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on-line viterbi algorithm and its relationship to random walks | in this paper, we introduce the on-line viterbi algorithm for decoding hidden markov models (hmms) in much smaller than linear space. our analysis on two-state hmms suggests that the expected maximum memory used to decode sequence of length $n$ with $m$-state hmm can be as low as $\theta(m\log n)$, without a significant slow-down compared to the classical viterbi algorithm. classical viterbi algorithm requires $o(mn)$ space, which is impractical for analysis of long dna sequences (such as complete human genome chromosomes) and for continuous data streams. we also experimentally demonstrate the performance of the on-line viterbi algorithm on a simple hmm for gene finding on both simulated and real dna sequences. |
capacity of a multiple-antenna fading channel with a quantized precoding matrix | given a multiple-input multiple-output (mimo) channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. here we analyze the performance of random vector quantization (rvq), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. we assume that channel elements are i.i.d. and known to the receiver, which relays the optimal (rate-maximizing) precoder codebook index to the transmitter using b bits. we first derive the large system capacity of beamforming (rank-one precoding matrix) as a function of b, where large system refers to the limit as b and the number of transmit and receive antennas all go to infinity with fixed ratios. with beamforming rvq is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. the performance of rvq is also compared with that of a simpler reduced-rank scalar quantization scheme in which the beamformer is constrained to lie in a random subspace. we subsequently consider a precoding matrix with arbitrary rank, and approximate the asymptotic rvq performance with optimal and linear receivers (matched filter and minimum mean squared error (mmse)). numerical examples show that these approximations accurately predict the performance of finite-size systems of interest. given a target spectral efficiency, numerical examples show that the amount of feedback required by the linear mmse receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback. |
refuting the pseudo attack on the reesse1+ cryptosystem | we illustrate through example 1 and 2 that the condition at theorem 1 in [8] dissatisfies necessity, and the converse proposition of fact 1.1 in [8] does not hold, namely the condition z/m - l/ak < 1/(2 ak^2) is not sufficient for f(i) + f(j) = f(k). illuminate through an analysis and ex.3 that there is a logic error during deduction of fact 1.2, which causes each of fact 1.2, 1.3, 4 to be invalid. demonstrate through ex.4 and 5 that each or the combination of qu+1 > qu * d at fact 4 and table 1 at fact 2.2 is not sufficient for f(i) + f(j) = f(k), property 1, 2, 3, 4, 5 each are invalid, and alg.1 based on fact 4 and alg.2 based on table 1 are disordered and wrong logically. further, manifest through a repeated experiment and ex.5 that the data at table 2 is falsified, and the example in [8] is woven elaborately. we explain why cx = ax * w^f(x) (% m) is changed to cx = (ax * w^f(x))^d (% m) in reesse1+ v2.1. to the signature fraud, we point out that [8] misunderstands the existence of t^-1 and q^-1 % (m-1), and forging of q can be easily avoided through moving h. therefore, the conclusion of [8] that reesse1+ is not secure at all (which connotes that [8] can extract a related private key from any public key in reesse1+) is fully incorrect, and as long as the parameter omega is fitly selected, reesse1+ with cx = ax * w^f(x) (% m) is secure. |
optimal routing for decode-and-forward based cooperation in wireless networks | we investigate cooperative wireless relay networks in which the nodes can help each other in data transmission. we study different coding strategies in the single-source single-destination network with many relay nodes. given the myriad of ways in which nodes can cooperate, there is a natural routing problem, i.e., determining an ordered set of nodes to relay the data from the source to the destination. we find that for a given route, the decode-and-forward strategy, which is an information theoretic cooperative coding strategy, achieves rates significantly higher than that achievable by the usual multi-hop coding strategy, which is a point-to-point non-cooperative coding strategy. we construct an algorithm to find an optimal route (in terms of rate maximizing) for the decode-and-forward strategy. since the algorithm runs in factorial time in the worst case, we propose a heuristic algorithm that runs in polynomial time. the heuristic algorithm outputs an optimal route when the nodes transmit independent codewords. we implement these coding strategies using practical low density parity check codes to compare the performance of the strategies on different routes. |
on the kolmogorov-chaitin complexity for short sequences | a drawback of kolmogorov-chaitin complexity (k) as a function from s to the shortest program producing s is its noncomputability which limits its range of applicability. moreover, when strings are short, the dependence of k on a particular universal turing machine u can be arbitrary. in practice one can approximate it by computable compression methods. however, such compression methods do not always provide meaningful approximations--for strings shorter, for example, than typical compiler lengths. in this paper we suggest an empirical approach to overcome this difficulty and to obtain a stable definition of the kolmogorov-chaitin complexity for short sequences. additionally, a correlation in terms of distribution frequencies was found across the output of two models of abstract machines, namely unidimensional cellular automata and deterministic turing machine. |
optimal routing for the gaussian multiple-relay channel with decode-and-forward | in this paper, we study a routing problem on the gaussian multiple relay channel, in which nodes employ a decode-and-forward coding strategy. we are interested in routes for the information flow through the relays that achieve the highest df rate. we first construct an algorithm that provably finds optimal df routes. as the algorithm runs in factorial time in the worst case, we propose a polynomial time heuristic algorithm that finds an optimal route with high probability. we demonstrate that that the optimal (and near optimal) df routes are good in practice by simulating a distributed df coding scheme using low density parity check codes with puncturing and incremental redundancy. |
general-purpose computing on a semantic network substrate | this article presents a model of general-purpose computing on a semantic network substrate. the concepts presented are applicable to any semantic network representation. however, due to the standards and technological infrastructure devoted to the semantic web effort, this article is presented from this point of view. in the proposed model of computing, the application programming interface, the run-time program, and the state of the computing virtual machine are all represented in the resource description framework (rdf). the implementation of the concepts presented provides a practical computing paradigm that leverages the highly-distributed and standardized representational-layer of the semantic web. |
wdm and directed star arboricity | a digraph is $m$-labelled if every arc is labelled by an integer in $\{1, \dots,m\}$. motivated by wavelength assignment for multicasts in optical networks, we introduce and study $n$-fibre colourings of labelled digraphs. these are colourings of the arcs of $d$ such that at each vertex $v$, and for each colour $\alpha$, $in(v,\alpha)+out(v,\alpha)\leq n$ with $in(v,\alpha)$ the number of arcs coloured $\alpha$ entering $v$ and $out(v,\alpha)$ the number of labels $l$ such that there is at least one arc of label $l$ leaving $v$ and coloured with $\alpha$. the problem is to find the minimum number of colours $\lambda_n(d)$ such that the $m$-labelled digraph $d$ has an $n$-fibre colouring. in the particular case when $d$ is $1$-labelled, $\lambda_1(d)$ is called the directed star arboricity of $d$, and is denoted by $dst(d)$. we first show that $dst(d)\leq 2\delta^-(d)+1$, and conjecture that if $\delta^-(d)\geq 2$, then $dst(d)\leq 2\delta^-(d)$. we also prove that for a subcubic digraph $d$, then $dst(d)\leq 3$, and that if $\delta^+(d), \delta^-(d)\leq 2$, then $dst(d)\leq 4$. finally, we study $\lambda_n(m,k)=\max\{\lambda_n(d) \tq d \mbox{is $m$-labelled} \et \delta^-(d)\leq k\}$. we show that if $m\geq n$, then $\ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + c \frac{m^2\log k}{n}$ for some constant $c$. we conjecture that the lower bound should be the right value of $\lambda_n(m,k)$. |
soft constraint abstraction based on semiring homomorphism | the semiring-based constraint satisfaction problems (semiring csps), proposed by bistarelli, montanari and rossi \cite{bmr97}, is a very general framework of soft constraints. in this paper we propose an abstraction scheme for soft constraints that uses semiring homomorphism. to find optimal solutions of the concrete problem, the idea is, first working in the abstract problem and finding its optimal solutions, then using them to solve the concrete problem. in particular, we show that a mapping preserves optimal solutions if and only if it is an order-reflecting semiring homomorphism. moreover, for a semiring homomorphism $\alpha$ and a problem $p$ over $s$, if $t$ is optimal in $\alpha(p)$, then there is an optimal solution $\bar{t}$ of $p$ such that $\bar{t}$ has the same value as $t$ in $\alpha(p)$. |
