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arxiv-676701 | math/0405082 | On the List and Bounded Distance Decodibility of the Reed-Solomon Codes | <|reference_start|>On the List and Bounded Distance Decodibility of the Reed-Solomon Codes: In this paper show that the list and bounded-distance decoding problems of certain bounds for the Reed-Solomon code are at least as hard as the discrete logarithm problem over finite fields.<|reference_end|> | arxiv | @article{cheng2004on,
title={On the List and Bounded Distance Decodibility of the Reed-Solomon Codes},
author={Qi Cheng and Daqing Wan},
journal={arXiv preprint arXiv:math/0405082},
year={2004},
archivePrefix={arXiv},
eprint={math/0405082},
primaryClass={math.NT cs.IT math.IT}
} | cheng2004on |
arxiv-676702 | math/0405577 | On $\psi$-basic bernoulli-wardian polynomials | <|reference_start|>On $\psi$-basic bernoulli-wardian polynomials: The wardian solution of any $\psi$-difference linear nonhomogeneous equation is found in the framework of the generalized finite operator calculus . Specifications to $q$-calculus case and the new one fibonomial calculus case are made explicit.<|reference_end|> | arxiv | @article{kwasniewski2004on,
title={On $\psi$-basic bernoulli-wardian polynomials},
author={A.K.Kwasniewski},
journal={Bulletin de la Societe des Sciences et des Lettres de
{\pounds}\'od\^e (54) Serie: Recherches sur les Deformations Vol. 45 (2004)
5-10},
year={2004},
archivePrefix={arXiv},
eprint={math/0405577},
primaryClass={math.CO cs.DM}
} | kwasniewski2004on |
arxiv-676703 | math/0405578 | $\psi$-Appell polynomials` solutions of an umbral difference nonhomogeneous equation | <|reference_start|>$\psi$-Appell polynomials` solutions of an umbral difference nonhomogeneous equation: One discovers why the solution of generalized umbral calculus difference nonhomogeneous equation in the form recently proposed by the author extends here now to generalized appellian delta operator and corresponding polynomials case almost automatically. The reason for that is just the proper framework of the generalized finite operator calculus recently being developed by the present author.<|reference_end|> | arxiv | @article{kwasniewski2004$\psi$-appell,
title={$\psi$-Appell polynomials` solutions of an umbral difference
nonhomogeneous equation},
author={A.K.Kwasniewski},
journal={Bulletin de la Societe des Sciences et des Lettres de
{\pounds}\'od\^e (54) Serie: Recherches sur les Deformations Vol. 45 (2004)
11-15},
year={2004},
archivePrefix={arXiv},
eprint={math/0405578},
primaryClass={math.CO cs.DM}
} | kwasniewski2004$\psi$-appell |
arxiv-676704 | math/0405591 | Fibonacci q-gaussian sequences | <|reference_start|>Fibonacci q-gaussian sequences: The summation formula within pascalian triangle resulting in the fibonacci sequence is extended to the $q$-binomial coefficients $q$-gaussian triangles.<|reference_end|> | arxiv | @article{kwasniewski2004fibonacci,
title={Fibonacci q-gaussian sequences},
author={A.K.Kwasniewski},
journal={Advanced Studies in Contemporary Mathematics vol. 8 (2004) No2
pp.121-124},
year={2004},
archivePrefix={arXiv},
eprint={math/0405591},
primaryClass={math.CO cs.DM}
} | kwasniewski2004fibonacci |
arxiv-676705 | math/0406006 | Fibonomial cumulative connection constants | <|reference_start|>Fibonomial cumulative connection constants: In this note we present examples of cumulative connection constants included new fibonomial ones. All examples posses combinatorial interpretation.<|reference_end|> | arxiv | @article{kwasniewski2004fibonomial,
title={Fibonomial cumulative connection constants},
author={A.K.Kwasniewski},
journal={Bulletin of the ICA vol. 44 (2005) 81-92},
year={2004},
archivePrefix={arXiv},
eprint={math/0406006},
primaryClass={math.CO cs.DM}
} | kwasniewski2004fibonomial |
arxiv-676706 | math/0406077 | A tutorial introduction to the minimum description length principle | <|reference_start|>A tutorial introduction to the minimum description length principle: This tutorial provides an overview of and introduction to Rissanen's Minimum Description Length (MDL) Principle. The first chapter provides a conceptual, entirely non-technical introduction to the subject. It serves as a basis for the technical introduction given in the second chapter, in which all the ideas of the first chapter are made mathematically precise. The main ideas are discussed in great conceptual and technical detail. This tutorial is an extended version of the first two chapters of the collection "Advances in Minimum Description Length: Theory and Application" (edited by P.Grunwald, I.J. Myung and M. Pitt, to be published by the MIT Press, Spring 2005).<|reference_end|> | arxiv | @article{grunwald2004a,
