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+Springer Nature 2021 LATEX template
+Multilingual Entity and Relation Extraction
+from Unified to Language-specific Training
+Zixiang Wang1, Jian Yang1, Tongliang Li1, Jiaheng
+Liu1, Ying Mo1, Jiaqi Bai1, Longtao He2 and Zhoujun Li1*
+1State Key Lab of Software Development Environment, Beihang
+University, Beijing, Beijing, China.
+2National Computer Network Emergency Response Technical
+Team/Coordination Center of China, Beijing, Beijing, China.
+*Corresponding author(s). E-mail(s): [email protected];
+Contributing authors: [email protected];
+[email protected]; [email protected];
+[email protected]; [email protected]; [email protected];
+[email protected];
+Abstract
+Entity and relation extraction is a key task in information extraction,
+where the output can be used for downstream NLP tasks. Existing
+approaches for entity and relation extraction tasks mainly focus on
+the English corpora and ignore other languages. Thus, it is critical to
+improving performance in a multilingual setting. Meanwhile, multilingual
+training is usually used to boost cross-lingual performance by trans-
+ferring knowledge from languages (e.g., high-resource) to other (e.g.,
+low-resource) languages. However, language interference usually exists
+in multilingual tasks as the model parameters are shared among all
+languages. In this paper, we propose a two-stage multilingual train-
+ing method and a joint model called Multilingual Entity and Relation
+Extraction framework (mERE) to mitigate language interference across
+languages. Specifically, we randomly concatenate sentences in differ-
+ent languages to train a Language-universal Aggregator (LA), which
+narrows the distance of embedding representations by obtaining the
+unified language representation. Then, we separate parameters to mit-
+igate interference via tuning a Language-specific Switcher (LS), which
+includes several independent sub-modules to refine the language-specific
+1
+arXiv:2301.04434v1  [cs.CL]  11 Jan 2023
+
+Springer Nature 2021 LATEX template
+2
+Article Title
+feature representation. After that, to enhance the relational triple extrac-
+tion, the sentence representations concatenated with the relation feature
+are used to recognize the entities. Extensive experimental results show
+that our method outperforms both the monolingual and multilingual
+baseline methods. Besides, we also perform detailed analysis to show
+that mERE is lightweight but effective on relational triple extraction
+and mERE is easy to transfer to other backbone models of multi-field
+tasks, which further demonstrates the effectiveness of our method.
+Keywords: Joint extraction, Information extraction, Multilingual entity and
+relation extraction, Relational triple
+1 Introduction
+Entity and relation extraction (ERE) contains two sub-tasks called named
+entity recognition (NER) [1–4] and relation classification (RC) [5, 6], which is
+the fundamental step of automatic knowledge graphs (KGs) [7] construction,
+knowledge discovery and intelligent question answering system. The results of
+ERE are typically described as a relational triple (h, r, t), where h and t are
+the head entity and the tail entity, respectively, and r denotes the relation
+between them. For example, for the sentence “Big Ben is in UK.” with a
+predefined relation called “Locate in”, an ideal relational triple of this sentence
+is expressed as (Big Ben, Locate in, UK).
+As a large amount of data is available from different languages on the
+Internet, it is important to utilize such valuable resources and develop multilin-
+gual entity and relation extraction models, which can operate across language
+barriers. However, most existing methods propose to solve ERE on English
+corpora, which can only deal with the monolingual extraction task. The main
+reason is that many languages suffer from the scarcity of corpora in ERE.
+Thus, multilingual training is proposed to help each other in a shared model,
+where the well-trained knowledge of high-resource languages can be trans-
+ferred to low-resource languages with a small amount of data. Recently, [8]
+propose a multilingual dataset called SMiLER, which is the first work to apply
+both monolingual and multilingual training. The authors in [8] introduce the
+multilingual entity and relation extraction model (i.e., HERBERTa) without
+considering interference across languages. However, such language interfer-
+ence is prevalent in multilingual tasks because of parameter sharing [9–11].
+As shown in Figure 1, to mitigate interference among languages, we propose
+to extract the feature representation of the corresponding language sentence.
+First, to facilitate the cross-lingual transfer among different languages, mul-
+tilingual representations are supposed to be closed under similar semantics
+using cross-lingual sentence-level concatenation. Then, based on the shared
+multilingual parameters, the language-specific representations derived from
+the independent modules can mitigate interference among multiple languages.
+
+Springer Nature 2021 LATEX template
+Article Title
+3
+Specifically, we propose a two-stage multilingual training method and an
+我爱吃苹果。
+amo le mele.
+I love apples.
+J'adore les pommes.
+…  
+Unified 
+Feature
+Chinese 
+Feature
+Italian 
+Feature
+English
+Feature
+French 
+Feature
+Fig. 1 This example includes 4 sentences from different languages, which express the same
+meaning. The four arrows represent four independent sentence representations extracted
+from different languages.
+effective model called multilingual Entity and Relation Extraction framework
+(mERE) to address the multilingual ERE task. In the first stage, we utilize a
+cross-lingual encoder to encode different language sentences and extract rela-
+tions directly. Then, we train the joint model with our Language-universal
+Aggregator (LA) to generate the unified language feature, which narrows the
+distance of similar semantic representation across languages. LA consists of
+a self-attention layer and is trained by random multi-sentences concatena-
+tion, which is used to learn semantic similarities in multilingual training. In
+the second stage, to alleviate the interference among languages, we freeze the
+parameters of LA and cross-lingual encoder in the first stage and optimize the
+independent parameters via fine-tuning the model with a Language-specific
+Switcher (LS), which consists of several independent sub-modules to produce
+the specific language features. Meanwhile, a selection mechanism is applied
+to choose the optimal group of sub-modules from LS, which enables the sub-
+module to share the same parameters with a certain group of languages. Such
+an automatic sub-module selection mechanism saves many model parameters
+when the number of languages is large. After that, each token representation
+is concatenated with the relation representation to enhance the recognition
+of the positions of entities in a sentence. Finally, in mERE, we adopt joint
+training to mitigate the error propagation problem.
+We conduct extensive experiments on the SMiLER benchmark of 14 lan-
+guages with 36 relations (including no relation) in total. The experimental
+results demonstrate that our method outperforms previous monolingual and
+multilingual ERE baseline methods by a large margin across languages, which
+demonstrates that our method can effectively mitigate language interference
+by improving representation quality among languages. Besides, we conduct
+detailed experiments to analyze how our method affects relational triple extrac-
+tion. Moreover, our method is simple but effective, and it is also easy to transfer
+to different backbone models of multi-field tasks with lightweight modules.
+
+Springer Nature 2021 LATEX template
+4
+Article Title
+2 Related Work
+Information Extraction Information extraction mainly focuses on extract-
+ing knowledge from unstructured text. A well-known system called Never-
+Ending Language Learner was reading the Web for almost 10 years to collect
+new instances of pre-defined relations and entity types [12]. Instead of the pre-
+defined entity and relation types, Open Information Extraction (OpenIE) has
+also attracted much attention during the past decade. A notable example is
+TextRunner [13], which utilizes a syntactic parser to extract triples from the
+Internet automatically. Many systems have been proposed subsequently, such
+as rule-based systems [14–16] and clause based systems [17, 18]. Recent super-
+vised methods are divided into three categories based on different architectures:
+(1) Generation-based models are typically sequence-to-sequence structure [19–
+21]. (2) Sequence labeling-based models using Begin Inside Outside (BIO)
+or Subject Relation Object None (SRON) to label every word in a sentence
+[22, 23]. (3) Span-based model takes advantage of span level feature which can
+be sufficiently exploited [24].
+Entity and Relation Extraction Early entity and relation extraction tasks
+use a pipeline approach, which are two separate subtasks including named
+entity recognition and relation classification. [25] first works on Recurrent Neu-
+ral Network (RNN) based model for extraction, capturing the semantics of the
+entity and its adjacent phrases through parsing trees. While [26] uses a syntac-
+tic tree-based RNN model to add weights to the important phrases. [27] first
+used a Convolutional Neural Network (CNN) structure to fuse the extracted
+word and sentence level features for extraction work. [28] uses a CNN structure
+based on a dependency tree to improve the performance. However, the pipeline
+approach has inevitable deficiencies: (1) The architecture ignores the interac-
+tions between entities and relations, causing the error propagation problem. (2)
+Some of the extracted entities are redundant in the named entity recognition
+phase, resulting in a degradation of performance in the relation classification
+phase.
+Most studies focus on the joint approach, which models entity recognition
+and relation classification in the same network and naturally relieves error
+propagation problem. The initial joint models are feature-based methods that
+heavily rely on NLP tools and manual efforts [29–32]. Recent joint models are
+typically neural network-based methods, which benefit from their excellent fea-
+ture learning capability. SPTree [33] is the first joint model based on the neural
+network method. Due to the two subtasks decoding with independent decoders
+but sharing parameters of the same encoding layers, this architecture also is
+known as parameters sharing. Following such kind of structure, [34] proposed
+an LSTM-based network that decodes entities and a CNN network to classify
+relations. [35, 36] employ CRF to improve performance of entity recognition.
+[37–40] use a pre-trained model called bidirectional encoder representation
+from transformers (BERT) to improve the accuracy of entity recognition. [41]
+proposes a multi-feature fusion sentence representation and decoder sequence
+annotation to handle the overlapping triples which are overlapped with one
+
+Springer Nature 2021 LATEX template
+Article Title
+5
+or two entities. Another architecture is joint decoding, which extracts entity
+pairs and corresponding relations simultaneously in one stage. NovelTagging
+[42] first proposes a tagging scheme to implement a joint decoding manner.
+But it cannot figure out the overlapping problem. The sequence-to-sequence
+scheme [43–46] models relational triples as a sequence, which can naturally
+deal with the nested entity and overlapping problem.
+Multilingual Models Multilingual models are a type of model that per-
+forms cross-lingual transfer among different languages, such as multilingual
+pre-training [47–51] and machine translation [11, 52–54]. Specifically, mBERT
+pre-trained on 104 languages in Wikipedia has a strong ability for cross-
+lingual transfer. Multilingual neural machine translation (MNMT) trains a
+single NMT model in multiple language pairs supporting translation direc-
+tions between multiple languages by sharing parameters [55–58]. Early studies
+mainly utilize high-resource languages to help low-resource languages and
+even perform zero-shot transfer translation [59, 60]. Recent studies focus on
+designing language-specific components to mitigate the language interference
+in shared parameters, especially on high-resource pairs [11, 61, 62]. Our method
+boosts the sentence representation quality from superior unified representation
+to further language-specific representation.
+Multilingual Entity and Relation Extraction Existing entity and rela-
+tion extraction datasets are insufficient in diversity and size. English is always
+used to be training corpora. [8] presents a new, large and diversified dataset
+Samsung MultiLingual Entity and Relation Extraction (SMiLER) dataset to
+entity and relation extraction both for English and multilingual setting. This
+is currently the most comprehensive and largest multilingual dataset.
+In this paper, we propose a multilingual entity and relation extraction
+framework called mERE with two-stage training strategies. In the first stage,
+we concatenate random sentences and use the self-attention mechanism [63]
+to learn the unified representation across languages. Inspired by MoE [64],
+we use several sub-modules with a selection mechanism to learn the specific
+representation of each language in the second stage. Such two-stage learning
+greatly improves the performance of relational triple extraction.
+3 Methodology
+In this section, we introduce the details of our training method for the multi-
+lingual joint extraction model as shown in Figure 2. We propose a two-stage
+training strategy. In the first stage, we train a Language-universal Aggrega-
+tor (LA) for learning the unified representations among multiple languages. In
+the second stage, we freeze the parameters and fine-tune the Language-specific
+Switcher (LS), which is applied to select specific feature representations of
+various languages.
+
+Springer Nature 2021 LATEX template
+6
+Article Title
+FR: Tour Eiffel à Paris.
+EN: Big Ben is in UK. 
+ES: España en Europa.
+IT: Torre pendente di Pisa in Italia.
+….
+Cross-lingual Pretrained Encoder
+Embeddings
+Classifier
+Relation
+[CLS]
+[CLS]
+𝜃1
+𝜃2
+𝜃3
+𝜃4
+Language-universal Aggregator
+Language-specific
+Switcher
+Entity1
+Entity2
+Big
+Ben
+UK
+Weighted sum
+NER
+Concatenate
+Encoder
+RC
+Switcher-based 
+Tuning
+NER
+LA
+Encoder
+RC
+NER
+LA
+LS
+Freeze
+Multilingual 
+Training
+Selection 
+Distribution
+Fig. 2 The left part shows the two-stage training strategy. The right part is our frame-
+work with Language-universal Aggregator (LA) for unified representation generation and
+Language-specific Switcher (LS) for language-specific feature extraction. We first train the
+LA with a concatenation of 2 random sentence representations, which are denoted as the
+green boxes (English) and yellow boxes (Italian) below the figure. Note that each sentence
+representation is directly regarded as input of LA during the evaluation stage. Then, we
+freeze part of the parameters and fine-tune the LS with all sub-modules during the training
+stage. The figure illustrates 4 sub-modules of LS with a top-2 strategy during evaluation.
+3.1 Task Formulation
+The goal of multilingual joint entity and relation extraction aims to identify all
+possible relational triples from sentences in different languages. Formally, given
+a sentence X from multilingual corpora D = {Dn}N
+n=1, where N represents
+the number of the all languages Lall = {Ln}N
+n=1. The probability of the target
+triple Y = {s, r, o} is defined as below:
+P(Y | X) = p(r | X; φ)p(s, o | X, r; ϕ),
+(1)
+where r denotes relation, s and o are subject (head entity) and object (tail
+entity), respectively. p(r | X; φ) means relation is only related to sentence X,
+and p(s, o | X, r; ϕ) means the entity pair (s, o) is related to both sentence X
+and the relation r that they shared.
+3.2 Language-aggregation Training
+We train the model with Language-universal Aggregator (LA) to learn the
+unified representation, which effectively narrows the distance of semantic
+representations across different languages. To obtain context representations
+of each token from the multilingual sentences, we utilize the cross-lingual
+pre-trained encoder for building a multilingual model. Given the sentence
+XLn = {xLn
+1 , . . . , xLn
+i
+, . . . , xLn
+m } with m tokens (including [CLS], [SEP] and
+
+Springer Nature 2021 LATEX template
+Article Title
+7
+[PAD]), xLn
+i
+∈ Rd is the i-th token embedding and d is the embedding size.
+The whole sentence is encoded by the cross-lingual pre-trained encoder:
+hLn = H(XLn; φ),
+(2)
+where hLn = {hLn
+1 , . . . , hLn
+i
+, . . . , hLn
+m } ∈ Rm×d represents the encoded rep-
+resentation and d is the hidden size. H denotes the cross-lingual pre-trained
+encoder. Meanwhile, a relation classifier W r ∈ Rd×U is used to project pooled
+output vector hp (from the [CLS] token) to the relation rc, where U is the
+number of relation types. The relation extraction is defined as:
+rc = hpW r,
+(3)
+To better learn the unified semantic representation among multiple lan-
+guages, we randomly sample s sentences of different languages from the
+training corpora to generate the cross-lingual representations using Equation 2
+and concatenate them to obtain hcat = [h
+LX1
+1
+, . . . , h
+LXi
+i
+, . . . , hLXs
+s
+], where LXi
+denotes the language symbol of the i-th sentence. Considering that each token
+needs to capture the dependency of inner-sentence and acquire semantic sim-
+ilarity representation of inter-sentence among languages, we train LA which
+applies the self-attention mechanism for fusing the information of the given
+concatenated representation:
+ˆhcat = SF(QKT
+√ϵ )V
+(4)
+where Q = hcatWq, K = hcatWk and V = hcatWv. SF represents the softmax
+operation. The three-parameter matrices Wq, Wk, and Wv are trainable. The
+term 1/√ϵ is the scaling factor. ˆhcat = {ˆh
+LX1
+1
+, . . . , ˆh
+LXi
+i
+, . . . , ˆhLXs
+s
+} and ˆh
+LXi
+i
+is
+i-th element. Instead of using language-specific features generated via Equation
+8, we directly utilize each element representation in ˆh
+LXi
+i
+to train the model
+via Equation 9.
+3.3 Language-specific Training
+To acquire features of a specific language, we freeze the parameters of language
+aggregation and cross-lingual encoder in the first training stage and fine-tune
+the model with LS. After obtaining the unified representation via LA, we
+extract the language-specific features via the LS with the selection mechanism
+from the unified representations.
+Given the language symbol Ln ∈ Lall(1 ≤ n ≤ N) and our LS θ =
+{θt}T
+t=1(1 ≤ t ≤ T , 1 ≤ T ≤ N), our selection mechanism is used to select
+corresponding sub-modules θf(Ln), in which f(·) is a function that maps a lan-
+guage to corresponding LS modules. To design an appropriate map function for
+our selection mechanism, each sentence is prefixed to the corresponding lan-
+guage symbol, which enables the model to correctly route sentences. Besides,
+
+Springer Nature 2021 LATEX template
+8
+Article Title
+all sub-modules from LS attend to the selection procedure during the training
+stage, which solves the undifferentiability problem. Specifically, the function
+ft(·) indicates the probability of selection of sub-module θt:
+ft (Ln) =
+exp
+�
+eLn
+t
+�
+�T
+i=1 exp
+�
+eLn
+i
+�
+(5)
+where eLn
+i
+is i-th element of the probability vector eLn = El[n]Wf. El ∈
+RN×d denotes the look-up table for all language prefix embeddings. The router
+matrix Wf ∈ Rd×T is used to project eLn which are normalized via a softmax
+distribution over the total T modules.
+For each sub-module θt from θ, we utilize Eθt(·) to transform unified feature
+representation ˆhLn into language-specific feature branch ˜hLn
+θt :
+˜hLn
+θt = Eθt(ˆhLn)
+(6)
+Eθt(ˆhLn) = LN
+�
+σ(ˆhLnWu)Wd + ˆhLn�
+(7)
+where ˆhLn ∈ Rm×d is an element of ˆhcat. Wu ∈ Rd×b and Wd ∈ Rb×d are
+projection matrices (b > d). σ is the ReLU activation function and LN(·) is
+the layer normalization function. The right part of Figure 2 corresponds to
+Equation 7.
+To ensure gradients are propagated to all sub-modules of LS {θt}T
+t=1, we
+apply the weighted average for obtaining the language-specific feature:
+˜hLn =
+T
+�
+t=1
+ft(Ln)Eθt
+�
+ˆhLn�
+(8)
+Note that for the whole process, function ft(Ln) in Equation 8 permits
+differentiability of the router.
+In the evaluation stage, it is necessary to prune several sub-module branches
+with the lowest selection probabilities to obtain the best performance. There-
+fore, we use the top-K strategy to select the best k(1 ≤ k ≤ T ) sub-modules
+with the highest probabilities to generate the language-specific representation.
+When k = T indicates all sub-modules involved in the calculation which means
+the selection mechanism is the same as the training stage. The mapping pro-
+cess is described as: Ln −→ {πLn
+1 , . . . , πLn
+i
+, . . . , πLn
+k } ∈ Π(k), where πLn
+i
+is
+one of the sub-module index that corresponds to language Ln and Π(k) is the
+space of all k-length combinations of Ck
+T in total.
+After obtaining the language-specific representation from LS, we create
+four matrices to recognize the head and tail positions of two named entities. To
+enhance the accuracy of recognition, we add a relation feature that constrains
+the extracted entities that are only related to the relevant relation. Formally,
+given a language-specific representation ˜hLn ∈ Rm×d of the m-length sentence
+
+Springer Nature 2021 LATEX template
+Article Title
+9
+and the relation vector re retrieved from relation embedding table Er ∈ RI×d,
+where I is the number of relations, the two entities are recognized as followed:
+entityx = (η((˜hLn ⊕ re)Wy))Uy
+(9)
+where the symbol collection entity={head, tail}, x={start,end} and y =
+{hs, he, ts, te}. We concatenate the relation vector with each token rep-
+resentation to enhance the recognition of entities, namely ˜hLn ⊕ re
+=
+{[˜hLn
+1 , re], . . . , [˜hLn
+i
+, re], . . . , [˜hLn
+m , re]} ∈ Rm×2d. Wy ∈ R2d×d are four down
+projection matrices and Uy ∈ Rd×1 are four index projection matrices. η
+denotes tanh activation function. Note that we use ground-truth relation as
+input in training entity recognition, which conforms to the joint training
+method in our architecture.
+3.4 Training Objective
+Our model presented in Figure 2 is trained jointly on multilingual ERE cor-
+pora. We first train the model only using a multilingual training strategy for
+our Language-universal Aggregator. Based on the unified language representa-
+tion, we fine-tune the model with Language-specific Switcher for learning the
+language-specific feature in the next step. The objective is to minimize the two
+training loss functions which are defined below:
+LLAT =
+M
+�
+m=1
+E(x,y)∼Dm[Lere(x, y; Θ)]
+(10)
+LLST =
+M
+�
+m=1
+E(x,y)∼Dm[Lere(x, y; Θ, θ)]
+(11)
+where D means multilingual entity and relation extraction training corpora
+and M denotes the number of the samples. Θ indicates shared parameters and
+θ is parameters in LS with selection mechanism. Lere is the loss function for
+entity and relation extraction, which is defined as below:
+Lere = α
+2 (Lstart
+h
++ L end
+h
++ L start
+t
++ L end
+t
+) + βLrel
+(12)
+where each L with any superscript is a cross-entropy loss. The subscripts with
+h and t indicate the head entity and tail entity respectively. The start and end
+of superscripts denote the first token index and last token index of an entity
+separately. Lrel is the loss function for relation classification. α and β are two
+weights on entity recognition loss and relation classification loss respectively.
+
+Springer Nature 2021 LATEX template
+10
+Article Title
+4 Experiments
+4.1 Datasets
+We evaluate our model on the dataset SMiLER [8], which is the largest
+and most diversified multilingual dataset for multilingual entity and relation
+extraction tasks with 14 languages from 36 relation types. The SMiLER con-
+sists of about 1.1M annotated sentences from Wikipedia and DBpedia, which
+includes English (En), Korean (Ko), Italian (It), French (Fr), German (De),
+Portuguese (Pt), Nederlands (Nl), Polish (Pl), Spanish (Es), Arabic (Ar), Rus-
+sian (Ru), Swedish (Sv), Farsi (Fa), Ukrainian (Uk). The relation types belong
+to roughly nine domains: location, organization, person, animal, art, device,
+measurement, event, and no relation. The statistics of SMiLER are shown in
+Table 1. As the development set in SMiLER is not publicly available, we only
+randomly extract the sentences from the training set to create new files with
+the same split ratio as the original paper.
+Table 1 The statistics of SMiLER dataset. English corpora include full-size, middle-size,
+and small-size. The languages are ordered from high-resource languages (left) to
+low-resource languages (right).
+Languages
+EN-full
+EN-mid
+It
+Fr
+De
+Pt
+Nl
+En-small
+Ko
+Pl
+Es
+Ar
+Ru
+Sv
+Fa
+Uk
+sentences num.
+748k
+269k
+76k
+62k
+53k
+45k
+40k
+35k
+20k
+17k
+12k
+9k
+7k
+5k
+3k
+1k
+relation types
+36
+36
+22
+22
+22
+22
+22
+32
+28
+22
+22
+9
+8
+22
+8
+7
+4.2 Implementation Details
+We conduct experiments on SMiLER, 14 languages in total. EN-small is
+treated as our English corpora. We utilize mBERT as our cross-lingual encoder.
+We train our model with AdamW, the learning rate is 3e-5 and weight decay
+is 0.1. The batch size is set to 16 on Tesla V100 GPU. The hidden size d is 768
+and dimension b of projection matrices Wu and Wd is 1024. The max sequence
+length is 256 and we concatenate 2 sentences during the first training stage. For
+the second training stage, we freeze most parameters in the first stage except
+the relation classifier and 8 matrices used to predict entities from Equation 9.
+The sub-module number T of LS is set to 6 (2 layers for 3 sub-modules and 1
+layer for the other). The epoch is set to 5 at the first stage. The max epoch of
+the second stage is set to 8 with an early stopping mechanism. The loss weights
+are set to 2 in named entity recognition and 1 in relation classification.
+In the evaluation stage, we set k = 3 in the top-K strategy to select the
+sub-modules in LS. We adopt standard micro-F1 metric to calculate scores on
+the models. The extracted entity pair is regarded as correct if the predictions
+of the head entity and tail entity are both the same as the ground truth. A
+triple is treated as correct if the entity pair and the corresponding relation
+type are all correct. no relation type is included in relation prediction. We
+also add a mask for the relation that is not absent in a language.
+
+Springer Nature 2021 LATEX template
+Article Title
+11
+4.3 Baselines
+As far as we know, the SMiLER is a new dataset and thus only an existing
+method for multilingual ERE without publishing source code. The relevant
+task is cross-lingual relation classification, which is also few in studies. There-
+fore, we reproduce the following competitive baselines to compare with our
+proposed approach for a fair comparison:
+• HEBERTa [8]: A multilingual entity and relation extraction framework
+called Hybrid Entity and Relation extraction BERT, which achieves the
+state-of-the-art performance on SMiLER. HERBERTa uses a pipeline train-
+ing manner that combines two independent BERT models. The first
+sub-model classifies the input sequence as one of 36 pre-defined relations
+(including no relation). The relation generated from the first sub-model is
+then fed to the second BERT and concatenated with the same input sequence
+as the input of the second model for entity recognition.
+• mBERT [65]: A cross-lingual model first uses the mBERT as a backbone
+for RC, which is trained on 104 languages with the corresponding Wikipedia
+dumps. We reproduce the results with the code shared at https://github.
+com/boun-tabi/RELX
+• MTMB [65]: A multilingual pre-training scheme called Matching the Mul-
+tilingual Blanks (MTMB). The framework shows several advantages against
+the mBERT on monolingual tasks and achieves significant improvements in
+cross-lingual transfer. Note that this framework is only designed for RC and
+not adapted to entity and relation extraction. Therefore, we simply modified
+the output layer of the baseline to conduct the ERE task.
+In addition to the above baselines, we also build a simplified multilin-
+gual joint entity and relation extraction framework called mERE-LS-LA as a
+basic structure which is concatenated relation representation with the sentence
+representation to enhance the extraction performance.
+Table 2 The F1 scores of different models. * denotes the model is reproduced by us on
+our experiment settings. - denotes that the language data is not involved both in the
+training and the evaluation stage. MONO, EURO, and SVO mean training data in 3
+different language groups. The languages are ordered from high-resource languages (left) to
+low-resource languages (right). The bold font number is the best score in each language.
+Test Sets
+AVG
+It
+Fr
+De
+Pt
+Nl
+En
+Ko
+Pl
+Es
+Ar
+Ru
+Sv
+Fa
+Uk
+HERBERTa*
+75.5
+83.9
+68.7
+71.5
+72.1
+78.5
+60.9
+80.4
+83.1
+60.0
+88.4
+79.4
+84.8
+79.6
+65.0
+mBERT*1
+75.2
+81.5
+68.2
+70.7
+71.0
+77.6
+59.9
+78.5
+81.1
+61.3
+89.5
+81.7
+81.5
+79.6
+70.0
+MTMB*1
+75.6
+80.9
+67.8
+70.9
+70.3
+79.1
+58.3
+79.3
+82.2
+58.2
+91.1
+74.1
+83.7
+77.8
+85.0
+mERE
+77.9
+81.7
+70.3
+73.4
+74.3
+81.1
+62.3
+82.7
+81.6
+64.7
+91.6
+83.1
+83.7
+79.6
+80.0
+mERE (EURO)
+70.9
+81.4
+70.2
+72.1
+74.2
+-
+62.2
+-
+-
+65.2
+-
+-
+-
+-
+-
+mERE (SVO)
+75.7
+81.3
+70.0
+72.9
+73.3
+80.6
+62.1
+-
+81.0
+64.7
+-
+83.1
+83.7
+-
+80.0
+mERE-LS
+77.2
+80.9
+69.7
+72.0
+73.5
+80.4
+62.2
+80.4
+81.6
+62.1
+91.6
+83.1
+84.8
+77.8
+80.0
+mERE-LS-LA (MONO)
+70.9
+81.2
+68.3
+67.1
+68.4
+77.9
+58.6
+79.3
+79.0
+48.4
+90.0
+72.5
+80.4
+66.7
+55.0
+mERE-LS-LA
+76.5
+81.3
+69.0
+71.9
+71.4
+80.3
+60.3
+76.4
+84.2
+60.7
+90.0
+83.9
+83.7
+77.8
+80.0
+1We modified the output layer to implement the entity recognition to accommodate the
+ERE task. We train the model in the joint training method.
+
+Springer Nature 2021 LATEX template
+12
+Article Title
+4.4 Models and Languages Comparison
+The results presented from the Tables are rounded to one decimal place. From
+Table 2, our method improves multilingual baselines by a large margin over pre-
+vious baselines. There is a 2.3% improvement on averaged F1 score compared
+with the previous strongest baseline MTMB which outperforms HERBERTa
+due to its strong multilingual pre-training scheme. Our mERE achieves the
+best scores on 8 out of 14 languages, especially on high-resource languages.
+The other 5 out of 6 languages achieve the second-best scores. Surprisingly,
+even our baseline mERE-LS-LA has 0.9% improvement over the MTMB. It
+seems that our basic structure is more effective on multilingual entity and rela-
+tion extraction tasks. Compared with mERE-LS that only uses LA, our full
+model mERE has nearly 0.7% F1 value improvement on average and yields
+similar or higher results on 13 languages except for Sv. The improvement can
+be attributed to our switcher-based language-specific training strategy, which
+finally extracts accurate information for entity recognition in each language.
+Compared with our baseline mERE-LS-LA, our full model mERE has nearly
+1.4% F1 value improvement on average which means mERE-LS also has nearly
+0.7% F1 value improvement on average. All such impressive results demon-
+strate that our full model mERE truly enhances the representation quality
+and mitigates language interference to a certain extent.
+We set several language groups to analyze the impact of different languages:
+(1)MONO: 14 languages in monolingual training. (2)EURO: It, Fr, Pt, De,
+Es, En. (3)SVO2: EURO, Ru, Sv, Nl, Pl, Uk. The default is all languages
+in multilingual training from Table 2. Compared with mERE-LS-LA training
+in multilingual corpora, we can observe that multilingual training achieves
+much higher results than mERE-LS-LA (MONO) monolingual training from
+Table 2, especially on low-resource languages. Such as improvements of Uk
+(25%), Fa (11.1%), and Ru (11.4%). It demonstrates that languages with less
+training data can benefit most from high-resource languages in multilingual
+training including ERE tasks. The results of the EURO family group are close
+to mERE. It is worth noting that Es achieves the best score in the EURO
+group. We conclude that Es benefits a lot from similarities of languages that
+are in the same language family even with less training data. In the SVO
+group, we can also visualize that most languages in EURO decrease slightly
+with the interference of other non-EURO languages. The different language
+families, or the languages with a big difference in syntactic structures might
+be the main interference among languages. However, compared with mERE
+(SVO), mERE yields the same results on low-resource languages and somewhat
+higher results on high-resource languages even the three non-SVO (Fa, Ar, and
+Ko) data involved during the training stage. We suppose that these non-SVO
+languages which are big different from others and are all low-resource may
+facilitate distinguishing high-resource languages in learning language-specific
+2SVO stands for the relative position of the Subject, Verb, and Object in the typical affirmative
+sentence. We treat Korean, Farsi, and Arabic as non-SVO languages. Arabic is VSO, while Korean
+and Farsi are SOV.
+
+Springer Nature 2021 LATEX template
+Article Title
+13
+features due to each sub-module from LS being independent, without sharing
+parameters in the same space. Lastly, we also observe some duplicated F1
+scores across low-resource languages. This phenomenon is caused by a small
+number of sentences in test sets.
+4.5 Entity and Relation Analysis
+Figure 3 shows F1 scores of relation and entity pair of mERE and mERE-LS-
+LA. We can observe that the relation classification seems to be easier than the
+named entity recognition. The correctness of entity pair extraction is the main
+bottleneck of the model performance. With the help of our LA and LS, mERE
+achieves higher results on entity pair recognition compared with mERE-LS-
+LA in general. Surprisingly, we can visualize that the performance of relation
+classification also has a slight improvement in mERE. We conclude that the
+improvement of the named entity recognition facilitates relation classification.
+Since information interaction between two sub-tasks can benefit each other in
+the joint training architecture.
+50
+55
+60
+65
+70
+75
+80
+85
+90
+95
+100
+Total
+It
+Fr
+De
+Pt
+Nl
+En
+Ko
+Pl
+Es
+Ar
+Ru
+Sv
+Fa
+Uk
+Relation(mERE)
+Entity Pair(mERE)
+Relation(mERE-LS-LA)
+Entity Pair(mERE-LS-LA)
+Fig. 3 The F1 scores of relations and entity pairs on all languages.
+F1 scores of detailed relation labels are shown in Figure 4. Most of the
+relations achieve higher F1 scores across languages, such as “no relation” and
+“has-type”. Part of relations differs widely across languages, such as relation
+“has-child”(F1 = 100 on Nl, F1 = 33 on De, F1 = 0 on Es). The big difference
+is caused by the number of relations of training data in each language. For
+some relations that occur F1 = 0 scores, we find out the relations (e.g won-
+award on Nl. has-parent on Pl. has-child on Es) are only one test sample.
+Such low results for some languages could be explained by a smaller number
+of relations in the test set.
+
+Springer Nature 2021 LATEX template
+14
+Article Title
+En
+It
+Fr
+Pt
+Es
+De
+Ar
+Nl
+Ru
+Pl
+Uk
+Sv
+Fa
+Ko
+no_relation
+is-where
+birth-place
+has-type
+movie-has-director
+has-occupation
+from-country
+has-genre
+has-author
+has-population
+headquarters
+is-member-of
+org-has-member
+has-parent
+org-has-founder
+has-spouse
+won-award
+has-nationality
+org-leader
+starring
+has-edu
+has-child
+event-year
+has-sibling
+has-length
+invented-when
+has-tourist-attraction
+has-lifespan
+first-product
+has-height
+has-highest-mountain
+invented-by
+has-weight
+post-code
+loc-leader
+eats
+85
+100
+100
+86
+91
+100
+100
+86
+100
+100
+75
+100
+97
+90
+96
+88
+81
+90
+85
+93
+97
+60
+89
+91
+92
+89
+89
+94
+84
+89
+50
+81
+84
+92
+92
+97
+100
+95
+100
+97
+91
+95
+100
+100
+100
+94
+76
+100
+99
+100
+92
+99
+100
+100
+100
+100
+59
+72
+68
+79
+67
+83
+100
+70
+100
+96
+100
+67
+100
+98
+25
+75
+30
+57
+56
+66
+72
+67
+0
+86
+91
+83
+75
+86
+67
+92
+100
+93
+100
+100
+100
+100
+100
+100
+94
+92
+100
+60
+100
+100
+100
+100
+100
+100
+94
+100
+96
+100
+100
+100
+99
+100
+100
+100
+100
+67
+100
+100
+83
+80
+78
+100
+100
+100
+100
+77
+92
+77
+88
+100
+82
+91
+100
+0
+100
+100
+96
+88
+100
+100
+95
+88
+100
+100
+86
+88
+100
+57
+100
+100
+100
+0
+100
+100
+83
+92
+90
+100
+100
+89
+100
+100
+100
+100
+89
+90
+60
+83
+86
+100
+50
+89
+95
+50
+50
+100
+0
+100
+79
+63
+92
+75
+67
+67
+0
+100
+100
+91
+75
+67
+100
+80
+100
+100
+100
+0
+100
+86
+67
+100
+50
+0
+33
+100
+0
+100
+92
+100
+0
+33
+100
+100
+100
+100
+67
+100
+100
+87
+83
+62
+80
+100
+100
+100
+100
+78
+100
+50
+100
+100
+88
+50
+56
+100
+0
+100
+100
+100
+100
+0
+20
+40
+60
+80
+100
+Fig. 4 The F1 scores of all relation labels on all languages. The darker color means a higher
+F1 score, while the lighter color means a lower F1 score.
+Figure 5 shows F1 scores of head entities and tail entities. We can observe
+that F1 scores of head entities are much higher than tail entities among most
+languages. It seems that head entities are easier to be recognized than tail
+entities. It is because the head entity always occurs at the beginning position
+of the sentence and thus the model probably memorizes the position, while the
+tail entity does not have any consistent position which is hard to predict.
+4.6 Ablation Study
+Sentences Concatenation To validate the effect of the number of sentences
+for learning the unified features among different languages, we conduct sev-
+eral experiments on the different numbers of sentences in concatenation. We
+learn from Figure 6 that there are evident F1 improvements with LA on dif-
+ferent concatenation numbers of sentences over only one sentence encoding.
+The multilingual model obtains the best performance when concatenating with
+the sentence pair. The increasing number of concatenated sentences has a
+slight decrease in performance. We conjecture that increasing the number of
+sentences may also bring somewhat interference.
+
+Springer Nature 2021 LATEX template
+Article Title
+15
+50
+55
+60
+65
+70
+75
+80
+85
+90
+95
+100
+Total It
+Fr
+De
+Pt
+Nl
+En
+Ko
+Pl
+Es
+Ar
+Ru
+Sv
+Fa
+Uk
+head entity
+tail entity
+Fig. 5 The performance of head entities (blue bar) and tail entities (orange bar) on different
+languages.
+1
+2
+3
+4
+Languages
+76.6
+76.7
+76.8
+76.9
+77.0
+77.1
+F1 score
+mERE-LS
+Fig. 6 The performance of sentences concatenation in the first training stage.
+Selection Mechanism To observe how the selection mechanism affects our
+model performance, we also train one-to-one sub-modules of LS called mERE14
+without using the selection mechanism in the second training stage. Each inde-
+pendent sub-module corresponds to a language and each sentence is routed via
+a language prefix which represents the number of sub-module. We can visualize
+from Figure 7 that increasing the number of parameters also improves obvi-
+ously over mERE-LS-LA. Nonetheless, the mERE14 will suffer from the sharp
+increasing training time and inference time, and big space consumption when
+the number of languages is large enough. Instead of increasing parameters,
+our Language-specific Switcher can effectively ameliorate extraction quality
+with only slight extra parameters and less time consumption. Since similar
+languages tend to select the same sub-modules from our LS. The mERE saves
+
+Springer Nature 2021 LATEX template
+16
+Article Title
+nearly 700M model capacity in our statistics and achieves better performance
+among most languages compared with mERE14. It is obvious that mERE is
+light and easy to transfer to other multi-field tasks. Selection Distribution
+It
+Fr
+De
+Pt
+Nl
+En
+Ko
+Pl
+Es
+Ar
+Ru
+Sv
+Fa
+Uk
+Languages
+60
+62
+64
+66
+68
+70
+72
+74
+76
+78
+80
+82
+84
+86
+88
+90
+92
+94
+F1 scores
+mERE-LS-LA
+mERE14
+mERE
+Fig. 7 The performance of three models on 14 languages. mERE14 utilizes 14 one-to-one
+sub-modules of LS without the selection mechanism. Each sub-module corresponds to a
+language.
+Figure 8 illustrates the heatmap of selection probability on 6 sub-modules from
+LS for each language. For each sub-module from top to bottom in Figure 8,
+we can visualize θ1 pays more attention to low-resource languages while θ4,
+θ5, and θ6 pay more attention to languages from the EURO family, which
+are mostly high-resource languages. The θ2 and θ3 seem to be more balanced
+on parameters sharing of languages except for 2 or 3 prominent languages.
+We conclude that some sub-modules are mainly used to extract features from
+similar languages and others are used to assist the specific languages.
+For each language from left to right, we can visualize that the selected
+sub-modules with higher probabilities are easy to distinguish in high-resource
+languages. In contrast, the selection probabilities across all sub-modules are
+relatively similar on low-resource languages in total. We conclude that train-
+ing data is rich enough to determine which way to route on high-resource
+languages and a more balanced selection decision is made on less training
+data. It is learned from Figure 8 that there are nearly 3 out of 6 prominently
+higher selection probabilities on the high-resource languages, and so do the
+low-resource languages with careful observation. It proves that only 3 sub-
+modules play the dominant role in refining the language-specific feature for
+each language. To avoid interference from the other irrelevant sub-modules,
+we adopt a top-K strategy to filter out 6 − k sub-modules with lower selec-
+tion probabilities in the evaluation stage. The top-6 strategy means selecting
+all sub-modules, which is the same as the training stage and the performance
+is relatively low (77.74) on average, while our mERE achieves the best perfor-
+mance (77.87) when adopting the top-3 strategy. It demonstrates that filtering
+out the least important sub-modules is necessary to enhance the prediction
+quality, which also reduces the redundant parameters in the evaluation. The
+
+Springer Nature 2021 LATEX template
+Article Title
+17
+top-1 achieves the worst performance (77.60), which demonstrates the part of
+sub-modules are also helpful for the task. Therefore, the best performance is
+obtained when the k value is balanced in all languages. Layer Number of
+It
+Fr
+De
+Pt
+Nl
+En
+Ko
+Pl
+Es
+Ar
+Ru
+Sv
+Fa
+Uk
+ 
+1 
+ 
+2 
+ 
+3 
+ 
+4 
+ 
+5 
+ 
+6 
+Fig. 8 The selection probability distributions of 6 sub-modules from LS on 14 languages.
+The sub-modules {θ}6
+1 are numbered from 1 to 6. The languages are ordered from high-
+resource languages (left) to low-resource languages (right). The darker color means a higher
+selection probability to the corresponding sub-module and a lower probability to select a
+certain sub-module when the color is lighter.
+Language-specific Switcher Table 3 used to evaluate the effect of the layer
+number of LS. We divide the 6 sub-modules into 2 groups (each group has the
+same layer number) with different combinations of layer numbers to accommo-
+date the scenarios, such as high- and low-resource language feature extraction.
+From Table 3, we can observe that the combination 1-2 achieves the best F1
+score on average. The combinations which are set to 1-1 and 4-4 also achieve
+better performance. With the increase or decrease of the layer number to a cer-
+tain degree, the performances are almost the same, which maintains relatively
+low averaged F1 scores. The full layer number combination 4-4 is an exception
+in the case, which demonstrates the performance still can be improved when
+the model capacity is large enough. According to the outcomes from Table 3,
+we conclude that the layer number of LS obviously impacts the results, with
+the best results attained when a balance is reached.
+5 Conclusion
+In this paper, we introduce a two-stage training method and a robust frame-
+work called mERE for multilingual entity and relation extraction, which
+ameliorates the sentence representation quality and mitigates the language
+interference among multiple languages. Specifically, we first learn the gener-
+alities across all languages to obtain the unified language representation via
+the Language-universal Aggregator and then learn the specialties of each lan-
+guage via the Language-specific Switcher. Experimental results demonstrate
+
+Springer Nature 2021 LATEX template
+18
+Article Title
+Table 3 The different layer numbers of sub-modules. Every 3 sub-modules in a group has
+the same layer numbers. Layer Num.01 and Layer Num.02 denote the layer number of the
+first group and second group respectively.
+Layer Num.01
+Layer Num.02
+AVG
+IT
+FR
+DE
+PT
+NL
+EN
+KO
+PL
+ES
+AR
+RU
+SV
+FA
+UK
+1
+1
+77.4
+81.3
+69.1
+72.1
+73.4
+80.4
+63.1
+81.9
+81.3
+63.4
+91.1
+85.4
+83.7
+77.8
+80.0
+1
+2
+77.9
+81.7
+70.3
+73.4
+74.3
+81.1
+62.3
+82.7
+81.6
+64.7
+91.6
+83.1
+83.7
+79.6
+80.0
+1
+3
+77.5
+81.5
+69.4
+72.8
+73.8
+81.1
+62.2
+81.9
+81.3
+64.7
+90.5
+83.1
+83.7
+79.6
+80.0
+1
+4
+77.5
+81.0
+70.2
+72.5
+74.1
+80.8
+62.2
+82.2
+81.3
+65.6
+90.5
+83.1
+83.7
+77.8
+80.0
+2
+2
+77.8
+81.7
+70.1
+73.1
+74.1
+81.0
+62.3
+81.9
+81.6
+66.1
+90.5
+83.1
+83.7
+79.6
+80.0
+2
+3
+77.4
+81.1
+70.2
+72.7
+74.1
+80.9
+62.1
+82.5
+81.3
+65.2
+90.5
+81.5
+83.7
+77.8
+80.0
+2
+4
+77.4
+81.3
+70.2
+72.2
+74.2
+81.0
+62.2
+81.4
+81.0
+64.7
+90.5
+81.5
+83.7
+79.6
+80.0
+3
+3
+77.4
+81.6
+70.4
+72.5
+73.3
+81.0
+62.1
+82.7
+81.0
+64.7
+91.1
+81.5
+83.7
+77.8
+80.0
+3
+4
+77.5
+81.5
+70.2
+73.3
+73.9
+81.4
+62.7
+83.0
+81.0
+64.3
+90.5
+82.3
+83.7
+77.8
+80.0
+4
+4
+77.7
+81.1
+70.2
+73.1
+74.2
+80.9
+62.3
+81.9
+81.6
+65.6
+90.5
+83.1
+83.7
+79.6
+80.0
+that our method significantly outperforms both monolingual and multilingual
+ERE baselines, which demonstrates that our framework can extract relational
+triples among various languages well. Moreover, our framework is also light
+and easy to transfer to other backbone models of multi-field tasks.
+In the future, we will pay more attention to complex multilingual relational
+triple extraction, such as overlapping relational triples or multiple relational
+triples. Besides, we will also do further research on a better contextual repre-
+sentation among multiple languages. Although there is a long way to experience
+in multilingual entity and relation extraction tasks, it is important to inves-
+tigate the valuable structured information in many other languages for the
+downstream NLP tasks.
+Acknowledgments.
+This work was supported in part by the National Nat-
+ural Science Foundation of China (Grant Nos. 62276017, U1636211, 61672081),
+the 2022 Tencent Big Travel Rhino-Bird Special Research Program, and the
+Fund of the State Key Laboratory of Software Development Environment
+(Grant No. SKLSDE-2021ZX-18).
+References
+[1] Huang, Z., Xu, W., Yu, K.: Bidirectional LSTM-CRF models for sequence
+tagging. CoRR abs/1508.01991 (2015) 1508.01991
+[2] Wang, J., Shou, L., Chen, K., Chen, G.: Pyramid: A layered model for
+nested named entity recognition. In: Jurafsky, D., Chai, J., Schluter,
+N., Tetreault, J.R. (eds.) Proceedings of the 58th Annual Meet-
+ing of the Association for Computational Linguistics, ACL 2020,
+Online, July 5-10, 2020, pp. 5918–5928. Association for Computational
+Linguistics, ??? (2020). https://doi.org/10.18653/v1/2020.acl-main.525.
+https://doi.org/10.18653/v1/2020.acl-main.525
+[3] Joshi, M., Chen, D., Liu, Y., Weld, D.S., Zettlemoyer, L., Levy, O.:
+Spanbert: Improving pre-training by representing and predicting spans.
+Trans. Assoc. Comput. Linguistics 8, 64–77 (2020). https://doi.org/10.
+1162/tacl a 00300
+
+Springer Nature 2021 LATEX template
+Article Title
+19
+[4] Tan, Z., Shen, Y., Zhang, S., Lu, W., Zhuang, Y.: A sequence-to-set net-
+work for nested named entity recognition. In: Zhou, Z. (ed.) Proceedings
+of the Thirtieth International Joint Conference on Artificial Intelligence,
+IJCAI 2021, Virtual Event / Montreal, Canada, 19-27 August 2021, pp.
+3936–3942. ijcai.org, ??? (2021). https://doi.org/10.24963/ijcai.2021/542.
+https://doi.org/10.24963/ijcai.2021/542
+[5] Levy, O., Seo, M., Choi, E., Zettlemoyer, L.: Zero-shot relation extraction
+via reading comprehension. In: Levy, R., Specia, L. (eds.) Proceedings
+of the 21st Conference on Computational Natural Language Learning
+(CoNLL 2017), Vancouver, Canada, August 3-4, 2017, pp. 333–342. Asso-
+ciation for Computational Linguistics, ??? (2017). https://doi.org/10.
+18653/v1/K17-1034. https://doi.org/10.18653/v1/K17-1034
+[6] Li, J., Wang, R., Zhang, N., Zhang, W., Yang, F., Chen, H.: Logic-guided
+semantic representation learning for zero-shot relation classification. In:
+Scott, D., Bel, N., Zong, C. (eds.) Proceedings of the 28th International
+Conference on Computational Linguistics, COLING 2020, Barcelona,
+Spain (Online), December 8-13, 2020, pp. 2967–2978. International Com-
+mittee on Computational Linguistics, ??? (2020). https://doi.org/10.
+18653/v1/2020.coling-main.265. https://doi.org/10.18653/v1/2020.coling-
+main.265
+[7] Lin, Q., Mao, R., Liu, J., Xu, F., Cambria, E.: Fusing topology contexts
+and logical rules in language models for knowledge graph completion. Inf.
+Fusion 90, 253–264 (2023). https://doi.org/10.1016/j.inffus.2022.09.020
+[8] Seganti, A., Firlag, K., Skowronska, H., Satlawa, M., Andruszkiewicz, P.:
+Multilingual entity and relation extraction dataset and model. In: Merlo,
+P., Tiedemann, J., Tsarfaty, R. (eds.) Proceedings of the 16th Conference
+of the European Chapter of the Association for Computational Linguis-
+tics: Main Volume, EACL 2021, Online, April 19 - 23, 2021, pp. 1946–1955.
+Association for Computational Linguistics, ??? (2021). https://doi.org/
+10.18653/v1/2021.eacl-main.166. https://doi.org/10.18653/v1/2021.eacl-
+main.166
+[9] Wang, Z., Lipton, Z.C., Tsvetkov, Y.: On negative interference in mul-
+tilingual models: Findings and A meta-learning treatment. In: Webber,
+B., Cohn, T., He, Y., Liu, Y. (eds.) Proceedings of the 2020 Confer-
+ence on Empirical Methods in Natural Language Processing, EMNLP
+2020, Online, November 16-20, 2020, pp. 4438–4450. Association for Com-
+putational Linguistics, ??? (2020). https://doi.org/10.18653/v1/2020.
+emnlp-main.359. https://doi.org/10.18653/v1/2020.emnlp-main.359
+[10] Gong, H., Li, X., Genzel, D.: Adaptive sparse transformer for multilingual
+translation. CoRR abs/2104.07358 (2021) 2104.07358
+
+Springer Nature 2021 LATEX template
+20
+Article Title
+[11] Yang, J., Yin, Y., Ma, S., Zhang, D., Li, Z., Wei, F.: High-resource
+language-specific training for multilingual neural machine translation. In:
+Raedt, L.D. (ed.) Proceedings of the Thirty-First International Joint Con-
+ference on Artificial Intelligence, IJCAI 2022, Vienna, Austria, 23-29 July
+2022, pp. 4461–4467. ijcai.org, ??? (2022). https://doi.org/10.24963/ijcai.
+2022/619. https://doi.org/10.24963/ijcai.2022/619
+[12] Mitchell, T.M., Cohen, W.W., Jr., E.R.H., Talukdar, P.P., Yang, B.,
+Betteridge, J., Carlson, A., Mishra, B.D., Gardner, M., Kisiel, B., Krish-
+namurthy, J., Lao, N., Mazaitis, K., Mohamed, T., Nakashole, N.,
+Platanios, E.A., Ritter, A., Samadi, M., Settles, B., Wang, R.C., Wijaya,
+D., Gupta, A., Chen, X., Saparov, A., Greaves, M., Welling, J.: Never-
+ending learning. Commun. ACM 61(5), 103–115 (2018). https://doi.org/
+10.1145/3191513
+[13] Yates, A., Banko, M., Broadhead, M., Cafarella, M.J., Etzioni, O., Soder-
+land, S.: Textrunner: Open information extraction on the web. In: Sidner,
+C.L., Schultz, T., Stone, M., Zhai, C. (eds.) Human Language Technology
+Conference of the North American Chapter of the Association of Com-
+putational Linguistics, Proceedings, April 22-27, 2007, Rochester, New
+York, USA, pp. 25–26. The Association for Computational Linguistics,
+??? (2007). https://aclanthology.org/N07-4013/
+[14] Fader, A., Soderland, S., Etzioni, O.: Identifying relations for open infor-
+mation extraction. In: Proceedings of the 2011 Conference on Empirical
+Methods in Natural Language Processing, EMNLP 2011, 27-31 July 2011,
+John McIntyre Conference Centre, Edinburgh, UK, A Meeting of SIG-
+DAT, a Special Interest Group of The ACL, pp. 1535–1545. ACL, ???
+(2011). https://aclanthology.org/D11-1142/
+[15] de S´a Mesquita, F., Schmidek, J., Barbosa, D.: Effectiveness and efficiency
+of open relation extraction. In: Proceedings of the 2013 Conference on
+Empirical Methods in Natural Language Processing, EMNLP 2013, 18-21
+October 2013, Grand Hyatt Seattle, Seattle, Washington, USA, A Meeting
+of SIGDAT, a Special Interest Group of The ACL, pp. 447–457. ACL, ???
+(2013). https://aclanthology.org/D13-1043/
+[16] White, A.S., Reisinger, D.A., Sakaguchi, K., Vieira, T., Zhang, S.,
+Rudinger, R., Rawlins, K., Durme, B.V.: Universal decompositional
+semantics on universal dependencies. In: Su, J., Carreras, X., Duh,
+K. (eds.) Proceedings of the 2016 Conference on Empirical Meth-
+ods in Natural Language Processing, EMNLP 2016, Austin, Texas,
+USA, November 1-4, 2016, pp. 1713–1723. The Association for Compu-
+tational Linguistics, ??? (2016). https://doi.org/10.18653/v1/d16-1177.
+https://doi.org/10.18653/v1/d16-1177
+
+Springer Nature 2021 LATEX template
+Article Title
+21
+[17] Corro, L.D., Gemulla, R.: Clausie: clause-based open information extrac-
+tion. In: Schwabe, D., Almeida, V.A.F., Glaser, H., Baeza-Yates,
+R., Moon, S.B. (eds.) 22nd International World Wide Web Con-
+ference, WWW ’13, Rio de Janeiro, Brazil, May 13-17, 2013, pp.
+355–366. International World Wide Web Conferences Steering Com-
+mittee / ACM, ??? (2013). https://doi.org/10.1145/2488388.2488420.
+https://doi.org/10.1145/2488388.2488420
+[18] Angeli, G., Premkumar, M.J.J., Manning, C.D.: Leveraging linguistic
+structure for open domain information extraction. In: Proceedings of the
+53rd Annual Meeting of the Association for Computational Linguistics
+and the 7th International Joint Conference on Natural Language Pro-
+cessing of the Asian Federation of Natural Language Processing, ACL
+2015, July 26-31, 2015, Beijing, China, Volume 1: Long Papers, pp.
+344–354. The Association for Computer Linguistics, ??? (2015). https:
+//doi.org/10.3115/v1/p15-1034. https://doi.org/10.3115/v1/p15-1034
+[19] Cui, L., Wei, F., Zhou, M.: Neural open information extraction. In:
+Gurevych, I., Miyao, Y. (eds.) Proceedings of the 56th Annual Meeting
+of the Association for Computational Linguistics, ACL 2018, Melbourne,
+Australia, July 15-20, 2018, Volume 2: Short Papers, pp. 407–413. Associa-
+tion for Computational Linguistics, ??? (2018). https://doi.org/10.18653/
+v1/P18-2065. https://aclanthology.org/P18-2065/
+[20] Kolluru, K., Aggarwal, S., Rathore, V., Mausam, Chakrabarti, S.: Imojie:
+Iterative memory-based joint open information extraction. In: Juraf-
+sky, D., Chai, J., Schluter, N., Tetreault, J.R. (eds.) Proceedings of
+the 58th Annual Meeting of the Association for Computational Lin-
+guistics, ACL 2020, Online, July 5-10, 2020, pp. 5871–5886. Association
+for Computational Linguistics, ??? (2020). https://doi.org/10.18653/v1/
+2020.acl-main.521. https://doi.org/10.18653/v1/2020.acl-main.521
+[21] Li, T., Wang, Z., Li, Z.: Low resource quantitative information extraction
+via structure searching and prefix-based text generation. AAAI Press, ???
+(2023)
+[22] Stanovsky, G., Michael, J., Zettlemoyer, L., Dagan, I.: Supervised open
+information extraction. In: Walker, M.A., Ji, H., Stent, A. (eds.) Pro-
+ceedings of the 2018 Conference of the North American Chapter of
+the Association for Computational Linguistics: Human Language Tech-
+nologies, NAACL-HLT 2018, New Orleans, Louisiana, USA, June 1-6,
+2018, Volume 1 (Long Papers), pp. 885–895. Association for Compu-
+tational Linguistics, ??? (2018). https://doi.org/10.18653/v1/n18-1081.
+https://doi.org/10.18653/v1/n18-1081
+[23] Kolluru, K., Adlakha, V., Aggarwal, S., Mausam, Chakrabarti, S.:
+
+Springer Nature 2021 LATEX template
+22
+Article Title
+Openie6: Iterative grid labeling and coordination analysis for open
+information
+extraction.
+In:
+Webber,
+B.,
+Cohn,
+T.,
+He,
+Y.,
+Liu,
+Y. (eds.) Proceedings of the 2020 Conference on Empirical Meth-
+ods in Natural Language Processing, EMNLP 2020, Online, Novem-
+ber 16-20, 2020, pp. 3748–3761. Association for Computational Lin-
+guistics, ??? (2020). https://doi.org/10.18653/v1/2020.emnlp-main.306.
+https://doi.org/10.18653/v1/2020.emnlp-main.306
+[24] Zhan, J., Zhao, H.: Span model for open information extraction on
+accurate corpus. In: The Thirty-Fourth AAAI Conference on Artificial
+Intelligence, AAAI 2020, The Thirty-Second Innovative Applications of
+Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Sympo-
+sium on Educational Advances in Artificial Intelligence, EAAI 2020, New
+York, NY, USA, February 7-12, 2020, pp. 9523–9530. AAAI Press, ???
+(2020)
+[25] Socher, R., Huval, B., Manning, C.D., Ng, A.Y.: Semantic composition-
+ality through recursive matrix-vector spaces. In: Tsujii, J., Henderson, J.,
+Pasca, M. (eds.) Proceedings of the 2012 Joint Conference on Empiri-
+cal Methods in Natural Language Processing and Computational Natural
+Language Learning, EMNLP-CoNLL 2012, July 12-14, 2012, Jeju Island,
+Korea, pp. 1201–1211. ACL, ??? (2012). https://aclanthology.org/D12-
+1110/
+[26] Hashimoto, K., Miwa, M., Tsuruoka, Y., Chikayama, T.: Simple cus-
+tomization of recursive neural networks for semantic relation classifica-
+tion. In: Proceedings of the 2013 Conference on Empirical Methods in
+Natural Language Processing, EMNLP 2013, 18-21 October 2013, Grand
+Hyatt Seattle, Seattle, Washington, USA, A Meeting of SIGDAT, a
+Special Interest Group of The ACL, pp. 1372–1376. ACL, ??? (2013).
+https://aclanthology.org/D13-1137/
+[27] Zeng, D., Liu, K., Lai, S., Zhou, G., Zhao, J.: Relation classification via
+convolutional deep neural network. In: Hajic, J., Tsujii, J. (eds.) COLING
+2014, 25th International Conference on Computational Linguistics, Pro-
+ceedings of the Conference: Technical Papers, August 23-29, 2014, Dublin,
+Ireland, pp. 2335–2344. ACL, ??? (2014). https://aclanthology.org/C14-
+1220/
+[28] Xu, K., Feng, Y., Huang, S., Zhao, D.: Semantic relation classifi-
+cation via convolutional neural networks with simple negative sam-
+pling. In: M`arquez, L., Callison-Burch, C., Su, J., Pighin, D., Marton,
+Y. (eds.) Proceedings of the 2015 Conference on Empirical Meth-
+ods in Natural Language Processing, EMNLP 2015, Lisbon, Portugal,
+September 17-21, 2015, pp. 536–540. The Association for Computa-
+tional Linguistics, ??? (2015). https://doi.org/10.18653/v1/d15-1062.
+
+Springer Nature 2021 LATEX template
+Article Title
+23
+https://doi.org/10.18653/v1/d15-1062
+[29] Roth, D., Yih, W.: A linear programming formulation for global inference
+in natural language tasks. In: Ng, H.T., Riloff, E. (eds.) Proceed-
+ings of the Eighth Conference on Computational Natural Language
+Learning, CoNLL 2004, Held in Cooperation with HLT-NAACL 2004,
+Boston, Massachusetts, USA, May 6-7, 2004, pp. 1–8. ACL, ??? (2004).
+https://aclanthology.org/W04-2401/
+[30] Kate, R.J., Mooney, R.J.: Joint entity and relation extraction using card-
+pyramid parsing. In: Lapata, M., Sarkar, A. (eds.) Proceedings of the
+Fourteenth Conference on Computational Natural Language Learning,
+CoNLL 2010, Uppsala, Sweden, July 15-16, 2010, pp. 203–212. ACL, ???
+(2010). https://aclanthology.org/W10-2924/
+[31] Yu, X., Lam, W.: Jointly identifying entities and extracting relations
+in encyclopedia text via A graphical model approach. In: Huang, C.,
+Jurafsky, D. (eds.) COLING 2010, 23rd International Conference on
+Computational Linguistics, Posters Volume, 23-27 August 2010, Beijing,
+China, pp. 1399–1407. Chinese Information Processing Society of China,
+??? (2010). https://aclanthology.org/C10-2160/
+[32] Li, Q., Ji, H.: Incremental joint extraction of entity mentions and rela-
+tions. In: Proceedings of the 52nd Annual Meeting of the Association
+for Computational Linguistics, ACL 2014, June 22-27, 2014, Baltimore,
+MD, USA, Volume 1: Long Papers, pp. 402–412. The Association for
+Computer Linguistics, ??? (2014). https://doi.org/10.3115/v1/p14-1038.
+https://doi.org/10.3115/v1/p14-1038
+[33] Miwa, M., Bansal, M.: End-to-end relation extraction using lstms on
+sequences and tree structures. In: Proceedings of the 54th Annual Meet-
+ing of the Association for Computational Linguistics, ACL 2016, August
+7-12, 2016, Berlin, Germany, Volume 1: Long Papers. The Association for
+Computer Linguistics, ??? (2016). https://doi.org/10.18653/v1/p16-1105.
+https://doi.org/10.18653/v1/p16-1105
+[34] Zheng, S., Hao, Y., Lu, D., Bao, H., Xu, J., Hao, H., Xu, B.: Joint
+entity and relation extraction based on a hybrid neural network. Neuro-
+computing 257, 59–66 (2017). https://doi.org/10.1016/j.neucom.2016.12.
+075
+[35] Tan, Z., Zhao, X., Wang, W., Xiao, W.: Jointly extracting multiple triplets
+with multilayer translation constraints. In: The Thirty-Third AAAI Con-
+ference on Artificial Intelligence, AAAI 2019, The Thirty-First Innovative
+Applications of Artificial Intelligence Conference, IAAI 2019, The Ninth
+AAAI Symposium on Educational Advances in Artificial Intelligence,
+EAAI 2019, Honolulu, Hawaii, USA, January 27 - February 1, 2019, pp.
+
+Springer Nature 2021 LATEX template
+24
+Article Title
+7080–7087. AAAI Press, ??? (2019). https://doi.org/10.1609/aaai.v33i01.
+33017080. https://doi.org/10.1609/aaai.v33i01.33017080
+[36] Liu, J., Chen, S., Wang, B., Zhang, J., Li, N., Xu, T.: Attention
+as relation: Learning supervised multi-head self-attention for relation
+extraction. In: Bessiere, C. (ed.) Proceedings of the Twenty-Ninth Inter-
+national Joint Conference on Artificial Intelligence, IJCAI 2020, pp.
+3787–3793. ijcai.org, ??? (2020). https://doi.org/10.24963/ijcai.2020/524.
+https://doi.org/10.24963/ijcai.2020/524
+[37] Wadden, D., Wennberg, U., Luan, Y., Hajishirzi, H.: Entity, relation,
+and event extraction with contextualized span representations. In: Inui,
+K., Jiang, J., Ng, V., Wan, X. (eds.) Proceedings of the 2019 Confer-
+ence on Empirical Methods in Natural Language Processing and the 9th
+International Joint Conference on Natural Language Processing, EMNLP-
+IJCNLP 2019, Hong Kong, China, November 3-7, 2019, pp. 5783–5788.
+Association for Computational Linguistics, ??? (2019). https://doi.org/
+10.18653/v1/D19-1585. https://doi.org/10.18653/v1/D19-1585
+[38] Eberts, M., Ulges, A.: Span-based joint entity and relation extraction
+with transformer pre-training. In: Giacomo, G.D., Catal´a, A., Dilkina,
+B., Milano, M., Barro, S., Bugar´ın, A., Lang, J. (eds.) ECAI 2020 - 24th
+European Conference on Artificial Intelligence, 29 August-8 September
+2020, Santiago de Compostela, Spain, August 29 - September 8, 2020 -
+Including 10th Conference on Prestigious Applications of Artificial Intel-
+ligence (PAIS 2020). Frontiers in Artificial Intelligence and Applications,
+vol. 325, pp. 2006–2013. IOS Press, ??? (2020). https://doi.org/10.3233/
+FAIA200321. https://doi.org/10.3233/FAIA200321
+[39] Ji, B., Yu, J., Li, S., Ma, J., Wu, Q., Tan, Y., Liu, H.: Span-based
+joint entity and relation extraction with attention-based span-specific
+and contextual semantic representations. In: Scott, D., Bel, N., Zong,
+C. (eds.) Proceedings of the 28th International Conference on Compu-
+tational Linguistics, COLING 2020, Barcelona, Spain (Online), Decem-
+ber 8-13, 2020, pp. 88–99. International Committee on Computational
+Linguistics, ??? (2020). https://doi.org/10.18653/v1/2020.coling-main.8.
+https://doi.org/10.18653/v1/2020.coling-main.8
+[40] Qiao, B., Zou, Z., Huang, Y., Fang, K., Zhu, X., Chen, Y.: A joint model
+for entity and relation extraction based on BERT. Neural Comput. Appl.
+34(5), 3471–3481 (2022). https://doi.org/10.1007/s00521-021-05815-z
+[41] Lai, T., Cheng, L., Wang, D., Ye, H., Zhang, W.: RMAN: relational
+multi-head attention neural network for joint extraction of entities and
+relations. Appl. Intell. 52(3), 3132–3142 (2022). https://doi.org/10.1007/
+s10489-021-02600-2
+
+Springer Nature 2021 LATEX template
+Article Title
+25
+[42] Zheng, S., Wang, F., Bao, H., Hao, Y., Zhou, P., Xu, B.: Joint extraction
+of entities and relations based on a novel tagging scheme. In: Barzilay, R.,
+Kan, M. (eds.) Proceedings of the 55th Annual Meeting of the Association
+for Computational Linguistics, ACL 2017, Vancouver, Canada, July 30 -
+August 4, Volume 1: Long Papers, pp. 1227–1236. Association for Compu-
+tational Linguistics, ??? (2017). https://doi.org/10.18653/v1/P17-1113.
+https://doi.org/10.18653/v1/P17-1113
+[43] Zeng, X., Zeng, D., He, S., Liu, K., Zhao, J.: Extracting relational facts
+by an end-to-end neural model with copy mechanism. In: Gurevych, I.,
+Miyao, Y. (eds.) Proceedings of the 56th Annual Meeting of the Associa-
+tion for Computational Linguistics, ACL 2018, Melbourne, Australia, July
+15-20, 2018, Volume 1: Long Papers, pp. 506–514. Association for Compu-
+tational Linguistics, ??? (2018). https://doi.org/10.18653/v1/P18-1047.
+https://aclanthology.org/P18-1047/
+[44] Zeng, X., He, S., Zeng, D., Liu, K., Liu, S., Zhao, J.: Learning the extrac-
+tion order of multiple relational facts in a sentence with reinforcement
+learning. In: Inui, K., Jiang, J., Ng, V., Wan, X. (eds.) Proceedings of the
+2019 Conference on Empirical Methods in Natural Language Processing
+and the 9th International Joint Conference on Natural Language Process-
+ing, EMNLP-IJCNLP 2019, Hong Kong, China, November 3-7, 2019, pp.
+367–377. Association for Computational Linguistics, ??? (2019). https:
+//doi.org/10.18653/v1/D19-1035. https://doi.org/10.18653/v1/D19-1035
+[45] Nayak, T., Ng, H.T.: Effective modeling of encoder-decoder archi-
+tecture
+for
+joint
+entity
+and
+relation
+extraction.
+In:
+The
+Thirty-
+Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, The
+Thirty-Second Innovative Applications of Artificial Intelligence Con-
+ference, IAAI 2020, The Tenth AAAI Symposium on Educational
+Advances
+in
+Artificial
+Intelligence,
+EAAI
+2020,
+New
+York,
+NY,
+USA, February 7-12, 2020, pp. 8528–8535. AAAI Press, ??? (2020).
+https://ojs.aaai.org/index.php/AAAI/article/view/6374
+[46] Wang, Z., Yang, L., Yang, J., Li, T., He, L., Li, Z.: A triple relation
+network for joint entity and relation extraction. Electronics 11(10) (2022).
+https://doi.org/10.3390/electronics11101535
+[47] Devlin, J., Chang, M., Lee, K., Toutanova, K.: BERT: pre-training of
+deep bidirectional transformers for language understanding. In: Burstein,
+J., Doran, C., Solorio, T. (eds.) Proceedings of the 2019 Conference of
+the North American Chapter of the Association for Computational Lin-
+guistics: Human Language Technologies, NAACL-HLT 2019, Minneapolis,
+MN, USA, June 2-7, 2019, Volume 1 (Long and Short Papers), pp.
+4171–4186. Association for Computational Linguistics, ??? (2019). https:
+//doi.org/10.18653/v1/n19-1423. https://doi.org/10.18653/v1/n19-1423
+
+Springer Nature 2021 LATEX template
+26
+Article Title
+[48] Yang, J., Ma, S., Zhang, D., Wu, S., Li, Z., Zhou, M.: Alternating language
+modeling for cross-lingual pre-training. In: AAAI 2020, pp. 9386–9393
+(2020)
+[49] Conneau,
+A.,
+Khandelwal,
+K.,
+Goyal,
+N.,
+Chaudhary,
+V.,
+Wen-
+zek, G., Guzm´an, F., Grave, E., Ott, M., Zettlemoyer, L., Stoy-
+anov, V.: Unsupervised cross-lingual representation learning at scale.
+In:
+Proceedings
+of
+the
+58th
+Annual
+Meeting
+of
+the
+Association
+for Computational Linguistics. Association for Computational Lin-
+guistics, Online (2020). https://doi.org/10.18653/v1/2020.acl-main.747.
+https://aclanthology.org/2020.acl-main.747
+[50] Yang, J., Ma, S., Dong, L., Huang, S., Huang, H., Yin, Y., Zhang, D.,
+Yang, L., Li, Z., Wei, F.: Ganlm: Encoder-decoder pre-training with
+an auxiliary discriminator. CoRR abs/2212.10218 (2022) 2212.10218.
+https://doi.org/10.48550/arXiv.2212.10218
+[51] Liu, J., Yu, T., Peng, H., Sun, M., Li, P.: Cross-lingual cross-modal con-
+solidation for effective multilingual video corpus moment retrieval. In:
+NAACL 2022, pp. 1854–1862 (2022)
+[52] Yang, J., Yin, Y., Ma, S., Zhang, D., Wu, S., Guo, H., Li, Z.,
+Wei, F.: UM4: unified multilingual multiple teacher-student model for
+zero-resource neural machine translation. In: Raedt, L.D. (ed.) Pro-
+ceedings of the Thirty-First International Joint Conference on Artifi-
+cial Intelligence, IJCAI 2022, Vienna, Austria, 23-29 July 2022, pp.
+4454–4460. ijcai.org, ??? (2022). https://doi.org/10.24963/ijcai.2022/618.
+https://doi.org/10.24963/ijcai.2022/618
+[53] Yang, J., Ma, S., Huang, H., Zhang, D., Dong, L., Huang, S., Muzio, A.,
+Singhal, S., Hassan, H., Song, X., Wei, F.: Multilingual machine transla-
+tion systems from microsoft for WMT21 shared task. In: WMT@EMNLP
+2021, pp. 446–455 (2021)
+[54] Guo, H., Liu, J., Huang, H., Yang, J., Li, Z., Zhang, D., Wei, F.: Lvp-
+m3: Language-aware visual prompt for multilingual multimodal machine
+translation. EMNLP (2022)
+[55] Firat, O., Cho, K., Bengio, Y.: Multi-way, multilingual neural machine
+translation with a shared attention mechanism. In: Knight, K., Nenkova,
+A., Rambow, O. (eds.) NAACL HLT 2016, The 2016 Conference
+of the North American Chapter of the Association for Computa-
+tional Linguistics: Human Language Technologies, San Diego California,
+USA, June 12-17, 2016, pp. 866–875. The Association for Compu-
+tational Linguistics, ??? (2016). https://doi.org/10.18653/v1/n16-1101.
+https://doi.org/10.18653/v1/n16-1101
+
+Springer Nature 2021 LATEX template
+Article Title
+27
+[56] Johnson, M., Schuster, M., Le, Q.V., Krikun, M., Wu, Y., Chen, Z., Tho-
+rat, N., Vi´egas, F.B., Wattenberg, M., Corrado, G., Hughes, M., Dean, J.:
+Google’s multilingual neural machine translation system: Enabling zero-
+shot translation. Trans. Assoc. Comput. Linguistics 5, 339–351 (2017).
+https://doi.org/10.1162/tacl a 00065
+[57] Fan, A., Bhosale, S., Schwenk, H., Ma, Z., El-Kishky, A., Goyal, S.,
+Baines, M., Celebi, O., Wenzek, G., Chaudhary, V., Goyal, N., Birch, T.,
+Liptchinsky, V., Edunov, S., Auli, M., Joulin, A.: Beyond english-centric
+multilingual machine translation. J. Mach. Learn. Res. 22, 107–110748
+(2021)
+[58] Lin, Z., Pan, X., Wang, M., Qiu, X., Feng, J., Zhou, H., Li, L.: Pre-training
+multilingual neural machine translation by leveraging alignment informa-
+tion. In: Webber, B., Cohn, T., He, Y., Liu, Y. (eds.) Proceedings of the
+2020 Conference on Empirical Methods in Natural Language Processing,
+EMNLP 2020, Online, November 16-20, 2020, pp. 2649–2663. Association
+for Computational Linguistics, ??? (2020). https://doi.org/10.18653/v1/
+2020.emnlp-main.210. https://doi.org/10.18653/v1/2020.emnlp-main.210
+[59] Aharoni, R., Johnson, M., Firat, O.: Massively multilingual neural
+machine translation. In: Burstein, J., Doran, C., Solorio, T. (eds.) Pro-
+ceedings of the 2019 Conference of the North American Chapter of the
+Association for Computational Linguistics: Human Language Technolo-
+gies, NAACL-HLT 2019, Minneapolis, MN, USA, June 2-7, 2019, Volume
+1 (Long and Short Papers), pp. 3874–3884. Association for Compu-
+tational Linguistics, ??? (2019). https://doi.org/10.18653/v1/n19-1388.
+https://doi.org/10.18653/v1/n19-1388
+[60] Zhang, B., Williams, P., Titov, I., Sennrich, R.: Improving massively
+multilingual neural machine translation and zero-shot translation. In:
+Jurafsky, D., Chai, J., Schluter, N., Tetreault, J.R. (eds.) Proceedings
+of the 58th Annual Meeting of the Association for Computational Lin-
+guistics, ACL 2020, Online, July 5-10, 2020, pp. 1628–1639. Association
+for Computational Linguistics, ??? (2020). https://doi.org/10.18653/v1/
+2020.acl-main.148. https://doi.org/10.18653/v1/2020.acl-main.148
+[61] V´azquez, R., Raganato, A., Tiedemann, J., Creutz, M.: Multilingual NMT
+with a language-independent attention bridge. In: Augenstein, I., Gella,
+S., Ruder, S., Kann, K., Can, B., Welbl, J., Conneau, A., Ren, X., Rei, M.
+(eds.) Proceedings of the 4th Workshop on Representation Learning for
+NLP, RepL4NLP@ACL 2019, Florence, Italy, August 2, 2019, pp. 33–39.
+Association for Computational Linguistics, ??? (2019). https://doi.org/
+10.18653/v1/w19-4305. https://doi.org/10.18653/v1/w19-4305
+[62] Philip, J., Berard, A., Gall´e, M., Besacier, L.: Monolingual adapters
+
+Springer Nature 2021 LATEX template
+28
+Article Title
+for zero-shot neural machine translation. In: Webber, B., Cohn, T.,
+He, Y., Liu, Y. (eds.) Proceedings of the 2020 Conference on Empir-
+ical Methods in Natural Language Processing, EMNLP 2020, Online,
+November 16-20, 2020, pp. 4465–4470. Association for Computational Lin-
+guistics, ??? (2020). https://doi.org/10.18653/v1/2020.emnlp-main.361.
+https://doi.org/10.18653/v1/2020.emnlp-main.361
+[63] Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez,
+A.N., Kaiser, L.u., Polosukhin, I.: Attention is all you need. In:
+Guyon, I., Luxburg, U.V., Bengio, S., Wallach, H., Fergus, R., Vish-
+wanathan, S., Garnett, R. (eds.) Advances in Neural Information
+Processing Systems, vol. 30. Curran Associates, Inc., ??? (2017).
+https://proceedings.neurips.cc/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-
+Paper.pdf
+[64] Shazeer, N., Mirhoseini, A., Maziarz, K., Davis, A., Le, Q., Hinton,
+G., Dean, J.: Outrageously large neural networks: The sparsely-gated
+mixture-of-experts layer. In: International Conference on Learning Rep-
+resentations (2017). https://openreview.net/forum?id=B1ckMDqlg
+[65] K¨oksal,
+A.,
+¨Ozg¨ur,
+A.:
+The
+RELX
+dataset
+and
+matching
+the
+multilingual blanks for cross-lingual relation classification. In: Find-
+ings
+of
+the
+Association
+for
+Computational
+Linguistics:
+EMNLP
+2020,
+pp.
+340–350.
+Association
+for
+Computational
+Linguistics,
+Online
+(2020).
+https://doi.org/10.18653/v1/2020.findings-emnlp.32.
+https://www.aclweb.org/anthology/2020.findings-emnlp.32
+