block locally optimal preconditioned eigenvalue xolvers (blopex) in hypre and petsc | we describe our software package block locally optimal preconditioned eigenvalue xolvers (blopex) publicly released recently. blopex is available as a stand-alone serial library, as an external package to petsc (``portable, extensible toolkit for scientific computation'', a general purpose suite of tools for the scalable solution of partial differential equations and related problems developed by argonne national laboratory), and is also built into {\it hypre} (``high performance preconditioners'', scalable linear solvers package developed by lawrence livermore national laboratory). the present blopex release includes only one solver--the locally optimal block preconditioned conjugate gradient (lobpcg) method for symmetric eigenvalue problems. {\it hypre} provides users with advanced high-quality parallel preconditioners for linear systems, in particular, with domain decomposition and multigrid preconditioners. with blopex, the same preconditioners can now be efficiently used for symmetric eigenvalue problems. petsc facilitates the integration of independently developed application modules with strict attention to component interoperability, and makes blopex extremely easy to compile and use with preconditioners that are available via petsc. we present the lobpcg algorithm in blopex for {\it hypre} and petsc. we demonstrate numerically the scalability of blopex by testing it on a number of distributed and shared memory parallel systems, including a beowulf system, sun fire 880, an amd dual-core opteron workstation, and ibm bluegene/l supercomputer, using petsc domain decomposition and {\it hypre} multigrid preconditioning. we test blopex on a model problem, the standard 7-point finite-difference approximation of the 3-d laplacian, with the problem size in the range $10^5-10^8$. |
cryptanalysis of group-based key agreement protocols using subgroup distance functions | we introduce a new approach for cryptanalysis of key agreement protocols based on noncommutative groups. this approach uses functions that estimate the distance of a group element to a given subgroup. we test it against the shpilrain-ushakov protocol, which is based on thompson's group f. |
maximizing maximal angles for plane straight-line graphs | let $g=(s, e)$ be a plane straight-line graph on a finite point set $s\subset\r^2$ in general position. the incident angles of a vertex $p \in s$ of $g$ are the angles between any two edges of $g$ that appear consecutively in the circular order of the edges incident to $p$. a plane straight-line graph is called $\phi$-open if each vertex has an incident angle of size at least $\phi$. in this paper we study the following type of question: what is the maximum angle $\phi$ such that for any finite set $s\subset\r^2$ of points in general position we can find a graph from a certain class of graphs on $s$ that is $\phi$-open? in particular, we consider the classes of triangulations, spanning trees, and paths on $s$ and give tight bounds in most cases. |
mixed membership stochastic blockmodels | observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. in this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. this model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. we develop a general variational inference algorithm for fast approximate posterior inference. we explore applications to social and protein interaction networks. |
sampling colourings of the triangular lattice | we show that the glauber dynamics on proper 9-colourings of the triangular lattice is rapidly mixing, which allows for efficient sampling. consequently, there is a fully polynomial randomised approximation scheme (fpras) for counting proper 9-colourings of the triangular lattice. proper colourings correspond to configurations in the zero-temperature anti-ferromagnetic potts model. we show that the spin system consisting of proper 9-colourings of the triangular lattice has strong spatial mixing. this implies that there is a unique infinite-volume gibbs distribution, which is an important property studied in statistical physics. our results build on previous work by goldberg, martin and paterson, who showed similar results for 10 colours on the triangular lattice. their work was preceded by salas and sokal's 11-colour result. both proofs rely on computational assistance, and so does our 9-colour proof. we have used a randomised heuristic to guide us towards rigourous results. |
tropical implicitization and mixed fiber polytopes | the software trim offers implementations of tropical implicitization and tropical elimination, as developed by tevelev and the authors. given a polynomial map with generic coefficients, trim computes the tropical variety of the image. when the image is a hypersurface, the output is the newton polytope of the defining polynomial. trim can thus be used to compute mixed fiber polytopes, including secondary polytopes. |
getting started in probabilistic graphical models | probabilistic graphical models (pgms) have become a popular tool for computational analysis of biological data in a variety of domains. but, what exactly are they and how do they work? how can we use pgms to discover patterns that are biologically relevant? and to what extent can pgms help us formulate new hypotheses that are testable at the bench? this note sketches out some answers and illustrates the main ideas behind the statistical approach to biological pattern discovery. |
stability of boundary measures | we introduce the boundary measure at scale r of a compact subset of the n-dimensional euclidean space. we show how it can be computed for point clouds and suggest these measures can be used for feature detection. the main contribution of this work is the proof a quantitative stability theorem for boundary measures using tools of convex analysis and geometric measure theory. as a corollary we obtain a stability result for federer's curvature measures of a compact, allowing to compute them from point-cloud approximations of the compact. |
interference and outage in clustered wireless ad hoc networks | in the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous poisson point process. in this paper, the node locations are assumed to form a poisson clustered process on the plane. we derive the distributional properties of the interference and provide upper and lower bounds for its ccdf. we consider the probability of successful transmission in an interference limited channel when fading is modeled as rayleigh. we provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds.we show that when the transmitter-receiver distance is large, the success probability is greater than that of a poisson arrangement. these results characterize the performance of the system under geographical or mac-induced clustering. we obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a poisson arrangement of nodes. for the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of poisson cluster processes, the palm characterization of poisson cluster processes and the campbell-mecke theorem. |
approximations of lovasz extensions and their induced interaction index | the lovasz extension of a pseudo-boolean function $f : \{0,1\}^n \to r$ is defined on each simplex of the standard triangulation of $[0,1]^n$ as the unique affine function $\hat f : [0,1]^n \to r$ that interpolates $f$ at the $n+1$ vertices of the simplex. its degree is that of the unique multilinear polynomial that expresses $f$. in this paper we investigate the least squares approximation problem of an arbitrary lovasz extension $\hat f$ by lovasz extensions of (at most) a specified degree. we derive explicit expressions of these approximations. the corresponding approximation problem for pseudo-boolean functions was investigated by hammer and holzman (1992) and then solved explicitly by grabisch, marichal, and roubens (2000), giving rise to an alternative definition of banzhaf interaction index. similarly we introduce a new interaction index from approximations of $\hat f$ and we present some of its properties. it turns out that its corresponding power index identifies with the power index introduced by grabisch and labreuche (2001). |
determinacy in a synchronous pi-calculus | the s-pi-calculus is a synchronous pi-calculus which is based on the sl model. the latter is a relaxation of the esterel model where the reaction to the absence of a signal within an instant can only happen at the next instant. in the present work, we present and characterise a compositional semantics of the s-pi-calculus based on suitable notions of labelled transition system and bisimulation. based on this semantic framework, we explore the notion of determinacy and the related one of (local) confluence. |
the cyborg astrobiologist: porting from a wearable computer to the astrobiology phone-cam | we have used a simple camera phone to significantly improve an `exploration system' for astrobiology and geology. this camera phone will make it much easier to develop and test computer-vision algorithms for future planetary exploration. we envision that the `astrobiology phone-cam' exploration system can be fruitfully used in other problem domains as well. |
p-adic modelling of the genome and the genetic code | the present paper is devoted to foundations of p-adic modelling in genomics. considering nucleotides, codons, dna and rna sequences, amino acids, and proteins as information systems, we have formulated the corresponding p-adic formalisms for their investigations. each of these systems has its characteristic prime number used for construction of the related information space. relevance of this approach is illustrated by some examples. in particular, it is shown that degeneration of the genetic code is a p-adic phenomenon. we have also put forward a hypothesis on evolution of the genetic code assuming that primitive code was based on single nucleotides and chronologically first four amino acids. this formalism of p-adic genomic information systems can be implemented in computer programs and applied to various concrete cases. |
separable and low-rank continuous games | in this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. included in this subclass are all finite games and polynomial games. we investigate the structure of equilibria in separable games. we show that these games admit finitely supported nash equilibria. motivated by the bounds on the supports of mixed equilibria in two-player finite games in terms of the ranks of the payoff matrices, we define the notion of the rank of an n-player continuous game and use this to provide bounds on the cardinality of the support of equilibrium strategies. we present a general characterization theorem that states that a continuous game has finite rank if and only if it is separable. using our rank results, we present an efficient algorithm for computing approximate equilibria of two-player separable games with fixed strategy spaces in time polynomial in the rank of the game. |