title={A tutorial introduction to the minimum description length principle},
author={Peter Grunwald},
journal={arXiv preprint arXiv:math/0406077},
year={2004},
archivePrefix={arXiv},
eprint={math/0406077},
primaryClass={math.ST cs.IT cs.LG math.IT stat.TH}
} | grunwald2004a |
arxiv-676707 | math/0406094 | Merging costs for the additive Marcus-Lushnikov process, and Union-Find algorithms | <|reference_start|>Merging costs for the additive Marcus-Lushnikov process, and Union-Find algorithms: Starting with a monodisperse configuration with $n$ size-1 particles, an additive Marcus-Lushnikov process evolves until it reaches its final state (a unique particle with mass $n$). At each of the $n-1$ steps of its evolution, a merging cost is incurred, that depends on the sizes of the two particles involved, and on an independent random factor. This paper deals with the asymptotic behaviour of the cumulated costs up to the $k$th clustering, under various regimes for $(n,k)$, with applications to the study of Union--Find algorithms.<|reference_end|> | arxiv | @article{chassaing2004merging,
title={Merging costs for the additive Marcus-Lushnikov process, and Union-Find
algorithms},
author={Philippe Chassaing, Regine Marchand},
journal={arXiv preprint arXiv:math/0406094},
year={2004},
archivePrefix={arXiv},
eprint={math/0406094},
primaryClass={math.PR cs.DS math.CO}
} | chassaing2004merging |
arxiv-676708 | math/0406140 | The structure and labelled enumeration of K_3,3-subdivision-free projective-planar graphs | <|reference_start|>The structure and labelled enumeration of K_3,3-subdivision-free projective-planar graphs: We consider the class F of 2-connected non-planar K_{3,3}-subdivision-free graphs that are embeddable in the projective plane. We show that these graphs admit a unique decomposition as a graph K_5 (the core) where the edges are replaced by two-pole networks constructed from 2-connected planar graphs. A method to enumerate these graphs in the labelled case is described. Moreover, we enumerate the homeomorphically irreducible graphs in F and homeomorphically irreducible 2-connected planar graphs. Particular use is made of two-pole directed series-parallel networks. We also show that the number m of edges of graphs in F with n vertices satisfies the bound m <=3n-6, for n >= 6.<|reference_end|> | arxiv | @article{gagarin2004the,
title={The structure and labelled enumeration of K_{3,3}-subdivision-free
projective-planar graphs},
author={Andrei Gagarin, Gilbert Labelle and Pierre Leroux (LaCIM, Universite
du Quebec a Montreal)},
journal={Pure Math. Appl. 16 (2005), no. 3, pp. 267-286},
year={2004},
archivePrefix={arXiv},
eprint={math/0406140},
primaryClass={math.CO cs.DM}
} | gagarin2004the |
arxiv-676709 | math/0406221 | Suboptimal behaviour of Bayes and MDL in classification under misspecification | <|reference_start|>Suboptimal behaviour of Bayes and MDL in classification under misspecification: We show that forms of Bayesian and MDL inference that are often applied to classification problems can be *inconsistent*. This means there exists a learning problem such that for all amounts of data the generalization errors of the MDL classifier and the Bayes classifier relative to the Bayesian posterior both remain bounded away from the smallest achievable generalization error.<|reference_end|> | arxiv | @article{grunwald2004suboptimal,
title={Suboptimal behaviour of Bayes and MDL in classification under
misspecification},
author={Peter Grunwald and John Langford},
journal={arXiv preprint arXiv:math/0406221},
year={2004},
archivePrefix={arXiv},
eprint={math/0406221},
primaryClass={math.ST cs.IT cs.LG math.IT stat.TH}
} | grunwald2004suboptimal |
arxiv-676710 | math/0406258 | The logarithmic fibbinomial formula | <|reference_start|>The logarithmic fibbinomial formula: Roman logarithmic binomial formula analogue has been found . It is presented here also for the case of fibonomial coefficients which recently have been given a combinatorial interpretation by the present author.<|reference_end|> | arxiv | @article{kwasniewski2004the,