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+Differentially Private Distributed Bayesian
+Linear Regression with MCMC
+Barı¸s Alparslan1, Sinan Yıldırım1, 2, and S¸. ˙Ilker Birbil3
+1Faculty of Engineering and Natural Sciences, Sabancı University, ˙Istanbul, Turkey∗
+2Center of Excellence in Data Analytics (VER˙IM), Sabancı University, ˙Istanbul, Turkey
+3Department of Business Analytics, University of Amsterdam, Amsterdam, The Netherlands
+February 1, 2023
+Abstract
+We propose a novel Bayesian inference framework for distributed differentially private
+linear regression. We consider a distributed setting where multiple parties hold parts of the
+data and share certain summary statistics of their portions in privacy-preserving noise. We
+develop a novel generative statistical model for privately shared statistics, which exploits a
+useful distributional relation between the summary statistics of linear regression. Bayesian
+estimation of the regression coefficients is conducted mainly using Markov chain Monte Carlo
+algorithms, while we also provide a fast version to perform Bayesian estimation in one iteration.
+The proposed methods have computational advantages over their competitors. We provide
+numerical results on both real and simulated data, which demonstrate that the proposed
+algorithms provide well-rounded estimation and prediction.
+Keywords: Differential privacy, linear regression, distributed learning, MCMC
+1
+Introduction
+Linear regression is a mathematical method that lies at the core of statistical research. Many
+researchers have been working on linear regression since the 19th century, and hence, many
+well-known solution methods exist. On a separate note, privacy-preserving statistical learning has
+gained popularity and importance in recent years, with differential privacy prevailing as the most
+commonly used definition for privacy (Dwork, 2006; Dwork et al., 2014a; Dankar and El Emam,
+2013). As a result, there is a recent but growing interest in differentially private linear regression.
+Many works in the data privacy literature do not mainly focus on regression but are motivated by
+or can be applied to regression. As an example, differentially private empirical risk minimisation
+(Chaudhuri et al., 2009; Bassily et al., 2014; Abadi et al., 2016; Kuru et al., 2022) can be applied to
+regression once it is cast as a data-driven optimisation problem. Many general-purpose Bayesian
+differentially private estimation methods can also be used in regression problems. Williams and
+Mcsherry (2010) is one of the first works that considered a hierarchical model for the privatised
+data and Bayesian estimation for the model parameters. Zhang et al. (2016) analyse several
+differential privacy mechanisms for posterior sampling and suggest using these mechanisms also
+∗The study was funded by the Scientific and Technological Research Council of Turkey (T¨UB˙ITAK) ARDEB
+Grant No 120E534. Barı¸s Alparslan and Sinan Yıldırım were supported by the project.
+1
+arXiv:2301.13778v1  [stat.ML]  31 Jan 2023
+
+for linear regression. Dimitrakakis et al. (2017) developed a posterior sampling query algorithm
+to combine differential privacy and Bayesian inference. Contrary to those one-sample approaches,
+general-purpose differentially private Markov chain Monte Carlo (MCMC) algorithms, which aim
+to identify the posterior distribution via iterative sampling, can also be applied to regression
+(Wang et al., 2015; Foulds et al., 2016; Wang et al., 2015; Yıldırım and Ermi¸s, 2019; Heikkil¨a
+et al., 2019; Gong, 2022; Alparslan and Yıldırım, 2022; Ju et al., 2022).
+Several works in the literature are somewhat more directly related to differentially private regression.
+Zhang et al. (2012) suggested a functional mechanism method, which is based on perturbing
+polynomial objective functions with privacy-preserving noise. As an alternative, Dwork et al.
+(2014b); Wang (2018) considered perturbation of summary statistics. Alabi et al. (2022) provide
+a technical discussion on different point estimation methods for differentially private simple linear
+regression, that is when we have a single feature. Ferrando et al. (2022) present a method to
+compute confidence intervals for the coefficients of linear regression. Cai et al. (2021) study the
+rates of convergence for parameter estimation with differential privacy via output perturbation,
+where a non-private estimator is perturbed. All those works consider point estimation of the
+linear regression parameters.
+In this paper, we focus on differential private distributed Bayesian inference for the parameters of
+linear regression. We use a novel hierarchical model that relies on a distributional relationship
+(Proposition 1) between the summary statistics of linear regression, which, to the best of our
+knowledge, has not been exploited so far. We propose Bayesian inference algorithms that take
+perturbations of summary statistics as observations. The general inferential tool we pick in this
+paper is MCMC, a well-known framework for iterative sampling from posterior distributions. As
+we shall see, the proposed MCMC algorithms in this paper already have lower computational
+complexities per iteration than their closest competitors in Bernstein and Sheldon (2019). Addi-
+tionally, we also propose much faster Bayesian estimation methods that perform estimation in
+one iteration. Finally, we assume a distributed setting where the total dataset is shared among
+multiple parties (data nodes), who want to collaborate for the inference of a common parameter,
+see e.g., Heikkil¨a et al. (2017) for such a setting. The non-distributed setting is just a special
+case (single data holder) for our methodology.
+This paper has connections with several works in the literature, yet it has significant differences
+from each of those, as we shall explain below.
+For the privacy-preserving mechanism, we consider adding noise to summary statistics of linear
+regression, similarly to Wang (2018); Bernstein and Sheldon (2019). The adaSSP framework of
+Wang (2018) motivates the fast Bayesian estimation methods developed in this paper. However,
+adaSSP is a point estimation method while we aim for a posterior distribution. The latter work,
+Bernstein and Sheldon (2019), is particularly related to this paper as they also study Bayesian
+linear regression with differential privacy using perturbed statistics of data. However, there are
+some important differences between our work and that of Bernstein and Sheldon (2019). These
+differences stem from the choice of summary statistics and the consequent hierarchical structure
+used for modelling linear regression. Those modelling differences lead to significant differences in
+the inference methods as well as significant computational advantages for our methods. Specifically,
+the computational complexity of our methods is O(d3), where d is the number of features. This
+order is much less than the O(d6) of Bernstein and Sheldon (2019). Finally, neither Wang (2018)
+nor Bernstein and Sheldon (2019) has considered a distributed learning setting like we do in
+2
+
+this paper, although both works can be modified for the distributed setting after moderate
+modifications.
+Foulds et al. (2016); Heikkil¨a et al. (2017) are other differentially Bayesian inference methods
+that target posterior distributions of perturbed summary statistics of sensitive data. The one by
+Heikkil¨a et al. (2017) is particularly interesting because they consider a distributed setting and
+present linear regression as their showcase example. However, we differ from those works in the
+way we model the perturbed statistics and in the choice of inference methods. Specifically, Foulds
+et al. (2016); Heikkil¨a et al. (2017) treat the perturbed statistics as if not perturbed, while we
+incorporate the effect of perturbation in our model.
+Recently, Alparslan and Yıldırım (2022) and Ju et al. (2022) employ data augmentation for
+modelling sensitive and privatised data and propose MCMC for Bayesian inference, the latter work
+having linear regression as a major application. Their methods have O(n) complexity per iteration
+in general where n is the number of instances in the data set, which can be slow when n is large.
+In contrast, our methods are scalable in data size since their computational complexities do not
+depend on n. We note that Alparslan and Yıldırım (2022, Section 4.2) also present an MCMC
+method scalable with n that exploits the approximate normality of additive summary statistics.
+However, a direct application of that would lead to an algorithm with O(d6) computational
+complexity (per iteration), like in Bernstein and Sheldon (2019).
+The paper is organised as follows: In Section 2 we review differential privacy. In Section 3 we lay
+out the hierarchical model for differentially private distributed linear regression with perturbed
+summary statistics. In Section 4, we present and discuss the aspects of the proposed inference
+algorithms. Section 5, we provide numerical experiments. We conclude in Section 6.
+Notation:
+Matrices and vectors are shown in bold-face notation. For a matrix A, its transpose,
+trace, and determinant (whenever they exist) are AT , tr(A), and |A|, respectively. For any
+sequence {ai}i≥0, we let ai:j = (ai, . . . , aj). We write x ∼ P to mean the random variable x
+has distribution P. N(m, Σ) stands for the multivariate normal distribution with mean m and
+covariance Σ. Wishart and inverse-Wishart distributions with scale matrix Λ and κ degrees of
+freedom are shown as W(Λ, κ) and IW(Λ, κ), respectively. IG(a, b) stands for the inverse-gamma
+distribution with shape and scale parameters a and b. We augment those notations with x to
+denote the respective probability density functions (pdf), e.g., as N(x; m, Σ).
+2
+Differential Privacy
+Differential privacy (Dwork, 2006, 2008) concerns randomised algorithms that run on sensitive,
+or usually private, data. A randomised algorithm takes an input data set D ∈ D and returns a
+random output in O, where the randomness is intrinsic to the algorithm. A differentially private
+algorithm constrains the difference between the probability distributions of the outputs obtained
+from neighbouring data sets. We say two data sets are neighbours if they differ by one individual’s
+piece of data.
+Definition 1 (Differential privacy). A randomised algorithm M : D �→ O is (ϵ, δ)-differentially
+private (DP) if for any pair of neighbouring data sets D, D′ ∈ D and for any subset O ⊆ O of the
+of support domain, it satisfies
+P[M(D) ∈ O] ≤ eϵP[M(D′) ∈ O] + δ.
+3
+
+The definition implies that smaller (ϵ, δ) leads to more privacy.
+Privacy-preserving algorithms often use noise-adding mechanisms. A popular noise-adding mecha-
+nism is the Gaussian mechanism (Dwork et al., 2006), which perturbs a function f : D �→ Rk of
+the sensitive data, for some k ≥ 1, with a random noise drawn from the Gaussian distribution.
+The amount of the added noise depends on the L2-sensitivity of the function, given by
+∆f =
+max
+neighbourD1,D2∈D∥f(D1) − f(D2)∥2.
+An (ϵ, δ)-DP Gaussian mechanism returns
+f(D) + ∆fσ(ϵ, δ)v,
+v ∼ N(0, Ik)
+(1)
+upon taking D as the input, where the quantity σ(ϵ, δ) ensures (ϵ, δ)-DP. In this work, we take
+σ(ϵ, δ) as the analytical solution given in Balle and Wang (2018, Algorithm 1) due to its tightness.
+The Gaussian mechanism is also central to other forms of privacy, such as zero-concentrated DP
+(Bun and Steinke, 2016) and Gaussian DP (Dong et al., 2022).
+In this paper, we consider (ϵ, δ)-DP as the type of privacy and the Gaussian mechanism to generate
+noisy observations. Moreover, the proposed methods in this paper never use the sensitive data
+once given the noisy observations generated using the Gaussian mechanism, hence exploiting the
+post-processing property of differential privacy (Dwork and Roth, 2014).
+Theorem 1 (Post-processing). If M : D �→ O be (ϵ, δ)-DP and let f : O → O′ be another mapping
+independent of D given M(D). Then fM : D �→ O′ with fM(D) = f(M(D)) is (ϵ, δ)-DP.
+3
+Differentially Private Distributed Linear Regression
+In this section, we present a new hierarchical model for differentially private distributed linear
+regression. For ease of exposition, we first present a model with a single data holder, then
+generalise the model for the distributed setting.
+3.1
+Basic Model and Privacy Setup
+Suppose we have a sequence of random variables {(xi, yi) : i = 1, . . . , n}, where xi ∈ X ⊆ Rd×1
+are the feature vectors and yi ∈ Y ⊆ R is the i’th response variable. We consider the normal
+linear regression to model the dependency between xi and yi. Specifically,
+yi = xT
+i θ + ei,
+ei
+i.i.d.
+∼ N(0, σ2
+y),
+i = 1, . . . , n,
+where θ ∈ Rd is the vector of the linear regression coefficients. We assume that the feature vectors
+xi’s are i.i.d. with distribution Px. Below, we will particularly focus on the case when Px can be
+assumed to be a normal distribution. However, we will also present algorithms for general Px.
+In matrix notation, the above can shortly be expressed as
+y = Xθ + e,
+e ∼ N(0, σ2
+yIn),
+where X =
+�
+xT
+1
+. . .
+xT
+n
+�T is the so-called design matrix, y =
+�
+y1
+. . .
+yn
+�T . Additionally, we
+also define the summary statistics of X and y given by
+S := XT X,
+z := XT y,
+4
+
+respectively. We assume a setup where S and z are privately released as the noisy summary
+statistics ˆS and ˆz are constructed as
+ˆS = S + σsM,
+(2)
+ˆz = z + σzv,
+v ∼ N(0, Id),
+(3)
+where M is a d × d symmetric matrix with its upper triangular elements drawn from N(0, 1).
+Dwork et al. (2014b) arrange σs and σz so that both (2) and (3) are (ϵ/2, δ/2) differentially
+private, leading to (ϵ, δ)-DP overall. Differently than Dwork et al. (2014b), we set
+σs = σz = ∆szσ(ϵ, δ),
+where σ(ϵ, δ) is given in Balle and Wang (2018, Algorithm 1), and ∆sz is the overall L2 sensitivity
+of [S, z], given by
+∆sz =
+�
+∥X∥4 + ∥X∥2∥Y ∥2
+with ∥X∥ = maxx∈X ∥x∥2 and ∥Y ∥ = maxy∈Y |y|.
+Based on the above relations, we shall represent a hierarchical model that enables Bayesian
+inference of θ given ˆS and ˆz. One important element of our modelling approach is the following
+result that establishes the conditional distribution of z given S, θ, and σ2
+y.
+Proposition 1. For the normal linear regression model, we have
+z|S, θ, σ2
+y ∼ N(Sθ, Sσ2
+y).
+Proof. First, note that,
+E[z|X, θ, σ2
+y] = E[XT Xθ + XT e] = Sθ,
+(4)
+Cov(z|X, θ, σ2
+y) = XT Xσ2
+y = Sσ2
+y,
+(5)
+and observe that both moments depend on X through its statistic S. Therefore, the conditional
+density of z given S, θ, and σ2
+y is
+p(z|X, θ, σ2
+y) = N(z; Sθ, Sσ2
+y).
+Next, define the function f : Rn×d �→ [0, ∞) with f(X) = p(z|X, θ, σ2
+y) and let CS,θ,σ2y = {X :
+XT X = S}, Since the function f is constant over CS,θ,σ2y, we can write
+p(z|S) =
+�
+CS,θ,σ2y
+fdPx = N(z; Sθ, Sσ2
+y),
+where the second equation is by moment equations in (4) and (5) above. This concludes the
+proof.
+Finally, we assign prior distributions for θ, σ2
+y as
+θ ∼ N(m, C),
+σ2
+y ∼ IG(a, b).
+(6)
+5
+
+At this point, it is worth discussing some important modelling differences between our work and
+Bernstein and Sheldon (2019). In Bernstein and Sheldon (2019), the central limit theorem (CLT)
+is applied to
+�
+S, z, yT y
+�
+, leading to a normality assumption for the whole vector. In contrast,
+we use the exact conditional distribution p(z|S, θ, σ2) thanks to Proposition 1. Moreover, unlike
+Bernstein and Sheldon (2019), we do not require a noisy version yT y, hence have a slight advantage
+of using less privacy-preserving noise. In summary, our model has a different hierarchical structure
+and requires less privacy-preserving noise.
+3.2
+Distributed Setting
+Next, we extend our model to the distributed setting, where the total data are shared among
+J ≥ 1 data holders as
+(X, y) = {(Xj, yj); j = 1, . . . , J}.
+(7)
+We let ni be number of rows in each xi, so that n = n1 + . . . + nJ. Each data holder j shares
+their own summary statistics Sj = XT
+j Xj, zj = XT
+j yj with privacy-preserving noise
+ˆSj = Sj + σsMj,
+ˆzj = z + σzvj,
+vj ∼ N(0, Id).
+(8)
+Note that, to preserve a given (ϵ, δ)-DP overall, each party must provide that level of privacy
+for their data, hence σs and σz are the same as before. The hierarchical structure of the overall
+model (specified for normally distributed xi’s) is shown in Figure 1.
+Figure 1: Differentially private distributed linear regression model (specified for normally distributed xi’s.)
+The distributed setting deserves separate consideration than the single data holder case for a couple
+of reasons: Firstly, the node-specific observations ( ˆS1, ˆz1), . . . , ( ˆSJ, ˆzJ) are altogether statistically
+more informative on θ than their aggregates �J
+j=1 ˆSj and �J
+j=1 ˆzj. This is because the aggregate
+versions are not sufficient statistics of the node-specific observations ( ˆS1, ˆz1), . . . , ( ˆSJ, ˆzJ) with
+respect to θ (even when σ2
+y is known.) Therefore, when the node-specific observations are available,
+one should not, in principle, trivially aggregate them and apply an inference method designed for
+J = 1 using those aggregates.
+Secondly, the partitioning of data as in (7) can be relevant to data privacy applications even
+outside the distributed learning framework, rendering the methodology in Section 4 useful in a
+6
+
+broader sense. For example, batches of (x, y)-type of data may be donated to a common data
+collector as in (8). At this point, a particular and interesting relation exists with pan-privacy
+applications (Dwork et al., 2010). Imagine that sensitive data from individuals are collected
+sequentially in time, and the data holder is concerned about possible intrusions into the memory
+where the sensitive data are stored. Then, one possible way to ensure the privacy of the data
+against such possible intrusions, which is the promise of pan-privacy, is to store the noisy statistics
+of every new batch of data and erase the original sensitive data. Then, at any time the data
+collector has data of the form ( ˆS1, ˆz1), . . . , ( ˆSJ, ˆzJ), each pair corresponding to a batch. As a
+result, inference algorithms as in Section 4 can be applied.
+4
+Algorithms for Bayesian Inference
+Bayesian inference targets the posterior distribution of the latent variables of the model, in
+particular θ, given the observations ˆS1:J and ˆz1:J. We present several Bayesian inference algorithms
+for the hierarchical model described in the previous section. In addition to other concerns like
+computational budget, the choice among those approaches mainly depends on the specification of
+Px as the distribution of S directly depends on it. In this paper, we have considered the following
+two cases and devised algorithms for each of them:
+1. In some cases it may be adequate to specify Px = N(0, Σx). This leads to S|Σx ∼ W(Σx, n).
+Further, to account for the uncertainty about the covariance Σx, one can treat it as a random
+variable with Σx ∼ IW(Λ, κ). Figure 1 shows the hierarchical structure of the distributed
+setting with those specifications. We defer discussing the conflict between the normality and
+boundedness assumptions to Remark 1 towards the end of Section 4.1.
+2. As the second case, we assume a general (non-normal) Px. A normal approximation, based on
+the CLT, could be considered for the distribution S (Wilson and Ghahramani, 2011). However,
+this would require the knowledge (or accurate estimation) of up to the fourth moments of Px
+as well as expensive computations for sampling S. We circumvent those difficulties by plugging
+in a point estimate of S given ˆS and use it during the sampling process as if it is the true
+S itself. Then, we develop two different algorithms for inference of θ, one being an MCMC
+algorithm and the other providing a closed form-solution for the posterior of θ following a
+rough point-wise estimation of σ2
+y. Note that these algorithms with fixed S do not require a
+distribution for x.
+Next, we provide the details of our approaches and the resulting algorithms.
+4.1
+Normally Distributed Features
+In this section, we present an MCMC algorithm for Bayesian inference for the differentially private
+distributed linear regression model when Px = N(0, Σx) and Σx ∼ IW(Λ, κ). The latent variables
+involved in this variant are θ, Σx, σ2
+y, S1:J, z1:J. Their posterior distribution given ˆS1:J, ˆz1:J can
+be written as
+p(θ, σ2
+y, Σx, z1:J, S1:J|ˆz1:J, ˆS1:J) ∝ p(θ)p(σ2
+y)p(Σx)
+J
+�
+j=1
+p(zj|θ, σ2
+y, S)p(Sj|Σx)p( ˆSj|Sj)p(ˆzj|zj).
+(9)
+7
+
+One could design an MCMC algorithm for this posterior distribution that updates θ, σ2
+y, Σx, z1:J,
+S1:J in turn based on their full conditional distributions. However, such an algorithm suffers from
+poor convergence because of a high posterior correlation between θ and z1:J (as verified in our
+numerical studies). It is well known that highly correlated variables result in poor convergence
+if they are updated one conditional on the other. To alleviate that problem, we work with the
+reduced model where z1:J are integrated out. The reduced model has θ, Σx, σ2
+y as its latent
+variables, whose joint posterior distribution can be written as
+p(θ, σ2
+y,Σx, S|ˆz, ˆS) ∝ p(θ)p(σ2
+y)p(Σx)
+J
+�
+j=1
+p(Sj|Σx)p( ˆSj|Sj)p(ˆzj|Sj, θ, σ2
+y),
+(10)
+where p(ˆz|S, θ, σ2
+y) = N(ˆz; Sθ, σ2
+ySθ + σ2
+zId).
+We would like to sample from the posterior distribution in (10) via MCMC that updates θ, σ2
+y,
+Σx, S1:J in turn based on their full conditional distributions. The variables θ and Σx enjoy
+closed-form full conditional distributions (see Appendix A for the derivations):
+Σx|S1:J, ˆS1:J, ˆz1:J ∼ IW
+�
+�Λ +
+J
+�
+j=1
+Sj, κ + n
+�
+� ,
+(11)
+θ|σ2
+y, ˆz, S1:J ∼ N(mp, Σp),
+(12)
+where the posterior moments for θ are
+Σ−1
+p
+=
+J
+�
+j=1
+Sj(σ2
+ySj + σ2
+zI)−1Sj + C−1,
+mp = Σp
+�
+�
+J
+�
+j=1
+Sj(σ2
+ySj + σ2
+zI)−1 ˆzj + C−1m
+�
+� .
+The full-conditional distributions of S1:J and σ2
+y have no closed form; hence we design Metropolis-
+Hastings (MH) moves to update them. For σ2
+y, one can simply use a random-walk MH move
+targeting p(σ2
+y|θ, S1:J, ˆz1:J). For S1:J, their full conditional distribution can be factorised as
+p(S1:J| ˆS1:J, ˆz1:J, Σx, σ2
+y, θ) =
+J
+�
+j=1
+p(Sj| ˆSj, ˆzj, Σx, σ2
+y, θ),
+where each factor is given by
+p(Sj| ˆSj, ˆzj, Σx, σ2
+y, θ) ∝ p(ˆzj|Sj, θ, σ2
+y)p(Sj|Σx)p( ˆSj|Sj).
+Thanks to that factorised form, each Sj can be updated with an MH move independently and
+in parallel. For the MH algorithm to update one Sj, we propose a new value from a Wishart
+distribution as S′
+j ∼ W(Sj/α, α), which has mean Sj and variance determined by α. In our
+experiments, we adjust a using ideas from the adaptive MCMC framework (Andrieu and Thoms,
+2008) to target an acceptance rate of around 0.2.
+Algorithm 1 represents the overall MCMC algorithm for the hierarchical model for differentially
+Bayesian distributed linear regression when Px is a normal distribution with a random covariance
+matrix having an inverse-Wishart distribution. We call this algorithm MCMC-normalX.
+8
+
+Algorithm 1: MCMC-normalX - one iteration
+Input: Current values of S1:J, θ, σ2
+y, Σx; observations ˆS1:J,ˆz1:J; noise variances σ2
+s, σ2
+z;
+proposal parameters a, σ2
+q; hyperparameters a, b, κ, Λ, m, C.
+Output: New sample of Σx, S, σ2
+y, θ
+1 Sample Σx using (11).
+2 for j = 1, 2, . . . J do
+3
+Update Sj via an MH move targeting p(Sj|Σx, θ, ˆzj).
+4 Sample θ using (12).
+5 Update σ2
+y via an MH move targeting p(σ2
+y|θ, S1:J, ˆz1:J).
+Remark 1. Admittedly, a potential concern is a conflict between the normality and boundedness
+assumptions (both for x and y). However, we also note that the collected data often happen
+to have some natural boundaries (which can be exploited to determine the sensitivity of the
+shared statistics), and yet the normal distribution is still used for modelling and subsequent
+inference mainly for sake of tractability. With the normality assumption, one can implement
+computationally efficient algorithms at the expense of minor modelling inaccuracies. While we
+acknowledge the methodologies in Alparslan and Yıldırım (2022, Section 4.2) and Ju et al. (2022)
+that can correctly incorporate the effect of truncation into inference, we remark that those methods
+pay the price of exactness by having O(n) computational complexity per iteration.
+4.2
+Features with a General Distribution
+The normality assumption for xi’s in Section 2 may not be adequate for some data sets. Moreover,
+when d is large, updating Sj’s can be the bottleneck of MCMC-normalX in Algorithm 1 in terms of
+computation time and convergence. We propose two algorithms to address both of those concerns.
+As it turns out, those algorithms provide accurate estimations even for the case of normally
+distributed features; see Section 5.1.
+Our approach for xi’s with a general distribution is based on estimating Sj’s from the beginning,
+using some principled estimation method, and fixing Sj’s to those estimates during the whole
+course of the inference procedure. In that way, we obtain a faster MCMC algorithm at the expense
+of targeting an approximate posterior distribution. Moreover, we have observed in our experiments
+that this variant is quite competitive in terms of accuracy, especially when the total number of
+nodes J increases. We call this variant MCMC-fixedS and present it in Algorithm 2.
+As for estimating Sj’s, one could simply consider taking the privately shared ˆSj as an estimator
+for Sj, but ˆSj is not necessarily a positive (semi-)definite matrix. Instead, we propose the nearest
+positive semi-definite matrix of to ˆSj as the estimator of Sj in terms of the Frobenius norm. (The
+nearest positive definite matrix to ˆSj does not exist.) To find the nearest positive semi-definite
+matrix, we follow Higham (1988) and apply the following procedure for each j = 1, . . . , J: (i)
+Calculate the eigendecomposition ˆSj = EDET , where E is a matrix of eigenvectors, and D is a
+diagonal matrix consisting of the eigenvalues λi. (ii) The nearest symmetric positive semi-definite
+matrix is �Sj = ED+ET , where D+ is a diagonal matrix with D+(i, i) = max{D(i, i), 0}.
+Note that �Sj found above is the maximum likelihood estimator of Sj given ˆSj (over the set
+of positive semi-definite matrices) since the conditional distribution of ˆSj given Sj is a normal
+9
+
+Algorithm 2: MCMC-fixedS - one iteration
+Input: Current values of θ, σ2
+y; estimates ˆS1:J, observations ˆz1:J; noise variance σ2
+z, and
+hyperparameters a, b, m, C.
+Output: New sample of σ2
+y, θ.
+1 Use S1:J = �S1:J throughout.
+2 Sample θ using (12).
+3 Update σ2
+y via an MH move targeting p(σ2
+y|θ, S1:J, ˆz1:J).
+Algorithm 3: Bayes-fixedS-fast
+Input: ˆS1:J, ˆz1:J; noise variance: σ2
+z; estimate ˜σ2
+y of σ2
+y; hyperparameters: m, C.
+Output: Estimate ˆθ.
+1 for j = 1, 2, . . . J do
+2
+Calculate the estimate �Sj for Sj using ˆSj.
+3
+Calculate Σj = �Sj(˜σ2
+y �Sj + σ2
+zI)−1 �Sj.
+4
+Calculate mj = �Sj(˜σ2
+y �Sj + σ2
+zI)−1 ˆzj.
+5 return Posterior moments of θ: Σ−1
+post = �J
+j=1 Σj + C−1,
+mpost = Σpost
+�
+C−1m + �J
+j=1 mj
+�
+.
+distribution with mean Sj.
+MCMC-fixedS in Algorithm 2 is faster than MCMC-normalX in Algorithm 1, since it avoids the step
+to update Sj’s, which constitutes the main computational burden on Algorithm 1. However,
+MCMC-fixedS can be made even faster by fixing σ2
+y also. As a crude estimator, we used ˜σ2
+y = ∥Y∥/3
+throughout the experiments. When σ2
+y is fixed in addition to S1:J, we end up with a non-iterative
+method where the posterior distribution of θ is calculated in closed form. We call the resulting
+algorithm Bayes-fixedS-fast and present it in Algorithm 3. Algorithm 3 does nothing but
+returns the moments of the posterior distribution of θ given �Sj’s, ˆzj’s, ˜σ2
+y, and the prior parameters
+for θ.
+4.3
+Computational Cost
+All our methods described in this section require O(d3) computation (per iteration for the iterative
+ones in Algorithms 1 and 2, or as a whole for the fast version in Algorithm 3) since they deal with
+d × d matrices. In contrast, as Bernstein and Sheldon (2019) apply CLT to the vector [S, z, yT y],
+their methods deal with covariance matrices of size (d2 + d + 1) explicitly, which leads to O(d6)
+computation per MCMC iteration. For even moderate d, this computational difference becomes
+dramatic and the latter may be prohibitive. Moreover, the complexity of our methods does not
+depend on n. This is in contrast to the O(n) complexity of general-purpose methods, such as
+Alparslan and Yıldırım (2022, Section 4.3) and Ju et al. (2022), that can be applied to linear
+regression.
+10
+
+4.4
+Extensions
+We mention two other variants of our methodology, deferring the details to Appendix B.
+Another solution for dealing with non-normal Px could be to average the feature vectors in X
+(and the corresponding response variables in y), so that the averaged rows of X can be modelled
+as approximately normal, due to CLT. This enables using the methods devised for normally
+distributed features. For the details of this approach, see Appendix B.1.
+Secondly, if the features are normally distributed but the data are not centred, we need to
+include the intercept parameter, which corresponds to appending xi with a one from the left, and
+MCMC-normalX does not directly apply. In that case, we can modify the hierarchical model that
+accommodates the non-centralised features and the intercept parameter and still benefit from
+the sampling techniques involved in MCMC-normalX in Algorithm 1. Appendix B.2 contains the
+details of the modified hierarchical model.
+5
+Numerical Experiments
+We present several numerical evaluations of the proposed methods, MCMC-normalX, MCMC-fixedS,
+and Bayes-fixedS-fast with simulated and real data. We compare our algorithms with two
+methods: adaSSP of Wang (2018) and the MCMC method of Bernstein and Sheldon (2019) for
+differentially private linear regression that we call MCMC-B&S. Note that adaSSP and MCMC-B&S
+are originally proposed for the non-distributed setting, that is, J = 1. For a comprehensive
+comparison, we have implemented their extensions for J ≥ 1. The details of those extensions are
+provided in Appendix C. In particular, we have carefully generalised the model in Bernstein and
+Sheldon (2019) for J ≥ 1 similarly as we have done for our model in Section 3.2. What we call
+MCMC-B&S is the adaptation of Bernstein and Sheldon (2019, Algorithm 1) for this generalised
+model (and (ϵ, δ)-DP). The code to replicate all of the experiments in this section can be found at
+https://github.com/sinanyildirim/Bayesian_DP_dist_LR.git.
+5.1
+Experiments with Simulated Data
+We have considered two different configurations, (n = 105, d = 2) and (n = 105, d = 5), for
+the problem size. For each (n, d), we have simulated the data as follows: We have generated
+θ ∼ N(0, Id), xi ∼ N(0, Σx) where Σx ∼ IW(Λ, κ) with κ = d + 1 and selected the scale matrix
+randomly as Λ = V T V , where V is a d × d matrix of i.i.d. variables from N(0, 1). The response
+variables y have been generated with σ2
+y = 1. For inference, we have used the same Λ, κ as above
+and a = 20, b = 0.5, m = 0d×1, C = (a − 1)/bId for the other hyperparameters.
+We have evaluated the methods at all combinations of J ∈ {1, 5, 10} and ϵ ∈ {0.1, 0.2, 0.5, 1, 2, 5, 10}.
+All the MCMC algorithms have been run for 104 iterations. For each (J, ϵ) pair, we have tried
+each method 50 times (each with different noisy observations) to obtain average performances.
+For performance metrics, we have looked at the mean squared errors (MSE) of (i) the estimates ˆθ,
+and (ii) the predictions ˆy(xtest) generated by the methods. For the Bayesian methods, ˆθ is taken as
+the mean posterior, which can be numerically estimated for the MCMC algorithms. For prediction
+performance, we have calculated E[ˆy(xtest) − ytest]2. For the Bayesian methods, ˆy(xtest) is the
+posterior predictive expectation of ytest at xtest. For adaSSP, we simply take ˆy(xtest) = xT
+test ˆθ.
+11
+
+The results are summarised in Figure 2. We observe that MCMC-fixedS and Bayes-fixedS-fast
+outperform adaSSP and MCMC-B&S in almost all cases both in terms of estimation and prediction.
+Comparing the full-scale algorithms MCMC-normalX and MCMC-B&S (that involve updates of S), we
+observe a clear advantage of MCMC-normalX at d = 2, but MCMC-B&S becomes more competitive at
+d = 5. This can be attributed to the fact that MCMC-B&S requires the extra statistic yT y, unlike
+MCMC-normalX, which causes MCMC-B&S to use more noisy statistics. This difference becomes more
+significant at small d, where the relative effect of the presence of yT y on the sensitivity is more
+significant. Finally, all methods improve as ϵ grows, which is expected.
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-9.5
+-9
+-8.5
+-8
+-7.5
+(log-)MSE: prediction, J = 1
+MCMC-normalX
+MCMC-fixedS
+Bayes-fixedS-fast
+MCMC-B&S
+adaSSP
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-9
+-8
+-7
+-6
+(log-)MSE: prediction, J = 5
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-9
+-8
+-7
+-6
+-5
+(log-)MSE: prediction, J = 10
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-10.5
+-10
+-9.5
+-9
+(log-)MSE: estimation J = 1
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-10.5
+-10
+-9.5
+-9
+-8.5
+-8
+-7.5
+(log-)MSE: estimation J = 5
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-10
+-9
+-8
+-7
+-6
+(log-)MSE: estimation J = 10
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-6
+-5
+-4
+-3
+-2
+(log-)MSE: prediction, J = 1
+MCMC-normalX
+MCMC-fixedS
+Bayes-fixedS-fast
+MCMC-B&S
+adaSSP
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-5
+-4
+-3
+-2
+-1
+(log-)MSE: prediction, J = 5
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-4
+-3
+-2
+-1
+0
+(log-)MSE: prediction, J = 10
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-3
+-2.5
+-2
+-1.5
+-1
+(log-)MSE: estimation J = 1
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-3
+-2.5
+-2
+-1.5
+-1
+(log-)MSE: estimation J = 5
+0.1
+0.2
+0.5
+1  
+2  
+5  
+10 
+0
+-2.5
+-2
+-1.5
+-1
+-0.5
+(log-)MSE: estimation J = 10
+Figure 2: Averaged prediction and estimation performances (over 50 runs). Top row: n = 105, d = 2, Bottom row:
+n = 105, d = 5.
+0
+10
+20
+d
+0
+2
+4
+6
+8 #10-3
+J = 1
+MCMC-normalX
+MCMC-fixedS
+MCMC-B&S
+0
+10
+20
+d
+0
+0.005
+0.01
+0.015
+0.02
+J = 5
+0
+10
+20
+d
+0
+0.01
+0.02
+0.03
+0.04
+J = 10
+Figure 3: Run times per iteration for MCMC algorithms
+We also compare the computation times of the MCMC algorithms MCMC-normalX, MCMC-fixedS,
+and MCMC-B&S1. Figure 3 shows the run-times of the algorithms vs d. The drastic difference in
+computational loads explained in Section 4.3 is also visible in the figure. While MCMC-B&S may be
+improved in terms of accuracy as d increases, the O(d6) dramatically slows it down.
+1The algorithms were run in MATLAB 2021b on an Apple M1 chip with 8 cores and 16 GB LPDDR4 memory.
+12
+
+5.2
+Experiments with Real Data
+For the real data case, we have used four different data sets from the UCI Machine Learning
+Repository. We have disregarded the columns including string data or key values (ID, name,
+date, etc.), and we have considered the most right-hand column as y. The finalised data sets are
+summarised below.
+data set
+n
+d
+hyperlinks
+power plant energy
+7655
+4
+view link
+bike sharing
+13904
+14
+view link
+air quality
+7486
+12
+view link
+3d road
+347900
+3
+view link
+For prediction, we have taken 80% of the data for training and the rest for testing. We present the
+average prediction performances (out of 50 runs) in Table 1 for each dataset and J with ϵ = 1. We
+observe that the prediction performances of the compared methods are close, while MCMC-fixed-S
+and Bayes-fixed-S are arguably the most stable ones. When J > 1 (the distributed data setting),
+those two methods beat adaSSP and MCMC-B&S more satisfactorily.
+Table 1: Averaged prediction performances (over 50 runs) for the real datasets - ϵ = 1
+J
+data sets
+MCMC-normalX
+MCMC-fixedS
+Bayes-fixedS-fast
+MCMC-B&S
+adaSSP
+J = 1
+PowerPlant
+0.0129
+0.0129
+0.0129
+0.0128
+0.0139
+BikeSharing
+0.0024
+0.0021
+0.0021
+0.0020
+0.0107
+AirQuality
+0.0060
+0.0057
+0.0057
+0.0062
+0.0066
+3droad
+0.0229
+0.0229
+0.0229
+0.0229
+0.0229