mumford dendrograms | an effective $p$-adic encoding of dendrograms is presented through an explicit embedding into the bruhat-tits tree for a $p$-adic number field. this field depends on the number of children of a vertex and is a finite extension of the field of $p$-adic numbers. it is shown that fixing $p$-adic representatives of the residue field allows a natural way of encoding strings by identifying a given alphabet with such representatives. a simple $p$-adic hierarchic classification algorithm is derived for $p$-adic numbers, and is applied to strings over finite alphabets. examples of dna coding are presented and discussed. finally, new geometric and combinatorial invariants of time series of $p$-adic dendrograms are developped. |
complexity of propositional proofs under a promise | we study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of cnf formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an explicitly specified function $\lam$ in the number of variables $n$. to this end, we develop propositional proof systems under different measures of promises (that is, different $\lam$) as extensions of resolution. this is done by augmenting resolution with axioms that, roughly, can eliminate sets of truth assignments defined by boolean circuits. we then investigate the complexity of such systems, obtaining an exponential separation in the average-case between resolution under different size promises: 1. resolution has polynomial-size refutations for all unsatisfiable 3cnf formulas when the promise is $\eps\cd2^n$, for any constant $0<\eps<1$. 2. there are no sub-exponential size resolution refutations for random 3cnf formulas, when the promise is $2^{\delta n}$ (and the number of clauses is $o(n^{3/2})$), for any constant $0<\delta<1$. |
efficient divide-and-conquer implementations of symmetric fsas | a deterministic finite-state automaton (fsa) is an abstract sequential machine that reads the symbols comprising an input word one at a time. an fsa is symmetric if its output is independent of the order in which the input symbols are read, i.e., if the output is invariant under permutations of the input. we show how to convert a symmetric fsa a into an automaton-like divide-and-conquer process whose intermediate results are no larger than the size of a's memory. in comparison, a similar result for general fsa's has been long known via functional composition, but entails an exponential increase in memory size. the new result has applications to parallel processing and symmetric fsa networks. |
on perfect, amicable, and sociable chains | let $x = (x_0,...,x_{n-1})$ be an n-chain, i.e., an n-tuple of non-negative integers $< n$. consider the operator $s: x \mapsto x' = (x'_0,...,x'_{n-1})$, where x'_j represents the number of $j$'s appearing among the components of x. an n-chain x is said to be perfect if $s(x) = x$. for example, (2,1,2,0,0) is a perfect 5-chain. analogously to the theory of perfect, amicable, and sociable numbers, one can define from the operator s the concepts of amicable pair and sociable group of chains. in this paper we give an exhaustive list of all the perfect, amicable, and sociable chains. |
resolution over linear equations and multilinear proofs | we develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. we demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, tseitin graph tautologies and the clique-coloring tautologies in these proof systems. using the (monotone) interpolation by a communication game technique we establish an exponential-size lower bound on refutations in a certain, considerably strong, fragment of resolution over linear equations, as well as a general polynomial upper bound on (non-monotone) interpolants in this fragment. we then apply these results to extend and improve previous results on multilinear proofs (over fields of characteristic 0), as studied in [raztzameret06]. specifically, we show the following: 1. proofs operating with depth-3 multilinear formulas polynomially simulate a certain, considerably strong, fragment of resolution over linear equations. 2. proofs operating with depth-3 multilinear formulas admit polynomial-size refutations of the pigeonhole principle and tseitin graph tautologies. the former improve over a previous result that established small multilinear proofs only for the \emph{functional} pigeonhole principle. the latter are different than previous proofs, and apply to multilinear proofs of tseitin mod p graph tautologies over any field of characteristic 0. we conclude by connecting resolution over linear equations with extensions of the cutting planes proof system. |
optimal causal inference: estimating stored information and approximating causal architecture | we introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. we study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. we show that, in the limit in which a model complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. from this, one can estimate the amount of historical information the process stores. more generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. for nonideal cases with finite data, we show how the correct number of underlying causal states can be found by optimal causal estimation. a previously derived model complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid over-fitting. |
obstructions to genericity in study of parametric problems in control theory | we investigate systems of equations, involving parameters from the point of view of both control theory and computer algebra. the equations might involve linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference as well as more complicated ones, which act trivially on the parameters. such a system can be identified algebraically with a certain left module over a non-commutative algebra, where the operators commute with the parameters. we develop, implement and use in practice the algorithm for revealing all the expressions in parameters, for which e.g. homological properties of a system differ from the generic properties. we use groebner bases and groebner basics in rings of solvable type as main tools. in particular, we demonstrate an optimized algorithm for computing the left inverse of a matrix over a ring of solvable type. we illustrate the article with interesting examples. in particular, we provide a complete solution to the "two pendula, mounted on a cart" problem from the classical book of polderman and willems, including the case, where the friction at the joints is essential . to the best of our knowledge, the latter example has not been solved before in a complete way. |
a dichotomy theorem for general minimum cost homomorphism problem | in the constraint satisfaction problem ($csp$), the aim is to find an assignment of values to a set of variables subject to specified constraints. in the minimum cost homomorphism problem ($minhom$), one is additionally given weights $c_{va}$ for every variable $v$ and value $a$, and the aim is to find an assignment $f$ to the variables that minimizes $\sum_{v} c_{vf(v)}$. let $minhom(\gamma)$ denote the $minhom$ problem parameterized by the set of predicates allowed for constraints. $minhom(\gamma)$ is related to many well-studied combinatorial optimization problems, and concrete applications can be found in, for instance, defence logistics and machine learning. we show that $minhom(\gamma)$ can be studied by using algebraic methods similar to those used for csps. with the aid of algebraic techniques, we classify the computational complexity of $minhom(\gamma)$ for all choices of $\gamma$. our result settles a general dichotomy conjecture previously resolved only for certain classes of directed graphs, [gutin, hell, rafiey, yeo, european j. of combinatorics, 2008]. |
bounding the betti numbers and computing the euler-poincar\'e characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials | let $\r$ be a real closed field, $ {\mathcal q} \subset \r[y_1,...,y_\ell,x_1,...,x_k], $ with $ \deg_{y}(q) \leq 2, \deg_{x}(q) \leq d, q \in {\mathcal q}, #({\mathcal q})=m,$ and $ {\mathcal p} \subset \r[x_1,...,x_k] $ with $\deg_{x}(p) \leq d, p \in {\mathcal p}, #({\mathcal p})=s$, and $s \subset \r^{\ell+k}$ a semi-algebraic set defined by a boolean formula without negations, with atoms $p=0, p \geq 0, p \leq 0, p \in {\mathcal p} \cup {\mathcal q}$. we prove that the sum of the betti numbers of $s$ is bounded by \[ \ell^2 (o(s+\ell+m)\ell d)^{k+2m}. \] this is a common generalization of previous results on bounding the betti numbers of closed semi-algebraic sets defined by polynomials of degree $d$ and 2, respectively. we also describe an algorithm for computing the euler-poincar\'e characteristic of such sets, generalizing similar algorithms known before. the complexity of the algorithm is bounded by $(\ell s m d)^{o(m(m+k))}$. |
convolutional entanglement distillation | we develop a theory of entanglement distillation that exploits a convolutional coding structure. we provide a method for converting an arbitrary classical binary or quaternary convolutional code into a convolutional entanglement distillation protocol. the imported classical convolutional code does not have to be dual-containing or self-orthogonal. the yield and error-correcting properties of such a protocol depend respectively on the rate and error-correcting properties of the imported classical convolutional code. a convolutional entanglement distillation protocol has several other benefits. two parties sharing noisy ebits can distill noiseless ebits ``online'' as they acquire more noisy ebits. distillation yield is high and decoding complexity is simple for a convolutional entanglement distillation protocol. our theory of convolutional entanglement distillation reduces the problem of finding a good convolutional entanglement distillation protocol to the well-established problem of finding a good classical convolutional code. |
conjugates of characteristic sturmian words generated by morphisms | this article is concerned with characteristic sturmian words of slope $\alpha$ and $1-\alpha$ (denoted by $c_\alpha$ and $c_{1-\alpha}$ respectively), where $\alpha \in (0,1)$ is an irrational number such that $\alpha = [0;1+d_1,\bar{d_2,...,d_n}]$ with $d_n \geq d_1 \geq 1$. it is known that both $c_\alpha$ and $c_{1-\alpha}$ are fixed points of non-trivial (standard) morphisms $\sigma$ and $\hat{\sigma}$, respectively, if and only if $\alpha$ has a continued fraction expansion as above. accordingly, such words $c_\alpha$ and $c_{1-\alpha}$ are generated by the respective morphisms $\sigma$ and $\hat{\sigma}$. for the particular case when $\alpha = [0;2,\bar{r}]$ ($r\geq1$), we give a decomposition of each conjugate of $c_\alpha$ (and hence $c_{1-\alpha}$) into generalized adjoining singular words, by considering conjugates of powers of the standard morphism $\sigma$ by which it is generated. this extends a recent result of lev\'{e} and s\ee bold on conjugates of the infinite fibonacci word. |