title={The logarithmic fibbinomial formula},
author={A.K.Kwasniewski},
journal={Adv. Stud. Contemp. Math. v.9 No.1 (2004) 19-26},
year={2004},
archivePrefix={arXiv},
eprint={math/0406258},
primaryClass={math.CO cs.DM}
} | kwasniewski2004the |
arxiv-676711 | math/0406353 | On metric Ramsey-type phenomena | <|reference_start|>On metric Ramsey-type phenomena: The main question studied in this article may be viewed as a nonlinear analogue of Dvoretzky's theorem in Banach space theory or as part of Ramsey theory in combinatorics. Given a finite metric space on n points, we seek its subspace of largest cardinality which can be embedded with a given distortion in Hilbert space. We provide nearly tight upper and lower bounds on the cardinality of this subspace in terms of n and the desired distortion. Our main theorem states that for any epsilon>0, every n point metric space contains a subset of size at least n^{1-\epsilon} which is embeddable in Hilbert space with O(\frac{\log(1/\epsilon)}{\epsilon}) distortion. The bound on the distortion is tight up to the log(1/\epsilon) factor. We further include a comprehensive study of various other aspects of this problem.<|reference_end|> | arxiv | @article{bartal2004on,
title={On metric Ramsey-type phenomena},
author={Yair Bartal, Nathan Linial, Manor Mendel, Assaf Naor},
journal={Ann. of Math. (2) 162 (2005), no. 2, 643--709},
year={2004},
doi={10.4007/annals.2005.162.643},
archivePrefix={arXiv},
eprint={math/0406353},
primaryClass={math.MG cs.DS}
} | bartal2004on |
arxiv-676712 | math/0406416 | Non-computable Julia sets | <|reference_start|>Non-computable Julia sets: We show that under the definition of computability which is natural from the point of view of applications, there exist non-computable quadratic Julia sets.<|reference_end|> | arxiv | @article{braverman2004non-computable,
title={Non-computable Julia sets},
author={Mark Braverman, Michael Yampolsky},
journal={arXiv preprint arXiv:math/0406416},
year={2004},
archivePrefix={arXiv},
eprint={math/0406416},
primaryClass={math.DS cs.CC}
} | braverman2004non-computable |
arxiv-676713 | math/0408122 | Perfect Delaunay Polytopes and Perfect Inhomogeneous Forms | <|reference_start|>Perfect Delaunay Polytopes and Perfect Inhomogeneous Forms: A lattice Delaunay polytope D is called perfect if it has the property that there is a unique circumscribing ellipsoid with interior free of lattice points, and with the surface containing only those lattice points that are the vertices of D. An inhomogeneous quadratic form is called perfect if it is determined by such a circumscribing ''empty ellipsoid'' uniquely up to a scale factor. Perfect inhomogeneous forms are associated with perfect Delaunay polytopes in much the way that perfect homogeneous forms are associated with perfect point lattices. We have been able to construct some infinite sequences of perfect Delaunay polytopes, one perfect polytope in each successive dimension starting at some initial dimension; we have been able to construct an infinite number of such infinite sequences. Perfect Delaunay polytopes are intimately related to the theory of Delaunay polytopes, and to Voronoi's theory of lattice types.<|reference_end|> | arxiv | @article{erdahl2004perfect,
title={Perfect Delaunay Polytopes and Perfect Inhomogeneous Forms},
author={Robert Erdahl, Andrei Ordine, and Konstantin Rybnikov},
journal={arXiv preprint arXiv:math/0408122},
year={2004},
archivePrefix={arXiv},
eprint={math/0408122},
primaryClass={math.NT cs.CC cs.CG math.MG quant-ph}
} | erdahl2004perfect |
arxiv-676714 | math/0408146 | Learning a Machine for the Decision in a Partially Observable Markov Universe | <|reference_start|>Learning a Machine for the Decision in a Partially Observable Markov Universe: In this paper, we are interested in optimal decisions in a partially observable Markov universe. Our viewpoint departs from the dynamic programming viewpoint: we are directly approximating an optimal strategic tree depending on the observation. This approximation is made by means of a parameterized probabilistic law. In this paper, a particular family of hidden Markov models, with input and output, is considered as a learning framework. A method for optimizing the parameters of these HMMs is proposed and applied. This optimization method is based on the cross-entropic principle.<|reference_end|> | arxiv | @article{dambreville2004learning,