+J = 5
+PowerPlant
+0.0133
+0.0134
+0.0134
+0.0136
+0.0235
+BikeSharing
+0.0174
+0.0045
+0.0045
+0.0086
+0.0382
+AirQuality
+0.0142
+0.0100
+0.0099
+0.0130
+0.0227
+3droad
+0.0229
+0.0229
+0.0229
+0.0229
+0.0229
+J = 10
+PowerPlant
+0.0142
+0.0143
+0.0143
+0.0143
+0.0351
+BikeSharing
+0.0812
+0.0082
+0.0082
+0.0137
+0.0526
+AirQuality
+0.0985
+0.0117
+0.0117
+0.0216
+0.0314
+3droad
+0.0229
+0.0229
+0.0229
+0.0229
+0.0229
+6
+Conclusion
+We propose a novel Bayesian inference framework, with MCMC being its main workhorse, for a
+differentially private distributed linear regression setting where the data is partitioned among the
+data holders. We provide several Bayesian inference algorithms suited to the developed hierarchical
+model for linear regression. Those algorithms can be preferred one over the other depending on
+the computational budget, model specifics, or how much we know about the underlying statistical
+facts of the data. We exploit the conditional structure between the summary statistics of linear
+regression, as given in Proposition 1, which leads to feasible algorithms with computational
+advantages over their competitors. The numerical experiments show that the proposed methods
+are competitive with their state-of-the-art alternatives in terms of accuracy.
+The extensions mentioned in Section 4.4 indicate potential future directions. There is also room
+13
+
+for improvement of MCMC-normalX. We chose the most common MH moves to update σ2
+y and
+Sj’s, without paying much attention to their efficiencies. Especially for large d, more advanced
+techniques, such as those stemming from Hamiltonian Monte Carlo (Neal, 2001) or pseudo-marginal
+MCMC (Andrieu and Roberts, 2009), may be employed to facilitate the mixing of the algorithm.
+7
+Acknowledgement
+The study was funded by the Scientific and Technological Research Council of Turkey (T¨UB˙ITAK)
+ARDEB Grant No 120E534.
+Supplementary material:
+The code to replicate the experiments in Section 5 can be found at
+https://github.com/sinanyildirim/Bayesian_DP_dist_LR.git.
+References
+Abadi, M., Chu, A., Goodfellow, I., McMahan, H. B., Mironov, I., Talwar, K., and Zhang, L.
+(2016). Deep learning with differential privacy. In Proceedings of the 2016 ACM SIGSAC
+Conference on Computer and Communications Security, CCS ’16, pages 308–318, New York,
+NY, USA. ACM. 1
+Alabi, D., McMillan, A., Sarathy, J., Smith, A., and Vadhan, S. (2022). Differentially private
+simple linear regression. Proceedings on Privacy Enhancing Technologies, 2022:184–204. 1
+Alparslan, B. and Yıldırım, S. (2022). Statistic selection and mcmc for differentially private
+bayesian estimation. Statistics and Computing, 32(5):66. 1, 1, 4.3
+Andrieu, C. and Roberts, G. O. (2009). The pseudo-marginal approach for efficient Monte Carlo
+computations. Annals of Statistics, 37(2):569–1078. 6
+Andrieu, C. and Thoms, J. (2008). A tutorial on adaptive mcmc. Statistics and Computing,
+18(4):343–373. 4.1
+Balle, B. and Wang, Y.-X. (2018). Improving the Gaussian mechanism for differential privacy:
+Analytical calibration and optimal denoising. In Dy, J. and Krause, A., editors, Proceedings of
+the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine
+Learning Research, pages 394–403. PMLR. 2, 3.1
+Bassily, R., Smith, A., and Thakurta, A. (2014). Private empirical risk minimization: Efficient
+algorithms and tight error bounds. In 2014 IEEE 55th Annual Symposium on Foundations of
+Computer Science, pages 464–473. 1
+Bernstein, G. and Sheldon, D. R. (2019). Differentially private bayesian linear regression. In
+Wallach, H., Larochelle, H., Beygelzimer, A., d'Alch´e-Buc, F., Fox, E., and Garnett, R., editors,
+Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc. 1, 3.1,
+4.3, 5, C.1, C.1
+Bun, M. and Steinke, T. (2016). Concentrated differential privacy: Simplifications, extensions,
+and lower bounds. In Proceedings, Part I, of the 14th International Conference on Theory of
+Cryptography - Volume 9985, pages 635–658, New York, NY, USA. Springer-Verlag New York,
+Inc. 2
+14
+
+Cai, T. T., Wang, Y., and Zhang, L. (2021). The cost of privacy: Optimal rates of convergence for
+parameter estimation with differential privacy. The Annals of Statistics, 49(5):2825 – 2850. 1
+Chaudhuri, K., Monteleoni, C., and Sarwate, A. D. (2009). Differentially private empirical risk
+minimization. 1
+Dankar, F. K. and El Emam, K. (2013). Practicing differential privacy in health care: A review.
+Trans. Data Priv., 6(1):35–67. 1
+Dimitrakakis, C., Nelson, B., Zhang, Z., Mitrokotsa, A., and Rubinstein, B. I. (2017). Differential
+privacy for bayesian inference through posterior sampling. Journal of machine learning research,
+18(11):1–39. 1
+Dong, J., Roth, A., and Su, W. J. (2022). Gaussian differential privacy. Journal of the Royal
+Statistical Society Series B, 84(1):3–37. 2
+Dwork, C. (2006). Differential privacy. In Bugliesi, M., Preneel, B., Sassone, V., and Wegener,
+I., editors, Automata, Languages and Programming, pages 1–12, Berlin, Heidelberg. Springer
+Berlin Heidelberg. 1, 2
+Dwork, C. (2008). Differential privacy: A survey of results. In Agrawal, M., Du, D., Duan, Z.,
+and Li, A., editors, Theory and Applications of Models of Computation, pages 1–19, Berlin,
+Heidelberg. Springer Berlin Heidelberg. 2
+Dwork, C., McSherry, F., Nissim, K., and Smith, A. (2006). Calibrating noise to sensitivity in
+private data analysis. In Theory of Cyrptography, pages 265–284. Springer. 2
+Dwork, C., Naor, M., Pitassi, T., Rothblum, G. N., and Yekhanin, S. (2010). Pan-private streaming
+algorithms. In ICS, pages 66–80. 3.2
+Dwork, C. and Roth, A. (2014). The algorithmic foundations of differential privacy. Found. Trends
+Theor. Comput. Sci., 9(3–4):211–407. 2
+Dwork, C., Roth, A., et al. (2014a). The algorithmic foundations of differential privacy. Foundations
+and Trends® in Theoretical Computer Science, 9(3–4):211–407. 1
+Dwork, C., Talwar, K., Thakurta, A., and Zhang, L. (2014b). Analyze gauss: Optimal bounds for
+privacy-preserving principal component analysis. In Proceedings of the Forty-Sixth Annual ACM
+Symposium on Theory of Computing, STOC ’14, page 11–20, New York, NY, USA. Association
+for Computing Machinery. 1, 3.1
+Ferrando, C., Wang, S., and Sheldon, D. (2022). Parametric bootstrap for differentially private
+confidence intervals. In Camps-Valls, G., Ruiz, F. J. R., and Valera, I., editors, Proceedings
+of The 25th International Conference on Artificial Intelligence and Statistics, volume 151 of
+Proceedings of Machine Learning Research, pages 1598–1618. PMLR. 1
+Foulds, J., Geumlek, J., and an Kamalika Chaudhuri, M. W. (2016). On the theory and practice
+of privacy-preserving Bayesian data analysis. Technical report, arxiv:1603.07294. 1
+Gong, R. (2022). Exact inference with approximate computation for differentially private data
+via perturbations. Journal of Privacy and Confidentiality, 12(2). 1
+15
+
+Heikkil¨a, M., Lagerspetz, E., Kaski, S., Shimizu, K., Tarkoma, S., and Honkela, A. (2017).
+Differentially private bayesian learning on distributed data. In Guyon, I., Luxburg, U. V.,
+Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., and Garnett, R., editors, Advances in
+Neural Information Processing Systems, volume 30. Curran Associates, Inc. 1
+Heikkil¨a, M. A., J¨alk¨o, J., Dikmen, O., and Honkela, A. (2019). Differentially private Markov
+chain Monte Carlo. In NeurIPS. 1
+Higham, N. J. (1988). Computing a nearest symmetric positive semidefinite matrix. Linear
+Algebra and its Applications, 103:103–118. 4.2
+Ju, N., Awan, J., Gong, R., and Rao, V. (2022). Data augmentation MCMC for bayesian inference
+from privatized data. In Oh, A. H., Agarwal, A., Belgrave, D., and Cho, K., editors, Advances
+in Neural Information Processing Systems. 1, 1, 4.3
+Kuru, N., Birbil, S. I., G¨urb¨uzbalaban, M., and Yıldırım, S. (2022).
+Differentially private
+accelerated optimization algorithms. SIAM Journal on Optimization, 32(2):795–821. 1
+Neal, R. (2001). Annealed importance sampling. Statistics and Computing, 11:125–139. 6
+Wang, Y.-X. (2018). Revisiting differentially private linear regression: optimal and adaptive
+prediction & estimation in unbounded domain. In UAI. 1, 5, C.2, C.2
+Wang, Y.-X., Fienberg, S., and Smola, A. (2015). Privacy for free: Posterior sampling and
+stochastic gradient monte carlo. In Bach, F. and Blei, D., editors, Proceedings of the 32nd
+International Conference on Machine Learning, volume 37 of Proceedings of Machine Learning
+Research, pages 2493–2502, Lille, France. PMLR. 1
+Williams, O. and Mcsherry, F. (2010). Probabilistic inference and differential privacy. In Lafferty,
+J., Williams, C., Shawe-Taylor, J., Zemel, R., and Culotta, A., editors, Advances in Neural
+Information Processing Systems, volume 23. Curran Associates, Inc. 1
+Wilson, A. G. and Ghahramani, Z. (2011). Generalised wishart processes. In Proceedings of the
+Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, UAI’11, page 736–744,
+Arlington, Virginia, USA. AUAI Press. 2
+Yıldırım, S. and Ermi¸s, B. (2019). Exact MCMC with differentially private moves. Statistics and
+Computing, 29(5):947–963. 1
+Zhang, J., Zhang, Z., Xiao, X., Yang, Y., and Winslett, M. (2012). Functional mechanism:
+Regression analysis under differential privacy. Proc. VLDB Endow., 5(11):1364–1375. 1
+Zhang, Z., Rubinstein, B., and Dimitrakakis, C. (2016). On the differential privacy of bayesian
+inference. Proceedings of the AAAI Conference on Artificial Intelligence, 30(1). 1
+16
+
+A
+Derivations for MCMC-normalX
+We reserve this section for the derivations required for our algorithm MCMC-normalX.
+Full Conditional Distribution of Σx:
+We note that
+p(Σx|S1:J, ˆS1:J, ˆz1:J) ∝ p(Σx)
+J
+�
+j=1
+p(Sj|Σx)
+=
+|Λ|dκ/2
+2dk/2Γd( κ
+2)|Σx|−(d+κ+1)/2e− 1
+2 tr(ΛΣ−1
+x )
+J
+�
+j=1
+|Sj|(nj−d−1)/2e− 1
+2 tr(Σ−1
+x Sj)
+2njd/2|Σx|nj/2Γd(nj/2)
+∝ |Σx|− n
+2 − (d+κ+1)
+2
+e− 1
+2 (� tr(Σ−1
+x Sj)+tr(ΛΣ−1
+x ))
+∝ |Σx|− (d+κ+n+1)
+2
+e− 1
+2 tr((� Sj+Λ)Σ−1
+x ).
+Therefore, we have
+Σx|S1:J, ˆS1:J, ˆz1:J ∼ IW
+�
+�Λ +
+J
+�
+j=1
+Sj, κ + n
+�
+� .
+Full Conditional Distribution of θ:
+The posterior of θ is proportional to
+p(θ|S1:J, σ2
+y, ˆz1:J) ∝ N(θ; m, C)p(ˆz1:J|S1:J, θ, σ2
+y).
+For the second factor, we have
+p(ˆz1:J|S1:J, θ, σ2
+y) ∝
+J
+�
+i=1
+p(ˆzj|Sj, θ, σ2
+y) =
+J
+�
+i=1
+N
+� ˆzj; Sjθ, σ2
+ySj + σ2
+zI
+�
+∝
+J
+�
+i=1
+exp
+�
+−1
+2(ˆzj − Sjθ)T (σ2
+ySj + σ2
+zI)−1(ˆzj − Sjθ)
+�
+∝ exp
+�
+�
+�−1
+2
+�
+�θT
+�
+��
+j
+Sj(σ2
+ySj + σ2
+zI)−1Sj
+�
+� θ − 2θT
+�
+��
+j
+Sj(σ2
+ySj + σ2
+zI)−1
+�
+� ˆzj
+�
+�
+�
+�
+� .
+Reorganising the terms, we end up with
+p(θ|S1:J, σ2
+y, ˆz1:J) ∝ exp
+�
+−1
+2
+�
+θT Σ−1
+postθ − 2θT Σ−1
+postmpost
+��
+,
+where Σ−1
+post = �
+j Sj(σ2
+ySj + σ2
+ZI)−1Sj + C−1 and mpost = Σpost[�
+j Sj(σ2
+ySj + σ2
+zI)−1)ˆzj +
+C−1m]. Therefore, θ|S1:J, σ2
+y, ˆz1:J ∼ N(mpost, Σpost).
+Acceptance Ratio for the MH Update of Sj:
+We drop the index j from Sj for simplicity.
+When S′ ∼ W(S/α, α), the proposal density is
+q(S′|S) = |S′|(α−d−1)/2e−tr[αS−1S′]/2
+|S/α|α/22αd/2Γd( α
+2 )
+= |S′|(α−d−1)/2e−tr[αS−1S′]/2
+|S|α/22αd/2Γd( α
+2 )
+αα/2.
+17
+
+Therefore, the acceptance ratio corresponding to this proposal is
+min
+�
+1, q(S|S′)
+q(S′|S)
+W(S′; njΣx, κ)p( ˆS| ˆS′)N(ˆz; S′θ, σ2
+ySθ + σ2
+zId)
+W(S; njΣx, κ)p( ˆS| ˆS)N(ˆz; Sθ, σ2ySθ + σ2zId)
+�
+,
+where the ratio of proposals becomes
+q(S|S′)
+q(S′|S) = |S|(α−d−1)/2|S|α/2e−tr[aS′−1S]/2
+|S′|(α−d−1)/2|S′|α/2e−tr[αS−1S′]/2 =
+� |S|
+|S′|
+�α−(d+1)/2
+eα(tr[S−1S′]−tr[S′−1S])/2.
+Acceptance Ratio for the MH Update of σ2
+y:
+To update σ2
+y, we use a random walk proposal
+σ2′
+y ∼ N(σ2
+y, σ2
+q). The resulting acceptance ratio is
+min
+�
+1,
+IG(σ2′
+y ; a, b) �J
+j=1 N(ˆzj; Sjθ, σ2′
+y Sjθ + σ2
+zId)
+IG(σ2y; a, b) �J
+j=1 N(ˆzj; Sjθ, σ2ySjθ + σ2zId)
+�
+B
+Other Variants
+This appendix is reserved for the details of the other variants mentioned in Section 4.4. For
+simplicity, we will assume a single data holder, i.e., J = 1; the extension to J > 1 should be
+straightforward.
+B.1
+Approximating Normality by Averaging
+When xi, i = 1, . . . , n are not normal, another approach that we propose is based on modifying
+the data to such that the rows of the modified feature matrix, called Xav, are averages of k > 1
+original features in X, and thus approximately normal, by the CLT. Specifically, let n be divisible
+by k so that m = n/k is an integer. Consider the m × n matrix
+A =
+1
+√
+k
+�
+����
+11×k
+01×k
+. . .
+01×k
+01×k
+11×k
+. . .
+01×k
+...
+...
+...
+...
+01×k
+01×k
+. . .
+11×k
+�
+����
+m×n
+,
+Then the matrix Xav = AX corresponds to constructing a shorter m × d matrix whose i’th
+column is the average of the rows (i − 1)k + 1, . . . , ik of X (scaled by 1/
+√
+k the preserve the
+norm). When k is large enough, we can make normality assumptions for the rows of Xav. Further,
+we consider
+yav := Ay = Xavθ + Ae,
+whose mean is Xavθ and covariance AAT σ2
+y. But, we have AAT = Im, so the covariance is σ2
+yIm.
+Therefore, the same hierarchical model in Figure 1 can be used for X′, y′ with their respective
+summary statistics
+zav = (Xav)T yav,
+Sav = (Xav)T Xav,
+as well as the noisy versions of those summary statistics to provide a given level of privacy. Note
+that Sav and zav have the same sensitivities as S and z, hence the same noise variances are
+needed for privacy. However, there is less information in Sav and zav due to averaging.
+18
+
+B.2
+Including the Intercept
+If we include the intercept parameter, which corresponds to appending xi with a 1 from the left,
+the design matrix will be changed from S to S0 =
+� n
+n¯xT
+n¯x
+S
+�
+, where ¯x = 1
+n
+�n
+i=1 xi. Also, note
+that S = (n − 1)�Σx + n¯x¯xT where �Σx is the sample covariance. Under the normality assumption
+for xi’s, ¯x ∼ N(m, Σx/n) and (n − 1)�Σx ∼ W(n − 1, Σx) are independent and have known
+distributions. Therefore, we can write a model that includes b = ¯x, ˆ
+Σx, and S0 where S0 replaces
+S in the standard model. More specifically, we have the following hierarchical model:
+θ ∼ N(m, C),
+Σx ∼ IW(Λ, κ),
+ˆ
+Σx|Σx ∼ W(n − 1, Σx),
+b|Σx ∼ N(µ, Σx/n),
+z|θ, Σ2
+y, ˆΣ, b ∼ N(S0θ, S0σ2
+y),
+ˆS| ˆΣ, b = N(S0, σ2
+sI),
+ˆz|z = N(z, σ2
+zI)
+with S0 =
+� n
+nbT
+nb
+(n − 1) ˆΣ + nbbT
+�
+.
+C
+Compared Methods
+Here, we provide the details of the methods which we compare with the proposed methods in
+this paper. Those methods are originally proposed for J = 1. However, for comparison, we
+implemented their natural extensions to the general (distributed) case J ≥ 1. The implementations
+of those methods can also be found in the code package provided for this paper.
+C.1
+MCMC-B&S Adapted to the Distributed Setting
+In Bernstein and Sheldon (2019), only J = 1 is considered, and the vector ss = [vec(S), z =
+XT y, u = yT y] is perturbed with privacy-preserving noise to generate the observations of
+the model. For J ≥ 1, we consider the following natural extension for generating perturbed
+observations ˆss = [vec( ˆSj), ˆzj, ˆuj] along with
+ˆSj = Sj + σdpMj,
+ˆzj = zj + vj,
+vj ∼ N(0, σ2
+dpId),
+ˆuj = uj + wj,
+wj ∼ N(0, σ2
+dp), (13)
+where σdp = σ(ϵ, δ)∆ss with ∆ss =
+�
+∥X∥4 + ∥X∥2∥Y∥2 + ∥Y∥4.
+For completeness, we provide the further specifics of the model: We take (θ, σ2
+y) ∼ NIG(a0, b0, m, Λ0)
+where Λ0 = C−1 and Px = N(0, Σx) with Σx ∼ IW(Λ, κ).
+During the comparisons, we set a0, b0, m, C, Λ, κ to the same values for both this model and our
+proposed model that assumes normally distributed features, i.e., Px = N(0, Σx). Then, we apply
+an extension of Bernstein and Sheldon (2019, Algorithm 1) suited to those observations. One
+iteration of that algorithm includes the following steps in order:
+• Calculate the D × 1 mean vector and D × D covariance matrix
+µss = E[ss],
+Σss = Cov[ss].
+This step requires the fourth moments N(0, Σx).
+• Sample ssj ∼ N(µ(j)
+post,ss, Σ(j)
+post,ss) with
+Σ(j)
+post,ss = (njΣss(θ)−1 + (1/σ2
+dp)I)−1,
+and
+µ(j)
+post,ss = Σ(j)
+post,ss(Σss(θ)−1µss + ˆssj/σ2
+dp).
+19
+
+• Sample Σx ∼ IW
+�
+Λ + �J
+j=1 Sj, n + κ
+�
+.
+• Sample (θ, σ2
+y) ∼ NIG(an, bn, mn, Λn) by sampling σ2
+y ∼ IG(an, bn), followed by sampling
+θ ∼ N(µn, σ2
+yΛ−1
+n ) with an = a0 + n/2, bn = 0.5u + mT C−1m − mT
+nΛnmn, and
+Λn = Λ0 +
+J
+�
+j=1
+Sj,
+mn = Λ−1
+n
+�
+�
+J
+�
+j=1
+zj + Λ0m
+�
+� ,
+.
+C.2
+A Variant of adaSSP for the Distributed Setting
+The adaSSP algorithm of (Wang, 2018) is originally designed for a single data holder, i.e., J = 1.
+In adaSSP, a differentially private estimate of θ is released as
+ˆθ = ( ˆS + λI)−1 ˆz.
+(14)
+Here, ˆS and ˆz are the privatised versions of S and z as in (2) and (3), except that ϵ and δ must be
+changed to 2ϵ/3 and 2δ/3 in those equations to provide (ϵ, δ) differential privacy. This is because
+adaSSP uses another parameter λ, which is also calculated from the sensitive data and a third of
+the privacy budget is spent for privatising that calculation. With v ∼ N(0, 1), λ is specifically
+calculated as
+λ = max{0, σ
+�
+d ln(6/δ) ln(2d2/ρ) − ˜λmin}
+with σ = ∥X∥2/(ϵ/3), λmin = min(eig(S)), and
+˜λmin = max{λmin +
+�
+ln(6/δ)σv − ln(6/δ)σv, 0}.
+We consider an extension of (Wang, 2018) for J ≥ 1. To perform the extension, we reflect on its
+tendency to approximate a (regularised) least square solution and consider the following estimate
+ˆθ =
+�
+�
+J
+�
+j=1
+ˆSj + I
+J
+�
+j=1
+λj
+�
+�
+−1 �
+�
+J
+�
+j=1
+ˆzj
+�
+� .
+(15)
+Here, ˆSj, ˆzj and λj are calculated in data node j separately from the other nodes. The estimation
+procedure in (15) does not properly account for the Bayesian paradigm but aggregates the shared
+ˆSj’s and ˆzj’s to approximate the (regularised) least squares solution.
+20
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+arXiv:2301.01692v1  [gr-qc]  3 Jan 2023
+Another Friedman-type solution that eliminates the problem of the divergent
+cosmological constant, implemented in the framework of the lattice regularization of
+the theory of gravity
+S.N. Vergeles∗
+Landau Institute for Theoretical Physics,
+Russian Academy of Sciences, Chernogolovka,
+Moscow region, 142432 Russia
+and
+Moscow Institute of Physics and Technology,
+Department of Theoretical Physics,
+Dolgoprudnyj, Moskow region, 141707 Russia
+Lattice regularization of the theory of gravity provides a new possibility for solving the problem
+of the divergent cosmological constant. The solution of the Einstein equation within the framework
+of the Friedmann paradigm with a finite bare cosmological constant is mathematically correct, since
+all local physical quantities (energy density including vacuum energy, etc.) on the lattice are finite.
+As a result, a solution is obtained that demonstrates an exponential growth of the cosmological scale
+factor a(t) in the initial period of evolution (inflation phase of the Universe) and then passes into a
+power law (a(t) ∝
+√
+t).
+PACS numbers: 04.60.Bc
+1.
+Introduction.
+In the fundamental review [1]
+the following facts were stated regarding the problem
+of divergent energy (divergent cosmological constant)
+of the ground state in quantum field theory:
+(i) In
+flat Minkowski space-time, these divergences, generally
+speaking, take place, but in the case of supersymmetric
+theories, the energies of the ground states strictly vanish.
+(ii) In curved space-time, even in the case of supergravity,
+the cosmological constant diverges. (iii) The superstring
+theory does not save the situation either.
+Since then, many papers have been published on this
+problem. Here we note only a few approaches to solving
+the problem, which seem to us very promising.
+The first approach is represented by works [2–7]. In
+these papers, efforts were made to solve the problem of
+the cosmological constant in detail, that is, through mi-
+croscopic analysis. In particular, the probability of the
+following process was calculated. Let there be a massive
+particle in the de Sitter space. This particle gives rise to
+a pair of the same particles for a sufficiently long period
+of time. This problem has been studied for both free and
+interacting fields.
+A similar statement of the problem
+for massive charged particles in the case of a flat space-
+time in the presence of a constant electric field leads to
+the creation of particle-antiparticle pair that weaken the
+initial electric field. In the case of de Sitter space, pair
+production also leads to a decrease in the cosmological
+constant with time. Unfortunately, in these works there
+is no study of the reverse influence of quantized mate-
+rial fields on the space-time geometry. It is possible that
+continued efforts in this direction will lead to a solution
+∗e-mail:[email protected]
+to the problem of the cosmological constant.
+In the paper [8] the mean of the energy-momentum
+tensor of a quantized scalar field is calculated in the case
+of an anisotropic metric, which is considered to be clas-
+sical and variable in time. Regularization is carried out
+in the usual way: the vacuum expectation value of the
+energy-momentum tensor, calculated in the case of a sta-
+tionary vacuum, is subtracted from the obtained value.
+The authors of the paper [9] study such models of
+field theory which, although not supersymmetric, have
+the same number of boson and fermion degrees of free-
+dom. In this case, the divergences of the highest, fourth
+degree are eliminated in the quantum mean of the energy-
+momentum tensor. It is shown what conditions the al-
+ready renormalized field masses must satisfy in order to
+reduce all other divergences.
+The work [10] seems to us to be interesting and com-
+plementary to the present work, since a bare cosmological
+constant is also introduced in [10], and the reduction of
+the huge vacuum energy is a dynamic effect, not a fine-
+tuning effect.
+Another interesting approach to solving the problem,
+using the macroscopic thermodynamic ideology, is pre-
+sented in [11] (see there also references for the articles
+of F.R. Klinkhamer and G.E. Volovik). The main idea
+of this approach is as follows. A bare cosmological con-
+stant is introduced into the system describing gravity and
+matter. The bare cosmological constant plays the role of
+the chemical potential µ. If the system comes to a state
+of thermodynamic equilibrium, then a large thermody-
+namic potential is of interest. Let Ω be a large thermo-
+dynamic potential for the spatial volume V . It is known
+that
+Ω(β, µ, V ) = −P(β, µ)V.
+(1)
+
+2
+Here, β stands for inverse temperature.
+In our case,
+β should be understood as the (imaginary) time dur-
+ing which the transition quantum amplitude (or partition
+function) is calculated. We have an obvious limitation for
+β values: |βH| ≪ 1, where H = ˙a/a is Hubble constant
+and a(t) is the cosmic scale factor. Otherwise, there can
+be no thermodynamic equilibrium.
+The standard spa-
+tially flat Robertson-Walker metric
+d s2 = (d x0)2 − a2(t)(d xα)2,
+α = 1, 2, 3
+(2)
+is used in [11]. Since the gravitational degrees of free-
+dom are exhausted by only one global parameter a(t),
+then the potential (1) is saturated with the degrees of
+freedom of matter. The main idea of the authors of the
+paper [11] is that in the case of thermal equilibrium (if it
+exists), the pressure on the right side of the equality (1)
+tends to zero, since there is no external pressure at all.
+Further, the effective energy-momentum tensor of matter
+is formed by the potential (1). Therefore, the effective
+energy density of matter, including the vacuum energy,
+under the condition of thermal equilibrium is estimated
+as ε ∼ Ω/V −→ 0. Thus the problem of the divergent
+cosmological constant is removed.
+The fundamental defect of all the papers cited here
+is the fact that the vacuum energy (in particular, the
+energy of zero-point oscillations) is not limited.
+Figu-
+ratively speaking, the Dirac sea has no bottom.
+And
+although the divergences in physical quantities are elim-
+inated by subtracting vacuum values from them, there
+remains a feeling of unsteadiness of the ground under
+the feet of the researcher. The reason for this is that in
+this case the characteristic divergences are power-law of
+the fourth degree.
+On the other hand, if the hypothesis is accepted that on
+ultra-small scales, space-time has the property of gran-
+ularity (this property is modeled by a lattice), then the
+formulation and solution of at least some problems turn
+out to be mathematically correct (see below).
+This work is an ideological continuation of the work
+[11]. The essential difference between the present paper
+and the paper [11] is that we assume a lattice regular-
+ization of the theory of gravity (see [12] and references
+there). Lattice regularization provides a new possibility
+for solving the problem of the divergent cosmological
+constant. The solution of the Einstein equation within
+the framework of the Friedmann paradigm with a finite
+bare cosmological constant is mathematically correct,
+since all local physical quantities (energy density in-
+cluding vacuum energy, etc.)
+on the lattice are finite.
+Our approach assumes that all physical quantities are
+determined by taking into account quantum zero point
+fluctuations.
+In particular, the energy density and
+pressure are mainly determined by quantum fluctua-
+tions. Since the equations considered here describe such
+large energy densities that, on the characteristic time
+intervals, have actions exceeding the Planck constant
+by a huge number of times, we assume the considered
+physical quantities to be classical and use the classical
+equations [13]. As a result, a solution is obtained that
+demonstrates an exponential growth of the scale factor
+in the initial period of evolution and then passes into a
+power law.
+2. Einstein equation and solution. We use the energy-
+momentum tensor of matter in the form of the energy-
+momentum tensor of an ideal relativistic fluid:
+T a
+b = (ε + p)U aUb − pδa
+b .
+(3)
+We work in an orthonormal basis in which the metric ten-
+sor ηab = diag(1, −1, −1, −1). On the right side of (3),
+the symbols ε and p denote the energy density and pres-
+sure, respectively, and these quantities also include vac-
+uum energy and pressure. Since fermionic fields, in con-
+trast to bosonic ones, make a negative contribution to the
+vacuum energy, but there are significantly more fermionic
+degrees of freedom than bosonic ones, we have ε < 0.
+Moreover, lattice regularization means that |ε|, |p| < ∞.
+Note that in (3) the pressure p is different from the pres-
+sure P(β, µ) in (1). A comparison of these values is given
+below. U a is the averaged 4-velocity of the macroscopic
+regions of the lattice. In our case U a = (1, 0, 0, 0). To
+compensate for the vacuum energy, a bare finite positive
+cosmological constant Λ0 is introduced into the Einstein
+equation[14]:
+Ra
+b −1
+2δa
+b R = 8πG
+c4 T a
+b + Λ0δa
+b .
+(4)
+We assume that the cosmological constant
+Λ0 = const ∼ l−2
+P ,
+lP ∼
+�
+8πGℏ
+c3
+∼ 10−32cm.
+(5)
+For the metric, we use ansatz (2). In order not to clutter
+up the formulas, we introduce the notation
+8πG
+c4 ε = ˜ε,
+8πG
+c4 p = ˜p.
+(6)
+All components of the Einstein equation are reduced to
+two equations:
+3 ˙a2
+a2 = Λ0 + ˜ε,
+2¨a
+a + ˙a2
+a2 = Λ0 − ˜p.
+(7)
+Here ˙a ≡ d a/ d x0.
+Another equation ∇aT a
+b = 0 is a
+consequence of equations (7), and therefore it does not
+need to be considered. Let us introduce the Hubble con-
+stant ˜H(t) ≡ ˙a/a, with the help of which Eqs. (7) are
+rewritten as follows:
+2 ˙˜H + (˜ε + ˜p) = 0,
+3 ˜H2 − (Λ0 + ˜ε) = 0.
+(8)
+So we have 3 unknown functions {˜ε(t), ˜p(t), ˜H(t)} and 2
+equations (8). The missing equation is the equation of
+state relating energy density and pressure. Regarding the
+equation of state, the following facts are reliably known:
+(i) in the case of real dusty matter, we have ˜p = 0; (ii) in
+
+3
+the case of real ultrarelativistic matter we have ˜p = ˜ε/3;
+in the case of vacuum energy and pressure, we have ˜p =
+−˜ε. In all three cases, the energy density and pressure
+are linearly related. Therefore, we propose to accept the
+following hypothesis:
+˜p = κΛ0 + (κ − 1)˜ε ←→ ˜ε + ˜p = κ(˜ε + Λ0).
+(9)
+This equation is linear and inhomogeneous with an un-
+known function κ(t), the asymptotics of which are fur-
+ther determined based on the known dynamics. The set
+of equations (8) and (9) has a solution:
+˙˜H = −3
+2κ ˜H2 → ˜H(t) = ˜H0
+�
+1 + 3
+2H0
+� t
+0
+κ(t′) d t′
+�−1
+,
+(10)
+˜ε(t) = −Λ0 + 3 ˜H2
+0
+�
+1 + 3
+2H0
+� t
+0
+κ(t′) d t′
+�−2
+,
+(11)
+˜p(t) = Λ0 + 3
+�
+κ(t) − 1
+� ˜H2
+0
+�
+1 + 3
+2H0
+� t
+0
+κ(t′) d t′
+�−2
+.
+(12)
+Here ˜H0 ≡ H0/c is the integration constant, ˜H(t) ≡
+H(t)/c, and H0 is the Hubble constant at the beginning
+of the inflation phase, [H(t)] = [H0] = s−1.
+We indicate some of the most obvious properties of the
+solution (10), (11), (12). The estimates given below are
+very rough. Let us accept the following estimates for the
+duration of the inflation time tinf, and for the constant
+Λ0:
+tinf ∼= 10−37s,
+H0 ∼= 1039s−1,
+˜H0 ∼= 1029cm−1. (13)
+Then H0tinf ∼= 100. Let’s take κ0 ≡ κ(t = 0) ∼= 1/150.
+Assume that during the time tinf the function κ changes
+insignificantly. Then for t < tinf the solutions (10), (11),
+(12) take the form
+˜H(t) ∼= ˜H0,
+˜ε(t) ∼= −˜p ∼= −Λ0 + 3 ˜H2
+0.
+(14)
+Thus, during inflation, the scale factor a(t) increased by
+(exp H0tinf) ≈ (exp 100) ≈ 1043 times.
+Assume that when t > tinf, the function κ(t) becomes
+equal to κ = 4/3. In this case, the solutions (10), (11),
+(12) give a power-law expansion:
+H(t) ∼= 1
+2t,
+˜ε(t) ∼= −Λ0 + 3
+4t2 ,
+˜p ∼= Λ0 + 1
+4t2 .
+(15)
+Solution (15) shows that the scale factor and the density
+of real matter change according to the well-known law,
+as well as the correct equation of state in the case of
+ultrarelativistic matter:
+a(t) ∝
+√
+t,
+ρreal =
+3
+32πGt2 ,
+preal = 1
+3εreal.
+(16)
+3. Thermodynamic considerations. Here, the possibil-
+ity of using a thermodynamic approach to this problem
+is briefly discussed, and some thermodynamic relations
+are also given. The purpose of this consideration is to
+(at least superficially) explain the state equation (9).
+The estimation (13) means that
+˜H2
+0 ≪ Λ0.
+(17)
+It can be seen from Eq. (11) that the maximum frequen-
+cies of the degrees of freedom of matter in the modern
+era are of the order of
+|ωmax| ∼ c
+�
+Λ0.
+(18)
+We are interested in small times when H ∼ H0 (see Eq.
+(10).
+Since at these times the space was many orders
+of magnitude more compact, then for small times the
+estimate |ωmax| ≫ c√Λ0 was valid. Consider the time
+interval ∆t ≲ H−1, for which we have
+∆a/a ∼ H∆t ≲ 1,
+∆t|ωmax| ≫ 1.
+(19)
+Taking into account Eq. (19), we can assume that for a
+time interval ∆t the thermodynamic equilibrium of the
+vacuum degrees of freedom is realized. This assumption
+cannot be extended to those degrees of freedom whose
+frequencies ∆t|ω| ≲ 1. But such degrees of freedom make
+a small contribution to the total energy-momentum ten-
+sor.
+When passing to the Euclidean signature by Wick’s
+rotation ∆t = −i∆τ [15], the parameter
+T ≡ β−1 = ℏ(∆τ)−1 ∼ ℏH
+(20)
+acquires the meaning of temperature. Let us determine
+the temperature value in Kelvin degrees at the begin-
+ning of the inflation process, when, according to some
+estimates H0 ∼ 1039s−1. Then
+T0 ∼ ℏH0
+k
+∼
+�
+1028�◦ K.
+(21)
+Here k is the Boltzmann constant. The temperature es-
+timate (21) is within the known temperature estimates
+in the initial phase of inflation.
+Once again, we note that thermodynamic considera-
+tions do not apply to low-frequency degrees of freedom.
+In particular, ordinary real matter may, generally speak-
+ing, not be in a state of thermal equilibrium.
+According to Eqs. (10) and (20) we have:
+ℏ d β ∼ d(1/H) = 3/2κ d t.
+But in the inflation phase a(t) = a0eHt, and so d t =
+H−1 d a/a. Thus we have:
+d β/β ∼ (3/2)κ d a/a.
+(22)
+Since the temperature decreases in the inflation phase, it
+can be seen from (22) that κ(t = 0) > 0.
+
+4
+It can be seen from the first Eq. (7) that the constant
+Λ0 cancels out the huge negative energy of the vacuum,
+so that in the era of power-law expansion only the rel-
+atively extremely small positive energy density of real
+matter affects the dynamics. From the given solution of
+Einstein’s equations, it can be seen that the huge value
+of pressure is also mainly reduced by the constant Λ0.
+In the presented solution we have ˜p ∼ −˜ε ∼ Λ0. Such a
+ratio of pressure and energy density of matter is dictated
+by the relativistic invariance of quantum states.
+We will show that the contraction of the enormous vac-
+uum pressure ˜p can be interpreted as a thermodynamic
+effect. Indeed, the contribution of the cosmological con-
+stant to the action for volume V =
+� �
+|g| d3 x and time
+interval ∆t is equal to
+i AΛ0 /ℏ = − ic4
+8πGℏΛ0V ∆t.
+(23)
+As a result of the Wick rotation according to the formula
+∆t = −i∆τ and due to (20) the action (23) is trans-
+formed to the form
+i AΛ0 /ℏ −→ −
+c4
+8πGℏΛ0V ∆τ = − c4
+8πGΛ0V β.
+(24)
+Adding (24) to the Euclidean action has the same effect
+as adding µNβ.
+Here N is the number of degrees of
+freedom on the part of the lattice contained in the volume
+V , and µ is the total chemical potential of the lattice.
+Equating the value (µNβ) to the value on the right side
+of the Eq. (24), we find:
+µ = − c4
+8πGΛ0
+V
+N .
+(25)
+Usually the chemical potential is the independent vari-
+able. But here it is a function of volume. Therefore, the
+total pressure is determined by a more complex formula:
+P(β, µ) = −
+� ∂Ω
+∂V
+�
+β,µ
+−
+�∂Ω
+∂µ
+�
+β,V
+∂µ
+∂V = p −
+c4
+8πGΛ0.
+(26)
+Here we have taken into account the equality N
+=
+−(∂Ω/∂µ)β,V and Eq. (25). On the left hand side of
+Eq. (26) the pressure P(β, µ) is the same as the pressure
+in Eq. (1). The above solution of the Einstein equations
+shows that P(β, µ) is negligible compared to the total
+pressure p of matter. This fact was pointed out and used
+in the work [11]
+The estimate ˜p ∼= Λ0 together with the vacuum energy
+hypothesis ˜ε ∼= −Λ0 justifies the equation of state (9). In
+both parts of equality (˜ε + ˜p) = κ(˜ε + Λ0), the diverging
+values of the quantities cancel each other out. This fact
+is the result of solving dynamic equations.
+A more accurate equation of state should be obtained
+by microscopic analysis in the spirit of the works [2–7].
+Acknowledgments
+I thank Prof. G.E. Volovik for awakening my interest
+in the thermodynamic study of the problem. I am grate-
+ful to Prof.
+E.T. Akhmedov for numerous discussions
+and advice in the course of work. This work was carried
+out as a part of the State Program 0033-2019-0005.
+[1] S. Weinberg, Reviews of modern physics 61, 1 (1989).
+[2] D. Krotov and A. M. Polyakov, Nuclear Physics B 849,
+410 (2011).
+[3] A. Polyakov, arXiv preprint arXiv:1209.4135 (2012).
+[4] E. Akhmedov, International Journal of Modern Physics
+D 23, 1430001 (2014).
+[5] E. Akhmedov, U. Moschella, and F. Popov, Physical Re-
+view D 99, 086009 (2019).
+[6] E. Akhmedov, Modern Physics Letters A 36, 2130020
+(2021).
+[7] A. Y. Kamenshchik, A. A. Starobinsky, and T. Var-
+danyan, The European Physical Journal C 82, 1 (2022).
+[8] Y. B. Zel’Dovich and A. Starobinskiˇı, Soviet Journal of
+Experimental and Theoretical Physics 34, 1159 (1972).
+[9] A. Y. Kamenshchik, A. A. Starobinsky, A. Tronconi,
+T. Vardanyan, and G. Venturi, The European Physical
+Journal C 78, 1 (2018).
+[10] S. Appleby and E. V. Linder, Journal of Cosmology and
+Astroparticle Physics 2020, 037 (2020).
+[11] F. Klinkhamer and G. Volovik, Physical Review D 105,
+084066 (2022).
+[12] S. Vergeles, Classical and Quantum Gravity 38, 085022
+(2021).
+[13] We mean the fact that according to (5), (6) and (11)
+we have the estimate (l3
+P tP ε)/ℏ ∼ 1. Here tP ∼ lP /c ∼
+10−43s is the Planck time. However, the inflation time
+tinf is several orders of magnitude longer than the Planck
+time (see (13)), and therefore (l3
+P tinfε)/ℏ ≫ 1. This
+means that in the Planck volume, on a time interval much
+greater than the Planckian but much less than the infla-
+tion time, the action of the system is much greater than
+the Planck constant, and therefore a classical description
+is possible.
+[14] In lattice theory [12], the cosmological constant is intro-
+duced in a natural way.
+[15] The correctness of the sign during Wick rotation is es-
+tablished by the example of the action of a scalar field.
+