occurrences of palindromes in characteristic sturmian words | this paper is concerned with palindromes occurring in characteristic sturmian words $c_\alpha$ of slope $\alpha$, where $\alpha \in (0,1)$ is an irrational. as $c_\alpha$ is a uniformly recurrent infinite word, any (palindromic) factor of $c_\alpha$ occurs infinitely many times in $c_\alpha$ with bounded gaps. our aim is to completely describe where palindromes occur in $c_\alpha$. in particular, given any palindromic factor $u$ of $c_\alpha$, we shall establish a decomposition of $c_\alpha$ with respect to the occurrences of $u$. such a decomposition shows precisely where $u$ occurs in $c_\alpha$, and this is directly related to the continued fraction expansion of $\alpha$. |
powers in a class of a-strict standard episturmian words | this paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic sturmian words. in particular, we explicitly determine all integer powers occurring in such infinite words, extending recent results of damanik and lenz (2003), who studied powers in sturmian words. the key tools in our analysis are canonical decompositions and a generalization of singular words, which were originally defined for the ubiquitous fibonacci word. our main results are demonstrated via some examples, including the $k$-bonacci word: a generalization of the fibonacci word to a $k$-letter alphabet ($k\geq2$). |
a characterization of fine words over a finite alphabet | to any infinite word w over a finite alphabet a we can associate two infinite words min(w) and max(w) such that any prefix of min(w) (resp. max(w)) is the lexicographically smallest (resp. greatest) amongst the factors of w of the same length. we say that an infinite word w over a is "fine" if there exists an infinite word u such that, for any lexicographic order, min(w) = au where a = min(a). in this paper, we characterize fine words; specifically, we prove that an infinite word w is fine if and only if w is either a "strict episturmian word" or a strict "skew episturmian word''. this characterization generalizes a recent result of g. pirillo, who proved that a fine word over a 2-letter alphabet is either an (aperiodic) sturmian word, or an ultimately periodic (but not periodic) infinite word, all of whose factors are (finite) sturmian. |
characterizations of finite and infinite episturmian words via lexicographic orderings | in this paper, we characterize by lexicographic order all finite sturmian and episturmian words, i.e., all (finite) factors of such infinite words. consequently, we obtain a characterization of infinite episturmian words in a "wide sense" (episturmian and episkew infinite words). that is, we characterize the set of all infinite words whose factors are (finite) episturmian. similarly, we characterize by lexicographic order all balanced infinite words over a 2-letter alphabet; in other words, all sturmian and skew infinite words, the factors of which are (finite) sturmian. |
a new distributed topology control algorithm for wireless environments with non-uniform path loss and multipath propagation | each node in a wireless multi-hop network can adjust the power level at which it transmits and thus change the topology of the network to save energy by choosing the neighbors with which it directly communicates. many previous algorithms for distributed topology control have assumed an ability at each node to deduce some location-based information such as the direction and the distance of its neighbor nodes with respect to itself. such a deduction of location-based information, however, cannot be relied upon in real environments where the path loss exponents vary greatly leading to significant errors in distance estimates. also, multipath effects may result in different signal paths with different loss characteristics, and none of these paths may be line-of-sight, making it difficult to estimate the direction of a neighboring node. in this paper, we present step topology control (stc), a simple distributed topology control algorithm which reduces energy consumption while preserving the connectivity of a heterogeneous sensor network without use of any location-based information. we show that the stc algorithm achieves the same or better order of communication and computational complexity when compared to other known algorithms that also preserve connectivity without the use of location-based information. we also present a detailed simulation-based comparative analysis of the energy savings and interference reduction achieved by the algorithms. the results show that, in spite of not incurring a higher communication or computational complexity, the stc algorithm performs better than other algorithms in uniform wireless environments and especially better when path loss characteristics are non-uniform. |
the graver complexity of integer programming | in this article we establish an exponential lower bound on the graver complexity of integer programs. this provides new type of evidence supporting the presumable intractability of integer programming. specifically, we show that the graver complexity of the incidence matrix of the complete bipartite graph $k_{3,m}$ satisfies $g(m)=\omega(2^m)$, with $g(m)\geq 17\cdot 2^{m-3}-7$ for every $m>3$ . |
toward psycho-robots | we try to perform geometrization of psychology by representing mental states, <<ideas>>, by points of a metric space, <<mental space>>. evolution of ideas is described by dynamical systems in metric mental space. we apply the mental space approach for modeling of flows of unconscious and conscious information in the human brain. in a series of models, models 1-4, we consider cognitive systems with increasing complexity of psychological behavior determined by structure of flows of ideas. since our models are in fact models of the ai-type, one immediately recognizes that they can be used for creation of ai-systems, which we call psycho-robots, exhibiting important elements of human psyche. creation of such psycho-robots may be useful improvement of domestic robots. at the moment domestic robots are merely simple working devices (e.g. vacuum cleaners or lawn mowers) . however, in future one can expect demand in systems which be able not only perform simple work tasks, but would have elements of human self-developing psyche. such ai-psyche could play an important role both in relations between psycho-robots and their owners as well as between psycho-robots. since the presence of a huge numbers of psycho-complexes is an essential characteristic of human psychology, it would be interesting to model them in the ai-framework. |
a complete proof of the graceful tree conjecture using the concept of edge degree | we show the graceful tree conjecture holds. |
h-decompositions | we show that for all graphs h of size n, the complete graph $k_{2n+1}$ has an $h$-decomposition. |
algebraic characterization of logically defined tree languages | we give an algebraic characterization of the tree languages that are defined by logical formulas using certain lindstr\"om quantifiers. an important instance of our result concerns first-order definable tree languages. our characterization relies on the usage of preclones, an algebraic structure introduced by the authors in a previous paper, and of the block product operation on preclones. our results generalize analogous results on finite word languages, but it must be noted that, as they stand, they do not yield an algorithm to decide whether a given regular tree language is first-order definable. |
an extension of a result concerning convex geometric graphs | we show a general result known as the erdos_sos conjecture: if $e(g)>{1/2}(k-1)n$ where $g$ has order $n$ then $g$ contains every tree of order $k+1$ as a subgraph. |
the extended edit distance metric | similarity search is an important problem in information retrieval. this similarity is based on a distance. symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high dimensional data objects. we propose a new distance metric that is applied to symbolic data objects and we test it on time series data bases in a classification task. we compare it to other distances that are well known in the literature for symbolic data objects. we also prove, mathematically, that our distance is metric. |
faster least squares approximation | least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. in a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with $n \gg d$. then, existing exact methods find a solution vector in $o(nd^2)$ time. we present two randomized algorithms that provide very accurate relative-error approximations to the optimal value and the solution vector of a least squares approximation problem more rapidly than existing exact algorithms. both of our algorithms preprocess the data with the randomized hadamard transform. one then uniformly randomly samples constraints and solves the smaller problem on those constraints, and the other performs a sparse random projection and solves the smaller problem on those projected coordinates. in both cases, solving the smaller problem provides relative-error approximations, and, if $n$ is sufficiently larger than $d$, the approximate solution can be computed in $o(nd \log d)$ time. |
a polynomial bound for untangling geometric planar graphs | to untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. pach and tardos [discrete comput. geom., 2002] asked if every n-vertex geometric planar graph can be untangled while keeping at least n^\epsilon vertices fixed. we answer this question in the affirmative with \epsilon=1/4. the previous best known bound was \omega((\log n / \log\log n)^{1/2}). we also consider untangling geometric trees. it is known that every n-vertex geometric tree can be untangled while keeping at least (n/3)^{1/2} vertices fixed, while the best upper bound was o(n\log n)^{2/3}. we answer a question of spillner and wolff [arxiv:0709.0170 2007] by closing this gap for untangling trees. in particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than 3(n^{1/2}-1) vertices fixed. moreover, we improve the lower bound to (n/2)^{1/2}. |