3dAzT4oBgHgl3EQfuf2L/content/tmp_files/load_file.txt

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+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='01692v1  [gr-qc]  3 Jan 2023  Another Friedman-type solution that eliminates the problem of the divergent  cosmological constant, implemented in the framework of the lattice regularization of  the theory of gravity  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Vergeles∗  Landau Institute for Theoretical Physics,  Russian Academy of Sciences, Chernogolovka,  Moscow region, 142432 Russia  and  Moscow Institute of Physics and Technology,  Department of Theoretical Physics,  Dolgoprudnyj, Moskow region, 141707 Russia  Lattice regularization of the theory of gravity provides a new possibility for solving the problem  of the divergent cosmological constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The solution of the Einstein equation within the framework  of the Friedmann paradigm with a finite bare cosmological constant is mathematically correct, since  all local physical quantities (energy density including vacuum energy, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=') on the lattice are finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  As a result, a solution is obtained that demonstrates an exponential growth of the cosmological scale  factor a(t) in the initial period of evolution (inflation phase of the Universe) and then passes into a  power law (a(t) ∝  √  t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  PACS numbers: 04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='Bc  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  In the fundamental review [1]  the following facts were stated regarding the problem  of divergent energy (divergent cosmological constant)  of the ground state in quantum field theory:  (i) In  flat Minkowski space-time, these divergences, generally  speaking, take place, but in the case of supersymmetric  theories, the energies of the ground states strictly vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (ii) In curved space-time, even in the case of supergravity,  the cosmological constant diverges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (iii) The superstring  theory does not save the situation either.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Since then, many papers have been published on this  problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Here we note only a few approaches to solving  the problem, which seem to us very promising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  The first approach is represented by works [2–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In  these papers, efforts were made to solve the problem of  the cosmological constant in detail, that is, through mi-  croscopic analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In particular, the probability of the  following process was calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Let there be a massive  particle in the de Sitter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' This particle gives rise to  a pair of the same particles for a sufficiently long period  of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' This problem has been studied for both free and  interacting fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  A similar statement of the problem  for massive charged particles in the case of a flat space-  time in the presence of a constant electric field leads to  the creation of particle-antiparticle pair that weaken the  initial electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In the case of de Sitter space, pair  production also leads to a decrease in the cosmological  constant with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Unfortunately, in these works there  is no study of the reverse influence of quantized mate-  rial fields on the space-time geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' It is possible that  continued efforts in this direction will lead to a solution  ∗e-mail:vergeles@itp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='ru  to the problem of the cosmological constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  In the paper [8] the mean of the energy-momentum  tensor of a quantized scalar field is calculated in the case  of an anisotropic metric, which is considered to be clas-  sical and variable in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Regularization is carried out  in the usual way: the vacuum expectation value of the  energy-momentum tensor, calculated in the case of a sta-  tionary vacuum, is subtracted from the obtained value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  The authors of the paper [9] study such models of  field theory which, although not supersymmetric, have  the same number of boson and fermion degrees of free-  dom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In this case, the divergences of the highest, fourth  degree are eliminated in the quantum mean of the energy-  momentum tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' It is shown what conditions the al-  ready renormalized field masses must satisfy in order to  reduce all other divergences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  The work [10] seems to us to be interesting and com-  plementary to the present work, since a bare cosmological  constant is also introduced in [10], and the reduction of  the huge vacuum energy is a dynamic effect, not a fine-  tuning effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Another interesting approach to solving the problem,  using the macroscopic thermodynamic ideology, is pre-  sented in [11] (see there also references for the articles  of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Klinkhamer and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Volovik).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The main idea  of this approach is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' A bare cosmological con-  stant is introduced into the system describing gravity and  matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The bare cosmological constant plays the role of  the chemical potential µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' If the system comes to a state  of thermodynamic equilibrium, then a large thermody-  namic potential is of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Let Ω be a large thermo-  dynamic potential for the spatial volume V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' It is known  that  Ω(β, µ, V ) = −P(β, µ)V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (1)  2  Here, β stands for inverse temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  In our case,  β should be understood as the (imaginary) time dur-  ing which the transition quantum amplitude (or partition  function) is calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' We have an obvious limitation for  β values: |βH| ≪ 1, where H = ˙a/a is Hubble constant  and a(t) is the cosmic scale factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Otherwise, there can  be no thermodynamic equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  The standard spa-  tially flat Robertson-Walker metric  d s2 = (d x0)2 − a2(t)(d xα)2,  α = 1, 2, 3  (2)  is used in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Since the gravitational degrees of free-  dom are exhausted by only one global parameter a(t),  then the potential (1) is saturated with the degrees of  freedom of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The main idea of the authors of the  paper [11] is that in the case of thermal equilibrium (if it  exists), the pressure on the right side of the equality (1)  tends to zero, since there is no external pressure at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Further, the effective energy-momentum tensor of matter  is formed by the potential (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Therefore, the effective  energy density of matter, including the vacuum energy,  under the condition of thermal equilibrium is estimated  as ε ∼ Ω/V −→ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Thus the problem of the divergent  cosmological constant is removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  The fundamental defect of all the papers cited here  is the fact that the vacuum energy (in particular, the  energy of zero-point oscillations) is not limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Figu-  ratively speaking, the Dirac sea has no bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  And  although the divergences in physical quantities are elim-  inated by subtracting vacuum values from them, there  remains a feeling of unsteadiness of the ground under  the feet of the researcher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The reason for this is that in  this case the characteristic divergences are power-law of  the fourth degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  On the other hand, if the hypothesis is accepted that on  ultra-small scales, space-time has the property of gran-  ularity (this property is modeled by a lattice), then the  formulation and solution of at least some problems turn  out to be mathematically correct (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  This work is an ideological continuation of the work  [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The essential difference between the present paper  and the paper [11] is that we assume a lattice regular-  ization of the theory of gravity (see [12] and references  there).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Lattice regularization provides a new possibility  for solving the problem of the divergent cosmological  constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The solution of the Einstein equation within  the framework of the Friedmann paradigm with a finite  bare cosmological constant is mathematically correct,  since all local physical quantities (energy density in-  cluding vacuum energy, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=')  on the lattice are finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Our approach assumes that all physical quantities are  determined by taking into account quantum zero point  fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  In particular, the energy density and  pressure are mainly determined by quantum fluctua-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Since the equations considered here describe such  large energy densities that, on the characteristic time  intervals, have actions exceeding the Planck constant  by a huge number of times, we assume the considered  physical quantities to be classical and use the classical  equations [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' As a result, a solution is obtained that  demonstrates an exponential growth of the scale factor  in the initial period of evolution and then passes into a  power law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Einstein equation and solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' We use the energy-  momentum tensor of matter in the form of the energy-  momentum tensor of an ideal relativistic fluid:  T a  b = (ε + p)U aUb − pδa  b .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (3)  We work in an orthonormal basis in which the metric ten-  sor ηab = diag(1, −1, −1, −1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' On the right side of (3),  the symbols ε and p denote the energy density and pres-  sure, respectively, and these quantities also include vac-  uum energy and pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Since fermionic fields, in con-  trast to bosonic ones, make a negative contribution to the  vacuum energy, but there are significantly more fermionic  degrees of freedom than bosonic ones, we have ε < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Moreover, lattice regularization means that |ε|, |p| < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Note that in (3) the pressure p is different from the pres-  sure P(β, µ) in (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' A comparison of these values is given  below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' U a is the averaged 4-velocity of the macroscopic  regions of the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In our case U a = (1, 0, 0, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' To  compensate for the vacuum energy, a bare finite positive  cosmological constant Λ0 is introduced into the Einstein  equation[14]:  Ra  b −1  2δa  b R = 8πG  c4 T a  b + Λ0δa  b .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (4)  We assume that the cosmological constant  Λ0 = const ∼ l−2  P ,  lP ∼  �  8πGℏ  c3  ∼ 10−32cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (5)  For the metric, we use ansatz (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In order not to clutter  up the formulas, we introduce the notation  8πG  c4 ε = ˜ε,  8πG  c4 p = ˜p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (6)  All components of the Einstein equation are reduced to  two equations:  3 ˙a2  a2 = Λ0 + ˜ε,  2¨a  a + ˙a2  a2 = Λ0 − ˜p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (7)  Here ˙a ≡ d a/ d x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Another equation ∇aT a  b = 0 is a  consequence of equations (7), and therefore it does not  need to be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Let us introduce the Hubble con-  stant ˜H(t) ≡ ˙a/a, with the help of which Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (7) are  rewritten as follows:  2 ˙˜H + (˜ε + ˜p) = 0,  3 ˜H2 − (Λ0 + ˜ε) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (8)  So we have 3 unknown functions {˜ε(t), ˜p(t), ˜H(t)} and 2  equations (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The missing equation is the equation of  state relating energy density and pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Regarding the  equation of state, the following facts are reliably known:  (i) in the case of real dusty matter, we have ˜p = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (ii) in  3  the case of real ultrarelativistic matter we have ˜p = ˜ε/3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  in the case of vacuum energy and pressure, we have ˜p =  −˜ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In all three cases, the energy density and pressure  are linearly related.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Therefore, we propose to accept the  following hypothesis:  ˜p = κΛ0 + (κ − 1)˜ε ←→ ˜ε + ˜p = κ(˜ε + Λ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (9)  This equation is linear and inhomogeneous with an un-  known function κ(t), the asymptotics of which are fur-  ther determined based on the known dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The set  of equations (8) and (9) has a solution:  ˙˜H = −3  2κ ˜H2 → ˜H(t) = ˜H0  �  1 + 3  2H0  � t  0  κ(t′) d t′  �−1  ,  (10)  ˜ε(t) = −Λ0 + 3 ˜H2  0  �  1 + 3  2H0  � t  0  κ(t′) d t′  �−2  ,  (11)  ˜p(t) = Λ0 + 3  �  κ(t) − 1  � ˜H2  0  �  1 + 3  2H0  � t  0  κ(t′) d t′  �−2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (12)  Here ˜H0 ≡ H0/c is the integration constant, ˜H(t) ≡  H(t)/c, and H0 is the Hubble constant at the beginning  of the inflation phase, [H(t)] = [H0] = s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  We indicate some of the most obvious properties of the  solution (10), (11), (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The estimates given below are  very rough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Let us accept the following estimates for the  duration of the inflation time tinf, and for the constant  Λ0:  tinf ∼= 10−37s,  H0 ∼= 1039s−1,  ˜H0 ∼= 1029cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (13)  Then H0tinf ∼= 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Let’s take κ0 ≡ κ(t = 0) ∼= 1/150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Assume that during the time tinf the function κ changes  insignificantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Then for t < tinf the solutions (10), (11),  (12) take the form  ˜H(t) ∼= ˜H0,  ˜ε(t) ∼= −˜p ∼= −Λ0 + 3 ˜H2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (14)  Thus, during inflation, the scale factor a(t) increased by  (exp H0tinf) ≈ (exp 100) ≈ 1043 times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Assume that when t > tinf, the function κ(t) becomes  equal to κ = 4/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In this case, the solutions (10), (11),  (12) give a power-law expansion:  H(t) ∼= 1  2t,  ˜ε(t) ∼= −Λ0 + 3  4t2 ,  ˜p ∼= Λ0 + 1  4t2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (15)  Solution (15) shows that the scale factor and the density  of real matter change according to the well-known law,  as well as the correct equation of state in the case of  ultrarelativistic matter:  a(t) ∝  √  t,  ρreal =  3  32πGt2 ,  preal = 1  3εreal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (16)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Thermodynamic considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Here, the possibil-  ity of using a thermodynamic approach to this problem  is briefly discussed, and some thermodynamic relations  are also given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The purpose of this consideration is to  (at least superficially) explain the state equation (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  The estimation (13) means that  ˜H2  0 ≪ Λ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (17)  It can be seen from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (11) that the maximum frequen-  cies of the degrees of freedom of matter in the modern  era are of the order of  |ωmax| ∼ c  �  Λ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (18)  We are interested in small times when H ∼ H0 (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Since at these times the space was many orders  of magnitude more compact, then for small times the  estimate |ωmax| ≫ c√Λ0 was valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Consider the time  interval ∆t ≲ H−1, for which we have  ∆a/a ∼ H∆t ≲ 1,  ∆t|ωmax| ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (19)  Taking into account Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (19), we can assume that for a  time interval ∆t the thermodynamic equilibrium of the  vacuum degrees of freedom is realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' This assumption  cannot be extended to those degrees of freedom whose  frequencies ∆t|ω| ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' But such degrees of freedom make  a small contribution to the total energy-momentum ten-  sor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  When passing to the Euclidean signature by Wick’s  rotation ∆t = −i∆τ [15], the parameter  T ≡ β−1 = ��(∆τ)−1 ∼ ℏH  (20)  acquires the meaning of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Let us determine  the temperature value in Kelvin degrees at the begin-  ning of the inflation process, when, according to some  estimates H0 ∼ 1039s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Then  T0 ∼ ℏH0  k  ∼  �  1028�◦ K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (21)  Here k is the Boltzmann constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The temperature es-  timate (21) is within the known temperature estimates  in the initial phase of inflation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Once again, we note that thermodynamic considera-  tions do not apply to low-frequency degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  In particular, ordinary real matter may, generally speak-  ing, not be in a state of thermal equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  According to Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (10) and (20) we have:  ℏ d β ∼ d(1/H) = 3/2κ d t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  But in the inflation phase a(t) = a0eHt, and so d t =  H−1 d a/a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Thus we have:  d β/β ∼ (3/2)κ d a/a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (22)  Since the temperature decreases in the inflation phase, it  can be seen from (22) that κ(t = 0) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  4  It can be seen from the first Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (7) that the constant  Λ0 cancels out the huge negative energy of the vacuum,  so that in the era of power-law expansion only the rel-  atively extremely small positive energy density of real  matter affects the dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' From the given solution of  Einstein’s equations, it can be seen that the huge value  of pressure is also mainly reduced by the constant Λ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  In the presented solution we have ˜p ∼ −˜ε ∼ Λ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Such a  ratio of pressure and energy density of matter is dictated  by the relativistic invariance of quantum states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  We will show that the contraction of the enormous vac-  uum pressure ˜p can be interpreted as a thermodynamic  effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Indeed, the contribution of the cosmological con-  stant to the action for volume V =  � �  |g| d3 x and time  interval ∆t is equal to  i AΛ0 /ℏ = − ic4  8πGℏΛ0V ∆t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (23)  As a result of the Wick rotation according to the formula  ∆t = −i∆τ and due to (20) the action (23) is trans-  formed to the form  i AΛ0 /ℏ −→ −  c4  8πGℏΛ0V ∆τ = − c4  8πGΛ0V β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (24)  Adding (24) to the Euclidean action has the same effect  as adding µNβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Here N is the number of degrees of  freedom on the part of the lattice contained in the volume  V , and µ is the total chemical potential of the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Equating the value (µNβ) to the value on the right side  of the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (24), we find:  µ = − c4  8πGΛ0  V  N .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (25)  Usually the chemical potential is the independent vari-  able.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' But here it is a function of volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Therefore, the  total pressure is determined by a more complex formula:  P(β, µ) = −  � ∂Ω  ∂V  �  β,µ  −  �∂Ω  ∂µ  �  β,V  ∂µ  ∂V = p −  c4  8πGΛ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  (26)  Here we have taken into account the equality N  =  −(∂Ω/∂µ)β,V and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' On the left hand side of  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (26) the pressure P(β, µ) is the same as the pressure  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' The above solution of the Einstein equations  shows that P(β, µ) is negligible compared to the total  pressure p of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' This fact was pointed out and used  in the work [11]  The estimate ˜p ∼= Λ0 together with the vacuum energy  hypothesis ˜ε ∼= −Λ0 justifies the equation of state (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' In  both parts of equality (˜ε + ˜p) = κ(˜ε + Λ0), the diverging  values of the quantities cancel each other out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' This fact  is the result of solving dynamic equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  A more accurate equation of state should be obtained  by microscopic analysis in the spirit of the works [2–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  Acknowledgments  I thank Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Volovik for awakening my interest  in the thermodynamic study of the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' I am grate-  ful to Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Akhmedov for numerous discussions  and advice in the course of work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' This work was carried  out as a part of the State Program 0033-2019-0005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Weinberg, Reviews of modern physics 61, 1 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [2] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Krotov and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Polyakov, Nuclear Physics B 849,  410 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Polyakov, arXiv preprint arXiv:1209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='4135 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [4] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Akhmedov, International Journal of Modern Physics  D 23, 1430001 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [5] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Akhmedov, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Moschella, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Popov, Physical Re-  view D 99, 086009 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [6] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Akhmedov, Modern Physics Letters A 36, 2130020  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Kamenshchik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Starobinsky, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Var-  danyan, The European Physical Journal C 82, 1 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [8] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Zel’Dovich and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Starobinskiˇı, Soviet Journal of  Experimental and Theoretical Physics 34, 1159 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Kamenshchik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Starobinsky, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Tronconi,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Vardanyan, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Venturi, The European Physical  Journal C 78, 1 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Appleby and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Linder, Journal of Cosmology and  Astroparticle Physics 2020, 037 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [11] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Klinkhamer and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Volovik, Physical Review D 105,  084066 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Vergeles, Classical and Quantum Gravity 38, 085022  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [13] We mean the fact that according to (5), (6) and (11)  we have the estimate (l3  P tP ε)/ℏ ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' Here tP ∼ lP /c ∼  10−43s is the Planck time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' However, the inflation time  tinf is several orders of magnitude longer than the Planck  time (see (13)), and therefore (l3  P tinfε)/ℏ ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content=' This  means that in the Planck volume, on a time interval much  greater than the Planckian but much less than the infla-  tion time, the action of the system is much greater than  the Planck constant, and therefore a classical description  is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [14] In lattice theory [12], the cosmological constant is intro-  duced in a natural way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}
+page_content='  [15] The correctness of the sign during Wick rotation is es-  tablished by the example of the action of a scalar field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dAzT4oBgHgl3EQfuf2L/content/2301.01692v1.pdf'}

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+arXiv:2301.04862v1  [cs.PL]  12 Jan 2023
+Naturalistic Static Program Analysis
+Mohammad Mehdi Pourhashem Kallehbasti
+Department of Electrical and Computer Engineering
+University of Science and Technology of Mazandaran
+P.O. Box 48518-78195, Behshahr, Iran
+[email protected]
+Mohammad Ghafari
+TU Clausthal, Germany
+[email protected]
+Abstract—Static program analysis development is a non-trivial
+and time-consuming task. We present a framework through
+which developers can define static program analyses in natural
+language. We show the application of this framework to identify
+cryptography misuses in Java programs, and we discuss how it
+facilitates static program analysis development for developers.
+Index Terms—Static program analysis, cryptography, natural
+language programming
+I. INTRODUCTION
+Static program analysis is the art of examining programs
+without requiring to execute the code. However, static analysis
+tools generate false positives and tuning them requires exper-
+tise. Likewise, program analysis development requires a deep
+knowledge of compiler or mastering an analysis framework.
+End-user programming is a set of techniques that enable
+end users to write programs at a level of complexity that is
+adequate to their practices, background, and skills. For in-
+stance, it includes visual languages to program robots through
+visual blocks [1], and simplified programming languages to
+translate English sentences to Bash commands [2]. We believe
+that end-user programming techniques can also help to hide the
+complexity of writing a static program analysis task for non-
+professional programmers and empower them in this domain.
+We introduce NASRA (NAturalistic Static pRogram Analy-
+sis), a framework that enables developers to define a program
+analysis task in natural language (NL), and it generates the
+corresponding Query Language (QL) query that underlies
+CodeQL program analysis engine.1 We illustrate the appli-
+cation of this framework to find cryptography misuses in Java
+programs. NASRA is open source and publicly available.2
+The ultimate goal of NASRA is to enable “naturalistic”
+static program analysis development in a way that developers
+can specify what they need without deep knowledge of static
+program analysis and how a specific framework works. Its
+higher level of abstraction than existing static analysis frame-
+works may facilitate a more intuitive formulation of program
+analysis tasks. Similarly, its agnostic nature to programming
+languages can provide a cross-language interface for program
+analysis, which obviates the need to learn the specifics of a
+program analysis framework. This paper presents a prelimi-
+nary step to realize the above goal.
+1https://codeql.github.com
+2https://doi.org/10.5281/zenodo.7495044
+II. THE NASRA FRAMEWORK
+Cryptography is an essential component to security, but it is
+one of the notorious topics where developers struggle a lot [3],
+[4]. Locating the init method invoked on a Cipher object
+is often deemed to be the first step to analyze cryptography
+code in Java programs. For instance, in CodeQL, one should
+write the following query to implement this task.
+from
+MethodAccess init
+where init.getMethod().getName() = "init" and
+init.getReceiverType().getName() = "Cipher"
+select init
+We have developed a framework, called NASRA, that
+enables a more intuitive formulation of the above task in the
+form below:
+An object of Cipher invokes init.
+NASRA is a rule-driven synthesizer. We rely on predefined
+rules due to a lack of trustworthy labeled examples required
+for a data-driven approach in this domain. NASRA receives a
+program analysis inquiry in natural language, applies semantic
+parsing, and generates CodeQL commands. The input inquiry
+should comply with a subset of the syntax of Attempto
+Controlled English (ACE) controlled natural language. We
+use Attempto Parsing Engine (APE), a tool that receives a
+series of ACE statements and produces the corresponding
+Discourse Representation Structures (DRS) that is a semantic
+representation of the input text. NASRA applies the translation
+rules, explained later in this section, on the given DRS and
+produces the corresponding CodeQL statements. Thanks to
+APE, the way one can formulate NASRA statements is very
+flexible and there is no need for absolute correspondence with
+the NASRA syntax. We chose CodeQL as our code analysis
+engine because it is an industry-leading and community-
+powered tool, and its publicly available to all GitHub users
+without any installation hassle. To employ NASRA for a new
+static analysis framework, only the transformation rules have
+to be adapted. To support a new application domain, we should
+identify the types of queries that the current syntax does not
+support, add the corresponding production rules to the syntax,
+and develop translations for them. NASRA is open source,
+and currently, supports program analysis tasks that concern
+cryptography misuses in Java programs.
+
+A. Syntax and Semantics
+Each NASRA query comprises one or more Statement. The
+syntax is shown below (terminals have different color).
+Query ::= Statement Query | Statement
+Statement ::= BasicStatement | LogicalStatement
+| Extension
+BasicStatement ::= Exp is (Exp | in List)
+Exp ::= Prefix Exp | type | ID | Literal
+Prefix ::= ((adjective|ε) attribute of)
+LogicalStatement ::= Statement and Statement |
+Statement or Statement | It is false that Statement
+| If Statement then Statement
+a) Expression: The smallest building block is Exp. It
+includes a Literal (String or int) or an ID (user defined
+identifier) that are directly mapped to CodeQL expressions.
+An Exp can also be a CodeQL type such as class, variable,
+and method access that are mapped to Class, Variable,
+and MethodAccess, respectively.
+b) Prefix: Each Exp can have an optional Prefix in
+the form of “attribute of” that indicates an attribute of
+the expression. For instance, name, type, argument, and
+method are attributes of an entity (i.e., Exp), and they cor-
+respond to getName(), getType(), getArgument(),
+and getMethod() methods in CodeQL, respectively.
+For example, “name of method1” is an Exp, where “name”
+is an attribute and method1 is an ID, and the whole expres-
+sion is translated to method1.getName() in CodeQL.
+Additionally, the attribute itself can have an optional
+ordinal
+number
+as
+an
+adjective,
+like
+second
+in
+the
+Exp “second argument of init” that is translated to
+“init.getArgument(1)”, where second is translated to
+1 as an argument according to zero-based numbering.
+Note that “attribute of” can be repeated several times, where
+each attribute may have an adjective. For example, the Exp
+“The type of the second argument of init” has one ID
+(i.e.,init) and two attributes (i.e., type and argument).
+c) Basic Statement: Each BasicStatement is a statement
+that can serve as a Boolean condition as well as an assumption.
+As a Boolean condition, BasicStatement produces equiva-
+lence of two Exps, as well as membership of an Exp in a list.
+In “Exp is Exp” structure, both sides of equivalence are Exps
+and they need to be equal, while in “Exp is in List” structure,
+the Exp needs to be equal to an item in a list. Accordingly, a
+statement like “arg1 is in ["RSA", "AES"].” is a disjunctive
+expression and can be rephrased to “arg1 is "RSA" or arg1
+is "AES".”, that is ultimately translated to “arg1 = "RSA"
+or arg1 = "AES"”.
+The syntax structure Exp is Exp can also produce as-
+sumptions when the second Exp is a CodeQL type. The
+assumptions are mapped to the from part of a CodeQL query.
+For instance, the statement “var1 is a variable.” translates to
+“Variable var1” and belongs to the from part.
+d) Logical Statement: A LogicalStatement can be a
+negation, conjunction, disjunction, or implication. For exam-
+ple, “If arg1 is "RSA" then arg2 is "AES".” is translated to
+“not (arg1 = "RSA") or arg2 = "AES"” in Cod-
+eQL, since p ⇒ q is equivalent to ¬p ∨ q.
+B. Extensibility
+One can extend NASRA to cover auxiliary statements and
+statement patterns. Their corresponding production rules are
+as follows.
+Extension ::= Pattern | AuxiliaryStatement
+We introduce these features through three statement pat-
+terns and one auxiliary statement that are helpful to cover
+constraints on using Java cryptography objects.
+1) Patterns: We present three patterns that extend Pattern
+nonterminal in the syntax. We discuss each in the following.
+a) Invocation: We use this pattern to state that a method
+is invoked by an instance of a specific class. It can also be
+used to make sure that there is no invocation of a method by
+any instance of a specific class.
+Pattern1 ::= An object of ID (invokes|does not invoke) ID.
+The NASRA query shown in Section II is an example of this
+pattern. The transformation follows a number of steps. First, a
+MethodAccess is declared with the same name used in the
+NASRA statement (i.e.,init). Then the conditions need to be
+added to the where part. Specifically, the name of the method
+of the MethodAccess init should be "init" that is
+stated in the second line. Finally, a MethodAccess has a
+receiver, that is the object invoking its method. In this case,
+the name of the type of the receiver should be "Cipher",
+that is expressed in CodeQL in the third line.
+If one needs to make sure that no invocation occurs, an
+existential quantifier must be used, as shown in the following.
+from
+where not
+(exists
+(MethodAccess
+init
+|
+init.getMethod().getName() = "init" and
+init.getReceiverType().getName() = "Cipher"))
+It means that there is no such MethodAccess init that
+has these conditions. We can state this in NASRA in the form
+below.
+An object of Cipher doesn’t invoke init.
+b) Partial order constraints: This pattern enables one to
+put partial order constraints on method invocations. In other
+words, one can enforce a method invocation to be preceded
+(or followed) by another method invocation.
+Pattern2::=MethodName (precedes|follows) MethodName.
+For example, there are two steps in CodeQL for stating that
+“invocation of getInstance is earlier than invocation of
+init”. First, one should specify that both methods are in the
+same scope. Next, the line number of the preceding method
+invocation has to be smaller than the line number of the other
+method invocation. This is shown below.
+
+getInstance.getEnclosingCallable()
+=
+init.getEnclosingCallable() and
+getInstance.getLocation().getEndLine()
+<
+init.getLocation().getEndLine()
+We can express this query in NASRA as follows.
+getInstance precedes init.
+c) Method signature constraint: It is possible to express
+signature of a method using Pattern3.
+Pattern3 ::= MethodName’s signature is List.
+A method signature can be seen as an ordered list of data
+types. This list contains names of data types as strings, such
+that the first string is the name of the first argument’s data
+type and so on. For example, the following NASRA query
+states that getInstance method has two arguments and
+the names of their types are "int" and "Certificate",
+respectively.
+getInstance’s signature is ["int", "Certificate"].
+This query is translated to the following CodeQL query.
+(count (getInstance.getAnArgument()) = 2) and
+getInstance.getArgument(0).getType().
+toString()="int" and getInstance.
+getArgument(1).getType().toString()=
+"Certificate"
+First, the number of arguments is set to the size of the user
+defined list, then the type of arguments are constrained one
+by one. count (method.getAnArgument()) returns
+the number of arguments of the method. getArgument(i)
+returns
+the
+argument number i
+in
+the
+given
+method,
+getType() returns the type of the given argument, and
+finally toString() converts the given data type to a String.
+2) AuxiliaryStatement: We aim to find misuses in code
+that violate one or more mandatory constraints. For instance,
+suppose that if the second argument of init method is
+"private key" then it is mandatory that the encryption al-
+gorithm, i.e., the second argument of getInstance method
+is "RSA", and also if the encryption algorithm is "AES"
+then it is mandatory that the mode of encryption, i.e., the
+first argument of the getInstance method, is "CBC". The
+following NASRA query will find such violations.
+It is false that if the type of the second argument of init
+is "PrivateKey", then the algorithm of getInstance’s
+first argument is "RSA" or it is false that if the algorithm of
+getInstance’s first argument is "AES" then the mode of
+getInstance’s first argument is "CBC".
+In order to find any violation of these constraints, dis-
+junction of their negation has to be stated in the query.3
+3For example, in “X is driving in an urban area(Cond1). It is necessary that
+X is driving slower than 60 km/h (Cons1). It is necessary that X fastens the
+seat belt (Cons2).”, the query needs to find an X that is driving in an urban
+area and is driving faster than 60 km/h or is not using the seat belt. If we
+assign a Boolean variable to each statement as mentioned in the statements, it
+should aim Cond1 ∧(¬Cons1 ∨¬Cons2) whose necessity part is translated
+to the disjunction of negation of two constraints.
+Nevertheless, the above statement becomes much longer and
+harder to comprehend as the number of constraints increases.
+We define auxiliary statements to ease the formulation as
+well as the comprehension of complex queries for developers.
+Particularly, NecessityStatements are auxiliary statements that
+enable developers to enforce mandatory constraints in short
+and independent statements. It starts with “It is necessary that”
+and follows the syntax below.
+NecessityStatement
+::=
+It is necessary that Statement.
+Therefore, instead of writing disjunction of negation of all
+constraints in one single statement, developers can benefit
+this construct (i.e., NecessiyStatement) to define all such
+constraints in several statements within a query. Accordingly,
+the single but long previous statement can be stated as two
+separate statements shown below.
+It is necessary that if the type of the second argument of init is
+"PrivateKey", then the algorithm of getInstance’s first
+argument is "RSA".
+It is necessary that if the algorithm of getInstance’s first
+argument is "AES" then the mode of getInstance’s first
+argument is "CBC".
+Necessity statements are treated differently from other state-
+ments. If there is only one NecessityStatement, its enclosing
+statement is negated and added to the where part of the
+CodeQL query. If there are more than one, e.g., n constraints
+Cons1, Cons2, ..., Consn, then the “(not T Cons1 or
+not T Cons2 or ... or not T Consn)” will be added
+to the where part, where T Consi is the translation of Consi.
+III. WORKING EXAMPLES
+Cipher is one of the most misused APIs in Java cryp-
+tography [4]. Listing 1 shows how to create a Cipher
+object in Java. We should call the Cipher’s getInstance
+method. This method receives a number of arguments. The
+first one is transformation that is a string containing
+three parts separated by “/”. These parts are algorithm,
+mode, and padding, respectively. Next, we should call the
+init method on the cipher object with two arguments to
+indicate the operation mode of the cipher, and to initialize
+this object with a Key or Certificate.
+Cipher cipher = Cipher.getInstance("AES/ECB/
+PKCS5Padding");
+cipher.init(Cipher.ENCRYPT_MODE,new SecretKeySpec(
+keyBytes, "AES"));
+Listing 1. Setting up the Cipher object in Java
+In the rest of this section, we present three different program
+analysis tasks to ensure secure use of Java Cipher.
+A. Key vs. Algorithm
+Task 1: If the key has a type of PublicKey, PrivateKey,
+or Certificate, or encryption mode is WRAP MODE or UN-
+WRAP MODE, then algorithm of transformation must be
+“RSA”.
+
+Listing 2 shows how to check this constraint in CodeQL.
+from MethodAccess getInstance, MethodAccess init
+where init.getMethod().getName() = "init" and init.
+getReceiverType().getName() = "Cipher" and
+getInstance.getMethod().getName() = "getInstance
+" and getInstance.getReceiverType().getName() =
+"Cipher" and (((init.getArgument(0).toString() =
+"Cipher.WRAP MODE" or init.getArgument(0).
+toString() = "Cipher.UNWRAP MODE") or (init.
+getArgument(1).getType().toString() = "java.
+security.PublicKey" or init.getArgument(1).
+getType().toString() = "java.security.PrivateKey
+" or init.getArgument(1).toString() = "java.
+security.cert.Certificate")) and not(getInstance
+.getArgument(0).toString().replaceAll("\","").
+splitAt("/",0) = "RSA"))
+select getInstance, init
+Listing 2. Key vs. Algorithm constraint in CodeQL
+This constraint can be expressed in NASRA as follows.
+An
+object
+of
+Cipher
+invokes
+init.
+An
+object
+of
+Cipher invokes getInstance. It is necessary that if
+init’s
+first
+argument
+is
+in
+["Cipher.WRAP_MODE",
+"Cipher.UNWRAP_MODE"]
+or
+the
+type
+of
+the
+second
+argument of init is in ["PublicKey", "PrivateKey",
+"Certificate"] then the algorithm of getInstance’s
+first argument is "RSA".
+B. Algorithm vs. Transformation Mode
+Task 2: If the algorithm of transformation is “RSA” then
+the mode of transformation must be either “” or “ECB”.
+Listing 3 shows the corresponding query to check this
+constraint in CodeQL. We should look for code in which the
+algorithm is “RSA”, but neither “ECB” nor “” is set for the
+mode.
+from MethodAccess getInstance
+where getInstance.getMethod().getName() = "
+getInstance" and getInstance.getReceiverType().
+getName() = "Cipher" and (getInstance.
+getArgument(0).toString().replaceAll("\"","").
+splitAt("/", 0) = "RSA") and not (getInstance.
+getArgument(0).toString().replaceAll("\"","").
+splitAt("/", 1) = "" or getInstance.getArgument
+(0).toString().replaceAll("\"","").splitAt("/",
+1) = "ECB")
+select getInstance
+Listing 3. Algorithm vs. Transformation Mode constraint in CodeQL
+This constraint can be expressed in NASRA as follows.
+An object of Cipher invokes getInstance. It is necessary
+that if the algorithm of getInstance’s first argument is
+"RSA" then the mode of getInstance’s first argument is in
+["", "ECB"].
+Thanks to Attempto Parsing Engine (APE), NASRA state-
+ments do not need to exactly follow the syntax rules meaning
+that a degree of freedom in paraphrasing is possible. For
+instance, the part “the algorithm of getInstance’s first
+argument is "RSA"” can also be written in two other forms:
+(i) the algorithm of the first argument of getInstance is
+"RSA".
+(ii) "RSA" is the algorithm of getInstance’s first argument.
+C. Transformation and Encryption Mode vs. Signature
+Task 3: If the transformation mode is either of “CBC”,
+“PCBC”, “CTR”, “CTS”, “CFB”, or “OFB”, and the en-
+cryption mode is not “Cipher.ENCRYPT MODE”, then the
+invoked init method should not have any of the following
+signature: init(encmode, cert), init(encmode, cert, ranGen),
+init(encmode, key), init(encmode, key, ranGen).
+Listing 4 presents how to enforce this constraint in CodeQL.
+from MethodAccess getInstance, MethodAccess init
+where init.getMethod().getName() = "init" and init.
+getReceiverType().getName() = "Cipher" and
+getInstance.getMethod().getName() = "getInstance
+" and getInstance.getReceiverType().getName() =
+"Cipher" and ((getInstance.getArgument(0).
+toString().replaceAll("\"","").splitAt("/", 1) =
+"CBC" or getInstance.getArgument(0).toString().
+replaceAll("\"","").splitAt("/", 1) = "PCBC" or
+getInstance.getArgument(0).toString().replaceAll
+("\"","").splitAt("/", 1) = "CTR" and
+getInstance.getArgument(0).toString().replaceAll
+("\"","").splitAt("/", 1) = "CTS" or getInstance
+.getArgument(0).toString().replaceAll("\"","").
+splitAt("/", 1) = "CFB" or getInstance.
+getArgument(0).toString().replaceAll("\"","").
+splitAt("/", 1) = "OFB") and not (init.
+getArgument(0).toString() = "Cipher.ENCRYPT_MODE
+")) and ((count (getInstance.getAnArgument()) =
+2 and getInstance.getArgument(0).getType().
+toString() = "int" and getInstance.getArgument
+(1).getType().toString() = "Certificate") or (
+count (getInstance.getAnArgument()) = 3 and
+getInstance.getArgument(0).getType().toString()
+= "int" and getInstance.getArgument(1).getType()
+.toString() = "Certificate" and getInstance.
+getArgument(2).getType().toString() = "
+SecureRandom") or (count (getInstance.
+getAnArgument()) = 2 and getInstance.getArgument
+(0).getType().toString() = "int" and getInstance
+.getArgument(1).getType().toString() = "Key") or
+(count (getInstance.getAnArgument()) = 3 and
+getInstance.getArgument(0).getType().toString()
+= "int" and getInstance.getArgument(1).getType()
+.toString() = "Key" and getInstance.getArgument
+(2).getType().toString() = "SecureRandom"))
+select init, getInstance
+Listing 4. Transformation and Encryption mode vs. Signature constraint in
+CodeQL
+The implementation of this task in NASRA is shown below.
+An
+object
+of
+Cipher
+invokes
+getInstance.
+An
+object
+of
+Cipher
+invokes
+init.
+It
+is
+necessary
+that
+if
+the
+mode
+of
+getInstance’s
+first
+argument
+is
+in
+["CBC","PCBC","CTR","CTS","CFB","OFB"]
+and
+init’s first argument is not "Cipher.ENCRYPT_MODE"
+then
+getInstance’s
+signature
+is
+not
+["int","Certificate"]
+and
+is
+not
+["int","Certificate","SecureRandom"]
+and
+is
+not
+["int","Key"]
+and
+is
+not
+["int","Key","SecureRandom"].
+D. Discussion
+Table I presents the number of distinct operators and
+operands (i.e., vocabulary), and the total number of operators
+and operands (i.e., length) needed for each analysis task.4
+4In NASRA, we consider user defined terminals such as init, “RSA”, and
+getInstance as operands and count the rest of language constructs as operators.
+
+TABLE I
+CODEQL VS. NASRA
+Analysis Task
+Vocabulary
+Length
+CodeQL
+NASRA
+CodeQL
+NASRA
+Key vs. Algorithm (III-A)
+32
+19
+179
+39
+Algorithm vs. Mode (III-B)
+27
+18
+107
+24
+Mode vs. Signature (III-C)
+42
+26
+434
+56
+Evidently, queries in NASRA are significantly shorter than
+queries in CodeQL (i.e., up to 87% reduction in length), and
+they consume a lot fewer programming constructs (i.e., up to
+38% fewer vocabularies). We computed Halstead complexity
+measures to estimate the coding time and the difficulty to
+write or understand these queries [5]. The results showed that
+developers require a lot less effort and time to develop these
+tasks in NASRA than in CodeQL.
+We also asked ten developers to share their opinion about
+queries in NASRA. They unanimously stated that they are
+succinct and easy to understand, and one commented that
+“these queries read like API documentation”.
+It is noteworthy that NASRA’s performance, i.e., how well
+it can detect API misuses, depends on its underlying analy-
+sis framework which is currently CodeQL. In other words,
+NASRA obviates the low-level details needed to define static
+program analyses, but the issues with false positives remain
+to be relevant. Moreover, despite being natural, the use of
+NASRA still requires knowledge of its syntax.
+IV. RELATED WORK
+Mapping a natural language statement into a formal repre-
+sentation has received great attention in the community but
+not much in the program analysis development domain.
+Schlegel
+et
+al.
+developed
+an
+end-user
+programming
+paradigm for Python, that maps natural language commands
+into Python code [6]. Landhauber et al. proposed a domain
+agnostic command interpreter that receives natural language
+commands in English and uses ontology to produce relevant
+API calls [7]. Yaghmazadeh et al. developed SQLIZER, a
+system to automatically synthesize SQL queries from a natural
+language [8]. Luo et al. investigated the translation from
+a natural language query to visualization with the goal of
+simplifying the creation of data visualizations [9].
+Heyman et al. developed a Python code completion tool
+that enriches developers’ code with the natural language de-
+scription of the intended data science task [10]. Nguyen et al.
+presented an approach that takes as input an English descrip-
+tion of a programming task and synthesizes the corresponding
+API code template for the task [11]. Desai et al. built a general
+framework for constructing program synthesizers that take
+natural language inputs and produce expressions in a target
+Domain Specific Language [12]. Zhai et al. proposed a search-
+based technique to automatically translate NL comments to
+formal program specifications that specify the expected pre
+and post conditions [13].
+The work presented in this paper is also related to cryp-
+tography domain. There exist tools that find cryptography
+misuses [14] and libraries that facilitate the adoption of
+cryptography for developers [15]. Nevertheless, none of them
+employed a natural language approach.
+V. CONCLUSION
+We introduced NASRA, an open-source framework to de-
+fine static program analyses in natural language. We demon-
+strated the application of this framework to find misuses in
+Java cryptography. The ultimate goal of NASRA is to enable
+a naturalistic way to develop static program analyses, which is
+usable for mainstream developers. To realize this goal, further
+studies are needed to determine NASRA’s effectiveness in
+real-world settings. The expressiveness of its queries and the
+effort required to extend it to other problem domains have to
+be investigated as well. Finally, automatic translation without
+pre-defined rules is also an exciting future research direction.
+REFERENCES
+[1] E. Barakova, J. Gillesen, B. Huskens, and T. Lourens, “End-user
+programming architecture facilitates the uptake of robots in social
+therapies,” Robotics and Autonomous Systems, vol. 61, no. 7, 2013.
+[2] X. V. Lin, C. Wang, L. Zettlemoyer, and M. D. Ernst, “NL2Bash:
+A corpus and semantic parser for natural language interface to the
+linux operating system,” in Proceedings of the Eleventh International
+Conference on Language Resources and Evaluation (LREC 2018), 2018.
+[3] M. Hazhirpasand, O. Nierstrasz, M. Shabani, and M. Ghafari, “Hurdles
+for developers in cryptography,” in 2021 IEEE International Conference
+on Software Maintenance and Evolution (ICSME), 2021, pp. 659–663.
+[4] M. Hazhirpasand, M. Ghafari, and O. Nierstrasz, “Java cryptography
+uses in the wild,” in Proceedings of the 14th ACM / IEEE International
+Symposium on Empirical Software Engineering and Measurement, 2020.
+[5] M. H. Halstead, Elements of Software Science (Operating and program-
+ming systems series).
+Elsevier Science Inc., 1977.
+[6] V. Schlegel, B. Lang, S. Handschuh, and A. Freitas, “Vajra: Step-by-
+step programming with natural language,” in Proceedings of the 24th
+International Conference on Intelligent User Interfaces, 2019.
+[7] M. Landh¨auber, S. Weigelt, and W. F. Tichy, “Nlci: A natural language
+command interpreter,” Automated Software Engg., vol. 24, no. 4, p.
+839–861, dec 2017.
+[8] N. Yaghmazadeh, Y. Wang, I. Dillig, and T. Dillig, “Sqlizer: Query
+synthesis from natural language,” Proc. ACM Program. Lang., vol. 1,
+no. OOPSLA, oct 2017.
+[9] Y. Luo, N. Tang, G. Li, J. Tang, C. Chai, and X. Qin, “Natural language
+to visualization by neural machine translation,” IEEE Transactions on
+Visualization and Computer Graphics, vol. 28, no. 1, pp. 217–226, 2022.
+[10] G. Heyman, R. Huysegems, P. Justen, and T. Van Cutsem, “Natural
+language-guided programming,” ser. Onward!, 2021, p. 39–55.
+[11] A. T. Nguyen, P. C. Rigby, T. Nguyen, D. Palani, M. Karanfil, and T. N.
+Nguyen, “Statistical translation of english texts to api code templates,”
+in 2018 IEEE International Conference on Software Maintenance and
+Evolution (ICSME), 2018, pp. 194–205.
+[12] A. Desai, S. Gulwani, V. Hingorani, N. Jain, A. Karkare, M. Marron,
+S. R, and S. Roy, “Program synthesis using natural language,” in Pro-
+ceedings of the 38th International Conference on Software Engineering,
+ser. ICSE ’16, 2016.
+[13] J. Zhai, Y. Shi, M. Pan, G. Zhou, Y. Liu, C. Fang, S. Ma, L. Tan,
+and X. Zhang, “C2s: Translating natural language comments to formal
+program specifications,” in Proceedings of the 28th ACM Joint Meeting
+on European Software Engineering Conference and Symposium on the
+Foundations of Software Engineering, ser. ESEC/FSE 2020, 2020.
+[14] Y. Zhang, M. M. A. Kabir, Y. Xiao, D. D. Yao, and N. Meng, “Automatic
+detection of java cryptographic api misuses: Are we there yet,” IEEE
+Transactions on Software Engineering, 2022.
+[15] S. Kafader and M. Ghafari, “Fluentcrypto: Cryptography in easy mode,”
+in 2021 IEEE International Conference on Software Maintenance and
+Evolution (ICSME), 2021, pp. 402–412.
+

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+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='04862v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='PL]  12 Jan 2023  Naturalistic Static Program Analysis  Mohammad Mehdi Pourhashem Kallehbasti  Department of Electrical and Computer Engineering  University of Science and Technology of Mazandaran  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Box 48518-78195, Behshahr, Iran  pourhashem@mazust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='ir  Mohammad Ghafari  TU Clausthal, Germany  mohammad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='ghafari@tu-clausthal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='de  Abstract—Static program analysis development is a non-trivial  and time-consuming task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We present a framework through  which developers can define static program analyses in natural  language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We show the application of this framework to identify  cryptography misuses in Java programs, and we discuss how it  facilitates static program analysis development for developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Index Terms—Static program analysis, cryptography, natural  language programming  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' INTRODUCTION  Static program analysis is the art of examining programs  without requiring to execute the code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' However, static analysis  tools generate false positives and tuning them requires exper-  tise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Likewise, program analysis development requires a deep  knowledge of compiler or mastering an analysis framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  End-user programming is a set of techniques that enable  end users to write programs at a level of complexity that is  adequate to their practices, background, and skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' For in-  stance, it includes visual languages to program robots through  visual blocks [1], and simplified programming languages to  translate English sentences to Bash commands [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We believe  that end-user programming techniques can also help to hide the  complexity of writing a static program analysis task for non-  professional programmers and empower them in this domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  We introduce NASRA (NAturalistic Static pRogram Analy-  sis), a framework that enables developers to define a program  analysis task in natural language (NL), and it generates the  corresponding Query Language (QL) query that underlies  CodeQL program analysis engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='1 We illustrate the appli-  cation of this framework to find cryptography misuses in Java  programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' NASRA is open source and publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='2  The ultimate goal of NASRA is to enable ���naturalistic”  static program analysis development in a way that developers  can specify what they need without deep knowledge of static  program analysis and how a specific framework works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Its  higher level of abstraction than existing static analysis frame-  works may facilitate a more intuitive formulation of program  analysis tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Similarly, its agnostic nature to programming  languages can provide a cross-language interface for program  analysis, which obviates the need to learn the specifics of a  program analysis framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' This paper presents a prelimi-  nary step to realize the above goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  1https://codeql.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='com  2https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='7495044  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' THE NASRA FRAMEWORK  Cryptography is an essential component to security, but it is  one of the notorious topics where developers struggle a lot [3],  [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Locating the init method invoked on a Cipher object  is often deemed to be the first step to analyze cryptography  code in Java programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' For instance, in CodeQL, one should  write the following query to implement this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  from  MethodAccess init  where init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getMethod().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "init" and  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getReceiverType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "Cipher"  select init  We have developed a framework, called NASRA, that  enables a more intuitive formulation of the above task in the  form below:  An object of Cipher invokes init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  NASRA is a rule-driven synthesizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We rely on predefined  rules due to a lack of trustworthy labeled examples required  for a data-driven approach in this domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' NASRA receives a  program analysis inquiry in natural language, applies semantic  parsing, and generates CodeQL commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The input inquiry  should comply with a subset of the syntax of Attempto  Controlled English (ACE) controlled natural language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We  use Attempto Parsing Engine (APE), a tool that receives a  series of ACE statements and produces the corresponding  Discourse Representation Structures (DRS) that is a semantic  representation of the input text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' NASRA applies the translation  rules, explained later in this section, on the given DRS and  produces the corresponding CodeQL statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Thanks to  APE, the way one can formulate NASRA statements is very  flexible and there is no need for absolute correspondence with  the NASRA syntax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We chose CodeQL as our code analysis  engine because it is an industry-leading and community-  powered tool, and its publicly available to all GitHub users  without any installation hassle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' To employ NASRA for a new  static analysis framework, only the transformation rules have  to be adapted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' To support a new application domain, we should  identify the types of queries that the current syntax does not  support, add the corresponding production rules to the syntax,  and develop translations for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' NASRA is open source,  and currently, supports program analysis tasks that concern  cryptography misuses in Java programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Syntax and Semantics  Each NASRA query comprises one or more Statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The  syntax is shown below (terminals have different color).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Query ::= Statement Query | Statement  Statement ::= BasicStatement | LogicalStatement  | Extension  BasicStatement ::= Exp is (Exp | in List)  Exp ::= Prefix Exp | type | ID | Literal  Prefix ::= ((adjective|ε) attribute of)  LogicalStatement ::= Statement and Statement |  Statement or Statement | It is false that Statement  | If Statement then Statement  a) Expression: The smallest building block is Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' It  includes a Literal (String or int) or an ID (user defined  identifier) that are directly mapped to CodeQL expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  An Exp can also be a CodeQL type such as class, variable,  and method access that are mapped to Class, Variable,  and MethodAccess, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  b) Prefix: Each Exp can have an optional Prefix in  the form of “attribute of” that indicates an attribute of  the expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' For instance, name, type, argument, and  method are attributes of an entity (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', Exp), and they cor-  respond to getName(), getType(), getArgument(),  and getMethod() methods in CodeQL, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  For example, “name of method1” is an Exp, where “name”  is an attribute and method1 is an ID, and the whole expres-  sion is translated to method1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() in CodeQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Additionally, the attribute itself can have an optional  ordinal  number  as  an  adjective,  like  second  in  the  Exp “second argument of init” that is translated to  “init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(1)”, where second is translated to  1 as an argument according to zero-based numbering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Note that “attribute of” can be repeated several times, where  each attribute may have an adjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' For example, the Exp  “The type of the second argument of init” has one ID  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=',init) and two attributes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', type and argument).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  c) Basic Statement: Each BasicStatement is a statement  that can serve as a Boolean condition as well as an assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  As a Boolean condition, BasicStatement produces equiva-  lence of two Exps, as well as membership of an Exp in a list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  In “Exp is Exp” structure, both sides of equivalence are Exps  and they need to be equal, while in “Exp is in List” structure,  the Exp needs to be equal to an item in a list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Accordingly, a  statement like “arg1 is in ["RSA", "AES"].” is a disjunctive  expression and can be rephrased to “arg1 is "RSA" or arg1  is "AES".”, that is ultimately translated to “arg1 = "RSA"  or arg1 = "AES"”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  The syntax structure Exp is Exp can also produce as-  sumptions when the second Exp is a CodeQL type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The  assumptions are mapped to the from part of a CodeQL query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  For instance, the statement “var1 is a variable.” translates to  “Variable var1” and belongs to the from part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  d) Logical Statement: A LogicalStatement can be a  negation, conjunction, disjunction, or implication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' For exam-  ple, “If arg1 is "RSA" then arg2 is "AES".” is translated to  “not (arg1 = "RSA") or arg2 = "AES"” in Cod-  eQL, since p ⇒ q is equivalent to ¬p ∨ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Extensibility  One can extend NASRA to cover auxiliary statements and  statement patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Their corresponding production rules are  as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Extension ::= Pattern | AuxiliaryStatement  We introduce these features through three statement pat-  terns and one auxiliary statement that are helpful to cover  constraints on using Java cryptography objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  1) Patterns: We present three patterns that extend Pattern  nonterminal in the syntax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We discuss each in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  a) Invocation: We use this pattern to state that a method  is invoked by an instance of a specific class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' It can also be  used to make sure that there is no invocation of a method by  any instance of a specific class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Pattern1 ::= An object of ID (invokes|does not invoke) ID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  The NASRA query shown in Section II is an example of this  pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The transformation follows a number of steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' First, a  MethodAccess is declared with the same name used in the  NASRA statement (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=',init).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Then the conditions need to be  added to the where part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Specifically, the name of the method  of the MethodAccess init should be "init" that is  stated in the second line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Finally, a MethodAccess has a  receiver, that is the object invoking its method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' In this case,  the name of the type of the receiver should be "Cipher",  that is expressed in CodeQL in the third line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  If one needs to make sure that no invocation occurs, an  existential quantifier must be used, as shown in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  from  where not  (exists  (MethodAccess  init  |  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getMethod().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "init" and  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getReceiverType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "Cipher"))  It means that there is no such MethodAccess init that  has these conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We can state this in NASRA in the form  below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  An object of Cipher doesn’t invoke init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  b) Partial order constraints: This pattern enables one to  put partial order constraints on method invocations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' In other  words, one can enforce a method invocation to be preceded  (or followed) by another method invocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Pattern2::=MethodName (precedes|follows) MethodName.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  For example, there are two steps in CodeQL for stating that  “invocation of getInstance is earlier than invocation of  init”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' First, one should specify that both methods are in the  same scope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Next, the line number of the preceding method  invocation has to be smaller than the line number of the other  method invocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' This is shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getEnclosingCallable()  =  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getEnclosingCallable() and  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getLocation().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getEndLine()  <  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getLocation().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getEndLine()  We can express this query in NASRA as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getInstance precedes init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  c) Method signature constraint: It is possible to express  signature of a method using Pattern3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Pattern3 ::= MethodName’s signature is List.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  A method signature can be seen as an ordered list of data  types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' This list contains names of data types as strings, such  that the first string is the name of the first argument’s data  type and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' For example, the following NASRA query  states that getInstance method has two arguments and  the names of their types are "int" and "Certificate",  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getInstance’s signature is ["int", "Certificate"].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  This query is translated to the following CodeQL query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  (count (getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getAnArgument()) = 2) and  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  toString()="int" and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getArgument(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString()=  "Certificate"  First, the number of arguments is set to the size of the user  defined list, then the type of arguments are constrained one  by one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' count (method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getAnArgument()) returns  the number of arguments of the method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' getArgument(i)  returns  the  argument number i  in  the  given  method,  getType() returns the type of the given argument, and  finally toString() converts the given data type to a String.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  2) AuxiliaryStatement: We aim to find misuses in code  that violate one or more mandatory constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' For instance,  suppose that if the second argument of init method is  "private key" then it is mandatory that the encryption al-  gorithm, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', the second argument of getInstance method  is "RSA", and also if the encryption algorithm is "AES"  then it is mandatory that the mode of encryption, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', the  first argument of the getInstance method, is "CBC".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The  following NASRA query will find such violations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  It is false that if the type of the second argument of init  is "PrivateKey", then the algorithm of getInstance’s  first argument is "RSA" or it is false that if the algorithm of  getInstance’s first argument is "AES" then the mode of  getInstance’s first argument is "CBC".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  In order to find any violation of these constraints, dis-  junction of their negation has to be stated in the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='3  3For example, in “X is driving in an urban area(Cond1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' It is necessary that  X is driving slower than 60 km/h (Cons1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' It is necessary that X fastens the  seat belt (Cons2).”, the query needs to find an X that is driving in an urban  area and is driving faster than 60 km/h or is not using the seat belt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' If we  assign a Boolean variable to each statement as mentioned in the statements, it  should aim Cond1 ∧(¬Cons1 ∨¬Cons2) whose necessity part is translated  to the disjunction of negation of two constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Nevertheless, the above statement becomes much longer and  harder to comprehend as the number of constraints increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  We define auxiliary statements to ease the formulation as  well as the comprehension of complex queries for developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Particularly, NecessityStatements are auxiliary statements that  enable developers to enforce mandatory constraints in short  and independent statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' It starts with “It is necessary that”  and follows the syntax below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  NecessityStatement  ::=  It is necessary that Statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Therefore, instead of writing disjunction of negation of all  constraints in one single statement, developers can benefit  this construct (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', NecessiyStatement) to define all such  constraints in several statements within a query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Accordingly,  the single but long previous statement can be stated as two  separate statements shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  It is necessary that if the type of the second argument of init is  "PrivateKey", then the algorithm of getInstance’s first  argument is "RSA".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  It is necessary that if the algorithm of getInstance’s first  argument is "AES" then the mode of getInstance’s first  argument is "CBC".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Necessity statements are treated differently from other state-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' If there is only one NecessityStatement, its enclosing  statement is negated and added to the where part of the  CodeQL query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' If there are more than one, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', n constraints  Cons1, Cons2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', Consn, then the “(not T Cons1 or  not T Cons2 or .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' or not T Consn)” will be added  to the where part, where T Consi is the translation of Consi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' WORKING EXAMPLES  Cipher is one of the most misused APIs in Java cryp-  tography [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Listing 1 shows how to create a Cipher  object in Java.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We should call the Cipher’s getInstance  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' This method receives a number of arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The  first one is transformation that is a string containing  three parts separated by “/”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' These parts are algorithm,  mode, and padding, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Next, we should call the  init method on the cipher object with two arguments to  indicate the operation mode of the cipher, and to initialize  this object with a Key or Certificate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Cipher cipher = Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getInstance("AES/ECB/  PKCS5Padding");' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='init(Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='ENCRYPT_MODE,new SecretKeySpec(  keyBytes, "AES"));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Listing 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Setting up the Cipher object in Java  In the rest of this section, we present three different program  analysis tasks to ensure secure use of Java Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Key vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Algorithm  Task 1: If the key has a type of PublicKey, PrivateKey,  or Certificate, or encryption mode is WRAP MODE or UN-  WRAP MODE, then algorithm of transformation must be  “RSA”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Listing 2 shows how to check this constraint in CodeQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  from MethodAccess getInstance, MethodAccess init  where init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getMethod().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "init" and init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getReceiverType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "Cipher" and  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getMethod().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "getInstance  " and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getReceiverType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() =  "Cipher" and (((init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() =  "Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='WRAP MODE" or init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  toString() = "Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='UNWRAP MODE") or (init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getArgument(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "java.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='PublicKey" or init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "java.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='PrivateKey  " or init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "java.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='cert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='Certificate")) and not(getInstance  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll("\\","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  splitAt("/",0) = "RSA"))  select getInstance, init  Listing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Key vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Algorithm constraint in CodeQL  This constraint can be expressed in NASRA as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  An  object  of  Cipher  invokes  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  An  object  of  Cipher invokes getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' It is necessary that if  init’s  first  argument  is  in  ["Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='WRAP_MODE",  "Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='UNWRAP_MODE"]  or  the  type  of  the  second  argument of init is in ["PublicKey", "PrivateKey",  "Certificate"] then the algorithm of getInstance’s  first argument is "RSA".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Algorithm vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Transformation Mode  Task 2: If the algorithm of transformation is “RSA” then  the mode of transformation must be either “” or “ECB”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Listing 3 shows the corresponding query to check this  constraint in CodeQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We should look for code in which the  algorithm is “RSA”, but neither “ECB” nor “” is set for the  mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  from MethodAccess getInstance  where getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getMethod().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "  getInstance" and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getReceiverType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getName() = "Cipher" and (getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  splitAt("/", 0) = "RSA") and not (getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  splitAt("/", 1) = "" or getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument  (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='splitAt("/",  1) = "ECB")  select getInstance  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Algorithm vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Transformation Mode constraint in CodeQL  This constraint can be expressed in NASRA as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  An object of Cipher invokes getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' It is necessary  that if the algorithm of getInstance’s first argument is  "RSA" then the mode of getInstance’s first argument is in  ["", "ECB"].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Thanks to Attempto Parsing Engine (APE), NASRA state-  ments do not need to exactly follow the syntax rules meaning  that a degree of freedom in paraphrasing is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' For  instance, the part “the algorithm of getInstance’s first  argument is "RSA"” can also be written in two other forms:  (i) the algorithm of the first argument of getInstance is  "RSA".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  (ii) "RSA" is the algorithm of getInstance’s first argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Transformation and Encryption Mode vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Signature  Task 3: If the transformation mode is either of “CBC”,  “PCBC”, “CTR”, “CTS”, “CFB”, or “OFB”, and the en-  cryption mode is not “Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='ENCRYPT MODE”, then the  invoked init method should not have any of the following  signature: init(encmode, cert), init(encmode, cert, ranGen),  init(encmode, key), init(encmode, key, ranGen).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Listing 4 presents how to enforce this constraint in CodeQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  from MethodAccess getInstance, MethodAccess init  where init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getMethod().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "init" and init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getReceiverType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "Cipher" and  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getMethod().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() = "getInstance  " and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getReceiverType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getName() =  "Cipher" and ((getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='splitAt("/", 1) =  "CBC" or getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  replaceAll("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='splitAt("/", 1) = "PCBC" or  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll  ("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='splitAt("/", 1) = "CTR" and  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll  ("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='splitAt("/", 1) = "CTS" or getInstance  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  splitAt("/", 1) = "CFB" or getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='replaceAll("\\"","").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  splitAt("/", 1) = "OFB") and not (init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='ENCRYPT_MODE  ")) and ((count (getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getAnArgument()) =  2 and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  toString() = "int" and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument  (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "Certificate") or (  count (getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getAnArgument()) = 3 and  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString()  = "int" and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType()  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "Certificate" and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getArgument(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "  SecureRandom") or (count (getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  getAnArgument()) = 2 and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument  (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "int" and getInstance  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "Key") or  (count (getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getAnArgument()) = 3 and  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString()  = "int" and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType()  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "Key" and getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getArgument  (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='getType().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='toString() = "SecureRandom"))  select init, getInstance  Listing 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Transformation and Encryption mode vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Signature constraint in  CodeQL  The implementation of this task in NASRA is shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  An  object  of  Cipher  invokes  getInstance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  An  object  of  Cipher  invokes  init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  It  is  necessary  that  if  the  mode  of  getInstance’s  first  argument  is  in  ["CBC","PCBC","CTR","CTS","CFB","OFB"]  and  init’s first argument is not "Cipher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='ENCRYPT_MODE"  then  getInstance’s  signature  is  not  ["int","Certificate"]  and  is  not  ["int","Certificate","SecureRandom"]  and  is  not  ["int","Key"]  and  is  not  ["int","Key","SecureRandom"].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Discussion  Table I presents the number of distinct operators and  operands (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', vocabulary), and the total number of operators  and operands (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', length) needed for each analysis task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='4  4In NASRA, we consider user defined terminals such as init, “RSA”, and  getInstance as operands and count the rest of language constructs as operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  TABLE I  CODEQL VS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' NASRA  Analysis Task  Vocabulary  Length  CodeQL  NASRA  CodeQL  NASRA  Key vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Algorithm (III-A)  32  19  179  39  Algorithm vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Mode (III-B)  27  18  107  24  Mode vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Signature (III-C)  42  26  434  56  Evidently, queries in NASRA are significantly shorter than  queries in CodeQL (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', up to 87% reduction in length), and  they consume a lot fewer programming constructs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', up to  38% fewer vocabularies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We computed Halstead complexity  measures to estimate the coding time and the difficulty to  write or understand these queries [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The results showed that  developers require a lot less effort and time to develop these  tasks in NASRA than in CodeQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  We also asked ten developers to share their opinion about  queries in NASRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' They unanimously stated that they are  succinct and easy to understand, and one commented that  “these queries read like API documentation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  It is noteworthy that NASRA’s performance, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', how well  it can detect API misuses, depends on its underlying analy-  sis framework which is currently CodeQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' In other words,  NASRA obviates the low-level details needed to define static  program analyses, but the issues with false positives remain  to be relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Moreover, despite being natural, the use of  NASRA still requires knowledge of its syntax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' RELATED WORK  Mapping a natural language statement into a formal repre-  sentation has received great attention in the community but  not much in the program analysis development domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Schlegel  et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  developed  an  end-user  programming  paradigm for Python, that maps natural language commands  into Python code [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Landhauber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' proposed a domain  agnostic command interpreter that receives natural language  commands in English and uses ontology to produce relevant  API calls [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Yaghmazadeh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' developed SQLIZER, a  system to automatically synthesize SQL queries from a natural  language [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' investigated the translation from  a natural language query to visualization with the goal of  simplifying the creation of data visualizations [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Heyman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' developed a Python code completion tool  that enriches developers’ code with the natural language de-  scription of the intended data science task [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Nguyen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  presented an approach that takes as input an English descrip-  tion of a programming task and synthesizes the corresponding  API code template for the task [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Desai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' built a general  framework for constructing program synthesizers that take  natural language inputs and produce expressions in a target  Domain Specific Language [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Zhai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' proposed a search-  based technique to automatically translate NL comments to  formal program specifications that specify the expected pre  and post conditions [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  The work presented in this paper is also related to cryp-  tography domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' There exist tools that find cryptography  misuses [14] and libraries that facilitate the adoption of  cryptography for developers [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Nevertheless, none of them  employed a natural language approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' CONCLUSION  We introduced NASRA, an open-source framework to de-  fine static program analyses in natural language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' We demon-  strated the application of this framework to find misuses in  Java cryptography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The ultimate goal of NASRA is to enable  a naturalistic way to develop static program analyses, which is  usable for mainstream developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' To realize this goal, further  studies are needed to determine NASRA’s effectiveness in  real-world settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' The expressiveness of its queries and the  effort required to extend it to other problem domains have to  be investigated as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Finally, automatic translation without  pre-defined rules is also an exciting future research direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  REFERENCES  [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Barakova, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Gillesen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Huskens, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Lourens, “End-user  programming architecture facilitates the uptake of robots in social  therapies,” Robotics and Autonomous Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 61, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 7, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [2] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Zettlemoyer, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Ernst, “NL2Bash:  A corpus and semantic parser for natural language interface to the  linux operating system,” in Proceedings of the Eleventh International  Conference on Language Resources and Evaluation (LREC 2018), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Hazhirpasand, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Nierstrasz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Shabani, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Ghafari, “Hurdles  for developers in cryptography,” in 2021 IEEE International Conference  on Software Maintenance and Evolution (ICSME), 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 659–663.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Hazhirpasand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Ghafari, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Nierstrasz, “Java cryptography  uses in the wild,” in Proceedings of the 14th ACM / IEEE International  Symposium on Empirical Software Engineering and Measurement, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Halstead, Elements of Software Science (Operating and program-  ming systems series).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Elsevier Science Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', 1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [6] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Schlegel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Lang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Handschuh, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Freitas, “Vajra: Step-by-  step programming with natural language,” in Proceedings of the 24th  International Conference on Intelligent User Interfaces, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Landh¨auber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Weigelt, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Tichy, “Nlci: A natural language  command interpreter,” Automated Software Engg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 24, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  839–861, dec 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [8] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Yaghmazadeh, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Wang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Dillig, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Dillig, “Sqlizer: Query  synthesis from natural language,” Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' ACM Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 1,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' OOPSLA, oct 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Luo, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Tang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Tang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Chai, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Qin, “Natural language  to visualization by neural machine translation,” IEEE Transactions on  Visualization and Computer Graphics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 28, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 217–226, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [10] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Heyman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Huysegems, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Justen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Van Cutsem, “Natural  language-guided programming,” ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Onward!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=', 2021, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 39–55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Nguyen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Rigby, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Nguyen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Palani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Karanfil, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  Nguyen, “Statistical translation of english texts to api code templates,”  in 2018 IEEE International Conference on Software Maintenance and  Evolution (ICSME), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 194–205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Desai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Gulwani, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Hingorani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Jain, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Karkare, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Marron,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' R, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Roy, “Program synthesis using natural language,” in Pro-  ceedings of the 38th International Conference on Software Engineering,  ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' ICSE ’16, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Zhai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Shi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Pan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Fang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Ma, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Tan,  and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Zhang, “C2s: Translating natural language comments to formal  program specifications,” in Proceedings of the 28th ACM Joint Meeting  on European Software Engineering Conference and Symposium on the  Foundations of Software Engineering, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' ESEC/FSE 2020, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [14] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Kabir, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Xiao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Yao, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Meng, “Automatic  detection of java cryptographic api misuses: Are we there yet,” IEEE  Transactions on Software Engineering, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content='  [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Kafader and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' Ghafari, “Fluentcrypto: Cryptography in easy mode,”  in 2021 IEEE International Conference on Software Maintenance and  Evolution (ICSME), 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}
+page_content=' 402–412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE4T4oBgHgl3EQfCwsd/content/2301.04862v1.pdf'}

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+arXiv:2301.13075v1  [quant-ph]  30 Jan 2023
+Threshold theorem in quantum annealing with deterministic analog control errors
+Manaka Okuyama1 and Masayuki Ohzeki1,2,3
+1Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
+2Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo,152-8551, Japan and
+3Sigma-i Co., Ltd., Tokyo 108-0075, Japan
+(Dated: January 31, 2023)
+We investigate the effect of deterministic analog control errors in the time-dependent Hamiltonian on iso-
+lated quantum dynamics. Deterministic analog control errors are formulated as time-dependent operators in the
+Schr¨odinger equation. We give an upper bound on the distance between two states in time evolution with and
+without deterministic analog control errors. As a result, we prove that, if the strength of deterministic analog
+control errors is less than the inverse of computational time, the final state in quantum dynamics without deter-
+ministic analog control errors can be obtained through a constant-order number of measurements in quantum
+dynamics with deterministic analog control errors.
+I.
+INTRODUCTION
+Quantum annealing [1–8] is an analog quantum computa-
+tion that utilizes continuous time evolution of quantum sys-
+tems, and, thereby, analog control errors of the parameters
+are inevitable in experimental systems. Because the theory
+of quantum error correction and suppression is incomplete
+in quantum annealing [9–13], estimating the effect of analog
+control errors is one of the most critical problems.
+There are two main types of analog control errors in quan-
+tum annealing.
+One is a stochastic control error [14–17],
+which represents an instantaneous parameter fluctuation. For
+this type of control error, recent studies [18, 19] proved that,
+if the strength of the stochastic control errors is less than the
+inverse of the computation time, information about the final
+state in quantum dynamics without analog control errors can
+be recovered from quantum dynamics with stochastic control
+errors. The other is deterministic control error, which is, for
+example, a bias acting on the magnetic field or a deviation in
+the value of the interaction. Deterministic control errors have
+been discussed so far in many literatures [20–26], but they are
+limited to specific problems.
+The present study investigates in general whether it is pos-
+sible to recover information about the target state, which is
+the final state in ideal time evolution, from quantum dynam-
+ics with deterministic analog control errors. We give an upper
+bound on the distance between two states in quantum dynam-
+ics with and without deterministic control errors using only in-
+formation about the deterministic control errors. Furthermore,
+using this bound, we prove that, if the strength of the deter-
+ministic control errors is less than the inverse of the computa-
+tion time, information about the target state can be recovered
+through a constant-order number of measurements in quan-
+tum dynamics with deterministic analog control errors. This
+result is intuitively obvious but it is important from the per-
+spective of experimental systems to give mathematical proof.
+The proof is based on the method proposed by Kieu to derive
+a quantum speed limit [27, 28].
+The organization of this paper is as follows. In Sec. II,
+we define the model and obtain the main result. Finally, our
+conclusion is presented in Sec. III.
+II.
+RESULT
+We consider the following isolated quantum dynamics:
+i d
+dt|ψ(t)⟩ = ˆH(t)|ψ(t)⟩,
+(1)
+where 0 ≤ t ≤ T and ℏ = 1. In general, it is difficult to com-
+pletely control the time-dependent Hamiltonian ˆH(t) without
+control errors in experimental systems. Deterministic ana-
+log control errors can take any form physically permissible
+but should also be described as a Hermitian operator since
+we consider isolated quantum dynamics. Thus, we incorpo-
+rate the deterministic analog control errors of ˆH(t) into the
+Schr¨odinger equation as a Hermitian operator ˆV(t). We ex-
+press the Schr¨odinger equation with deterministic analog con-
+trol errors as follows:
+i d
+dt|φ(t)⟩ = ( ˆH(t) + ˆV(t))|φ(t)⟩.
+(2)
+Then, we obtain the following result.
+Theorem 1. The distance between two final states |ψ(T)⟩ and
+|φ(T)⟩ is bounded from above by
+∥ |ψ(T)⟩ − |φ(T)⟩ ∥ ≤ v,
+(3)
+where ∥ |a⟩ ∥ ≡ √⟨a|a⟩, v ≡
+� T
+0 dt
+��� ˆV(t)
+���, and
+��� ˆA
+��� is the eigen-
+value of ˆA with the largest absolute value.
+Proof of Theorem 1. From Eqs. (1) and (2), we obtain
+d
+dt(|ψ(t)⟩ − |φ(t)⟩) = −i ˆH(t)(|ψ(t)⟩ − |φ(t)⟩) + i ˆV(t) |φ(t)⟩ ,(4)
+and
+d
+dt∥ |ψ(t)⟩ − |φ(t)⟩ ∥2 = 2 Re
+�
+(⟨ψ(t)| − ⟨φ(t)|) d
+dt(|ψ(t)⟩ − |φ(t)⟩)
+�
+= 2 Re
+�
+(⟨ψ(t)| − ⟨φ(t)|)i ˆV(t) |φ(t)⟩
+�
+≤ 2∥ |ψ(t)⟩ − |φ(t)⟩ ∥ · ∥ ˆV(t) |φ(t)⟩ ∥,
+(5)
+where we used the Cauchy-Schwartz inequality. On the other
+hand, we find
+d
+dt∥ |ψ(t)⟩ − |φ(t)⟩ ∥2 = 2∥ |ψ(t)⟩ − |φ(t)⟩ ∥ · d
+dt∥ |ψ(t)⟩ − |φ(t)⟩ ∥.
+(6)
+
+2
+Thus, we obtain
+d
+dt∥ |ψ(t)⟩ − |φ(t)⟩ ∥ ≤ ∥ ˆV(t) |φ(t)⟩ ∥ ≤ ∥ ˆV(t)∥.
+(7)
+Finally, by integrating both sides from 0 to T, we arrive at Eq.
+(3).
+□
+It is worth mentioning that the right hand side of Eq. (3)
+contains only information about the control errors ˆV and not
+about ˆH(t).
+The inequality (3) makes sense only if v < 2 is satisfied
+because
+∥ |ψ(T)⟩ − |φ(T)⟩ ∥ =
+�
+2 − 2 Re ⟨ψ(t)|φ(t)⟩ ≤ 2.
+(8)
+In particular, when the strength of deterministic control errors
+is less than the inverse of the computation time,
+��� ˆV(t)
+��� <
+√
+2
+T ,
+(9)
+we have
+∥ |ψ(T)⟩ − |φ(T)⟩ ∥ ≤ v <
+√
+2.
+(10)
+This means that the two final states have non-zero overlap
+Re ⟨ψ(T)|φ(T)⟩ ≥ 1 − v2
+2 > 0.
+(11)
+Then, it is possible to recover the information about |ψ(T)⟩
+from |φ(T)⟩.
+For example, we expand the two final states |ψ(T)⟩ and
+|φ(T)⟩ as
+|ψ(T)⟩ =
+�
+n
+Cn |n⟩ ,
+(12)
+|φ(T)⟩ =
+�
+n
+Dn |n⟩ ,
+(13)
+where |n⟩ is the measurement basis. We are interested in the
+mth eigenstate of the measurement basis and its probability
+amplitude Cm is given by
+|Cm|2 = 1 − ǫ2,
+(14)
+with 0 ≤ ǫ < 1. Then, we arrive at:
+Corollary 2. If
+1 − v2/2 > ǫ ≥ 0,
+(15)
+then the probability amplitude of the mth eigenstate in the
+Schr¨odinger equation with deterministic analog control errors
+(2) takes a non-zero value,
+|Dm| ≥ 1 − v2
+2 − ǫ
+√
+1 − ǫ2 > 0.
+(16)
+Corollary 2 states that the number of measurements re-
+quired to obtain |m⟩ is independent of the computation time
+T in quantum dynamics with deterministic analog control er-
+rors (2). Thus, under the condition (15), deterministic control
+errors do not seriously affect the efficiency of quantum anneal-
+ing.
+The condition (15) can be rewritten as
+� T
+0
+dt
+��� ˆV(t)
+��� <
+�
+2(1 − ǫ).
+(17)
+It may seem difficult to satisfy this condition for large T.
+However, when T is large, the parameters should change
+slowly and the strength of the analog control errors is expected
+to be smaller. Thus, the condition (15) is not far from experi-
+mental systems and may be acceptable.
+Proof of Corollary 2. From Eq. (11), we obtain
+0 < 1 − v2
+2 ≤ Re ⟨ψ(T)|φ(T)⟩ ≤ | ⟨ψ(T)|φ(T)⟩ |
+≤
+�
+n
+|CnDn| =
+√
+1 − ǫ2|Dm| +
+�
+n(�m)
+|CnDn|
+≤
+√
+1 − ǫ2|Dm| + ǫ
+�
+1 − |Dm|2|
+≤
+√
+1 − ǫ2|Dm| + ǫ,
+(18)
+where we used the Cauchy-Schwartz inequality. Thus, using
+Eq. (15), we obtain
+|Dm| ≥
+1 − v2
+2 − ǫ
+√
+1 − ǫ2 > 0.
+(19)
+□
+III.
+CONCLUSIONS
+We have established a threshold theorem that provides a
+sufficient condition for obtaining the target state in isolated
+quantum dynamics with any deterministic analog control er-
+ror.
+We have considered only deterministic analog control er-
+rors. A similar threshold theorem for stochastic analog control
+errors has already been obtained in Ref. [18]. For both types
+of analog control error, the same point is that, if the strength
+of the control errors is less than the inverse of the computation
+time, the target state can be obtained through a constant-order
+number of measurements in quantum dynamics with analog
+control errors. It is an interesting future problem to combine
+these results.
+Finally, we emphasize that we do not impose any assump-
+tions on time evolution. Considering a specific schedule for
+each problem, such as adiabatic time evolution, might im-
+prove the present results.
+The present work was financially supported by JSPS KAK-
+ENHI Grant No. 19H01095, 20H02168 and 21K13848.
+
+3
+[1] T. Kadowaki and H. Nishimori, Quantum annealing in the trans-
+verse Ising model, Phys. Rev. E 58, 5355 (1998).
+[2] P. Ray, B. K. Chakrabarti, and A. Chakrabarti, Sherrington-
+Kirkpatrick model in a transverse field: Absence of replica
+symmetry breaking due to quantum fluctuations, Phys. Rev. B
+39, 11828 (1989).
+[3] J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli, Quantum
+Annealing of a Disordered Magnet, Science 284, 779 (1999).
+[4] J. Brooke, T. F. Rosenbaum, and G. Aeppli, Tunable Quantum
+Tunneling of Magnetic Domain Walls, Nature (London) 413,
+610 (2001).
+[5] G. E. Santoro, R. Martoˇn´ak, E. Tosatti, and R. Car, Theory of
+Quantum Annealing of an Ising Spin Glass, Science 295, 2427
+(2002).
+[6] E.
+Farhi,
+J.
+Goldstone,
+S.
+Gutmann,
+and
+M.
+Sipser,
+Quantum
+Computation
+by
+Adiabatic
+Evolution,
+arXiv:
+quant-ph/0001106.
+[7] D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd,
+and O. Regev, Adiabatic Quantum Computation is Equivalent
+to Standard Quantum Computation, SIAM J. Comput. 37, 166
+(2007).
+[8] A. Mizel, D. A. Lidar, and M. Mitchell, Simple Proof of Equiv-
+alence between Adiabatic Quantum Computation and the Cir-
+cuit Model, Phys. Rev. Lett. 99, 070502 (2007).
+[9] S. P. Jordan, E. Farhi, and P. W. Shor, Error-correcting codes
+for adiabatic quantum computation, Phys. Rev. A 74, 052322
+(2006).
+[10] D. A. Lidar, Towards Fault Tolerant Adiabatic Quantum Com-
+putation, Phys. Rev. Lett. 100, 160506 (2008).
+[11] G. Quiroz and D. A. Lidar, High-fidelity adiabatic quan-
+tum computation via dynamical decoupling, Phys. Rev. A 86,
+042333 (2012).
+[12] K. L. Pudenz, T. Albash, and D. A. Lidar, Error-corrected quan-
+tum annealing with hundreds of qubits, Nat. Commun. 5, 3243
+(2014).
+[13] D. Venturelli, S. Mandr´a, S. Knysh, B. O’Gorman, R. Biswas,
+and V. Smelyanskiy, Quantum Optimization of Fully Connected
+Spin Glasses, Phys. Rev. X 5, 031040 (2015)
+[14] E. Wong and M. Zakai, On the Convergence of Ordinary Inte-
+grals to Stochastic Integrals, Ann. Math. Stat. 36, 1560 (1965).
+[15] C. W. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag,
+Berlin, 1999).
+[16] A. Dutta, A. Rahmani, and A. del Campo, Anti-Kibble-Zurek
+Behavior in Crossing the Quantum Critical Point of a Thermally
+Isolated System Driven by a Noisy Control Field, Phys. Rev.
+Lett. 117, 080402 (2016).
+[17] M.-Z. Ai, J.-M. Cui, R. He, Z.-H. Qian, X.-X. Gao, Y.-F.
+Huang, C.-F. Li and G.-C. Guo, Experimental verification of
+anti-Kibble-Zurek behavior in a quantum system under a noisy
+control field, Phys. Rev. A 103, 012608 (2021).
+[18] M. Okuyama, K. Ohki, and M. Ohzeki, Threshold theorem in
+isolated quantum dynamics with stochastic control errors, Phil.
+Trans. R. Soc. A. 381, 20210412 (2023).
+[19] K. Kobayashi, Bound on the closed quantum dynamics under
+stochastic noise, arXiv:2211.14862.
+[20] A. M. Childs, E. Farhi, and J. Preskill, Robustness of adiabatic
+quantum computation, Phys.Rev. A 65, 012322 (2002).
+[21] J. Roland and N. J. Cerf, Noise resistance of adiabatic quan-
+tum computation using random matrix theory, Phys. Rev. A 71,
+032330 (2005).
+[22] K. C. Young, R. B-Kohout, D. A. Lidar, Adiabatic quantum
+optimization with the wrong Hamiltonian, Phys. Rev. A 88,
+062314 (2013).
+[23] S. Mandr`a, G. G. Guerreschi, and A. Aspuru-Guzik, Adiabatic
+quantum optimization in the presence of discrete noise: Re-
+ducing the problem dimensionality, Phys. Rev. A 92, 062320
+(2015).
+[24] S. Muthukrishnan, T. Albash, and D. A. Lidar, Sensitivity of
+quantum speedup by quantum annealing to a noisy oracle, Phys.
+Rev. A 99, 032324 (2019).
+[25] A. Pearson, M. A., I. Hen, and D. A. Lidar, Analog errors in
+quantum annealing: doom and hope, npj Quantum Inf. 5, 107
+(2019).
+[26] T. Albash, V. Martin-Mayor, and I. Hen, Analog errors in Ising
+machines, Quantum Sci. Technol. 4, 02LT03 (2019).
+[27] T. D. Kieu, A Class of Time-Energy Uncertainty Relations for
+Time-dependent Hamiltonians, Proc. R. Soc. A 475, 20190148
+(2019).
+[28] M.
+Okuyama
+and
+M.
+Ohzeki,
+A
+useful
+fundamental
+speed limit for the imaginary-time Schrodinger equation,
+arXiv:1806.09040.
+