on the critical exponent of generalized thue-morse words | for certain generalized thue-morse words t, we compute the "critical exponent", i.e., the supremum of the set of rational numbers that are exponents of powers in t, and determine exactly the occurrences of powers realizing it. |
analyzing covert social network foundation behind terrorism disaster | this paper addresses a method to analyze the covert social network foundation hidden behind the terrorism disaster. it is to solve a node discovery problem, which means to discover a node, which functions relevantly in a social network, but escaped from monitoring on the presence and mutual relationship of nodes. the method aims at integrating the expert investigator's prior understanding, insight on the terrorists' social network nature derived from the complex graph theory, and computational data processing. the social network responsible for the 9/11 attack in 2001 is used to execute simulation experiment to evaluate the performance of the method. |
a multi-level blocking distinct degree factorization algorithm | we give a new algorithm for performing the distinct-degree factorization of a polynomial p(x) over gf(2), using a multi-level blocking strategy. the coarsest level of blocking replaces gcd computations by multiplications, as suggested by pollard (1975), von zur gathen and shoup (1992), and others. the novelty of our approach is that a finer level of blocking replaces multiplications by squarings, which speeds up the computation in gf(2)[x]/p(x) of certain interval polynomials when p(x) is sparse. as an application we give a fast algorithm to search for all irreducible trinomials x^r + x^s + 1 of degree r over gf(2), while producing a certificate that can be checked in less time than the full search. naive algorithms cost o(r^2) per trinomial, thus o(r^3) to search over all trinomials of given degree r. under a plausible assumption about the distribution of factors of trinomials, the new algorithm has complexity o(r^2 (log r)^{3/2}(log log r)^{1/2}) for the search over all trinomials of degree r. our implementation achieves a speedup of greater than a factor of 560 over the naive algorithm in the case r = 24036583 (a mersenne exponent). using our program, we have found two new primitive trinomials of degree 24036583 over gf(2) (the previous record degree was 6972593). |
a numerical algorithm for zero counting. i: complexity and accuracy | we describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. the algorithm performs o(n d kappa(f)) iterations where n is the number of polynomials (as well as the dimension of the ambient space), d is a bound on the polynomials' degree, and kappa(f) is a condition number for the system. each iteration uses an exponential number of operations. the algorithm uses finite-precision arithmetic and a polynomial bound for the precision required to ensure the returned output is correct is exhibited. this bound is a major feature of our algorithm since it is in contrast with the exponential precision required by the existing (symbolic) algorithms for counting real zeros. the algorithm parallelizes well in the sense that each iteration can be computed in parallel polynomial time with an exponential number of processors. |
on compositions of numbers and graphs | the main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. these problems are of general interest for discrete mathematics including a new twig of a bough of theory of graphs i.e. a given graph compositions. the problems result from and are served in the entourage of series of exercises with hints based predominantly on the second reference and other related recent papers. |
node discovery problem for a social network | methods to solve a node discovery problem for a social network are presented. covert nodes refer to the nodes which are not observable directly. they transmit the influence and affect the resulting collaborative activities among the persons in a social network, but do not appear in the surveillance logs which record the participants of the collaborative activities. discovering the covert nodes is identifying the suspicious logs where the covert nodes would appear if the covert nodes became overt. the performance of the methods is demonstrated with a test dataset generated from computationally synthesized networks and a real organization. |
analog chaos-based secure communications and cryptanalysis: a brief survey | a large number of analog chaos-based secure communication systems have been proposed since the early 1990s exploiting the technique of chaos synchronization. a brief survey of these chaos-based cryptosystems and of related cryptanalytic results is given. some recently proposed countermeasures against known attacks are also introduced. |
cryptanalysis of an image encryption scheme based on a new total shuffling algorithm | chaotic systems have been broadly exploited through the last two decades to build encryption methods. recently, two new image encryption schemes have been proposed, where the encryption process involves a permutation operation and an xor-like transformation of the shuffled pixels, which are controlled by three chaotic systems. this paper discusses some defects of the schemes and how to break them with a chosen-plaintext attack. |
cryptanalysis of a computer cryptography scheme based on a filter bank | this paper analyzes the security of a recently-proposed signal encryption scheme based on a filter bank. a very critical weakness of this new signal encryption procedure is exploited in order to successfully recover the associated secret key. |
an interface group for process components | we take a process component as a pair of an interface and a behaviour. we study the composition of interacting process components in the setting of process algebra. we formalize the interfaces of interacting process components by means of an interface group. an interesting feature of the interface group is that it allows for distinguishing between expectations and promises in interfaces of process components. this distinction comes into play in case components with both client and server behaviour are involved. |
on the operating unit size of load/store architectures | we introduce a strict version of the concept of a load/store instruction set architecture in the setting of maurer machines. we take the view that transformations on the states of a maurer machine are achieved by applying threads as considered in thread algebra to the maurer machine. we study how the transformations on the states of the main memory of a strict load/store instruction set architecture that can be achieved by applying threads depend on the operating unit size, the cardinality of the instruction set, and the maximal number of states of the threads. |
a thread calculus with molecular dynamics | we present a theory of threads, interleaving of threads, and interaction between threads and services with features of molecular dynamics, a model of computation that bears on computations in which dynamic data structures are involved. threads can interact with services of which the states consist of structured data objects and computations take place by means of actions which may change the structure of the data objects. the features introduced include restriction of the scope of names used in threads to refer to data objects. because that feature makes it troublesome to provide a model based on structural operational semantics and bisimulation, we construct a projective limit model for the theory. |
predicting relevant empty spots in social interaction | an empty spot refers to an empty hard-to-fill space which can be found in the records of the social interaction, and is the clue to the persons in the underlying social network who do not appear in the records. this contribution addresses a problem to predict relevant empty spots in social interaction. homogeneous and inhomogeneous networks are studied as a model underlying the social interaction. a heuristic predictor function approach is presented as a new method to address the problem. simulation experiment is demonstrated over a homogeneous network. a test data in the form of baskets is generated from the simulated communication. precision to predict the empty spots is calculated to demonstrate the performance of the presented approach. |
asymptotic capacity of wireless ad hoc networks with realistic links under a honey comb topology | we consider the effects of rayleigh fading and lognormal shadowing in the physical interference model for all the successful transmissions of traffic across the network. new bounds are derived for the capacity of a given random ad hoc wireless network that reflect packet drop or capture probability of the transmission links. these bounds are based on a simplified network topology termed as honey-comb topology under a given routing and scheduling scheme. |
algorithmic arithmetic fewnomial theory i: one variable | withdrawn by the authors due to an error in the proof of the finite field result (thm. 1.5): the random primes used in the proof need not avoid the exceptional primes from lemma 2.7, thus leaving thm. 1.5 unproved. |
natural realizations of sparsity matroids | a hypergraph g with n vertices and m hyperedges with d endpoints each is (k,l)-sparse if for all sub-hypergraphs g' on n' vertices and m' edges, m'\le kn'-l. for integers k and l satisfying 0\le l\le dk-1, this is known to be a linearly representable matroidal family. motivated by problems in rigidity theory, we give a new linear representation theorem for the (k,l)-sparse hypergraphs that is natural; i.e., the representing matrix captures the vertex-edge incidence structure of the underlying hypergraph g. |
an estimation of distribution algorithm with intelligent local search for rule-based nurse rostering | this paper proposes a new memetic evolutionary algorithm to achieve explicit learning in rule-based nurse rostering, which involves applying a set of heuristic rules for each nurse's assignment. the main framework of the algorithm is an estimation of distribution algorithm, in which an ant-miner methodology improves the individual solutions produced in each generation. unlike our previous work (where learning is implicit), the learning in the memetic estimation of distribution algorithm is explicit, i.e. we are able to identify building blocks directly. the overall approach learns by building a probabilistic model, i.e. an estimation of the probability distribution of individual nurse-rule pairs that are used to construct schedules. the local search processor (i.e. the ant-miner) reinforces nurse-rule pairs that receive higher rewards. a challenging real world nurse rostering problem is used as the test problem. computational results show that the proposed approach outperforms most existing approaches. it is suggested that the learning methodologies suggested in this paper may be applied to other scheduling problems where schedules are built systematically according to specific rules |