9tFPT4oBgHgl3EQfYzRy/content/tmp_files/load_file.txt

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+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='13075v1  [quant-ph]  30 Jan 2023  Threshold theorem in quantum annealing with deterministic analog control errors  Manaka Okuyama1 and Masayuki Ohzeki1,2,3  1Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan  2Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo,152-8551, Japan and  3Sigma-i Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=', Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=', Tokyo 108-0075, Japan  (Dated: January 31, 2023)  We investigate the effect of deterministic analog control errors in the time-dependent Hamiltonian on iso-  lated quantum dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Deterministic analog control errors are formulated as time-dependent operators in the  Schr¨odinger equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' We give an upper bound on the distance between two states in time evolution with and  without deterministic analog control errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' As a result, we prove that, if the strength of deterministic analog  control errors is less than the inverse of computational time, the final state in quantum dynamics without deter-  ministic analog control errors can be obtained through a constant-order number of measurements in quantum  dynamics with deterministic analog control errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  INTRODUCTION  Quantum annealing [1–8] is an analog quantum computa-  tion that utilizes continuous time evolution of quantum sys-  tems, and, thereby, analog control errors of the parameters  are inevitable in experimental systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Because the theory  of quantum error correction and suppression is incomplete  in quantum annealing [9–13], estimating the effect of analog  control errors is one of the most critical problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  There are two main types of analog control errors in quan-  tum annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  One is a stochastic control error [14–17],  which represents an instantaneous parameter fluctuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' For  this type of control error, recent studies [18, 19] proved that,  if the strength of the stochastic control errors is less than the  inverse of the computation time, information about the final  state in quantum dynamics without analog control errors can  be recovered from quantum dynamics with stochastic control  errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' The other is deterministic control error, which is, for  example, a bias acting on the magnetic field or a deviation in  the value of the interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Deterministic control errors have  been discussed so far in many literatures [20–26], but they are  limited to specific problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  The present study investigates in general whether it is pos-  sible to recover information about the target state, which is  the final state in ideal time evolution, from quantum dynam-  ics with deterministic analog control errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' We give an upper  bound on the distance between two states in quantum dynam-  ics with and without deterministic control errors using only in-  formation about the deterministic control errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Furthermore,  using this bound, we prove that, if the strength of the deter-  ministic control errors is less than the inverse of the computa-  tion time, information about the target state can be recovered  through a constant-order number of measurements in quan-  tum dynamics with deterministic analog control errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' This  result is intuitively obvious but it is important from the per-  spective of experimental systems to give mathematical proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  The proof is based on the method proposed by Kieu to derive  a quantum speed limit [27, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  The organization of this paper is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' II,  we define the model and obtain the main result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Finally, our  conclusion is presented in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  RESULT  We consider the following isolated quantum dynamics:  i d  dt|ψ(t)⟩ = ˆH(t)|ψ(t)⟩,  (1)  where 0 ≤ t ≤ T and ℏ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' In general, it is difficult to com-  pletely control the time-dependent Hamiltonian ˆH(t) without  control errors in experimental systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Deterministic ana-  log control errors can take any form physically permissible  but should also be described as a Hermitian operator since  we consider isolated quantum dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Thus, we incorpo-  rate the deterministic analog control errors of ˆH(t) into the  Schr¨odinger equation as a Hermitian operator ˆV(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' We ex-  press the Schr¨odinger equation with deterministic analog con-  trol errors as follows:  i d  dt|φ(t)⟩ = ( ˆH(t) + ˆV(t))|φ(t)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (2)  Then, we obtain the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' The distance between two final states |ψ(T)⟩ and  |φ(T)⟩ is bounded from above by  ∥ |ψ(T)⟩ − |φ(T)⟩ ∥ ≤ v,  (3)  where ∥ |a⟩ ∥ ≡ √⟨a|a⟩, v ≡  � T  0 dt  ��� ˆV(t)  ���, and  ��� ˆA  ��� is the eigen-  value of ˆA with the largest absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' From Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' (1) and (2), we obtain  d  dt(|ψ(t)⟩ − |φ(t)⟩) = −i ˆH(t)(|ψ(t)⟩ − |φ(t)⟩) + i ˆV(t) |φ(t)⟩ ,(4)  and  d  dt∥ |ψ(t)⟩ − |φ(t)⟩ ∥2 = 2 Re  �  (⟨ψ(t)| − ⟨φ(t)|) d  dt(|ψ(t)⟩ − |φ(t)⟩)  �  = 2 Re  �  (⟨ψ(t)| − ⟨φ(t)|)i ˆV(t) |φ(t)⟩  �  ≤ 2∥ |ψ(t)⟩ − |φ(t)⟩ ∥ · ∥ ˆV(t) |φ(t)⟩ ∥,  (5)  where we used the Cauchy-Schwartz inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' On the other  hand, we find  d  dt∥ |ψ(t)⟩ − |φ(t)⟩ ∥2 = 2∥ |ψ(t)⟩ − |φ(t)⟩ ∥ · d  dt∥ |ψ(t)⟩ − |φ(t)⟩ ∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (6)  2  Thus, we obtain  d  dt∥ |ψ(t)⟩ − |φ(t)⟩ ∥ ≤ ∥ ˆV(t) |φ(t)⟩ ∥ ≤ ∥ ˆV(t)∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (7)  Finally, by integrating both sides from 0 to T, we arrive at Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  □  It is worth mentioning that the right hand side of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' (3)  contains only information about the control errors ˆV and not  about ˆH(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  The inequality (3) makes sense only if v < 2 is satisfied  because  ∥ |ψ(T)⟩ − |φ(T)⟩ ∥ =  �  2 − 2 Re ⟨ψ(t)|φ(t)⟩ ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (8)  In particular, when the strength of deterministic control errors  is less than the inverse of the computation time,  ��� ˆV(t)  ��� <  √  2  T ,  (9)  we have  ∥ |ψ(T)⟩ − |φ(T)⟩ ∥ ≤ v <  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (10)  This means that the two final states have non-zero overlap  Re ⟨ψ(T)|φ(T)⟩ ≥ 1 − v2  2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (11)  Then, it is possible to recover the information about |ψ(T)⟩  from |φ(T)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  For example, we expand the two final states |ψ(T)⟩ and  |φ(T)⟩ as  |ψ(T)⟩ =  �  n  Cn |n⟩ ,  (12)  |φ(T)⟩ =  �  n  Dn |n⟩ ,  (13)  where |n⟩ is the measurement basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' We are interested in the  mth eigenstate of the measurement basis and its probability  amplitude Cm is given by  |Cm|2 = 1 − ǫ2,  (14)  with 0 ≤ ǫ < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Then, we arrive at:  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' If  1 − v2/2 > ǫ ≥ 0,  (15)  then the probability amplitude of the mth eigenstate in the  Schr¨odinger equation with deterministic analog control errors  (2) takes a non-zero value,  |Dm| ≥ 1 − v2  2 − ǫ  √  1 − ǫ2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (16)  Corollary 2 states that the number of measurements re-  quired to obtain |m⟩ is independent of the computation time  T in quantum dynamics with deterministic analog control er-  rors (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Thus, under the condition (15), deterministic control  errors do not seriously affect the efficiency of quantum anneal-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  The condition (15) can be rewritten as  � T  0  dt  ��� ˆV(t)  ��� <  �  2(1 − ǫ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (17)  It may seem difficult to satisfy this condition for large T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  However, when T is large, the parameters should change  slowly and the strength of the analog control errors is expected  to be smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Thus, the condition (15) is not far from experi-  mental systems and may be acceptable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Proof of Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' (11), we obtain  0 < 1 − v2  2 ≤ Re ⟨ψ(T)|φ(T)⟩ ≤ | ⟨ψ(T)|φ(T)⟩ |  ≤  �  n  |CnDn| =  √  1 − ǫ2|Dm| +  �  n(�m)  |CnDn|  ≤  √  1 − ǫ2|Dm| + ǫ  �  1 − |Dm|2|  ≤  √  1 − ǫ2|Dm| + ǫ,  (18)  where we used the Cauchy-Schwartz inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Thus, using  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' (15), we obtain  |Dm| ≥  1 − v2  2 − ǫ  √  1 − ǫ2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  (19)  □  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  CONCLUSIONS  We have established a threshold theorem that provides a  sufficient condition for obtaining the target state in isolated  quantum dynamics with any deterministic analog control er-  ror.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  We have considered only deterministic analog control er-  rors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A similar threshold theorem for stochastic analog control  errors has already been obtained in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' For both types  of analog control error, the same point is that, if the strength  of the control errors is less than the inverse of the computation  time, the target state can be obtained through a constant-order  number of measurements in quantum dynamics with analog  control errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' It is an interesting future problem to combine  these results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Finally, we emphasize that we do not impose any assump-  tions on time evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Considering a specific schedule for  each problem, such as adiabatic time evolution, might im-  prove the present results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  The present work was financially supported by JSPS KAK-  ENHI Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 19H01095, 20H02168 and 21K13848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  3  [1] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Kadowaki and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Nishimori, Quantum annealing in the trans-  verse Ising model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' E 58, 5355 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Ray, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Chakrabarti, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Chakrabarti, Sherrington-  Kirkpatrick model in a transverse field: Absence of replica  symmetry breaking due to quantum fluctuations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' B  39, 11828 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Brooke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Bitko, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rosenbaum, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Aeppli, Quantum  Annealing of a Disordered Magnet, Science 284, 779 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Brooke, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rosenbaum, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Aeppli, Tunable Quantum  Tunneling of Magnetic Domain Walls, Nature (London) 413,  610 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [5] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Santoro, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Martoˇn´ak, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Tosatti, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Car, Theory of  Quantum Annealing of an Ising Spin Glass, Science 295, 2427  (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [6] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Farhi,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Goldstone,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Gutmann,  and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Sipser,  Quantum  Computation  by  Adiabatic  Evolution,  arXiv:  quant-ph/0001106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Aharonov, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' van Dam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Kempe, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Landau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lloyd,  and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Regev, Adiabatic Quantum Computation is Equivalent  to Standard Quantum Computation, SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 37, 166  (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Mizel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lidar, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Mitchell, Simple Proof of Equiv-  alence between Adiabatic Quantum Computation and the Cir-  cuit Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 99, 070502 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Jordan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Farhi, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Shor, Error-correcting codes  for adiabatic quantum computation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 74, 052322  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lidar, Towards Fault Tolerant Adiabatic Quantum Com-  putation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 100, 160506 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [11] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Quiroz and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lidar, High-fidelity adiabatic quan-  tum computation via dynamical decoupling, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 86,  042333 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [12] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Pudenz, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Albash, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lidar, Error-corrected quan-  tum annealing with hundreds of qubits, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 5, 3243  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Venturelli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Mandr´a, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Knysh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' O’Gorman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Biswas,  and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Smelyanskiy, Quantum Optimization of Fully Connected  Spin Glasses, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' X 5, 031040 (2015)  [14] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Wong and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Zakai, On the Convergence of Ordinary Inte-  grals to Stochastic Integrals, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 36, 1560 (1965).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [15] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Gardiner and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Zoller, Quantum Noise (Springer-Verlag,  Berlin, 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Dutta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rahmani, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' del Campo, Anti-Kibble-Zurek  Behavior in Crossing the Quantum Critical Point of a Thermally  Isolated System Driven by a Noisy Control Field, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 117, 080402 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Ai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Cui, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' He, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Qian, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Gao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Li and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Guo, Experimental verification of  anti-Kibble-Zurek behavior in a quantum system under a noisy  control field, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 103, 012608 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Okuyama, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Ohki, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Ohzeki, Threshold theorem in  isolated quantum dynamics with stochastic control errors, Phil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 381, 20210412 (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [19] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Kobayashi, Bound on the closed quantum dynamics under  stochastic noise, arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='14862.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Childs, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Farhi, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Preskill, Robustness of adiabatic  quantum computation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 65, 012322 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Roland and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Cerf, Noise resistance of adiabatic quan-  tum computation using random matrix theory, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 71,  032330 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Young, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' B-Kohout, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lidar, Adiabatic quantum  optimization with the wrong Hamiltonian, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 88,  062314 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Mandr`a, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Guerreschi, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Aspuru-Guzik, Adiabatic  quantum optimization in the presence of discrete noise: Re-  ducing the problem dimensionality, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 92, 062320  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Muthukrishnan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Albash, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lidar, Sensitivity of  quantum speedup by quantum annealing to a noisy oracle, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 99, 032324 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Pearson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=', I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Hen, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Lidar, Analog errors in  quantum annealing: doom and hope, npj Quantum Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 5, 107  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [26] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Albash, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Martin-Mayor, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Hen, Analog errors in Ising  machines, Quantum Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' 4, 02LT03 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [27] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Kieu, A Class of Time-Energy Uncertainty Relations for  Time-dependent Hamiltonians, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content=' A 475, 20190148  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Okuyama  and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='  Ohzeki,  A  useful  fundamental  speed limit for the imaginary-time Schrodinger equation,  arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}
+page_content='09040.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9tFPT4oBgHgl3EQfYzRy/content/2301.13075v1.pdf'}

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+Revealing Rheological Parameters of Cotton-stitch-modified Cotton Fabrics by 
+Three-Network Modeling (TNM) of Materials 
+Harmony Werth1, #, Kazi Zihan Hossain1, #,  M. Rashed Khan1,* 
+1Department of Chemical and Materials Engineering, University of Nevada, Reno 
+#contributed equally 
+*Corresponding author: [email protected] 
+Abstract 
+Cotton threads and fabrics are the most used textile materials and have garnered 
+widespread interest for smart textiles to capture human-centered cyber-physical and 
+human-health-related bioanalytical data. Cotton threads are sewn (manually or digitally) 
+into fabrics to achieve functional and fashion stitches that soften or stiffen the base fabric. 
+There has been limited investigation into the influence of a single stitch on the mechanical 
+properties of knitted cotton fabric. Such understanding may become critical to producing 
+optimized textile-based composites/smart materials involving sewing operations. While 
+stitching operations are investigated in numerous ways to produce a range of smart 
+wearables, herein, we demonstrate the rheological modification of base cotton fabric 
+induced by two types of singular stitches (straight and zigzag). We have sewn simple 
+straight and zigzag cotton stitches to investigate the rheological modification of the base 
+cotton fabrics. Uniaxial stress-strain experimental data, combined with constitutive 
+modeling (i.e., three-network model, TNM) obtained from the calibration software 
+(MCalibration), revealed the feasibility of a data-driven approach to investigate the 
+rheological parameters. Our experimental analyses, combined with the calibrated data, 
+suggest a 99.99% confidence in assessing the influence of a single stitch on knitted cotton 
+fabrics. We have also used distributed strain energy to analyze the mechanics and failure 
+of the base and stitched fabrics. Our study may enable the design and study of integrating 
+smart threads in cotton fabrics to produce smart wearables, e-textile, biomedical and e-
+fashion textiles.    
+ 
+ 
+ 
+ 
+ 
+ 
+
+Introduction 
+Knitted cotton fabrics have been utilized in everyday garment materials and 
+emerged as one of the popular base materials to generate smart wearables. In this article, 
+we reveal rheological parameters- also known as phenomenological parameters, of 
+cotton-stitch-modified cotton fabrics, harnessing Three Network Models (TNM).1,2 We 
+produce two types of stitches for demonstrations to modify the mechanical behavior of 
+knitted cotton fabrics. While the utility of cotton fabrics is ubiquitous, and numerous 
+demonstrations are currently published in the literature, our study focuses on 
+understanding the tuned mechanics of cotton fabrics by sewn stitches and unravels data 
+that we often overlook through stress-strain analyses. Anisotropy of knitted cotton fabric 
+and its modified structural properties exhibited deformations during mechanical 
+performance analyses.3 Several studies focused on understanding knit fabrics, fabric 
+elongation, deformation, and failures at critical applied stress.4–10 Advanced applications 
+on knitted fabrics are approached mainly by trial and error methods where in-plane 
+stitches are randomly generated, leaving a knowledge gap in understanding the impact 
+of final sewn stitches on fabrics. Sewing- one of the ancient fabric manufacturing 
+techniques, loops a thread into fabrics, leveraging an analog or computerized sewing 
+machine. Different sewing stages,11 sewing parameters,12, and sewing machines13,14 
+have also been reported to alter the properties of the sewing thread. The looping process 
+integrates different threads and produces entanglements with aesthetic colors, body 
+shapes, and on-demand geometries. Different stitch patterns have also been reported to 
+change the rheological behavior of the sewing thread.15,16 However, the rheological 
+impact on the fabric due to stitching has not been adequately investigated. While the 
+original purpose of sewing has been joining two pieces of fabric together, the most 
+advanced applications integrate smart threads so that biomedical, biochemical, and 
+biological analyses can be performed in situ.17,18 From the design of fashion to human-
+centered smart wearables, state-of-sewing leverages many stitch patterns; however, a 
+data-informed approach to dissect the role of sewn stitches in manipulating the final 
+fabrics' properties is currently lacking in the literature.  
+Using a sewing machine, sewn stitches create entanglements between two 
+threads- an upper and a bobbin thread, the bottom thread. During the entanglement, the 
+sewing needle loops the upper thread between the bottom thread through the fabric, and 
+the threads entangle. When the tension of both threads matches, the entanglement lays 
+in-plane of the fabric on both sides with minimal damage.19 The resulting stitch can be 
+varied in numerous ways to create functional and non-functional patterns based on the 
+types of sewing threads, fabric types, or choice of materials for the final composite 
+structures.20 Concurrently, stitches are used to bind two or more layers of fabric together, 
+which is known as a seam. To determine the impact of stitches on the mechanical 
+behavior of fabrics, a few research groups have tested seams in woven cotton fabric.21–
+23 A few investigations on the mechanical behavior of seams in knitted fabrics are also 
+available in the literature.24,25 However, studies involving a single stitch thread to modify 
+the mechanical behavior of cotton fabric are currently lacking for a single layer of fabric. 
+Such studies, we believe, will become significantly crucial for future applications, i.e., 
+electronic textiles- because reducing materials consumption at an optimum number of 
+
+trials and errors seems crucial to pursue robust design configurations during the 
+development of smart threads and electronic fabrics.  
+The base fabric and thread used in this work are made from cotton. We assume 
+both as an elastomeric network for modeling. Elastomers having 3,000 to 10,000 
+repeating 
+units 
+exhibit 
+structural 
+flexibility 
+and 
+experience 
+stretch-induced 
+softening/hardening (also known as Mullins damage) under applied loads.26 For data 
+calibration, we use TNM in MCalibration software which maps the entire stress-strain 
+spectra from the uniaxial test. The TNM is also knowns as a phenomenological model to 
+describe deformation-induced structural evolution (i.e., the transition between soft to stiff 
+network) and how strain-energy density becomes redistributed (i.e., hysteresis) 
+throughout the experiments. Different hyperelastic models have been utilized in the 
+literature to represent the rheological behavior of fabrics.27–31 However, according to our 
+knowledge, this work presents the constitutive modeling of stitched fabrics with TNM for 
+the first time.  The data-calibration process in MCalibration can start using default or user-
+induced settings. For this study, we have chosen to start calibration using default settings 
+in MCalibration. The kinematics of the TNM consists of three parallel molecular networks. 
+We have assumed spring-dashpot domains connected in parallel for the first two, and the 
+third one is only a spring depicting the hyperelasticity of the first two networks. The semi-
+crystalline domains are captured through the spring dashpots. While a single network can 
+be used to evaluate the property of the entire composite structure, we have chosen TNM 
+to capture effective viscoplasticity.1  
+ 
+Here, we have chosen two types of sewing stitches: straight and zigzag, to 
+establish and reveal rheological parameters of cotton-stitch modified cotton fabrics, 
+harnessing TNM. These stitches are common in sewn garments and are pre-programmed 
+into the default settings of modern sewing machines. Also, we investigate several 
+variations of the zigzag stitch that has varying stitch length and width. A commercial 
+sewing machine creates stitches with 100% cotton materials (i.e., threads and fabrics). 
+For our analyses, we investigate the surface topography of the fabric and samples with 
+sewn stitches using optical and scanning electron microscope (SEM) images. We perform 
+(a) uniaxial stress-strain and (b) repeated cyclic tests in an Instron to dissect the 
+mechanical behaviors of the (a) base fabric, (b) base threads, and (c) threads-laid-fabric 
+structures. The uniaxial stress-strain analyses have revealed three regions of interest 
+(i.e., elastic, yield, and viscoplastic). Also, we have investigated the permanent failure of 
+the entire composite (fracture) to find the extremities of experimental analyses. The cyclic 
+tests provide information about hysteresis, which we leverage to understand distributed 
+strain-energy density and the loss due to hysteresis. We outline calibration using TNM in 
+MCalibration to provide a simple route to test the impact of specific sewing patterns on 
+the mechanical behavior of the final fabric. We hypothesize that the thread, which has 
+significantly denser strain energy, shifts the fabric's macroscale stress-strain behavior 
+after stitching. We proved our hypothesis through the uniaxial test and then altered the 
+stitch length to investigate the factors that cause specific changes in the stress-strain 
+behavior. The understanding developed by investigating the changes in mechanical 
+behavior can be used to optimize the mechanical properties of a composite made with 
+cotton thread and fabric. 
+
+Materials and Methods 
+Our experiments were performed to determine a constitutive equation to represent the 
+behavior of cotton fabric with different types of stitches. This was accomplished by 
+analyzing uniaxial stress-strain curves for each component (cotton fabric and cotton 
+thread) and different variations of the overall composite (straight stitched fabric, zigzag 
+stitch, and fabric with stitching holes but no thread).  
+Materials 
+The fabric used in this experiment was 100% cotton jersey knit with a unit weight of 427 
+g/m2 obtained from Hobby Lobby Stores, Inc. The measured thickness of the fabric was 
+0.45 mm. Similarly, the thread used in this experiment was a 50-weight, 4-ply, 100% 
+cotton thread of Sew-Ology Brand from Hobby Lobby Stores, Inc., produced for machine 
+quilting. The measured outer diameter of the thread was 0.30 mm. The same thread was 
+used for the top and bobbin threads for all samples prepared and presented in this work.  
+Sample Preparation 
+We used a Brother SE600 sewing machine from Amazon to create stitches of manually 
+adjustable length and width. The tension was selected so that the tension on the bobbin 
+thread and the upper thread were equal, preventing the bottom thread from showing on 
+the top or vice-versa, as is common sewing practice. A swatch of fabric approximately 20 
+cm in length was cut with scissors and then sewn wale-wise with the appropriate type of 
+stitch for the sample. Two samples were prepared with stitching: straight stitched and 
+zigzag stitched. The straight stitch was 2 mm in length. The zigzag stitches were (listed 
+as stitch length x stitch width): 2x5 mm, 1x5 mm, 3x5 mm, 2x3 mm, and 2x4 mm. Several 
+samples without any sewn stitches were also prepared for comparison. The fabric 
+samples were then cut to the same size with a Cricut Maker fabric cutter bought from 
+Amazon, allowing for accurate and reproducible sample cutting. For every sample, the 
+fabric was cut to the dimensions of 6 cm in length by 2 cm in width. Sample cutting was 
+done carefully to keep the stitching in the center of the sample. Damaged or samples with 
+uncentered stitches were discarded without any analysis.   
+Image Acquisition 
+Olympus SZ61 Stereo-microscope loaded with an Amscope MU1000-HS camera was 
+used to capture the optical microscopic images. Secondary electron images of the 
+samples were captured using a Thermo Scientific Scios 2 SEM. For SEM imaging, small 
+representative samples were cut and loaded on the sample holder with double-sided 
+carbon tape. Attention was given to keeping the stitch undamaged while loading on the 
+holder. Since the samples were nonconductive, samples were sputter-coated with Gold 
+(Au) to create a ~10 nm layer on the surface of the sample before imaging. Further optical 
+images were captured with the camera on an iPhone 13 mini. 
+Experimental Methods 
+
+The data was collected using an Instron 5982 test machine for uniaxial tensile testing. 
+The tested area was 4 cm by 2 cm. The extra centimeter on each side allowed the grip to 
+hold the sample during testing. Each sample type was examined with tensile testing to 
+determine the stress and strain until failure at a 40 mm/min strain rate. Cyclic testing of 
+four cycles was then conducted for specific samples up to a sustainable strain level for 
+that sample type. Samples with straight stitches could only withstand slightly more than 
+10% strain. Therefore, cyclic tests with straight stitches were conducted up to 10% strain. 
+For comparison, cyclic testing up to 10% strain was also conducted for unaltered fabric 
+samples and the 2x5 mm zigzag stitch.  
+Strain-energy Density Calculation  
+Using the trapezoidal rule, we calculated strain-energy density from the time-dependent 
+force and stress data at varying strain rates. The area under the stress-strain or force-
+strain curve is divided into equal-time steps. Each small area under the curve is added 
+until we reach the last data point to get the total area under the curve. The reported energy 
+density from different observations is the total after each experimental stress-strain 
+observation.  
+Constitutive Modeling of Different Fabrics 
+An initial prediction of the strain energy density of the straight stitched sample was 
+obtained based on the data collected from the unaltered fabric and thread samples. In 
+order to obtain the prediction, the strain energy density of the straight stitch sample and 
+the unaltered fabric was obtained by finding the area under the stress-strain curve of the 
+sample with the trapezoidal rule. The strain energy density was calculated up to 4.5% 
+strain because the thread samples failed around 5% strain. The strain energy of the 
+samples was calculated by multiplying the strain energy density by the volume of the 
+sample. The volume of the fabric was calculated using the sample's length, width, and 
+thickness. The thread volume was calculated from the measured diameter and length of 
+the thread sample. The straight stitch sample can be approximated by one sample of 
+fabric and two samples of thread, so the volume of the straight stitch sample was 
+calculated by adding the volume of the unaltered fabric and two threads. Similarly, the 
+predicted strain energy of the straight stitch sample was calculated by adding the strain 
+energy of the unaltered fabric and two threads. The prediction for the strain energy density 
+of the straight stitched sample could then be obtained by dividing the predicted stored 
+energy by the calculated volume. 
+MCalibration, from PolymerFEM,32 was used to obtain parameters for a material model 
+capable of representing the mechanical behavior of the fabric samples prepared in this 
+work. MCalibration fits the experimentally collected uniaxial stress-strain data to the 
+PolyUMod Three Network model.2 An average of the stress-strain behavior of each 
+sample type was obtained first. This set of averaged data was then processed using the 
+MCalibration software tools to prepare the data for calibration. The default settings were 
+used for the calibration. The calibrated parameters were exported and analyzed after the 
+automatic convergence of the calibration process.  
+
+Results and Discussion 
+Surface Topography 
+We formed two different types of stitches on the base fabric. Figures 1a and 1b are top-
+down optical microscope images of the base and sewn fabrics for visual inspection. 
+Figure 1b is a zoomed-in visual inspection of Figure 1a to identify differences between a 
+straight stitch and a zigzag stitch on the in-laid fabric. These images show that the straight 
+and zigzag stitches went through the fabric without significant internal damage. The 
+straight stitch shown in Figures 1a(ii) and 1b(ii) do not have significant bunching due to 
+the stitch compared with the only fabric shown in Figures 1a(i) and 1b(i); However, a 
+meandering network of the zigzag stitches caused the fabric within the stitch to 
+significantly bunch together, as shown in Figures 1 a(iii) and 1b(iii). The fabric is unable 
+to maintain its shape during sewing and is pulled into the stitch instead. The structural 
+stiffness and flexibility of the fabric may have contributed to the bunching, as observed 
+within the stitch dimensions. Figure 1c is the sewn fabric's SEM images to investigate the 
+surface topography of the stitches and fabric. SEM images in Figure 1c(i) and Figure 1c(ii) 
+reveal the undamaged fabric by fibers. From these visual inspections, we assume the 
+fabric remains structurally robust during the sewing and stitches only alter the mechanical 
+behavior.  
+ 
+Figure 1:  (a) Images were taken of samples under normal lighting conditions for visual inspection. 
+(b) A stereoscope was used to examine the samples. (c) Secondary electron SEM images were 
+taken of the fabric and sewn stitches. 
+Uniaxial Tensile Behavior 
+We investigated plain thread, plain fabric, and stitched fabrics using Instron for 
+mechanical behavior analyses. The uniaxial tensile test behavior of plain thread is shown 
+
+a(i)
+b(i)
+c(i)
+Cotton
+Fabric
+a(ii)
+b(i)
+500μm
+Straight
+Fabric<
+Stich
+Stitch
+c(ii)
+b(ili)
+Zigzag
+Stitch
+5 mm
+2 mm
+500 μmin Figure 2a, and the plain fabric is shown in Figure 2b. For comparison, Figure 2b also 
+shows the behaviors of straight and zigzag (2x5mm) stitched fabrics. Four other zigzag 
+stitched fabrics' behavior is shown in Figure 2c. Figures 2d and 2e show the side view of 
+a zigzag stitched fabric loaded into Intron during tensile testing and at the end of failure 
+analyses.  
+We tested two samples of the plain threads, and both samples' behavior is shown 
+in Figure 2a. The plain thread failed at 5% strain but exhibited the highest strain energy 
+density compared to other samples tested. In contrast to the plain thread, the cotton fabric 
+in Figure 2b exhibited reproducible stretchability of up to 70% strain in two samples. The 
+inclusion of straight stitches into the plain fabric induced failure at ~12% strain, and the 
+zigzag stitched sample failed at ~32% strain.  
+The unaltered fabric had the highest stain at the point of failure, shown in Figure 
+2b, between 60-80%, with a strain energy density of around 1.0 MJ/m3 at failure. In 
+comparison, the thread samples had a strain energy density of approximately 5.0 MJ/m3 
+at failure, which occurred at around 5% strain. The strain energy density of the unaltered 
+fabric and thread at 4.5% were 4.19x10-4 MJ/m3 and 4.64 MJ/m3, respectively. Examining 
+the stress-strain data for the cotton fabric and the cotton thread individually, we conclude 
+that combining these materials would result in a sample with a strain energy density that 
+falls between the different materials at a given strain. The samples with sewn straight 
+stitches of 2mm length failed between 10-15% strain. At a strain of 4.5%, the straight 
+stitched samples exhibited an average strain energy density of 1.88x10-3 MJ/m3. A 
+prediction of the strain energy density of the straight stitched samples at 4.5% was 
+obtained using the experimental values of the thread and fabric alone. The predicted 
+value was 7.2x10-2 MJ/m3, more significant than the measured strain energy density. This 
+discrepancy is expected as the sewing process exposes the thread to dynamic loads and 
+friction known to reduce the strength of the thread.33 Overall, the sample with sewn 
+straight stitches failed at all fabric samples' lowest stress and strain. The cause of the low 
+stress and strain at failure is suspected to be the structure of the stitches, which cannot 
+withstand as much strain as the fabric. The fabric, with a higher elongation at failure than 
+the thread, can deform under the load. Therefore, the thread in the straight stitch 
+withstands the load for the entire sample until the thread breaks, equivalent to sample 
+failure. It was observed that the thread failed before the fabric in all samples with straight 
+stitches. 
+Samples with zigzag stitches of 2mm length and 5mm width also failed at stress 
+and strain lower than the unaltered fabric but higher strain than the straight stitched 
+sample. An analysis of the strain energy density of the 2x5mm zigzag sample reveals 
+aspects of the mechanical behavior. At strains below 20%, the strain energy density of 
+the 2x5mm zigzag sample is indistinguishable from the strain energy density of the fabric; 
+Therefore, the fabric's mechanical properties dominate the thread's properties in the 
+2x5mm zigzag sample at strains under 20%. At 30% strain, the strain energy density of 
+the zigzag sample is nearly double that of the fabric sample. The departure of the 2x5mm 
+zigzag sample from the mechanical behavior of the fabric indicates that at strains above 
+20%, the thread is the dominant influence on the mechanical behavior. This behavior is 
+
+investigated further in zigzag samples with varying stitch lengths and widths, as indicated 
+in Figure 2c. 
+ 
+Figure 2: (a) The graph of the stress-strain curve for the samples of the cotton thread indicates 
+maximum stress of approximately 100MPa at a strain of approximately 4.5% before failure. (b) 
+The graph shows the stress-strain curves of the unaltered fabric, fabric with straight stitches of 
+2mm length, and fabric with zigzag stitches of a length of 2mm and a width of 5mm. (c) The stress-
+strain graph shows the impact of varying the properties of zigzag stitches. (d) An image of a 
+sample with 1x5mm zigzag stitches shows the condition of the sample before uniaxial tensile 
+loading. (e) An image of a sample with 1x5mm zigzag stitches shows the condition of the sample 
+after uniaxial tensile loading. Notably, the fabric has failed while the sewn thread is intact. 
+During uniaxial tensile testing, it was revealed that stitch length and width are both critical 
+factors that influence the tensile behavior of the samples with zigzag stitches. Figure 2 
+(c) shows stress-strain curves for samples with zigzag stitches of varying length and 
+width. The fabric samples with 2x5mm, 2x4mm, and 3x5mm zigzag stitches failed at a 
+higher strain than those with straight stitches but at a similar stress. As with the 2x5mm 
+sample, the 2x4mm and 3x5mm had similar strain energy densities at low strain until the 
+thread became a dominant influence. The 1x5mm zigzag sample exhibited drastically 
+
+(a)
+25
+Thread Sample 1
+b
+FabricOnly 1
+-ThreadSample2
+★—FabricOnly2
+- Straight Stitch 1
+100
+8 -
+- Straight Stitch 2
+—2x5mm Zigzag Stitch 1
+Stress (MPa)
+Stress (MPa)
+75
+2x5mm Zigzag Stitch 2
+6.
+50-
+4
+25 
+2.
+0
+0.
+0
+2
+6
+8
+10
+0
+20
+40
+60
+80
+100
+Strain (%)
+Strain (%)
+(c)
+10
+(d)
+2x4mm
+e
+一1x5mm
+2x3mm
+8-
+★一3x5mm
+FabricStress (Mpa)
+6
+Zigzag
+Stitch
+Failure
+4 
+Point
+2-
+Sample
+Grip
+0：
+0
+20
+40
+60
+80
+100
+Strain (%)different behavior from the other samples with zigzag stitches. The strain energy density 
+of the 1x5mm zigzag samples matched that of the unaltered fabric sample up to 
+approximately 60% strain, indicating that the stitches had little impact on the tensile 
+behavior of the sample overall. The 1x5mm samples also had more extended elongation 
+at failure than the unaltered fabric sample. The structure of the zigzag stitch contributes 
+to the behavior of all the zigzag samples. Since zigzag stitches have both a stitch length 
+and a stitch width, the stitch could change shape as the fabric elongates.  
+Figures 2(d) and (e) show a 1x5mm zigzag sample before and after uniaxial tensile 
+testing. After testing, the stitches are longer in the direction parallel to loading and shorter 
+in the direction perpendicular to loading compared to before tensile testing. In other 
+words, the stitch could shrink in the direction perpendicular to loading while elongating in 
+the direction of loading. A shorter stitch length results in more threads in the sample, 
+which allows the stitches to deform enough to match the elongation of the fabric. The 
+consequence of the stitch deformation is that the fabric withstands the load while the stitch 
+can deform, but the stitch bears the load when it is no longer able to match the elongation 
+of the fabric. Eventually, the load exhausts the ability of the stitch to deform, which is 
+when the strain energy density of the zigzag sample deviates from that of the unaltered 
+fabric. It was observed that the sewn thread had snapped in all samples after the sample 
+had failed during tensile testing, except for the 1x5mm zigzag sample. The 1x5mm zigzag 
+sample in Figure 2(c) had a shorter stitch length. Another point of interest is shown in 
+Figure 2(e), which shows that the thread was intact after the fabric failed, which is the 
+opposite of all other samples that contained sewn stitches. Therefore, it is possible to 
+alter stitch properties to alter the fabric's tensile behavior, and the properties determine 
+the extent of the influence from the thread and the fabric at particular strains. 
+Repeated Cycling Behavior 
+The unaltered fabric sample, straight stitch sample, and 2x5mm zigzag stitch sample 
+were examined under cyclic loading to analyze stress softening and hysteresis. Any 
+fabrics are subjected to cyclic loading during use from body movements such as the 
+expansion of the chest during breathing or the movement of joints. An analysis of the 
+behavior of the fabric samples during cyclic loading provides information that can inform 
+design decisions. All samples were strained up to 10% because the straight stitch 
+samples failed at approximately 12% strain. Hysteresis, the change in behavior from the 
+loading to the unloading cycle, was observed in all samples, as shown in Figure 3. Across 
+all samples, the most extensive hysteresis occurred during the first cycle. Additionally, all 
+samples had the highest strain energy density during the loading of the first cycle. The 
+hysteresis between the loading and unloading cycle of the overall sample is impacted by 
+the relationship between the yarns' properties and the fabric's structure. The plastic 
+deformation of the yarns, which relates to the slippage and viscoelasticity of the fibers 
+within the yarn, influences hysteresis.10 The structure dictates the number and nature of 
+the contact points between loops of thread, which impacts the friction during loading. 
+Friction is the main factor determining the amount of hysteresis that will occur.5 In the 
+samples with stitches, the causes of tensile hysteresis are further complicated by the 
+presence the stitched threads, which impact the overall properties and structure of the 
+
+sample. In Figure 3b, the straight stitch sample showed more hysteresis than the zigzag 
+stitched sample shown in Figure 3c, indicating that the straight stitched threads 
+experienced more plastic deformation than the zigzag stitched threads. The difference in 
+the plastic deformation experienced in the threads relates to the behavior observed in the 
+uniaxial tensile testing. The straight-stitched thread sustains more of the load for the entire 
+sample than the zigzag stitch; the thread in the straight-stitched sample experiences more 
+plastic deformation. Repeated cycles allow for an investigation of the hysteresis in 
+additional cycles and an analysis of the stress-softening behavior of the samples. The 
+second cycle revealed that stress softening occurred in all samples between the first and 
+second cycles, which can be observed in whole Figure 3 as a reduction in the strain 
+energy density of the loading curve between the first and second cycles. The unaltered 
+fabric sample in Figure 3a showed a minor stress softening, which can be attributed to 
+the significant difference between the maximum strain during cyclic loading and the strain 
+required to cause failure. Since the unaltered fabric sample has minor unrecoverable 
+deformation at the 10% strain tested in this experiment, minimal stress softening 
+occurred. In additional cycles after the second cycle, hysteresis in the fabric sample and 
+the zigzag sample remained the same; however, hysteresis decreased slightly in the 
+straight stitched sample from the second to the third cycle. The decrease in hysteresis is 
+attributable to the stress softening in the straight stitch sample between the second and 
+the third cycles, which indicates that further unrecoverable deformation occurred during 
+each cycle. In comparison, the fabric and the zigzag stitch samples do not experience 
+significant unrecoverable deformation in cycles after the second cycle. 
+ 
+
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure 2: (a) The unaltered fabric sample showed less stress softening than the 2x5mm zigzag 
+stitch sample but still showed hysteresis. (b) The straight stitch sample had the most stress 
+softening and also showed hysteresis. (c) The cyclic loading of the 2x5mm zigzag stitch sample 
+showed stress softening after the first cycle and hysteresis. 
+ 
+ 
+
+(a)
+0.06
+-OnlyFabricCycle1
+-OnlyFabricCycle2
+OnlyFabric Cycle3
+★一
+Only Fabric Cycle 4
+Stress (Mpa)
+0.04 -
+0.02
+0.00+
+0
+10
+5
+Strain (%)
+(b)
+1.0
+StraightStitchCycle1
+-Straight StitchCycle2
+Straight Stitch Cycle3
+0.8 -
+★一
+Straight Stitch Cycle 4
+0.2 -
+0.0 +
+5
+10
+Strain (%)
+(c)
+0.06
+2x5mmZigzagCycle1
+—2x5mmZigzagCycle2
+2x5mmZigzagCycle3
+★一
+2x5mmZigzagCycle4
+Stress (Mpa)
+0.04
+0.02
+0.00
+0
+5
+10
+Strain (%)Revealing rheological parameters of Fabric and Composite Systems 
+The TNM is a powerful constitutive model capturing the flow and deformation (rheology) 
+behaviors of materials. Bergstrom and Bischoff explained the mathematical details of the 
+TNM in their work.1 While the stress-strain analysis directly measures the mechanical 
+behavior, the rheological parameters we often overlook in stress-strain analyses can be 
+revealed through constitutive models. Studies on such parameters also enable data-
+informed design decisions.  
+We used MCalibration software to perform rheological analyses using TNM and calibrate 
+the TNM parameters to assess unaltered and altered fabrics. MCalibration software 
+begins calibration with a set of initially estimated parameter values by observing the 
+experimental data. It tries to reduce the deviation between the predicted and the 
+experimental behavior by continuously updating the parameters. This process is also 
+known as data calibration and rheological parameter identification. When the coefficient 
+of determination or the R2 value stops changing significantly by reaching convergence, 
+the software reveals the rheological parameters in its user interface. The experimental 
+data and MCalibration predicted data with their respective R2 fitness are shown in Figure 
+4, indicating that the TNM model effectively captures the uniaxial tensile behavior of 
+unaltered, straight- and zigzag-stitched fabrics. The predicted data fits closely with the 
+experimental data for all investigated samples with this method. The prediction of the 
+2x5mm zigzag sample in Figure 4a matched with an R2 fitness of 0.999, which was a 
+closer fit than the unaltered fabric sample or the straight stitch sample. The reason for the 
+closer match indicates that the 2x5mm zigzag sample had behavior closest to that of a 
+thermoplastic polymer, which is the material on which the TNM is based. Furthermore, 
+the calibration calculates the material model parameters, revealing information about the 
+behavior of the samples that cannot be determined from an analysis of the experimental 
+data alone. Table 1 shows several such parameters. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Figure 3: The material calibration with the PolyUMod TNM resulted in a good prediction for (a) 
+the unaltered fabric sample, (b) the 2mm straight stitch sample, and (c) the 2x5mm zigzag sample. 
+ 
+
+(a)
+3
+ExperimentalFabricData
+Predicted Fabric Data
+2.5
+Stress
+1.5
+1
+0.5
+R2Fitness=0.997
+0
+0
+10
+20
+3040
+50
+6070
+Strain (%)
+(b)
+1.5
+ExperimentalStraightStitchData
+-Predicted Straight StitchData
+1.25
+(MPa)
+1
+stress
+0.75
+0.5
+0.25
+R2Fitness=0.99
+0
+0
+2.5
+5
+7.5
+10
+12.5
+Strain (%)
+(c)
+0.7
+Experimental2x5mmZigzagData
+-Predicted2x5mmZigzagData
+0.6
+0.5
+(edw) :
+0.4
+0.3
+0.2
+0.1
+R2Fitness=0.999
+0
+0
+5
+10
+15
+520
+25
+30
+Strain (%)Table 1: The Three-Network Model (TNM) parameters of unaltered fabric, straight 
+stitch, and the 2x5 mm Zigzag stitch 
+Description 
+Symbol 
+Unit 
+Unaltered 
+Fabric 
+Straight Stitch 
+2x5 mm Zigzag 
+Shear modulus of network 
+A 
+𝜇� 
+KPa 
+11.40 
+77.95 
+0.65 
+Locking stretch 
+𝜆� 
+- 
+1.08 
+1.02 
+1.04 
+Bulk modulus 
+𝜅 
+KPa 
+656.37 
+1369.34 
+1194.72 
+Flow resistance of network 
+A 
+𝜏̂� 
+KPa 
+127.80 
+901.91 
+352.31 
+Stress exponential of 
+network A 
+𝑚� 
+- 
+3.83 
+11.11 
+9.59 
+Initial shear modulus of 
+network B 
+𝜇�� 
+KPa 
+96.46 
+15.05 
+40.75 
+Final shear modulus of 
+network B 
+𝜇�� 
+KPa 
+96.46 
+9.31 
+58.99 
+Evolution rate of 𝜇� 
+𝛽 
+- 
+9.69 
+10.20 
+10.50 
+Flow resistance of network 
+B 
+𝜏̂� 
+KPa 
+348.78 
+1226.80 
+636.76 
+Stress exponential of 
+network B 
+𝑚� 
+- 
+7.89 
+9.65 
+10.85 
+Shear modulus of network 
+C 
+𝜇� 
+KPa 
+398.95 
+1180.98 
+207.47 
+Earlier investigation27  on assessing the hyperelastic material model calibrated 
+parameters, leveraging Mooney-Rivlin, Ogden, neo-Hookean, Arruda Boyce, Gent, Yeoh, 
+and Blatz-Ko constitutive models. The higher-order Mooney-Rivlin and Yeoh models fitted 
+the experimental data properly. The Arruda-Boyce model also showed good relation with 
+the experimental data. Also, we noticed a similarity in the stress-strain behavior from that 
+investigation that is close to our unaltered fabric behavior shown in Figure 2(b). We want 
+to compare the parameters we obtained with that literature27. We noted a shear modulus 
+of 3.8913 KPa, and a limiting locking stretch (𝜆�,���� of 0.65907 from that investigation. 
+The Cauchy stress acting on any networks in the TNM model is based on the Arruda-
+Boyce or eight-chain model.1 The reported shear modulus and the shear modulus of the 
+Network A of the unaltered fabric are also not significantly different here. As the shear 
+modulus of the Arruda-Boyce model gets distributed in three networks, we should only 
+compare the locking stretch directly. The locking stretch is defined as the ratio of the 
+current chain length and the initial chain length. From the literature, the relation between 
+the locking stretch (𝜆�� and limited locking stretch can be found,34,35, which is 
+𝜆� � �1
+3 �𝜆�,���
+�
+�
+2
+𝜆�,���
+� 
+
+The reported limiting locking stretch converted to 𝜆� will be 1.0753, which is very close to 
+our reported locking stretch value of the unaltered fabric, 1.08. Additionally, for all the 
+samples, the locking stretch was close to 1, indicating that the sample did not go through 
+a significant strain level. The locking stretch values of the straight stitch and the zigzag 
+stitch are also smaller than the unaltered fabric, indicating less deformation observed in 
+Figure 2(b). The final calibrated parameters depend significantly on the initially guessed 
+parameters. It would be easier to compare the parameters between three samples if an 
+identical set of initial values was used. As we are using the uniaxial tensile testing here, 
+bulk modulus should not impact the predicted behavior significantly. 36 In the TNM, 
+network A and B utilize separate energy activation mechanisms to represent the 
+amorphous and semi-crystalline domains. Network C represents the large strain response 
+controlled by entropic resistance. The shear modulus and the flow resistance of network 
+A in the straight stitch are significantly higher than the other two samples indicating higher 
+resistance by the spring represented in the network. Figure 4(b) also indicates that up to 
+10% strain straight-stitched fabric is stiffer than the other two matching the observation in 
+the parameters. Comparatively close initial and final shear modulus of network B and 
+almost similar evolution rates indicate a similar effective shear modulus for all the 
+samples. The flow resistance of network B and the shear modulus of network C of the 
+straight-stitched sample are also higher, indicating higher stiffness of the materials.  
+Conclusion 
+This work determined that altering the parameters of the stitching when sewing 
+with cotton thread into a single layer of jersey-knit cotton fabric impacts the strain-energy 
+density, hysteresis, and stress softening of the sample. When examined with optical and 
+scanning electron microscopes, the stitched samples did not show damage to the fabric 
+from the sewing process. The stitch type and parameters of a zigzag stitch were shown 
+to directly impact the sample's behavior under uniaxial tensile loading. Depending on the 
+stitch type, the fabric can be altered to have a higher or lower strain energy density at 
+certain strains. We also note that stitches capable of less elongation than the fabric will 
+increase the strain energy density at lower strains and result in failure at a lower strain. 
+Stitches that can match or exceed the elongation may have minimal impact on the strain 
+energy density of the sample at the same strains as a sample without stitches but will fail 
+at higher strains, resulting in a higher strain energy density at failure. Stitches will also 
+impact the hysteresis and stress softening of the sample. Also, stitches capable of less 
+elongation than the fabric will be subjected to higher stress during loading, resulting in 
+plastic deformation and more significant hysteresis and stress softening during cyclic 
+loading. The tensile and cyclic tests reveal that the mechanical behavior of samples 
+composed of fabric with stitches varies greatly depending on the relationships between 
+the property of the materials and their structure. When data from tensile tests were 
+calibrated with the PolyUMod TNM, the materials presented in this work matched well 
+with the calibrated model; therefore, materials calibration provides an opportunity to aid 
+the selection of materials and structure by offering insight into hidden parameters that 
+allow for a data-driven approach to design.  
+
+Limitations of this work include the number of materials and structures investigated, as 
+the behavior observed may differ from samples with different compositions and 
+structures. Furthermore, many other properties may be impacted by the presence of 
+sewing stitches that were not investigated in this paper, such as abrasive strength, 
+bursting strength, torsional properties, ability to withstand washing and drying, and many 
+other characteristics. Future works may investigate the impact of additional types of 
+stitches on fabrics of different materials and structures and analyze additional properties 
+of the samples. 
+Acknowledgments 
+MRK acknowledges the funding support from VPRI's startup account. HW 
+acknowledges the Nevada undergraduate research award (NURA) fund from the 
+Undergraduate Research Office, and KZH acknowledges funding from the College of 
+Engineering Dean's Office at the University of Nevada, Reno. HW acknowledges 
+contributions from Sydney Fields, Jake Kattelman, Thomas Kaps, and Braden Norris for 
+the MSE 470 (Polymer Engineering instructed by MRK) in-class project. KZH 
+acknowledges the opportunity to train and mentor all the groups in CHE/MSE 470 and 
+Brian Perdue in CHE 495 using the concepts from this article. MRK acknowledges the 
+support received from Dean's Office to purchase Instron 5982 with Dr. Jefferey Lacombe, 
+Dr. Bin Li, and Zachary Karmiol. 
+ 
+ 
+References 
+1.  Bergstrom JS, Bischoff JE. An Advanced Thermomechanical Constitutive Model for 
+UHMWPE. Int J Struct Chang Solids 2010; 2: 31–39. 
+2.  PolyUMod 
+Three 
+Network 
+(TN) 
+Model. 
+PolymerFEM.com, 
+https://polymerfem.com/three-network-model/ (2020, accessed 21 February 2022). 
+3.  Penava Ž, Penava DŠ, Miloš L. Experimental and analytical analyses of the knitted 
+fabric off-axes tensile test. Text Res J 2021; 91: 62–72. 
+4.  Mohamed A, Messiry ME. Analysis Of The Effect Of Cyclic Loading On Cotton-
+Spandex Knitted Fabric. pp. 1–6. 
+5.  Dusserre G. Modelling the hysteretic wale-wise stretching behaviour of technical 
+plain knits. Eur J Mech - ASolids 2015; 51: 160–171. 
+6.  Li Q, Wang Y, Jiang S, et al. Investigation into tensile hysteresis of polyurethane-
+containing textile substrates for coated strain sensors. Mater Des 2020; 188: 108451. 
+
+7.  Andrews BAK, McSherry WF, Frick JG, et al. Recovery from Tensile Strain in Knitted 
+Cotton Fabric after Cross-Linking. Text Res J 1971; 41: 387–391. 
+8.  Choi M-S, Ashdown SP. Effect of Changes in Knit Structure and Density on the 
+Mechanical and Hand Properties of Weft-Knitted Fabrics for Outerwear. Text Res J 
+2000; 70: 1033–1045. 
+9.  Liu R, Lao TT, Wang SX. Impact of Weft Laid-in Structural Knitting Design on Fabric 
+Tension Behavior and Interfacial Pressure Performance of Circular Knits. J Eng 
+Fibers Fabr 2013; 8: 155892501300800420. 
+10.  Abdessalem SB, Abdelkader YB, Mokhtar S, et al. Influence of Elastane 
+Consumption on Plated Plain Knitted Fabric Characteristics. J Eng Fibers Fabr 2009; 
+4: 155892500900400420. 
+11.  Midha VK, Mukhopadhyay A, Chatopadhyay R, et al. Studies on the Changes in 
+Tensile Properties of Sewing Thread at Different Sewing Stages. Text Res J 2009; 
+79: 1155–1167. 
+12.  Midha VK, Mukhopadhyay A, Chattopadhyay R, et al. Effect of Process and Machine 
+Parameters on Changes in Tensile Properties of Threads during High-speed 
+Industrial Sewing. Text Res J 2010; 80: 491–507. 
+13.  Sundaresan G, Salhotra KR, Hari PK. Strength reduction in sewing threads during 
+high speed sewing in industrial lockstitch machine: Part II: Effect of thread and fabric 
+properties. Int J Cloth Sci Technol 1998; 10: 64–79. 
+14.  Sundaresan G, Hari PK, Salhotra KR. Strength reduction of sewing threads during 
+high speed sewing in an industrial lockstitch machine: Part I - mechanism of thread 
+strength reduction. Int J Cloth Sci Technol 1997; 9: 334–345. 
+15.  Rengasamy RS, Wesley S. Tensile Behavior of Different Types of Sewing Threads 
+Observed under Simple-Tensile, Loop and Knot Tests. J Text Appar Technol Manag; 
+7, https://ojs.cnr.ncsu.edu/index.php/JTATM/article/view/1390 (2011, accessed 9 
+September 2022). 
+16.  Abrishami S, Ezazshahabi N, Mousazadegan F. Analysis of the stress relaxation 
+behaviour of sewing threads in the straight and loop form. J Text Inst 2021; 112: 
+596–609. 
+17.  Villanueva R, Ganta D, Guzman C. Mechanical, in-situ electrical and thermal 
+properties of wearable conductive textile yarn coated with polypyrrole/carbon black 
+composite. Mater Res Express 2018; 6: 016307. 
+18.  Ardalan S, Hosseinifard M, Vosough M, et al. Towards smart personalized 
+perspiration analysis: An IoT-integrated cellulose-based microfluidic wearable patch 
+
+for smartphone fluorimetric multi-sensing of sweat biomarkers. Biosens Bioelectron 
+2020; 168: 112450. 
+19.  Ukponmwan JO, Mukhopadhyay A, Chatterjee KN. Sewing Threads. Text Prog 
+2000; 30: 1–91. 
+20.  Yıldız EZ, Pamuk O. The parameters affecting seam quality: a comprehensive 
+review. Res J Text Appar 2021; 25: 309–329. 
+21.  Sülar V, Meşegül C, Kefsiz H, et al. A comparative study on seam performance of 
+cotton and polyester woven fabrics. J Text Inst 2015; 106: 19–30. 
+22.  Rogina-Car B, Schwarz I, Kovačević S. Analysis of Woven Fabric at the Place of the 
+Sewn Seam. AUTEX Res J 2018; 18: 216–220. 
+23.  Akter M, Khan MR. The effect of stitch types and sewing thread types on seam 
+strength for cotton apparel. Int J Sci Eng Res; 6. 
+24.  Wang L, Chan LK, Hu X. INFLUENCE OF STITCH DENSITY TO STITCHES 
+PROPERTIES OF KNITTED PRODUCTS. Res J Text Appar 2001; 5: 46–53. 
+25.  Admassu Y, Edae A, Getahun G, et al. Experimental analysis on the effect of fabric 
+structures and seam performance characteristics of weft knitted cotton apparels. J 
+Eng Fibers Fabr 2022; 17: 15589250221113480. 
+26.  Qi HJ, Boyce MC. Constitutive model for stretch-induced softening of the stress–
+stretch behavior of elastomeric materials. J Mech Phys Solids 2004; 52: 2187–2205. 
+27.  Julio García Ruíz M, Yarime Suárez González L. Comparison of hyperelastic 
+material models in the analysis of fabrics. Int J Cloth Sci Technol 2006; 18: 314–325. 
+28.  Khiêm VN, Krieger H, Itskov M, et al. An averaging based hyperelastic modeling and 
+experimental analysis of non-crimp fabrics. Int J Solids Struct 2018; 154: 43–54. 
+29.  Gong Y, Peng X, Yao Y, et al. An anisotropic hyperelastic constitutive model for 
+thermoplastic woven composite prepregs. Compos Sci Technol 2016; 128: 17–24. 
+30.  Peng X, Guo Z, Du T, et al. A simple anisotropic hyperelastic constitutive model for 
+textile fabrics with application to forming simulation. Compos Part B Eng 2013; 52: 
+275–281. 
+31.  Peng XQ, Guo ZY, Zia-Ur-Rehman, et al. A Simple Anisotropic Fiber Reinforced 
+Hyperelastic Constitutive Model for Woven Composite Fabrics. Int J Mater Form 
+2010; 3: 723–726. 
+
+32.  MCalibration. PolymerFEM.com, https://polymerfem.com/mcalibration/ (accessed 
+21 February 2022). 
+33.  Geršak J, Knez B. REDUCTION IN THREAD STRENGTH AS A CAUSE OF 
+LOADING IN THE SEWING PROCESS. Int J Cloth Sci Technol 1991; 3: 6–12. 
+34.  Bergstrom JS. Mechanics of Solid Polymers: Theory and Computational Modeling. 
+William Andrew, 2015. 
+35.  Nguyen H-D, Huang S-C. The Uniaxial Stress–Strain Relationship of Hyperelastic 
+Material Models of Rubber Cracks in the Platens of Papermaking Machines Based 
+on Nonlinear Strain and Stress Measurements with the Finite Element Method. 
+Materials 2021; 14: 7534. 
+36.  Jorgen. How Important is the Bulk Modulus in FEA? PolymerFEM.com, 
+https://polymerfem.com/how-important-is-the-bulk-modulus/ (2021, accessed 17 
+November 2022). 
+ 
+ 
+

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+Quantum Hairy Black Hole Formation and Horizon Quantum Mechanics
+R. T. Cavalcanti∗ and J. M. Hoff da Silva†
+Departamento de F´ısica, Universidade Estadual Paulista (Unesp), Guaratinguet´a 12516-410, Brazil
+After introducing the gravitational decoupling method and the hairy black hole recently derived
+from it, we investigate the formation of quantum hairy black holes by applying the horizon quan-
+tum mechanics formalism. It enables us to determine how external fields, characterized by hairy
+parameters, affect the probability of spherically symmetric black hole formation and the generalized
+uncertainty principle.
+I.
+INTRODUCTION
+Given their intrinsic connection with intense gravitational fields, solid theoretical basis [1–3], and several observa-
+tional results corroborating their existences, black holes play a central role in contemporary high-energy physics and
+astrophysics [4–7]. Despite the characterization of the horizon of stationary black hole solutions being well-known
+within general relativity [3, 8], the nature of the horizons of non-stationary or stationary solutions beyond general
+relativity is still a source of extensive research [9–12]. The investigation of black holes is not restricted to astrophysical
+objects; they are also expected to be formed whenever a high concentration of energy is confined to a small region of
+spacetime, producing so-called quantum black holes [7, 13–17]. However, the precise formation mechanism of classical
+and quantum black holes is still unknown. Although we do not have a theory of quantum gravity, phenomenology
+suggests that some features of quantum black holes are expected to be model-independent [7]. From a certain scale,
+candidate theories should modify the results of general relativity, giving birth to some alternatives to Einsteins’s
+theory of gravity [18, 19]. Examples could allow for the presence of non-minimal coupled fundamental fields or higher
+derivative terms during the action, which directly affects the uniqueness theorems of black holes in general relativity.
+The famous no-hair theorem is not preserved outside the general relativity realm. These solutions lead to effects that
+are potentially detectable near the horizon of astrophysical black holes [20–22], or in quantum black holes’ formation
+[23, 24], and may provide hints for the quantum path.
+One of the major challenges in general relativity is finding physically relevant solutions to Einstein’s field equations.
+On the other hand, deriving new solutions from other previously known ones is a widespread technique. This approach
+is precisely what the so-called gravitational decoupling (GD) method intends to achieve. It has recently commanded
+the community’s attention due to its simplicity and effectiveness [25–27] in generating new, exact analytical solutions
+by considering additional sources to the stress-energy tensor. The recent description of anisotropic stellar distribu-
+tions [28, 29], whose predictions might be tested in astrophysical observations [30–33], as well as the hairy black hole
+solutions by gravitational decoupling, are particularly interesting. The latter describes a black hole with hair sourced
+by generic fields, possibly of quantum nature, surrounding the vacuum Schwarzschild solution [27]. Exciting results
+have been found during investigation of this solution [34–36].
+From the quantum side, one of the key features of quantum gravity phenomenology is the generalized uncertainty
+principle (GUP), which modifies the Heisenberg uncertainty principle accordingly
+∆x∆p ≳ ℏ
+�
+1 + ϵ(∆p)2�
+.
+(1)
+This expression of the GUP, which stems from different approaches to quantum gravity [37–46], characterizes a
+minimum scale length ∆x. This feature emerges quite naturally in the horizon quantum mechanics formalism (HQM)
+[16, 47]. In addition to the GUP, HQM also provides an estimation of the probability of quantum black hole formation.
+In a scenario of extra-dimensional spacetimes, the HQM gave an explanation for the null results of quantum black
+hole formation in current colliders [23, 24]. Could it also tell us something about a mechanism for decreasing the
+fundamental scale to something near the scale of current colliders? Our aim is to investigate the quantitative and
+qualitative effects of black hole hair, regarding the probability of black hole formation and the GUP by applying the
+horizon quantum mechanics formalism.
+This paper is organized as follows: Section II is dedicated to reviewing the gravitational decoupling procedure, the
+metric for GD hairy black holes, and an approximation for the horizon radius. In Section III, we apply the horizon
+∗Electronic address: [email protected]
+†Electronic address: julio.hoff@unesp.br
+arXiv:2301.00319v1  [gr-qc]  1 Jan 2023
+
+2
+quantum mechanics formalism to the hairy black hole solution of the previous section. We compare the probability of
+quantum black hole formation and the GUPs of hairy black holes for a range of hair parameters, unveiling the effects
+of the hair fields. Finally, Section IV is dedicated to conclusions and discussion.
+II.
+HAIRY BLACK HOLES AND HORIZON RADIUS
+Starting from Einstein’s field equations
+Gµν = 8π ˇTµν,
+(2)
+where Gµν = Rµν − 1
+2Rgµν denotes the Einstein tensor, the gravitational decoupling (GD) [25] method takes the
+energy–momentum tensor decomposed as
+ˇTµν = Tµν + Θµν.
+(3)
+Here, Tµν is the source of a known solution to general relativity, while Θµν introduces a new field or extension of the
+gravitational sector. From ∇µ Gµν = 0, we also have ∇µ ˇT µν = 0. The effective density and the tangential and radial
+pressures can be determined by examining the field equations
+ˇρ = ρ + Θ 0
+0 ,
+(4a)
+ˇpt = p − Θ 2
+2 ,
+(4b)
+ˇpr = p − Θ 1
+1 .
+(4c)
+The idea is to deform a known solution to split the field equations in a sector containing the known solution with
+source Tµν and a decoupled one governing the deformation, encompassing Θµν. In fact, assuming a known spherically
+symmetric metric,
+ds2 = −eκ(r)dt2 + eζ(r)dr2 + r2dΩ2,
+(5)
+and deforming κ(r) and ζ(r) as
+κ(r) �→ κ(r) + αf2(r),
+(6a)
+e−ζ(r) �→ e−ζ(r) + αf1(r),
+(6b)
+the resulting decoupled field equations read
+8π Θ 0
+0
+= α
+�f1
+r2 + f ′
+1
+r
+�
+,
+(7a)
+8π Θ 1
+1 − α e−ζ f ′
+2
+r
+= α f1
+� 1
+r2 + κ′(r) + αf ′
+2(r)
+r
+�
+,
+(7b)
+8πΘ 2
+2 −αf1Z1(r) =αf ′
+1
+4
+�
+κ′(r) + αf ′
+2(r)+ 2
+r
+�
++αZ2(r),
+(7c)
+where [25]
+Z1(r) = α2f ′
+2 (r)2 + 2 α
+�
+f ′
+2 (r) κ′ (r) + f ′
+2 (r)
+r
++ f ′′
+2 (r)
+�
++ κ′ (r)2 + 2 κ′ (r)
+r
++ 2 κ′′ (r) ,
+(8a)
+Z2(r) = αe−ζ
+�
+2f ′′
+2 + f 2′
+2 + 2f ′
+2
+r
++ 2κ′f ′
+2 − ζ′f ′
+2
+�
+.
+(8b)
+The above equations state that if the deformation parameter α goes to zero, then Θµν must go to zero. It is worth
+mentioning that for extended geometric deformation, that is, for f2 ̸= 0, the sources are not individually conserved
+in general. However, as discussed in [26], in this case, the decoupling of the field equations without an exchange of
+energy is allowed in two scenarios: (a) when Tµν is a barotropic fluid whose equation of state is T00 = T11 or (b) for
+vacuum regions of the first system Tµν = 0. When minimal geometric deformation is applied, on the other hand, the
+sources are shown to be individually conserved [25, 26].
+Assuming the Schwarzschild solution to be the known one and requiring a well-defined horizon structure [27], from
+grr = − 1
+gtt follows
+�
+1 − 2M
+r
+� �
+eαf2(r) − 1
+�
+= αf1(r).
+(9)
+
+3
+Therefore, one is able to write
+ds2 = −
+�
+1 − 2M
+r
+�
+eαf2(r)dt2+
+�
+1 − 2M
+r
+�−1
+e−α f2(r)dr2 + r2 dΩ2.
+(10)
+Further, assuming strong energy conditions,
+ˇρ + ˇpr + 2 ˇpt ≥ 0,
+(11a)
+ˇρ + ˇpr ≥ 0,
+(11b)
+ˇρ + ˇpt ≥ 0,
+(11c)
+and managing the field equations, a new hairy black hole solution was found [27]
+ds2 = −f(r)dt2 +
+1
+f(r)dr2 + r2dΩ2,
+(12)
+where
+f(r) = 1 − 2GM + αℓ
+r
++ αe−
+r
+GM .
+(13)
+The dimensionless parameter 0 ≤ α ≤ 1 tracks the deformation of the Schwarzschild black hole, e is the Euler constant,
+and ℓ is the direct effect of the nonvanishing additional font Θµν. Notice that by taking α = 0, the Schwarzschild
+solution is restored. Further, the ℓ parameter is limited to 2GM/e2 ≤ ℓ ≤ 1 due to the assumption of a strong energy
+condition. In extreme cases, ℓ = 2GM/e2 and
+fe(r) = 1 − 2GM
+r
++ α
+�
+e−
+r
+GM − 2GM
+e2 r
+�
+.
+(14)
+The hairy black hole has a single horizon, located at r = rH, such that
+�
+1 + αe− rH
+GM
+�
+rH = 2GM + αℓ.
+(15)
+Such an equation has no analytical solution. Nevertheless, a very accurate analytical approximation is found by Taylor
+expanding it around the Schwarzschild horizon radius rS = 2GM,
+rH
+GM ≈ 4
+�
+αℓe2/GM − 3 α + e2�
+αℓe2/GM − 4 α + 2 e2 .
+(16)
+Figure 1 shows a comparison between the exact and approximated horizon radii for different values of the hairy
+parameters. In the following section, we are going to use Equation (16) for the analytical expression of the hairy black
+hole’s horizon radius.
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+ℓ
+GM
+2.0
+2.1
+2.2
+2.3
+2.4
+2.5
+2.6
+2.7
+2.8
+rH
+GM
+α = 0.00
+α = 0.20
+α = 0.40
+α = 0.60
+α = 0.80
+α = 1.0
+Exact
+FIG. 1: The radius of the hairy black hole horizon rH as a function of ℓ for different values of the parameter α. The colored
+dashed lines represent the approximated radius, and the gray lines are the exact ones. It shows how the hairy horizon deviates
+from the Schwarzschild horizon for an increasing α and ℓ. The ranges for α and ℓ were fixed due to the assumption of a strong
+energy condition [27].
+
+4
+III.
+THE HORIZON QUANTUM MECHANICS FORMALISM
+Horizon quantum mechanics (also known as horizon wave function formalism) is an effective approach capable of
+providing the signatures of black hole physics to the Planck scale [48–51] (see [47] for a comprehensive review). The
+main idea is to extend quantum mechanics and gravity further than the current experimental limits. In such an
+approach, we face the conceptual challenge of consistently describing classical and quantum mechanical objects, such
+as horizons and particles. This is achieved by assigning wave functions to the quantum black hole horizon. This
+association allows the use of quantum mechanical machinery to distinguish between particles and quantum black
+holes and to estimate the GUPs. Nevertheless, first, we must choose a model describing the particle wave function to
+derive the results. Due to the previous results’ simplicity and efficiency, we shall use the Gaussian model.
+From classical general relativity, we know that the horizons of black holes are described by trapping surfaces, whose
+locations are determined by
+gij∇ir∇jr = 0 ,
+(17)
+where ∇ir is orthogonal to the surfaces of the constant area A = 4πr2. A trapping surface then exists if there are
+values of r and t such that the gravitational radius RH satisfies
+RH(r, t) ≥ r .
+(18)
+Considering a spinless point-particle of mass m, an uncertainty in the spatial particle localization of the same order
+of the Compton scale λm ≃ ℏ/m = lp mp/m follows from the uncertainty principle, where lp and mp are the Planck
+length and mass, respectively. Arguing that quantum mechanics gives a more precise description of physics, RH makes
+sense only if it is larger than the Compton wavelength associated with the same mass, namely RH ≳ λm. Thus, for
+the Schwarzschild radius RS = 2Gm = 2 lp
+mp m,
+lp m/mp ≳ lp mp/m
+=⇒
+m ≳ mp .
+(19)
+This suggests that the Planck mass is the minimum mass such that the Schwarzchild radius can be defined.
+From quantum mechanics, the spectral decomposition of a spherically symmetric matter distribution is given by
+the expression
+|ψS⟩ =
+�
+E
+C(E) |ψE⟩ ,
+(20)
+with the usual eigenfunction equation
+ˆH |ψE⟩ = E |ψE⟩ ,
+(21)
+regardless of the specific form of the actual Hamiltonian operator ˆH. Using the energy spectrum and inverting the
+expression of the Schwarzschild radius, we have
+E = mp
+rH
+2lp
+.
+(22)
+Putting it back into the wave function, one can define the (unnormalized) horizon wave function as
+ψH(rH) = C
+�
+mp
+rH
+2lp
+�
+(23)
+whose normalization is fixed, as usual, by the inner product
+⟨ψH | φH⟩ = 4π
+� ∞
+0
+ψ∗
+H(rH)φH(rH)r2
+HdrH.
+(24)
+However, the classical radius RH is thus replaced by the expected value of the operator ˆRH. From the uncertainty
+of the expectation value, it follows that the radius will necessarily be “fuzzy”, similar to the position of the source
+itself. The next aspect one has to approach to establish a criterion for deciding if a mass distribution does or does
+not form a black hole is if it lies inside its horizon of radius r = rH. From quantum mechanics, one finds that it is
+given by the product
+P<(r < rH) = PS(r < rH)PH(rH),
+(25)
+
+5
+where the first term,
+PS(r < rH) = 4π
+� rH
+0
+|ψS(r)|2r2dr,
+(26)
+is the probability that the particle resides inside the sphere of radius r = rH, while the second term,
+PH(rH) = 4πr2
+H|ψH(rH)|2
+(27)
+is the probability density that the value of the gravitational radius is rH. Finally, the probability that the particle
+described by the wave function ψS is a BH will be given by the integral of (25) over all possible values of the horizon
+radius rH. Namely,
+PBH =
+� ∞
+0
+P<(r < rH)drH,
+(28)
+which is one of the main outcomes of the formalism.
+A.
+Gaussian Sources
+The previous construction can be made explicit by applying the Gaussian model for the wave function. To implement
+this idea, let us recall that spectral decomposition is also assumed to be valid for momentum. Therefore, from (20),
+⟨p |ψS⟩ = C(p) ≡ ψH(p). The Gaussian wave function for ψS scales as r2 in the position space and leads to a Gaussian
+wave function in the momentum space, scaling as p2, naturally. Finally, since the dispersion relation relates p2 with
+energy, we are able to have ⟨p |ψS⟩ = ψH(rH) via (22). Hence, starting with a Gaussian wave function, we can describe
+a spherically symmetric massive particle at rest, such as
+ψS(r) =
+e− r2
+2 l2
+(l √π)3/2 .
+(29)
+The corresponding function in momentum space is thus given by
+˜ψS(p) = 4π
+� ∞
+0
+sin(rp)
+√
+8π3rp
+e− r2
+2 l2
+(l √π)3/2 r2dr
+=
+e−
+p2
+2 ∆2
+(∆ √π)3/2 ,
+(30)
+where ∆ = mp lp/l is the spread of the wave packet in momentum space, whose width l the Compton length of the
+particle should diminish,
+l ≥ λm ∼ mp lp
+m
+.
+(31)
+In addition to the straightforward handling of a Gaussian wave packet, it is also relevant to recall that the Gaussian
+wave function leads to a minimal uncertainty for the expected values computed with it. Had we used another wave
+function, it would certainly imply a worsening uncertainty, eventually leading to unnecessary extra difficulties relating
+to the HQM and GUP (see next section). Back to our problem, assuming the relativistic mass-shell relation in flat
+space [48]
+p2 = E2 − m2 ,
+(32)
+the energy E of the particle is expressed in terms of the related horizon radius rH = RH(E), following from Equation
+(16),
+E = αmpℓe2 +
+�
+α − e2�
+mprH
+2 (2 α − e2)lp
+.
+(33)
+
+6
+Thus, from Equations (30) and (33), one finds the the horizon wave function of the hairy black hole
+ψH(rH) = NHΘ(rH − RH) e(C2r2
+H+C1rH+C0),
+where
+C0 = − α2l2m2
+pℓ2e4
+8 (2 α − e2)2l2p
+,
+C1 = −
+�
+α − e2�
+αl2m2
+pℓe2
+4 (2 α − e2)2l2p
+,
+C2 = −
+�
+α − e2�2l2m2
+p
+8 (2 α − e2)2l2p
+.
+(34)
+The Heaviside step function Θ appears above due to the imposition E ≥ m. The normalisation factor NH is fixed
+according to
+N −2
+H
+= 4π
+� ∞
+0
+|ψH(rH)|2 r2
+H drH.
+The normalized horizon wave function is thus given as follows
+ψH(rH) = −
+2 C
+3
+2
+2 e
+A(rH )
+2
+√π
+�
+4 C1C2eA(RH) −
+�
+2
+√
+2C2Γ
+� 3
+2 , −A(RH)
+�
++
+√
+2πC2
+1
+�
+erf
+� √
+2(2 C2RH+C1)
+2 √−C2
+�
+− 1
+��√−C2
+,
+(35)
+A(x) = 4 C2
+2x2 + 4 C1C2x + C2
+1
+2 C2
+.
+Here, Γ(s, x) denotes the upper incomplete Euler–Gamma function and erf(x) the error function. The expression above
+has two classes of parameters. Two of these, α and ℓ, are related to the hairy black hole, and two are non-fixed a priori:
+the particle mass m, encoded in RH, and the Gaussian width l. The resulting probability PBH = PBH(l, m, ℓ, α) will
+also depend on the same parameters.
+According to the previous discussion, before finding the probability distribution, we have first to find the probability
+that the particle resides inside a sphere with the radius r = rH. From Equations (26) and (29), one obtains
+PS(r < rH) = 4π
+� rH
+0
+|ψS(r)|2r2dr =
+2
+√π γ
+�3
+2, r2
+H
+l2
+�
+,
+with γ(s, x) = Γ(s) − Γ(s, x), the lower incomplete Gamma function.
+Equations (27) and (35) yield PH(rH), as
+depicted in Figure 2.
+0
+1
+2
+3
+4
+5
+mprH
+lpm
+0
+1
+PH(rH)
+l = 0.50
+l = 1.0
+l = 1.5
+l = 2.0
+FIG. 2: The probability density for the value of the gravitational radius is rH for α = ℓ/(GM) = 0.5 and different values of
+the Gaussian width.
+Combining the previous results, one finds that the probability density for the particle resides within its own
+gravitational radius
+P<(r < rH) = 8√πγ
+�3
+2, r2
+H
+l2
+�
+r2
+H|ψH(rH)|2.
+
+7
+The probability of the particle described by the Gaussian to be a black hole is finally given by
+PBH(l, m, ℓ, α) = 8√π
+� ∞
+RH
+γ
+�3
+2, r2
+H
+l2
+�
+r2
+H|ψH(rH)|2,
+(36)
+which has to be calculated numerically. Assuming the Gaussian width has the same order as the particle Compton
+length, we could set l ∼ m−1 on Equation (36) and find the probability depending on either l or m. On the other
+hand, by departing again from Equation (31), we may set values for m in terms of the Planck mass and find the
+probability in this scenario. Applying l ∼ m−1 yields
+PBH(l, ℓ, α) = 8√π
+� ∞
+RH
+γ
+�3
+2, r2
+H
+l2
+�
+r2
+H|ψH(rH)|2,
+(37)
+or
+PBH(m, ℓ, α) = 8√π
+� ∞
+RH
+γ
+�3
+2, r2
+Hm2
+�
+r2
+H|ψH(rH)|2.
+(38)
+The resulting probabilities are shown in Figure 3 below. Figure 4 displays the probability for m given as a fraction of
+the Planck mass.
+0
+1
+2
+3
+4
+5
+l
+lp
+0
+1
+PBH
+ℓmp
+lpm = α = 0.00
+ℓmp
+lpm = α = 0.30
+ℓmp
+lpm = α = 0.60
+ℓmp
+lpm = α = 0.90
+1
+2
+m
+mp
+0
+1
+PBH
+ℓmp
+lpm = α = 0.00
+ℓmp
+lpm = α = 0.30
+ℓmp
+lpm = α = 0.60
+ℓmp
+lpm = α = 0.90
+FIG. 3: The probability of a ”particle” being a black hole depending on the Gaussian width or mass, assuming l ∼ m−1.
+1
+2
+3
+4
+5
+l
+lp
+0
+1
+PBH
+ℓmp
+lpm = α = 0.00
+ℓmp
+lpm = α = 0.30
+ℓmp
+lpm = α = 0.60
+ℓmp
+lpm = α = 0.90
+FIG. 4: The probability of a ”particle” being a black hole depending on the Gaussian width and mass m given as a fraction of
+the Planck mass, with m = mp (solid), m = 3mp/4 (dashed), and m = mp/2 (dotted).
+
+8
+B.
+HQM and GUP
+Since the horizon quantum mechanics formalism applies the standard wave function description for particles, a
+natural question is whether it affects the Heisenberg uncertainty principle. As mentioned, it produces a GUP similar
+to that produced by Equation (1). In quantum mechanics, the uncertainty principle may be derived by calculating
+the uncertainty associated with the wave function. Here, we start from the same point. From the Gaussian wave
+function (29), the particle size uncertainty is given by
+∆r2
+0 = ⟨r2⟩ − ⟨r⟩2
+= 4π
+� ∞
+0
+|ψS(r)|2r4dr −
+�
+4π
+� ∞
+0
+|ψS(r)|2r3dr
+�2
+= 3π − 8
+2π
+l2.
+(39)
+One might find the uncertainty of the horizon radius in an analogous way,1
+∆r2
+H = ⟨r2
+H⟩ − ⟨rH⟩2.
+(40)
+The total radial uncertainty can now be taken as a linear combination of the quantities calculated above, ∆r =
+∆r0 + ϵ∆rH. For the uncertainty in momentum, we have
+∆p2 = ⟨p2⟩ − ⟨p⟩2 = 3π − 8
+2π
+m2
+pl2
+p
+l2
+.
+Note that the momentum uncertainty and the width l are related such that ∆p ∼ 1/l. Using this fact in ∆r =
+∆r0 + ϵ∆rH, one is able to find
+∆r
+lp
+= 3π − 8
+2π
+mp
+∆p + ϵ∆H
+�∆p
+mp
+�
+,
+(41)
+which is similar to the GUP discussed previously. The function ∆H also depends on the wave function and hairy black
+hole parameters. Figure 5 shows the behavior of the GUP as a function of the momentum uncertainty, taking ϵ = 1.
+There, we can see a minimum ∆r placed around the Planck scale. From the GUP expression, it is straightforward
+to see that a larger ϵ means significant correction to the quantum mechanics’ uncertainty. The hairy parameters,
+however, have a small qualitative effect on fixing the minimum scale. As shown in Figure 5, their effects become
+prominent for a large ∆p.
+1
+2
+∆p
+mp
+1
+2
+∆r
+lp
+ℓmp
+lpm = α = 0.00
+ℓmp
+lpm = α = 0.30
+ℓmp
+lpm = α = 0.60
+ℓmp
+lpm = α = 0.90
+FIG. 5: GUP profile emerged from the horizon wave function formalism for ϵ = 1. The dotted line represents the particle size
+uncertainty ∆r0, the dashed line represents the uncertainty of the horizon radius ∆rH, and the solid lines describe the GUP.
+1 The analytical expression of ∆r2
+H is huge and little enlightening.
+
+9
+IV.
+DISCUSSION
+A few years ago, effective theories suggested lowering the scale of quantum black hole formation to TeV. Thus, in
+principle, it became experimentally accessible. In spite of no quantum black holes being detected, solid theoretical
+results point out that such objects should exist in nature [7, 14]. They could give us valuable hints about quantum
+gravity features [7, 13, 14]. One of this paper’s motivating questions was whether a generic black hole hair could
+significantly change the scale of quantum black hole formation. However, regarding the analysis carried out here, the
+hairy black holes look qualitatively similar to the Schwarzschild one, with a probability PBH of a similar shape and a
+related GUP, leading to the existence of a minimum length scale. Nevertheless, one of the main results of the present
+paper is that the existence of hair increases the probability PBH. This is indeed a point to be stressed. Its explanation
+rests upon the fact that the hairy black hole radius is slightly larger than the one for Schwarzschild. This implies
+that, although the scale of quantum black hole formation is still beyond the current experimental scale, additional
+fields may lower such scale. Those results might impact future colliders’ estimations of quantum black holes coming
+from alternative theories of gravity and potentially stimulate investigations of specific models of quantum hairy black
+holes [17].
+Acknowledgements
+R.T.C. thanks Unesp—AGRUP for the financial support. J.M.H.d.S. thanks CNPq (grant No. 303561/2018-1) for
+the financial support.
+[1] Hawking, S.W.; Ellis, G.F.R. The Large Scale Structure of Space-Time; Cambridge Monographs on Mathematical Physics,
+Cambridge University Press: Cambridge, UK, 2011. https://doi.org/10.1017/CBO9780511524646.
+[2] Chandrasekhar,
+S.
+The
+Mathematical
+Theory
+of
+Black
+Holes.
+Fundam.
+Theor.
+Phys.
+1984,
+9,
+5–26.
+https://doi.org/10.1007/978-94-009-6469-3 2.
+[3] Frolov, V.P.; Novikov, I.D., Eds. Black Hole Physics: Basic Concepts and New Developments; Kluwer Academic Publishers:
+Dordrecht, The Netherlands, 1998. https://doi.org/10.1007/978-94-011-5139-9.
+[4] Abbott, B.P.; et al.
+Observation of Gravitational Waves from a Binary Black Hole Merger.
+Phys. Rev. Lett. 2016,
+116, 061102, https://doi.org/10.1103/PhysRevLett.116.061102.
+[5] Cardoso, V.; Pani, P. Testing the nature of dark compact objects: A status report. Living Rev. Relativ. 2019, 22, 4,
+https://doi.org/10.1007/s41114-019-0020-4.
+[6] Barack, L.; et al. Black holes, gravitational waves and fundamental physics: A roadmap. Class. Quant. Grav. 2019,
+36, 143001, https://doi.org/10.1088/1361-6382/ab0587.
+[7] Calmet,
+X.,
+Ed.
+Quantum
+Aspects
+of
+Black
+Holes;
+Springer:
+Berlin/Heidelberg,
+Germany,
+2015.
+https://doi.org/10.1007/978-3-319-10852-0.
+[8] Wald,
+R.M.
+General
+Relativity;
+Chicago
+Univ.
+Pr.:
+Chicago,
+IL,
+USA,
+1984.
+https://doi.org/10.7208/chicago/9780226870373.001.0001.
+[9] Faraoni, V. Cosmological and Black Hole Apparent Horizons; Springer: Berlin/Heidelberg, Germany, 2015; Volume 907.
+https://doi.org/10.1007/978-3-319-19240-6.
+[10] Ashtekar,
+A.;
+Krishnan,
+B.
+Dynamical
+horizons
+and
+their
+properties.
+Phys. Rev. D
+2003,
+68,
+104030,
+https://doi.org/10.1103/ PhysRevD.68.104030.
+[11] Ashtekar, A.; Galloway, G.J. Some uniqueness results for dynamical horizons. Adv. Theor. Math. Phys. 2005, 9, 1–30,
+https://doi.org/10.4310/ATMP.2005.v9.n1.a1.
+[12] Gourgoulhon, E.; Jaramillo, J.L.
+New theoretical approaches to black holes.
+New Astron. Rev. 2008, 51, 791–798,
+https://doi.org/10.1016/j.newar.2008.03.026.
+[13] Calmet, X.; Casadio, R.
+What is the final state of a black hole merger?
+Mod. Phys. Lett. A 2018, 33, 1850124,
+https://doi.org/10.1142/S0217732318501249.
+[14] Calmet, X.; Kuipers, F. Black holes in quantum gravity. Nuovo Cim. C 2022, 45, 37, https://doi.org/10.1393/ncc/i2022-
+22037-4.
+[15] Casadio,
+R.;
+Orlandi,
+A.
+Quantum
+Harmonic
+Black
+Holes.
+JHEP
+2013,
+08,
+025,
+https://doi.org/10.1007/JHEP08(2013)025.
+[16] Casadio, R.; Giugno, A.; Micu, O.; Orlandi, A. Black holes as self-sustained quantum states, and Hawking radiation.
+Phys. Rev. D 2014, 90, 084040, https://doi.org/10.1103/PhysRevD.90.084040.
+[17] Calmet, X.; Casadio, R.; Hsu, S.D.H.; Kuipers, F. Quantum Hair from Gravity. Phys. Rev. Lett. 2022, 128, 111301,
+https://doi.org/10.1103/PhysRevLett.128.111301.
+[18] Will, C.M.
+The Confrontation between General Relativity and Experiment.
+Living Rev. Relativ. 2014, 17, 4,
+https://doi.org/ 10.12942/lrr-2014-4.
+
+10
+[19] Berti, E.; et al. Testing General Relativity with Present and Future Astrophysical Observations. Class. Quant. Grav.
+2015, 32, 243001, https://doi.org/10.1088/0264-9381/32/24/243001.
+[20] Kanti, P.; Bakopoulos, A.; Pappas, N. Scalar-Gauss-Bonnet Theories: Evasion of No-Hair Theorems and novel black-hole
+solutions. PoS 2019, CORFU2018, 091. https://doi.org/10.22323/1.347.0091.
+[21] Sotiriou, T.P.; Zhou, S.Y. Black hole hair in generalized scalar-tensor gravity: An explicit example. Phys. Rev. D 2014,
+90, 124063, https://doi.org/10.1103/PhysRevD.90.124063.
+[22] Cavalcanti, R.T.; Alves, K.d.S.; Hoff da Silva, J.M. Near-Horizon Thermodynamics of Hairy Black Holes from Gravitational
+Decoupling. Universe 2022, 8, 363, https://doi.org/10.3390/universe8070363.
+[23] Casadio, R.; Cavalcanti, R.T.; Giugno, A.; Mureika, J. Horizon of quantum black holes in various dimensions. Phys. Lett.
+B 2016, 760, 36–44, https://doi.org/10.1016/j.physletb.2016.06.042.
+[24] Arsene, N.; Casadio, R.; Micu, O.
+Quantum production of black holes at colliders.
+Eur. Phys. J. C 2016, 76, 384,
+https://doi.org/10.1140/epjc/s10052-016-4228-0.
+[25] Ovalle, J. Decoupling gravitational sources in general relativity: From perfect to anisotropic fluids. Phys. Rev. D 2017,
+95, 104019, https://doi.org/10.1103/PhysRevD.95.104019.
+[26] Ovalle, J. Decoupling gravitational sources in general relativity: The extended case. Phys. Lett. B 2019, 788, 213–218,
+https://doi.org/10.1016/j.physletb.2018.11.029.
+[27] Ovalle, J.; Casadio, R.; Contreras, E.; Sotomayor, A. Hairy black holes by gravitational decoupling. Phys. Dark Univ.
+2021, 31, 100744, https://doi.org/10.1016/j.dark.2020.100744.
+[28] da Rocha, R.a. MGD Dirac stars. Symmetry 2020, 12, 508, https://doi.org/10.3390/sym12040508.
+[29] Tello-Ortiz, F.; Malaver, M.; Rinc´on, A.; Gomez-Leyton, Y. Relativistic anisotropic fluid spheres satisfying a non-linear
+equation of state. Eur. Phys. J. C 2020, 80, 371, https://doi.org/10.1140/epjc/s10052-020-7956-0.
+[30] da Rocha, R. Minimal geometric deformation of Yang-Mills-Dirac stellar configurations. Phys. Rev. D 2020, 102, 024011,
+https://doi.org/10.1103/PhysRevD.102.024011.
+[31] Fernandes-Silva, A.; Ferreira-Martins, A.J.; da Rocha, R. Extended quantum portrait of MGD black holes and information
+entropy. Phys. Lett. B 2019, 791, 323–330, https://doi.org/10.1016/j.physletb.2019.03.010.
+[32] da
+Rocha,
+R.
+Dark
+SU(N)
+glueball
+stars
+on
+fluid
+branes.
+Phys.
+Rev.
+D
+2017,
+95,
+124017,
+https://doi.org/10.1103/PhysRevD.95.124017.
+[33] Da Rocha, R.; Tomaz, A.A. Holographic entanglement entropy under the minimal geometric deformation and extensions.
+Eur. Phys. J. C 2019, 79, 1035, https://doi.org/10.1140/epjc/s10052-019-7558-x.
+[34] Ovalle, J.; Contreras, E.; Stuchlik, Z.
+Kerr–de Sitter black hole revisited.
+Phys. Rev. D 2021, 103, 084016,
+https://doi.org/10.1103/ PhysRevD.103.084016.
+[35] Meert, P.; da Rocha, R. Gravitational decoupling, hairy black holes and conformal anomalies. Eur. Phys. J. C 2022,
+82, 175, https://doi.org/10.1140/epjc/s10052-022-10121-6.
+[36] Cavalcanti, R.T.; de Paiva, R.C.; da Rocha, R. Echoes of the gravitational decoupling: Scalar perturbations and quasinor-
+mal modes of hairy black holes. Eur. Phys. J. Plus 2022, 137, 1185, https://doi.org/10.1140/epjp/s13360-022-03407-x.
+[37] Gross,
+D.J.;
+Mende,
+P.F.
+String Theory Beyond the Planck Scale.
+Nucl. Phys. B 1988,
+303, 407–454.
+https://doi.org/10.1016/0550-3213(88)90390-2.
+[38] Konishi, K.; Paffuti, G.; Provero, P.
+Minimum Physical Length and the Generalized Uncertainty Principle in String
+Theory. Phys. Lett. B 1990, 234, 276–284. https://doi.org/10.1016/0370-2693(90)91927-4.
+[39] Amati, D.; Ciafaloni, M.; Veneziano, G. Can Space-Time Be Probed Below the String Size? Phys. Lett. B 1989, 216, 41–47.
+https://doi.org/10.1016/0370-2693(89)91366-X.
+[40] Rovelli, C.; Smolin, L. Discreteness of area and volume in quantum gravity. Nucl. Phys. B 1995, 442, 593–622; Erratum
+in Nucl. Phys. B 1995, 456, 753–754, https://doi.org/10.1016/0550-3213(95)00150-Q.
+[41] Scardigli, F. Generalized uncertainty principle in quantum gravity from micro - black hole Gedanken experiment. Phys.
+Lett. B 1999, 452, 39–44, https://doi.org/10.1016/S0370-2693(99)00167-7.
+[42] Maggiore,
+M.
+A Generalized uncertainty principle in quantum gravity.
+Phys. Lett. B 1993,
+304, 65–69,
+https://doi.org/10.1016/0370-2693(93)91401-8.
+[43] Hossenfelder,
+S.
+Minimal Length Scale Scenarios for Quantum Gravity.
+Living Rev. Relativ. 2013,
+16, 2,
+https://doi.org/10.12942/lrr-2013-2.
+[44] Casadio, R.; Micu, O.; Nicolini, P. Minimum length effects in black hole physics. Fundam. Theor. Phys. 2015, 178, 293–322,
+https://doi.org/10.1007/978-3-319-10852-0 10.
+[45] Sprenger, M.; Nicolini, P.; Bleicher, M. Physics on Smallest Scales—An Introduction to Minimal Length Phenomenology.
+Eur. J. Phys. 2012, 33, 853–862, https://doi.org/10.1088/0143-0807/33/4/853.
+[46] Tawfik, A.N.; Diab, A.M.
+Review on Generalized Uncertainty Principle.
+Rept. Prog. Phys. 2015, 78, 126001,
+https://doi.org/ 10.1088/0034-4885/78/12/126001.
+[47] Casadio, R.; Giugno, A.; Micu, O. Horizon quantum mechanics: A hitchhiker’s guide to quantum black holes. Int. J. Mod.
+Phys. D 2016, 25, 1630006, https://doi.org/10.1142/S0218271816300068.
+[48] Casadio, R. Localised particles and fuzzy horizons: A tool for probing Quantum Black Holes. arXiv 2013, arXiv:1305.3195.
+[49] Casadio, R.; Giugno, A.; Giusti, A.; Lenzi, M. Quantum Formation of Primordial Black holes. Gen. Relativ. Grav. 2019,
+51, 103, https://doi.org/10.1007/s10714-019-2587-1.
+[50] Casadio,
+R.;
+Micu,
+O.
+Horizon Quantum Mechanics of collapsing shells.
+Eur. Phys. J. C 2018,
+78, 852,
+https://doi.org/10.1140/ epjc/s10052-018-6326-7.
+[51] Casadio, R.; Giugno, A.; Giusti, A. Global and Local Horizon Quantum Mechanics. Gen. Relativ. Grav. 2017, 49, 32,
+https://doi.org/10.1007/s10714-017-2198-7.
+