instruction sequences with dynamically instantiated instructions | we study sequential programs that are instruction sequences with dynamically instantiated instructions. we define the meaning of such programs in two different ways. in either case, we give a translation by which each program with dynamically instantiated instructions is turned into a program without them that exhibits on execution the same behaviour by interaction with some service. the complexity of the translations differ considerably, whereas the services concerned are equally simple. however, the service concerned in the case of the simpler translation is far more powerful than the service concerned in the other case. |
evolving localizations in reaction-diffusion cellular automata | we consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in each one state. we employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules is required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems. |
reconstruction of markov random fields from samples: some easy observations and algorithms | markov random fields are used to model high dimensional distributions in a number of applied areas. much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the markov random fields. we analyze a simple algorithm for reconstructing the underlying graph defining a markov random field on $n$ nodes and maximum degree $d$ given observations. we show that under mild non-degeneracy conditions it reconstructs the generating graph with high probability using $\theta(d \epsilon^{-2}\delta^{-4} \log n)$ samples where $\epsilon,\delta$ depend on the local interactions. for most local interaction $\eps,\delta$ are of order $\exp(-o(d))$. our results are optimal as a function of $n$ up to a multiplicative constant depending on $d$ and the strength of the local interactions. our results seem to be the first results for general models that guarantee that {\em the} generating model is reconstructed. furthermore, we provide explicit $o(n^{d+2} \epsilon^{-2}\delta^{-4} \log n)$ running time bound. in cases where the measure on the graph has correlation decay, the running time is $o(n^2 \log n)$ for all fixed $d$. we also discuss the effect of observing noisy samples and show that as long as the noise level is low, our algorithm is effective. on the other hand, we construct an example where large noise implies non-identifiability even for generic noise and interactions. finally, we briefly show that in some simple cases, models with hidden nodes can also be recovered. |
two-connected graphs with prescribed three-connected components | we adapt the classical 3-decomposition of any 2-connected graph to the case of simple graphs (no loops or multiple edges). by analogy with the block-cutpoint tree of a connected graph, we deduce from this decomposition a bicolored tree tc(g) associated with any 2-connected graph g, whose white vertices are the 3-components of g (3-connected components or polygons) and whose black vertices are bonds linking together these 3-components, arising from separating pairs of vertices of g. two fundamental relationships on graphs and networks follow from this construction. the first one is a dissymmetry theorem which leads to the expression of the class b=b(f) of 2-connected graphs, all of whose 3-connected components belong to a given class f of 3-connected graphs, in terms of various rootings of b. the second one is a functional equation which characterizes the corresponding class r=r(f) of two-pole networks all of whose 3-connected components are in f. all the rootings of b are then expressed in terms of f and r. there follow corresponding identities for all the associated series, in particular the edge index series. numerous enumerative consequences are discussed. |
entanglement-assisted quantum convolutional coding | we show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. we exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. our construction produces a calderbank-shor-steane (css) entanglement-assisted quantum convolutional code from two arbitrary classical binary convolutional codes. the rate and error-correcting properties of the classical convolutional codes directly determine the corresponding properties of the resulting entanglement-assisted quantum convolutional code. we explain how to encode our css entanglement-assisted quantum convolutional codes starting from a stream of information qubits, ancilla qubits, and shared entangled bits. |
distinguishing short quantum computations | distinguishing logarithmic depth quantum circuits on mixed states is shown to be complete for qip, the class of problems having quantum interactive proof systems. circuits in this model can represent arbitrary quantum processes, and thus this result has implications for the verification of implementations of quantum algorithms. the distinguishability problem is also complete for qip on constant depth circuits containing the unbounded fan-out gate. these results are shown by reducing a qip-complete problem to a logarithmic depth version of itself using a parallelization technique. |
algorithmic permutation of part of the torah | a small part of the torah is arranged into a two dimensional array. the characters are then permuted using a simple recursive deterministic algorithm. the various permutations are then passed through three stochastic filters and one deterministic filter to identify the permutations which most closely approximate readable biblical hebrew. of the 15 billion sequences available at the second level of recursion, 800 pass the a priori thresholds set for each filter. the resulting "biblical hebrew" text is available for inspection and the generation of further material continues. |
on the monotonicity of the generalized marcum and nuttall q-functions | monotonicity criteria are established for the generalized marcum q-function, $\emph{q}_{m}$, the standard nuttall q-function, $\emph{q}_{m,n}$, and the normalized nuttall q-function, $\mathcal{q}_{m,n}$, with respect to their real order indices m,n. besides, closed-form expressions are derived for the computation of the standard and normalized nuttall q-functions for the case when m,n are odd multiples of 0.5 and $m\geq n$. by exploiting these results, novel upper and lower bounds for $\emph{q}_{m,n}$ and $\mathcal{q}_{m,n}$ are proposed. furthermore, specific tight upper and lower bounds for $\emph{q}_{m}$, previously reported in the literature, are extended for real values of m. the offered theoretical results can be efficiently applied in the study of digital communications over fading channels, in the information-theoretic analysis of multiple-input multiple-output systems and in the description of stochastic processes in probability theory, among others. |
on the maximum span of fixed-angle chains | soss proved that it is np-hard to find the maximum 2d span of a fixed-angle polygonal chain: the largest distance achievable between the endpoints in a planar embedding. these fixed-angle chains can serve as models of protein backbones. the corresponding problem in 3d is open. we show that three special cases of particular relevance to the protein model are solvable in polynomial time. when all link lengths and all angles are equal, the maximum 3d span is achieved in a flat configuration and can be computed in constant time. when all angles are equal and the chain is simple (non-self-crossing), the maximum flat span can be found in linear time. in 3d, when all angles are equal to 90 deg (but the link lengths arbitrary), the maximum 3d span is in general nonplanar but can be found in quadratic time. |
episturmian words: a survey | in this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of sturmian words on two letters. after recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words. some properties of factors are described, including factor complexity, palindromes, fractional powers, frequencies, and return words. we also consider lexicographical properties of episturmian words, as well as their connection to the balance property, and related notions such as finite episturmian words, arnoux-rauzy sequences, and "episkew words" that generalize the skew words of morse and hedlund. |
palindromic richness | in this paper, we study combinatorial and structural properties of a new class of finite and infinite words that are 'rich' in palindromes in the utmost sense. a characteristic property of so-called "rich words" is that all complete returns to any palindromic factor are themselves palindromes. these words encompass the well-known episturmian words, originally introduced by the second author together with x. droubay and g. pirillo in 2001. other examples of rich words have appeared in many different contexts. here we present the first unified approach to the study of this intriguing family of words. amongst our main results, we give an explicit description of the periodic rich infinite words and show that the recurrent balanced rich infinite words coincide with the balanced episturmian words. we also consider two wider classes of infinite words, namely "weakly rich words" and almost rich words (both strictly contain all rich words, but neither one is contained in the other). in particular, we classify all recurrent balanced weakly rich words. as a consequence, we show that any such word on at least three letters is necessarily episturmian; hence weakly rich words obey fraenkel's conjecture. likewise, we prove that a certain class of almost rich words obeys fraenkel's conjecture by showing that the recurrent balanced ones are episturmian or contain at least two distinct letters with the same frequency. lastly, we study the action of morphisms on (almost) rich words with particular interest in morphisms that preserve (almost) richness. such morphisms belong to the class of "p-morphisms" that was introduced by a. hof, o. knill, and b. simon in 1995. |