DNE1T4oBgHgl3EQfWQQt/content/tmp_files/2301.03111v1.pdf.txt

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+arXiv:2301.03111v1  [math.PR]  8 Jan 2023
+Stochastic Reservoir Calculations
+Steven Finch
+January 8, 2023
+Abstract.
+Prabhu (1958) obtained the stationary distribution of storage
+level Zt in a reservoir of finite volume v, given an inflow Xt and an outflow
+Yt.
+Time t is assumed to be discrete, Xt ∼ Gamma(p, µ) are independent
+and p is a positive integer.
+The mean inflow is p/µ; the target outflow is
+m (constant).
+We attempt to clarify intricate details, often omitted in the
+literature, by working through several examples.
+Of special interest are the
+probabilities of depletion (Zt = 0) and spillage (Zt = v).
+For prescribed
+{v, p, µ}, what value of m minimizes both of these?
+Let v > 0, p be a positive integer, µ > 0 and m > 0. At each time t = 1, 2, 3, . . .,
+a reservoir of volume v absorbs an inflow Xt ∼ Gamma(p, µ) and simultaneously
+releases an outflow 0 ≤ Yt ≤ m, depending on availablity. More precisely,
+Yt = min {Xt + Zt, m}
+where 0 ≤ Zt ≤ v is the storage level.
+Independence across time is assumed.
+Our
+interest is in the probability density function of Zt in the limit as t → ∞. We need
+not explicitly refer to Yt again, as Zt+1 can be defined recursively without it:
+Zt+1 = max {0, min {Xt + Zt − m, v}} ,
+Z1 = v/2.
+Let n = ⌊v/m⌋ and δ = v − m n.
+In words, δ is 0 if and only if v is an integer
+multiple of m, and δ is otherwise > 0. Let
+λ = (−1)p−1µp exp(−µ m).
+The graph of the PDF for Zt is piecewise smooth and contains at most n + 1 arcs, as
+well as point masses at z = 0 and z = v. The arcs are identified by j = 0, 1, 2, . . ., n
+from left to right, and correspond to open subintervals
+max {(j − 1)m + δ, 0} < z < min {j m + δ, v}
+of 0 < z < v. Prabhu [1] impressively obtained the cumulative distribution function
+F(z) = 1 − exp [µ(v − z)]
+p−1
+�
+r=0
+αr
+n−j
+�
+q=0
+(−λ)q (v − q m − z)q p+r
+(q p + r)!
+0Copyright © 2023 by Steven R. Finch. All rights reserved.
+1
+
+Stochastic Reservoir Calculations
+2
+that shall occupy us for the remainder of this paper.
+The αr coefficients are found
+by solving a system of p linear equations with coefficients drs for r, s = 0, 1, . . . , p−1.
+These will be defined shortly.
+Special considerations apply to endpoints.
+Let κ = n − 1 if δ = 0 and κ = n
+otherwise. The depletion probability, i.e., odds for the reservoir to be dry, is
+F(0) = 1 − exp(µ v)
+p−1
+�
+r=0
+αr
+κ
+�
+q=0
+(−λ)q (v − q m)q p+r
+(q p + r)!
+.
+In contrast, the spillage probability, i.e., odds for the reservoir to be full, is just
+1 − F(v) = α0.
+Minimizing the chance of both zero supply (harmful) and oversupply (wasteful) is
+clearly important. Other quantities of interest include the total deficit, i.e., unsatis-
+fied demand, over a specified time duration; and total surplus, i.e., unwanted supply
+(because v < ∞) that necessarily leaks into the environment.
+For r = 0, 1, . . . , p − 1, the linear system
+αr − λ
+p−1
+�
+s=0
+drs αs = (−µ)r exp [−µ(v + m)]
+p−r−1
+�
+s=0
+[µ(v + m)]s
+s!
+requires solution, where
+drs = (−1)p+r−1
+n
+�
+q=0
+(−λ)q
+v
+�
+q m
+(t − q m)q p+s(t + m)p−r−1
+(q p + s)!(p − r − 1)!
+dt.
+The integral can be easily expressed in closed-form.
+Prabhu’s CDF formula, given gamma-distributed inflow, extends a PDF formula
+discovered earlier by Moran [2], given exponentially distributed inflow (p = 1).
+We
+have not studied [2] in depth.
+More discussion of [1] appears in [3, 4, 5, 6].
+The
+treatment in [7, 8] is, however, most pragmatic and useful for our purposes.
+Henceforth we fix v = 1 and explore results for selected {p, µ, m}. It is surprising,
+more than fifty years after the publication of Prabhu’s work, that greater attention
+has not been paid to this research [7].
+We can only imagine that intricate details,
+often lost in theoretical summaries, have conspired to prevent greater understanding
+and widespread recognition.
+Our hope is that working through a few examples will
+help to improve matters.
+
+Stochastic Reservoir Calculations
+3
+1.
+{p, µ, m} =
+�
+1, 2, 1
+2
+�
+The mean inflow is p/µ = 1/2 and the target outflow is m = 1/2.
+Clearly n =
+⌊1/m⌋ = 2 and δ = 1 − m n = 0, i.e., there is no offset.
+The arcs j = 0, 1, 2
+correspond to intervals
+0 < z < 0,
+0 < z < 1/2,
+1/2 < z < 1
+and thus j = 0 can be ignored (being empty). Prabhu’s formula gives F(z) as
+1 − 1
+2 exp [µ(1 − z)] [2 − (1 − 2z) λ] α0
+for j = 1 and
+1 − exp [µ(1 − z)] α0
+for j = 2. The linear equation
+(1 − λ d00)α0 = exp
+�
+−3
+2µ
+�
+coupled with
+d00 = 1 − 1
+8λ
+and λ = 2e−1 give
+α0 =
+8
+8 − 8λ + λ2 exp
+�
+−3
+2µ
+�
+= 0.15000227...
+as the spillage probability. Because κ = n − 1 = 1,
+F(0) = 1 − 1
+2 exp(µ) (2 − λ) α0 = 0.29937324...
+is the depletion probability.
+One may have expected these two probabilities to be
+almost equal (since 1/µ = 1/2 = m and by a certain symmetry), but this is not true.
+The derivative f(z) of F(z) is plotted in Figure 1.
+2.
+{p, µ, m} =
+�
+1, 2, 1
+3
+�
+The mean inflow is p/µ = 1/2 and the target outflow is m = 1/3.
+Clearly n =
+⌊1/m⌋ = 3 and δ = 1 − m n = 0, i.e., there is no offset.
+The arcs j = 0, 1, 2, 3
+correspond to intervals
+0 < z < 0,
+0 < z < 1/3,
+1/3 < z < 2/3,
+2/3 < z < 1
+
+Stochastic Reservoir Calculations
+4
+and thus j = 0 can be ignored (being empty). Prabhu’s formula gives F(z) as
+1 − 1
+18 exp [µ(1 − z)]
+�
+18 − 6 (2 − 3z) λ + (1 − 3z)2λ2�
+α0
+for j = 1,
+1 − 1
+3 exp [µ(1 − z)] [3 − (2 − 3z) λ] α0
+for j = 2 and
+1 − exp [µ(1 − z)] α0
+for j = 3. The linear equation
+(1 − λ d00)α0 = exp
+�
+−4
+3µ
+�
+coupled with
+d00 = 1 − 2
+9λ +
+1
+162λ2
+and λ = 2e−2/3 give
+α0 =
+162
+162 − 162λ + 36λ2 − λ3 exp
+�
+−4
+3µ
+�
+= 0.34604845...
+as the spillage probability. Because κ = n − 1 = 1,
+F(0) = 1 − 1
+18 exp(µ)
+�
+18 − 12λ + λ2�
+α0 = 0.04363903...
+is the depletion probability. While α0 < F(0) in Section 1, we have α0 > F(0) here.
+This outcome suggests examining a value of m between 1/3 and 1/2. The derivative
+f(z) of F(z) is plotted in Figure 2.
+3.
+{p, µ, m} =
+�
+1, 2, 2
+5
+�
+The mean inflow is p/µ = 1/2 and the target outflow is m = 2/5.
+Clearly n =
+⌊1/m⌋ = 2 and δ = 1 − m n = 1/5, i.e., the offset is nonzero.
+The arcs j = 0, 1, 2
+correspond to intervals
+0 < z < 1/5,
+1/5 < z < 3/5,
+3/5 < z < 1;
+note that j = 0 has length only 1/5. Prabhu’s formula gives F(z) as
+1 − 1
+50 exp [µ(1 − z)]
+�
+50 − 10 (3 − 5z) λ + (1 − 5z)2λ2�
+α0
+
+Stochastic Reservoir Calculations
+5
+for j = 0,
+1 − 1
+5 exp [µ(1 − z)] [5 − (3 − 5z) λ] α0
+for j = 1 and
+1 − exp [µ(1 − z)] α0
+for j = 2. The linear equation
+(1 − λ d00)α0 = exp
+�
+−7
+5µ
+�
+coupled with
+d00 = 1 − 9
+50λ +
+1
+750λ2
+and λ = 2e−4/5 give
+α0 =
+750
+750 − 750λ + 135λ2 − λ3 exp
+�
+−7
+5µ
+�
+= 0.24745701...
+as the spillage probability. Because κ = n = 2,
+F(0) = 1 − 1
+50 exp(µ)
+�
+50 − 30λ + λ2�
+α0 = 0.12789671...
+is the depletion probability. The values α0 and F(0) are closer than in the previous
+two sections; a choice of m that is intermediate to 2/5 and 1/2 should make these
+coincident.
+We estimate that m = 0.44276 meets this objective (with 0.199 as the
+common probability). On the other hand, if our goal is to minimize the unweighted
+combination α0 + F(0), then m = 0.38 achieves the goal (with sum 0.372).
+The
+derivative f(z) of F(z) is plotted in Figure 3.
+4.
+{p, µ, m} =
+�
+2, 4, 1
+2
+�
+The mean inflow is p/µ = 1/2 and the target outflow is m = 1/2.
+Clearly n =
+⌊1/m⌋ = 2 and δ = 1 − m n = 0, i.e., there is no offset.
+The arcs j = 0, 1, 2
+correspond to intervals
+0 < z < 0,
+0 < z < 1/2,
+1/2 < z < 1
+and thus j = 0 can be ignored (being empty). Prabhu’s formula gives F(z) as
+1 − 1
+48 exp [µ(1 − z)]
+��
+48 − 6 (1 − 2z)2 λ
+�
+α0 +
+�
+48 − 48z − (1 − 2z)3 λ
+�
+α1
+�
+for j = 1 and
+1 − exp [µ(1 − z)] {α0 + (1 − z)α1}
+
+Stochastic Reservoir Calculations
+6
+for j = 2. The linear equations
+(1 − λ d00)α0 − λ d01α1 = exp
+�
+−3
+2µ
+� �
+1 + 3
+2µ
+�
+,
+λ d10α0 − (1 − λ d11)α1 = exp
+�
+−3
+2µ
+�
+µ
+coupled with
+d00 = −1 + 11
+384λ,
+d01 = − 7
+12 +
+7
+1920λ,
+d10 = 1 − 1
+48λ,
+d11 = 1
+2 −
+1
+384λ
+and λ = −16e−2 give
+α0 = 1
+2
+2 + 3µ − 2λ µ d01 − λ (2 + 3µ) d11
+1 − λ (d00 + d11) + λ2 (d00d11 − d01d10) exp
+�
+−3
+2µ
+�
+,
+α1 = 1
+2
+−2µ + 2λ µ d00 + λ (2 + 3µ) d10
+1 − λ (d00 + d11) + λ2 (d00d11 − d01d10) exp
+�
+−3
+2µ
+�
+;
+the spillage probability is hence α0 = 0.13554701.... Because κ = n − 1 = 1,
+F(0) = 1 − 1
+48 exp(µ) [(48 − 6λ) α0 + (48 − λ)α1] = 0.22163253...
+is the depletion probability. The mode of Gamma(2, µ) is 1/µ > 0 whereas the mode
+of Gamma(1, µ) is 0; a small inflow is less likely for p = 2 than for p = 1, thus F(0)
+is noticeably smaller than in Section 1.
+The tail of Gamma(2, µ) is fatter than the
+tail of Gamma(1, µ); a large inflow is more likely for p = 2 than for p = 1, however
+α0 is paradoxically smaller than in Section 1 (but only slightly). The derivative f(z)
+of F(z) is plotted in Figure 4.
+5.
+Invariance
+One verification of Prabhu’s formula is based on simulation (easily programmed, since
+the recurrence for Zt is straightforward).
+Another verification is more esoteric: to
+confirm that the formula is invariant under the transformation
+�
+v, p
+µ, m
+�
+�−→
+�
+˜v, p
+˜µ, ˜m
+�
+=
+� v
+m,
+p
+m µ, 1
+�
+in the sense that spillage & depletion probabilities should remain constant and storage
+level CDF arguments should simply scale by m. First,
+˜n =
+� ˜v
+˜m
+�
+=
+� v
+m
+�
+= n,
+
+Stochastic Reservoir Calculations
+7
+˜λ = (−1)p−1˜µp exp[−˜µ ˜m] = (−1)p−1(m µ)p exp[−m µ · 1] = mpλ
+and
+˜drs = (−1)p+r−1
+n
+�
+q=0
+(−˜λ)q
+˜v
+�
+q ˜m
+(t − q ˜m)q p+s(t + ˜m)p−r−1
+(q p + s)!(p − r − 1)!
+dt
+= (−1)p+r−1
+n
+�
+q=0
+mp q(−λ)q
+v/m
+�
+q
+(t − q)q p+s(t + 1)p−r−1
+(q p + s)!(p − r − 1)! dt
+= (−1)p+r−1
+n
+�
+q=0
+mp q(−λ)q
+v
+�
+q m
+( u
+m − q)q p+s( u
+m + 1)p−r−1
+(q p + s)!(p − r − 1)!
+du
+m
+upon setting u = m t, du = m dt; thus
+˜drs = (−1)p+r−1
+n
+�
+q=0
+mp q(−λ)q
+mp q+s+p−r−1+1
+v
+�
+q m
+(u − q m)q p+s(u + m)p−r−1
+(q p + s)!(p − r − 1)!
+du
+= m−(p−r+s)drs.
+Second,
+˜αr − ˜λ
+p−1
+�
+s=0
+˜drs ˜αs = (−˜µ)r exp [−˜µ(˜v + ˜m)]
+p−r−1
+�
+s=0
+[˜µ(˜v + ˜m)]s
+s!
+implies
+˜αr − mpλ
+p−1
+�
+s=0
+m−(p−r+s)drs ˜αs = mr(−µ)r exp [−µ(v + m)]
+p−r−1
+�
+s=0
+[µ(v + m)]s
+s!
+because ˜µ(˜v + ˜m) = m µ
+� v
+m + 1
+�
+= µ(v + m); therefore
+m−r ˜αr − λ
+p−1
+�
+s=0
+m−sdrs ˜αs = (−µ)r exp [−µ(v + m)]
+p−r−1
+�
+s=0
+[µ(v + m)]s
+s!
+which is immediately satisfied by ˜αr = mrαr. In particular, ˜α0 = α0. Third,
+˜δ = ˜v − ˜m n = v − m n
+m
+= δ
+m.
+
+Stochastic Reservoir Calculations
+8
+Figure 1: Plot of storage level density w = f(z) for {p, µ, m} =
+�
+1, 2, 1
+2
+�
+.
+Finally, given j,
+˜F(z) = 1 − exp [˜µ(˜v − z)]
+p−1
+�
+r=0
+˜αr
+n−j
+�
+q=0
+(−˜λ)q (˜v − q ˜m − z)q p+r
+(q p + r)!
+= 1 − exp
+�
+(m µ)
+� v
+m − z
+�� p−1
+�
+r=0
+mrαr
+n−j
+�
+q=0
+mp q(−λ)q ( v
+m − q − z)q p+r
+(q p + r)!
+= 1 − exp [µ(v − m z)]
+p−1
+�
+r=0
+mrαr
+n−j
+�
+q=0
+mp q(−λ)q
+mp q+r
+(v − q m − m z)q p+r
+(q p + r)!
+= F(m z)
+for (j − 1) ˜m + ˜δ < z < j ˜m + ˜δ, i.e., (j − 1)m + δ < m z < j m + δ. In the same way,
+˜F(0) = F(0), with the upper summation limit n − j replaced by ˜κ = κ.
+6.
+Inquiry
+Moran [9, 10] introduced a different model – in continuous time – for an infinite
+volume reservoir. Let X(t) ∼ Gamma(t, 1/ρ) denote the total inflow over the interval
+(0, t], assumed to be a nonnegative stochastic process with stationary independent
+increments, where 0 < ρ < 1 is constant.
+In particular, E(X(T)) = ρ t.
+Let the
+
+M
+8'0
+0.6
+0.4
+0.2
+0.0
+0.2
+0.4
+0.6
+8:0
+1.0Stochastic Reservoir Calculations
+9
+Figure 2: Plot of storage level density w = f(z) for {p, µ, m} =
+�
+1, 2, 1
+3
+�
+.
+Figure 3: Plot of storage level density w = f(z) for {p, µ, m} =
+�
+1, 2, 2
+5
+�
+.
+
+w
+1.2
+1.0
+0.8
+0.6
+0.4
+0.2
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0M
+1.2
+1.0
+0.8
+0.6
+0.4
+0.2
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0Stochastic Reservoir Calculations
+10
+Figure 4: Plot of storage level density w = f(z) for {p, µ, m} =
+�
+2, 4, 1
+2
+�
+.
+outflow be continuous and at unit rate except when the reservoir is empty. We have
+Z(t) = Z(0) + X(t) − t +
+t
+�
+0
+1{Z(τ)=0} dτ
+where 1Ω is the indicator function of Ω ⊆ R. By a limiting argument (from discrete
+to continuous), the PDF of Z(t) as t → ∞ has Laplace transform [11]
+(1 − ρ)θ
+θ − ln (1 + ρ θ),
+Re(θ) > 0
+which Daniels [12] inverted to yield
+f(z) = −(1 − ρ)
+∞
+�
+0
+d
+dz
+(z + w)w−1 exp [−(z + w)/ρ]
+ρwΓ(w)
+dw,
+z > 0
+with a point mass 1 − ρ at z = 0.
+We seek an experimental approach to verify
+this PDF.
+How might one efficiently simulate Z(t) for suitably large t?
+Offers of
+assistance would be most appreciated.
+We wonder too if Prabhu’s formula could
+possibly be reconfigured to play a role in this inquiry.
+The fact that v < ∞ earlier
+but v = ∞ here is an issue; the fact that Xt was the precise inflow at time t whereas
+X(t) is an accumulated inflow over (0, t] is another issue.
+
+0.8
+0.6
+0.4
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0Stochastic Reservoir Calculations
+11
+7.
+Acknowledgements
+Khaled Hamed was so kind to answer several questions of mine; this paper would not
+have been possible without his very helpful articles [7, 8]. In particular, he appears
+to be the first author to specify the role of the offset δ when v is not an integer
+multiple of m.
+I am grateful to innumerable software developers.
+The symbolic
+manipulations described here are tailor-made for Mathematica, and the simulations
+employed here to check predictions are ideal for R.
+References
+[1] N. U. Prabhu, On the integral equation for the finite dam, Quart. J. Math. 9
+(1958) 183–188; MR0099726.
+[2] P. A. P. Moran, A probability theory of dams and storage systems: modifications
+of the release rules, Austral. J. Appl. Sci. 6 (1955) 117–130; MR0077807.
+[3] P. A. P. Moran, The Theory of Storage, Wiley, 1959, pp. 39–51; MR0114254.
+[4] N. U. Prabhu, Queues and Inventories, Wiley, 1965, pp. 209–213; MR0211494.
+[5] P. Lochert and R. M. Phatarfod, On the problem of discretization in dam theory,
+Water Resources Research 15 (1979) 1593-1597.
+[6] E. H. Lloyd, The stochastic reservoir: exact and approximate evaluations of
+storage distribution, J. Hydrology 151 (1993) 65–107.
+[7] K. H. Hamed, On the implementation of Prabhu’s exact solution of the stochastic
+reservoir equation, Adv. in Water Resources 32 (2009) 594–606.
+[8] K. H. Hamed, Stochastic reservoir analysis, from Handbook of Engineering Hy-
+drology, ed. S. Eslamian, CRC Press, 2014, pp. 531–548.
+[9] P. A. P. Moran, A probability theory of a dam with a continuous release, Quart.
+J. Math. 7 (1956) 130–137; MR0101573.
+[10] J. Gani, Problems in the probability theory of storage systems, J. Royal Statist.
+Soc. Ser. B 19 (1957) 181–206; MR0092289.
+[11] D. G. Kendall, Some problems in the theory of dams, J. Royal Statist. Soc. Ser.
+B 19 (1957) 207–212.
+[12] H. E. Daniels, Discussion on the papers by Dr. Gani and Mr. Kendall, J. Royal
+Statist. Soc. Ser. B 19 (1957) 224–225.
+
+Stochastic Reservoir Calculations
+12
+Steven Finch
+MIT Sloan School of Management
+Cambridge, MA, USA
+steven fi[email protected]
+

DNE1T4oBgHgl3EQfWQQt/content/tmp_files/load_file.txt

@@ -0,0 +1,319 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf,len=318
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='03111v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='PR]  8 Jan 2023  Stochastic Reservoir Calculations  Steven Finch  January 8, 2023  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Prabhu (1958) obtained the stationary distribution of storage  level Zt in a reservoir of finite volume v, given an inflow Xt and an outflow  Yt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Time t is assumed to be discrete, Xt ∼ Gamma(p, µ) are independent  and p is a positive integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The mean inflow is p/µ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' the target outflow is  m (constant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  We attempt to clarify intricate details, often omitted in the  literature, by working through several examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Of special interest are the  probabilities of depletion (Zt = 0) and spillage (Zt = v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  For prescribed  {v, p, µ}, what value of m minimizes both of these?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Let v > 0, p be a positive integer, µ > 0 and m > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' At each time t = 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=',  a reservoir of volume v absorbs an inflow Xt ∼ Gamma(p, µ) and simultaneously  releases an outflow 0 ≤ Yt ≤ m, depending on availablity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' More precisely,  Yt = min {Xt + Zt, m}  where 0 ≤ Zt ≤ v is the storage level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Independence across time is assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Our  interest is in the probability density function of Zt in the limit as t → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' We need  not explicitly refer to Yt again, as Zt+1 can be defined recursively without it:  Zt+1 = max {0, min {Xt + Zt − m, v}} ,  Z1 = v/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Let n = ⌊v/m⌋ and δ = v − m n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  In words, δ is 0 if and only if v is an integer  multiple of m, and δ is otherwise > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Let  λ = (−1)p−1µp exp(−µ m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The graph of the PDF for Zt is piecewise smooth and contains at most n + 1 arcs, as  well as point masses at z = 0 and z = v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The arcs are identified by j = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', n  from left to right, and correspond to open subintervals  max {(j − 1)m + δ, 0} < z < min {j m + δ, v}  of 0 < z < v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Prabhu [1] impressively obtained the cumulative distribution function  F(z) = 1 − exp [µ(v − z)]  p−1  �  r=0  αr  n−j  �  q=0  (−λ)q (v − q m − z)q p+r  (q p + r)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  0Copyright © 2023 by Steven R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Finch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' All rights reserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  1  Stochastic Reservoir Calculations  2  that shall occupy us for the remainder of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The αr coefficients are found  by solving a system of p linear equations with coefficients drs for r, s = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' , p−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  These will be defined shortly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Special considerations apply to endpoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Let κ = n − 1 if δ = 0 and κ = n  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The depletion probability, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', odds for the reservoir to be dry, is  F(0) = 1 − exp(µ v)  p−1  �  r=0  αr  κ  �  q=0  (−λ)q (v − q m)q p+r  (q p + r)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  In contrast, the spillage probability, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', odds for the reservoir to be full, is just  1 − F(v) = α0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Minimizing the chance of both zero supply (harmful) and oversupply (wasteful) is  clearly important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Other quantities of interest include the total deficit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', unsatis-  fied demand, over a specified time duration;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' and total surplus, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', unwanted supply  (because v < ∞) that necessarily leaks into the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  For r = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' , p − 1, the linear system  αr − λ  p−1  �  s=0  drs αs = (−µ)r exp [−µ(v + m)]  p−r−1  �  s=0  [µ(v + m)]s  s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  requires solution, where  drs = (−1)p+r−1  n  �  q=0  (−λ)q  v  �  q m  (t − q m)q p+s(t + m)p−r−1  (q p + s)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' (p − r − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The integral can be easily expressed in closed-form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Prabhu’s CDF formula, given gamma-distributed inflow, extends a PDF formula  discovered earlier by Moran [2], given exponentially distributed inflow (p = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  We  have not studied [2] in depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  More discussion of [1] appears in [3, 4, 5, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The  treatment in [7, 8] is, however, most pragmatic and useful for our purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Henceforth we fix v = 1 and explore results for selected {p, µ, m}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' It is surprising,  more than fifty years after the publication of Prabhu’s work, that greater attention  has not been paid to this research [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  We can only imagine that intricate details,  often lost in theoretical summaries, have conspired to prevent greater understanding  and widespread recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Our hope is that working through a few examples will  help to improve matters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Stochastic Reservoir Calculations  3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  {p, µ, m} =  �  1, 2, 1  2  �  The mean inflow is p/µ = 1/2 and the target outflow is m = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Clearly n =  ⌊1/m⌋ = 2 and δ = 1 − m n = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', there is no offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The arcs j = 0, 1, 2  correspond to intervals  0 < z < 0,  0 < z < 1/2,  1/2 < z < 1  and thus j = 0 can be ignored (being empty).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Prabhu’s formula gives F(z) as  1 − 1  2 exp [µ(1 − z)] [2 − (1 − 2z) λ] α0  for j = 1 and  1 − exp [µ(1 − z)] α0  for j = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The linear equation  (1 − λ d00)α0 = exp  �  −3  2µ  �  coupled with  d00 = 1 − 1  8λ  and λ = 2e−1 give  α0 =  8  8 − 8λ + λ2 exp  �  −3  2µ  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='15000227.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  as the spillage probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Because κ = n − 1 = 1,  F(0) = 1 − 1  2 exp(µ) (2 − λ) α0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='29937324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  is the depletion probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  One may have expected these two probabilities to be  almost equal (since 1/µ = 1/2 = m and by a certain symmetry), but this is not true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The derivative f(z) of F(z) is plotted in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  {p, µ, m} =  �  1, 2, 1  3  �  The mean inflow is p/µ = 1/2 and the target outflow is m = 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Clearly n =  ⌊1/m⌋ = 3 and δ = 1 − m n = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', there is no offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The arcs j = 0, 1, 2, 3  correspond to intervals  0 < z < 0,  0 < z < 1/3,  1/3 < z < 2/3,  2/3 < z < 1  Stochastic Reservoir Calculations  4  and thus j = 0 can be ignored (being empty).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Prabhu’s formula gives F(z) as  1 − 1  18 exp [µ(1 − z)]  �  18 − 6 (2 − 3z) λ + (1 − 3z)2λ2�  α0  for j = 1,  1 − 1  3 exp [µ(1 − z)] [3 − (2 − 3z) λ] α0  for j = 2 and  1 − exp [µ(1 − z)] α0  for j = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The linear equation  (1 − λ d00)α0 = exp  �  −4  3µ  �  coupled with  d00 = 1 − 2  9λ +  1  162λ2  and λ = 2e−2/3 give  α0 =  162  162 − 162λ + 36λ2 − λ3 exp  �  −4  3µ  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='34604845.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  as the spillage probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Because κ = n − 1 = 1,  F(0) = 1 − 1  18 exp(µ)  �  18 − 12λ + λ2�  α0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='04363903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  is the depletion probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' While α0 < F(0) in Section 1, we have α0 > F(0) here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  This outcome suggests examining a value of m between 1/3 and 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The derivative  f(z) of F(z) is plotted in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  {p, µ, m} =  �  1, 2, 2  5  �  The mean inflow is p/µ = 1/2 and the target outflow is m = 2/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Clearly n =  ⌊1/m⌋ = 2 and δ = 1 − m n = 1/5, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', the offset is nonzero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The arcs j = 0, 1, 2  correspond to intervals  0 < z < 1/5,  1/5 < z < 3/5,  3/5 < z < 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  note that j = 0 has length only 1/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Prabhu’s formula gives F(z) as  1 − 1  50 exp [µ(1 − z)]  �  50 − 10 (3 − 5z) λ + (1 − 5z)2λ2�  α0  Stochastic Reservoir Calculations  5  for j = 0,  1 − 1  5 exp [µ(1 − z)] [5 − (3 − 5z) λ] α0  for j = 1 and  1 − exp [µ(1 − z)] α0  for j = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The linear equation  (1 − λ d00)α0 = exp  �  −7  5µ  �  coupled with  d00 = 1 − 9  50λ +  1  750λ2  and λ = 2e−4/5 give  α0 =  750  750 − 750λ + 135λ2 − λ3 exp  �  −7  5µ  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='24745701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  as the spillage probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Because κ = n = 2,  F(0) = 1 − 1  50 exp(µ)  �  50 − 30λ + λ2�  α0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='12789671.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  is the depletion probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The values α0 and F(0) are closer than in the previous  two sections;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' a choice of m that is intermediate to 2/5 and 1/2 should make these  coincident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  We estimate that m = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='44276 meets this objective (with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='199 as the  common probability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' On the other hand, if our goal is to minimize the unweighted  combination α0 + F(0), then m = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='38 achieves the goal (with sum 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='372).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The  derivative f(z) of F(z) is plotted in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  {p, µ, m} =  �  2, 4, 1  2  �  The mean inflow is p/µ = 1/2 and the target outflow is m = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Clearly n =  ⌊1/m⌋ = 2 and δ = 1 − m n = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', there is no offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The arcs j = 0, 1, 2  correspond to intervals  0 < z < 0,  0 < z < 1/2,  1/2 < z < 1  and thus j = 0 can be ignored (being empty).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Prabhu’s formula gives F(z) as  1 − 1  48 exp [µ(1 − z)]  ��  48 − 6 (1 − 2z)2 λ  �  α0 +  �  48 − 48z − (1 − 2z)3 λ  �  α1  �  for j = 1 and  1 − exp [µ(1 − z)] {α0 + (1 − z)α1}  Stochastic Reservoir Calculations  6  for j = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The linear equations  (1 − λ d00)α0 − λ d01α1 = exp  �  −3  2µ  � �  1 + 3  2µ  �  ,  λ d10α0 − (1 − λ d11)α1 = exp  �  −3  2µ  �  µ  coupled with  d00 = −1 + 11  384λ,  d01 = − 7  12 +  7  1920λ,  d10 = 1 − 1  48λ,  d11 = 1  2 −  1  384λ  and λ = −16e−2 give  α0 = 1  2  2 + 3µ − 2λ µ d01 − λ (2 + 3µ) d11  1 − λ (d00 + d11) + λ2 (d00d11 − d01d10) exp  �  −3  2µ  �  ,  α1 = 1  2  −2µ + 2λ µ d00 + λ (2 + 3µ) d10  1 − λ (d00 + d11) + λ2 (d00d11 − d01d10) exp  �  −3  2µ  �  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  the spillage probability is hence α0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='13554701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='. Because κ = n − 1 = 1,  F(0) = 1 − 1  48 exp(µ) [(48 − 6λ) α0 + (48 − λ)α1] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='22163253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  is the depletion probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The mode of Gamma(2, µ) is 1/µ > 0 whereas the mode  of Gamma(1, µ) is 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' a small inflow is less likely for p = 2 than for p = 1, thus F(0)  is noticeably smaller than in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The tail of Gamma(2, µ) is fatter than the  tail of Gamma(1, µ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' a large inflow is more likely for p = 2 than for p = 1, however  α0 is paradoxically smaller than in Section 1 (but only slightly).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' The derivative f(z)  of F(z) is plotted in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Invariance  One verification of Prabhu’s formula is based on simulation (easily programmed, since  the recurrence for Zt is straightforward).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Another verification is more esoteric: to  confirm that the formula is invariant under the transformation  �  v, p  µ, m  �  �−→  �  ˜v, p  ˜µ, ˜m  �  =  � v  m,  p  m µ, 1  �  in the sense that spillage & depletion probabilities should remain constant and storage  level CDF arguments should simply scale by m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' First,  ˜n =  � ˜v  ˜m  �  =  � v  m  �  = n,  Stochastic Reservoir Calculations  7  ˜λ = (−1)p−1˜µp exp[−˜µ ˜m] = (−1)p−1(m µ)p exp[−m µ · 1] = mpλ  and  ˜drs = (−1)p+r−1  n  �  q=0  (−˜λ)q  ˜v  �  q ˜m  (t − q ˜m)q p+s(t + ˜m)p−r−1  (q p + s)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' (p − r − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  dt  = (−1)p+r−1  n  �  q=0  mp q(−λ)q  v/m  �  q  (t − q)q p+s(t + 1)p−r−1  (q p + s)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' (p − r − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' dt  = (−1)p+r−1  n  �  q=0  mp q(−λ)q  v  �  q m  ( u  m − q)q p+s( u  m + 1)p−r−1  (q p + s)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' (p − r − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  du  m  upon setting u = m t, du = m dt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' thus  ˜drs = (−1)p+r−1  n  �  q=0  mp q(−λ)q  mp q+s+p−r−1+1  v  �  q m  (u − q m)q p+s(u + m)p−r−1  (q p + s)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' (p − r − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  du  = m−(p−r+s)drs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Second,  ˜αr − ˜λ  p−1  �  s=0  ˜drs ˜αs = (−˜µ)r exp [−˜µ(˜v + ˜m)]  p−r−1  �  s=0  [˜µ(˜v + ˜m)]s  s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  implies  ˜αr − mpλ  p−1  �  s=0  m−(p−r+s)drs ˜αs = mr(−µ)r exp [−µ(v + m)]  p−r−1  �  s=0  [µ(v + m)]s  s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  because ˜µ(˜v + ˜m) = m µ  � v  m + 1  �  = µ(v + m);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' therefore  m−r ˜αr − λ  p−1  �  s=0  m−sdrs ˜αs = (−µ)r exp [−µ(v + m)]  p−r−1  �  s=0  [µ(v + m)]s  s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  which is immediately satisfied by ˜αr = mrαr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' In particular, ˜α0 = α0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Third,  ˜δ = ˜v − ˜m n = v − m n  m  = δ  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Stochastic Reservoir Calculations  8  Figure 1: Plot of storage level density w = f(z) for {p, µ, m} =  �  1, 2, 1  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Finally, given j,  ˜F(z) = 1 − exp [˜µ(˜v − z)]  p−1  �  r=0  ˜αr  n−j  �  q=0  (−˜λ)q (˜v − q ˜m − z)q p+r  (q p + r)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  = 1 − exp  �  (m µ)  � v  m − z  �� p−1  �  r=0  mrαr  n−j  �  q=0  mp q(−λ)q ( v  m − q − z)q p+r  (q p + r)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  = 1 − exp [µ(v − m z)]  p−1  �  r=0  mrαr  n−j  �  q=0  mp q(−λ)q  mp q+r  (v − q m − m z)q p+r  (q p + r)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  = F(m z)  for (j − 1) ˜m + ˜δ < z < j ˜m + ˜δ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=', (j − 1)m + δ < m z < j m + δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' In the same way,  ˜F(0) = F(0), with the upper summation limit n − j replaced by ˜κ = κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Inquiry  Moran [9, 10] introduced a different model – in continuous time – for an infinite  volume reservoir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Let X(t) ∼ Gamma(t, 1/ρ) denote the total inflow over the interval  (0, t], assumed to be a nonnegative stochastic process with stationary independent  increments, where 0 < ρ < 1 is constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  In particular, E(X(T)) = ρ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content="  Let the  M  8'0  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='6  8:0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='0Stochastic Reservoir Calculations  9  Figure 2: Plot of storage level density w = f(z) for {p, µ, m} =  �  1, 2, 1  3  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Figure 3: Plot of storage level density w = f(z) for {p, µ, m} =  �  1, 2, 2  5  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  w  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
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+page_content='0M  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
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+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
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+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='0Stochastic Reservoir Calculations  10  Figure 4: Plot of storage level density w = f(z) for {p, µ, m} =  �  2, 4, 1  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  outflow be continuous and at unit rate except when the reservoir is empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' We have  Z(t) = Z(0) + X(t) − t +  t  �  0  1{Z(τ)=0} dτ  where 1Ω is the indicator function of Ω ⊆ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' By a limiting argument (from discrete  to continuous), the PDF of Z(t) as t → ∞ has Laplace transform [11]  (1 − ρ)θ  θ − ln (1 + ρ θ),  Re(θ) > 0  which Daniels [12] inverted to yield  f(z) = −(1 − ρ)  ∞  �  0  d  dz  (z + w)w−1 exp [−(z + w)/ρ]  ρwΓ(w)  dw,  z > 0  with a point mass 1 − ρ at z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  We seek an experimental approach to verify  this PDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  How might one efficiently simulate Z(t) for suitably large t?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Offers of  assistance would be most appreciated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  We wonder too if Prabhu’s formula could  possibly be reconfigured to play a role in this inquiry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The fact that v < ∞ earlier  but v = ∞ here is an issue;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' the fact that Xt was the precise inflow at time t whereas  X(t) is an accumulated inflow over (0, t] is another issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
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+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='0Stochastic Reservoir Calculations  11  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Acknowledgements  Khaled Hamed was so kind to answer several questions of mine;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' this paper would not  have been possible without his very helpful articles [7, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' In particular, he appears  to be the first author to specify the role of the offset δ when v is not an integer  multiple of m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  I am grateful to innumerable software developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  The symbolic  manipulations described here are tailor-made for Mathematica, and the simulations  employed here to check predictions are ideal for R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  References  [1] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Prabhu, On the integral equation for the finite dam, Quart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' 9  (1958) 183–188;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' MR0099726.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Moran, A probability theory of dams and storage systems: modifications  of the release rules, Austral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' 6 (1955) 117–130;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' MR0077807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Moran, The Theory of Storage, Wiley, 1959, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' 39–51;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' MR0114254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [4] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Prabhu, Queues and Inventories, Wiley, 1965, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' 209–213;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' MR0211494.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [5] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Lochert and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Phatarfod, On the problem of discretization in dam theory,  Water Resources Research 15 (1979) 1593-1597.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [6] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Lloyd, The stochastic reservoir: exact and approximate evaluations of  storage distribution, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Hydrology 151 (1993) 65–107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [7] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Hamed, On the implementation of Prabhu’s exact solution of the stochastic  reservoir equation, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' in Water Resources 32 (2009) 594–606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [8] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Hamed, Stochastic reservoir analysis, from Handbook of Engineering Hy-  drology, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Eslamian, CRC Press, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' 531–548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [9] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Moran, A probability theory of a dam with a continuous release, Quart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' 7 (1956) 130–137;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' MR0101573.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Gani, Problems in the probability theory of storage systems, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Royal Statist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' B 19 (1957) 181–206;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' MR0092289.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Kendall, Some problems in the theory of dams, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Royal Statist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  B 19 (1957) 207–212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  [12] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Daniels, Discussion on the papers by Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Gani and Mr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Kendall, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content=' Royal  Statist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
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+page_content=' B 19 (1957) 224–225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='  Stochastic Reservoir Calculations  12  Steven Finch  MIT Sloan School of Management  Cambridge, MA, USA  steven finch@harvard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}
+page_content='edu' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNE1T4oBgHgl3EQfWQQt/content/2301.03111v1.pdf'}

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