computational approach to the emergence and evolution of language - evolutionary naming game model | computational modelling with multi-agent systems is becoming an important technique of studying language evolution. we present a brief introduction into this rapidly developing field, as well as our own contributions that include an analysis of the evolutionary naming-game model. in this model communicating agents, that try to establish a common vocabulary, are equipped with an evolutionarily selected learning ability. such a coupling of biological and linguistic ingredients results in an abrupt transition: upon a small change of the model control parameter a poorly communicating group of linguistically unskilled agents transforms into almost perfectly communicating group with large learning abilities. genetic imprinting of the learning abilities proceeds via baldwin effect: initially unskilled communicating agents learn a language and that creates a niche in which there is an evolutionary pressure for the increase of learning ability. under the assumption that communication intensity increases continuously with finite speed, the transition is split into several transition-like changes. it shows that the speed of cultural changes, that sets an additional characteristic timescale, might be yet another factor affecting the evolution of language. in our opinion, this model shows that linguistic and biological processes have a strong influence on each other and this effect certainly has contributed to an explosive development of our species. |
an algorithm for road coloring | a coloring of edges of a finite directed graph turns the graph into finite-state automaton. the synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. a coloring of edges of a directed graph of uniform outdegree (constant outdegree of any vertex) is synchronizing if the coloring turns the graph into a deterministic finite automaton possessing a synchronizing word. the road coloring problem is the problem of synchronizing coloring of a directed finite strongly connected graph of uniform outdegree if the greatest common divisor of the lengths of all its cycles is one. the problem posed in 1970 had evoked a noticeable interest among the specialists in the theory of graphs, automata, codes, symbolic dynamics as well as among the wide mathematical community. a polynomial time algorithm of $o(n^3)$ complexity in the most worst case and quadratic in majority of studied cases for the road coloring of the considered graph is presented below. the work is based on recent positive solution of the road coloring problem. the algorithm was implemented in the package testas |
a pyramidal evolutionary algorithm with different inter-agent partnering strategies for scheduling problems | this paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. the effects of different partner selection schemes amongst the agents on solution quality are examined for two multiple-choice optimisation problems. it is shown that partnering strategies that exploit problem-specific knowledge are superior and can counter inappropriate (sub-) fitness measurements. |
on the effects of idiotypic interactions for recommendation communities in artificial immune systems | it has previously been shown that a recommender based on immune system idiotypic principles can out perform one based on correlation alone. this paper reports the results of work in progress, where we undertake some investigations into the nature of this beneficial effect. the initial findings are that the immune system recommender tends to produce different neighbourhoods, and that the superior performance of this recommender is due partly to the different neighbourhoods, and partly to the way that the idiotypic effect is used to weight each neighbours recommendations. |
a recommender system based on the immune network | the immune system is a complex biological system with a highly distributed, adaptive and self-organising nature. this paper presents an artificial immune system (ais) that exploits some of these characteristics and is applied to the task of film recommendation by collaborative filtering (cf). natural evolution and in particular the immune system have not been designed for classical optimisation. however, for this problem, we are not interested in finding a single optimum. rather we intend to identify a sub-set of good matches on which recommendations can be based. it is our hypothesis that an ais built on two central aspects of the biological immune system will be an ideal candidate to achieve this: antigen - antibody interaction for matching and antibody - antibody interaction for diversity. computational results are presented in support of this conjecture and compared to those found by other cf techniques. |
the danger theory and its application to artificial immune systems | over the last decade, a new idea challenging the classical self-non-self viewpoint has become popular amongst immunologists. it is called the danger theory. in this conceptual paper, we look at this theory from the perspective of artificial immune system practitioners. an overview of the danger theory is presented with particular emphasis on analogies in the artificial immune systems world. a number of potential application areas are then used to provide a framing for a critical assessment of the concept, and its relevance for artificial immune systems. |
partnering strategies for fitness evaluation in a pyramidal evolutionary algorithm | this paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. the effects of different partner selection schemes for (sub-)fitness evaluation purposes are examined for two multiple-choice optimisation problems. it is shown that random partnering strategies perform best by providing better sampling and more diversity. |
on minimality of convolutional ring encoders | convolutional codes are considered with code sequences modelled as semi-infinite laurent series. it is wellknown that a convolutional code c over a finite group g has a minimal trellis representation that can be derived from code sequences. it is also wellknown that, for the case that g is a finite field, any polynomial encoder of c can be algebraically manipulated to yield a minimal polynomial encoder whose controller canonical realization is a minimal trellis. in this paper we seek to extend this result to the finite ring case g = z_{p^r} by introducing a socalled "p-encoder". we show how to manipulate a polynomial encoding of a noncatastrophic convolutional code over z_{p^r} to produce a particular type of p-encoder ("minimal p-encoder") whose controller canonical realization is a minimal trellis with nonlinear features. the minimum number of trellis states is then expressed as p^gamma, where gamma is the sum of the row degrees of the minimal p-encoder. in particular, we show that any convolutional code over z_{p^r} admits a delay-free p-encoder which implies the novel result that delay-freeness is not a property of the code but of the encoder, just as in the field case. we conjecture that a similar result holds with respect to catastrophicity, i.e., any catastrophic convolutional code over z_{p^r} admits a noncatastrophic p-encoder. |
a bayesian optimisation algorithm for the nurse scheduling problem | a bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurses assignment. unlike our previous work that used gas to implement implicit learning, the learning in the proposed algorithm is explicit, ie. eventually, we will be able to identify and mix building blocks directly. the bayesian optimization algorithm is applied to implement such explicit learning by building a bayesian network of the joint distribution of solutions. the conditional probability of each variable in the network is computed according to an initial set of promising solutions. subsequently, each new instance for each variable is generated, ie in our case, a new rule string has been obtained. another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. if stopping conditions are not met, the conditional probabilities for all nodes in the bayesian network are updated again using the current set of promising rule strings. computational results from 52 real data instances demonstrate the success of this approach. it is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems. |
strategic alert throttling for intrusion detection systems | network intrusion detection systems are themselves becoming targets of attackers. alert flood attacks may be used to conceal malicious activity by hiding it among a deluge of false alerts sent by the attacker. although these types of attacks are very hard to stop completely, our aim is to present techniques that improve alert throughput and capacity to such an extent that the resources required to successfully mount the attack become prohibitive. the key idea presented is to combine a token bucket filter with a realtime correlation algorithm. the proposed algorithm throttles alert output from the ids when an attack is detected. the attack graph used in the correlation algorithm is used to make sure that alerts crucial to forming strategies are not discarded by throttling. |
movie recommendation systems using an artificial immune system | we apply the artificial immune system (ais) technology to the collaborative filtering (cf) technology when we build the movie recommendation system. two different affinity measure algorithms of ais, kendall tau and weighted kappa, are used to calculate the correlation coefficients for this movie recommendation system. from the testing we think that weighted kappa is more suitable than kendall tau for movie problems. |
investigating artificial immune systems for job shop rescheduling in changing environments | artificial immune system can be used to generate schedules in changing environments and it has been proven to be more robust than schedules developed using a genetic algorithm. good schedules can be produced especially when the number of the antigens is increased. however, an increase in the range of the antigens had somehow affected the fitness of the immune system. in this research, we are trying to improve the result of the system by rescheduling the same problem using the same method while at the same time maintaining the robustness of the schedules. |
artificial immune systems (ais) - a new paradigm for heuristic decision making | over the last few years, more and more heuristic decision making techniques have been inspired by nature, e.g. evolutionary algorithms, ant colony optimisation and simulated annealing. more recently, a novel computational intelligence technique inspired by immunology has emerged, called artificial immune systems (ais). this immune system inspired technique has already been useful in solving some computational problems. in this keynote, we will very briefly describe the immune system metaphors that are relevant to ais. we will then give some illustrative real-world problems suitable for ais use and show a step-by-step algorithm walkthrough. a comparison of ais to other well-known algorithms and areas for future work will round this keynote off. it should be noted that as ais is still a young and evolving field, there is not yet a fixed algorithm template and hence actual implementations might differ somewhat from the examples given here. |
on the complexity of finding gapped motifs | this paper has been withdrawn by the corresponding author because the newest version is now published in journal of discrete algorithms. |
mimo networks: the effects of interference | multiple-input/multiple-output (mimo) systems promise enormous capacity increase and are being considered as one of the key technologies for future wireless networks. however, the decrease in capacity due to the presence of interferers in mimo networks is not well understood. in this paper, we develop an analytical framework to characterize the capacity of mimo communication systems in the presence of multiple mimo co-channel interferers and noise. we consider the situation in which transmitters have no information about the channel and all links undergo rayleigh fading. we first generalize the known determinant representation of hypergeometric functions with matrix arguments to the case when the argument matrices have eigenvalues of arbitrary multiplicity. this enables the derivation of the distribution of the eigenvalues of gaussian quadratic forms and wishart matrices with arbitrary correlation, with application to both single user and multiuser mimo systems. in particular, we derive the ergodic mutual information for mimo systems in the presence of multiple mimo interferers. our analysis is valid for any number of interferers, each with arbitrary number of antennas having possibly unequal power levels. this framework, therefore, accommodates the study of distributed mimo systems and accounts for different positions of the mimo interferers. |
doubly-generalized ldpc codes: stability bound over the bec | the iterative decoding threshold of low-density parity-check (ldpc) codes over the binary erasure channel (bec) fulfills an upper bound depending only on the variable and check nodes with minimum distance 2. this bound is a consequence of the stability condition, and is here referred to as stability bound. in this paper, a stability bound over the bec is developed for doubly-generalized ldpc codes, where the variable and the check nodes can be generic linear block codes, assuming maximum a posteriori erasure correction at each node. it is proved that in this generalized context as well the bound depends only on the variable and check component codes with minimum distance 2. a condition is also developed, namely the derivative matching condition, under which the bound is achieved with equality. |
a connection between palindromic and factor complexity using return words | in this paper we prove that for any infinite word w whose set of factors is closed under reversal, the following conditions are equivalent: (i) all complete returns to palindromes are palindromes; (ii) p(n) + p(n+1) = c(n+1) - c(n) + 2 for all n, where p (resp. c) denotes the palindromic complexity (resp. factor complexity) function of w, which counts the number of distinct palindromic factors (resp. factors) of each length in w. |
new type stirling like numbers - an email style letter | the notion of the fibonacci cobweb poset from [1] has been naturally extended to any admissible sequence $f$ in [2] where it was also recognized that the celebrated prefab notion of bender and goldman [3] - (see also [4,5]) - admits such an extension so as to encompass the new type combinatorial objects from [2] as leading examples. recently the present author had introduced also [6] two natural partial orders in there: one $\leq$ in grading-natural subsets of cobweb`s prefabs sets [2] and in the second proposal one endows the set sums of the so called "prefabiants" with such another partial order that one arrives at bell-like numbers including fibonacci triad sequences introduced by the present author in [7]. here we quote the basic observations concerning the new type stirling like numbers as they appear in [6]. for more on notation, stirling like numbers of the first kind and for proofs - see [6]. |
exploiting problem structure in a genetic algorithm approach to a nurse rostering problem | there is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. however, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and constraints that typically occurs in such problems. in order to overcome this, successful implementations frequently make use of problem specific knowledge. this paper is concerned with the development of a ga for a nurse rostering problem at a major uk hospital. the structure of the constraints is used as the basis for a co-evolutionary strategy using co-operating sub-populations. problem specific knowledge is also used to define a system of incentives and disincentives, and a complementary mutation operator. empirical results based on 52 weeks of live data show how these features are able to improve an unsuccessful canonical ga to the point where it is able to provide a practical solution to the problem |
well-centered triangulation | meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual voronoi diagram). this is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. we prove that well-centered meshes also have optimality properties and relationships to delaunay and minmax angle triangulations. we present an iterative algorithm that seeks to transform a given triangulation in two or three dimensions into a well-centered one by minimizing a cost function and moving the interior vertices while keeping the mesh connectivity and boundary vertices fixed. the cost function is a direct result of a new characterization of well-centeredness in arbitrary dimensions that we present. ours is the first optimization-based heuristic for well-centeredness, and the first one that applies in both two and three dimensions. we show the results of applying our algorithm to small and large two-dimensional meshes, some with a complex boundary, and obtain a well-centered tetrahedralization of the cube. we also show numerical evidence that our algorithm preserves gradation and that it improves the maximum and minimum angles of acute triangulations created by the best known previous method. |
essential variables and positions in terms | the paper deals with $\sigma-$composition of terms, which allows us to extend the derivation rules in formal deduction of identities. the concept of essential variables and essential positions of terms with respect to a set of identities is a key step in the simplification of the process of formal deduction. $\sigma-$composition of terms is defined as replacement between $\sigma$-equal terms. this composition induces $\sigma r-$deductively closed sets of identities. in analogy to balanced identities we introduce and investigate $\sigma-$balanced identities for a given set of identities $\sigma$. |
fixed point and aperiodic tilings | an aperiodic tile set was first constructed by r.berger while proving the undecidability of the domino problem. it turned out that aperiodic tile sets appear in many topics ranging from logic (the entscheidungsproblem) to physics (quasicrystals) we present a new construction of an aperiodic tile set that is based on kleene's fixed-point construction instead of geometric arguments. this construction is similar to j. von neumann self-reproducing automata; similar ideas were also used by p. gacs in the context of error-correcting computations. the flexibility of this construction allows us to construct a "robust" aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. this property was not known for any of the existing aperiodic tile sets. |
capacity of general discrete noiseless channels | this paper concerns the capacity of the discrete noiseless channel introduced by shannon. a sufficient condition is given for the capacity to be well-defined. for a general discrete noiseless channel allowing non-integer valued symbol weights, it is shown that the capacity--if well-defined--can be determined from the radius of convergence of its generating function, from the smallest positive pole of its generating function, or from the rightmost real singularity of its complex generating function. a generalisation is given for pringsheim's theorem and for the exponential growth formula to generating functions of combinatorial structures with non-integer valued symbol weights. |
pure exploration for multi-armed bandit problems | we consider the framework of stochastic multi-armed bandit problems and study the possibilities and limitations of forecasters that perform an on-line exploration of the arms. these forecasters are assessed in terms of their simple regret, a regret notion that captures the fact that exploration is only constrained by the number of available rounds (not necessarily known in advance), in contrast to the case when the cumulative regret is considered and when exploitation needs to be performed at the same time. we believe that this performance criterion is suited to situations when the cost of pulling an arm is expressed in terms of resources rather than rewards. we discuss the links between the simple and the cumulative regret. one of the main results in the case of a finite number of arms is a general lower bound on the simple regret of a forecaster in terms of its cumulative regret: the smaller the latter, the larger the former. keeping this result in mind, we then exhibit upper bounds on the simple regret of some forecasters. the paper ends with a study devoted to continuous-armed bandit problems; we show that the simple regret can be minimized with respect to a family of probability distributions if and only if the cumulative regret can be minimized for it. based on this equivalence, we are able to prove that the separable metric spaces are exactly the metric spaces on which these regrets can be minimized with respect to the family of all probability distributions with continuous mean-payoff functions. |
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