title={Learning a Machine for the Decision in a Partially Observable Markov
Universe},
author={Frederic Dambreville (DGA/CTA/DT/GIP)},
journal={arXiv preprint arXiv:math/0408146},
year={2004},
archivePrefix={arXiv},
eprint={math/0408146},
primaryClass={math.GM cs.AI cs.LG}
} | dambreville2004learning |
arxiv-676715 | math/0408365 | Quasi-concave functions on antimatroids | <|reference_start|>Quasi-concave functions on antimatroids: In this paper we consider quasi-concave set functions defined on antimatroids. There are many equivalent axiomatizations of antimatroids, that may be separated into two categories: antimatroids defined as set systems and antimatroids defined as languages. An algorthmic characterization of antimatroids, that considers them as set systems, was given in (Kempner, Levit 2003). This characterization is based on the idea of optimization using set functions defined as minimum values of linkages between a set and the elements from the set complement. Such set functions are quasi-concave. Their behavior on antimatroids was studied in (Kempner, Muchnik 2003), where they were applied to constraint clustering. In this work we investigate a duality between quasi-concave set functions and linkage functions. Our main finding is that quasi-concave set functions on an antimatroid may be represented as minimum values of some monotone linkage functions.<|reference_end|> | arxiv | @article{levit2004quasi-concave,
title={Quasi-concave functions on antimatroids},
author={Vadim E. Levit and Yulia Kempner},
journal={arXiv preprint arXiv:math/0408365},
year={2004},
archivePrefix={arXiv},
eprint={math/0408365},
primaryClass={math.CO cs.DM}
} | levit2004quasi-concave |
arxiv-676716 | math/0409429 | Bounding Fastest Mixing | <|reference_start|>Bounding Fastest Mixing: In a series of recent works, Boyd, Diaconis, and their co-authors have introduced a semidefinite programming approach for computing the fastest mixing Markov chain on a graph of allowed transitions, given a target stationary distribution. In this paper, we show that standard mixing-time analysis techniques--variational characterizations, conductance, canonical paths--can be used to give simple, nontrivial lower and upper bounds on the fastest mixing time. To test the applicability of this idea, we consider several detailed examples including the Glauber dynamics of the Ising model--and get sharp bounds.<|reference_end|> | arxiv | @article{roch2004bounding,
title={Bounding Fastest Mixing},
author={S. Roch},
journal={arXiv preprint arXiv:math/0409429},
year={2004},
archivePrefix={arXiv},
eprint={math/0409429},
primaryClass={math.PR cs.DM math.CO math.ST stat.TH}
} | roch2004bounding |
arxiv-676717 | math/0409548 | On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel | <|reference_start|>On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel: This paper considers the model of an arbitrary distributed signal x observed through an added independent white Gaussian noise w, y=x+w. New relations between the minimal mean square error of the non-causal estimator and the likelihood ratio between y and \omega are derived. This is followed by an extended version of a recently derived relation between the mutual information I(x;y) and the minimal mean square error. These results are applied to derive infinite dimensional versions of the Fisher information and the de Bruijn identity. The derivation of the results is based on the Malliavin calculus.<|reference_end|> | arxiv | @article{zakai2004on,
title={On mutual information, likelihood-ratios and estimation error for the
additive Gaussian channel},
author={Moshe Zakai},
journal={IEEE Trans. on Information Theory, Vol. 51(9), pp. 3017-3024,
Sept. 2005},
year={2004},
doi={10.1109/TIT.2005.853297},
archivePrefix={arXiv},
eprint={math/0409548},
primaryClass={math.PR cs.IT math.IT math.ST stat.TH}
} | zakai2004on |
arxiv-676718 | math/0410068 | Combinatorial group theory and public key cryptography | <|reference_start|>Combinatorial group theory and public key cryptography: After some excitement generated by recently suggested public key exchange protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al., it is a prevalent opinion now that the conjugacy search problem is unlikely to provide sufficient level of security if a braid group is used as the platform. In this paper we address the following questions: (1) whether choosing a different group, or a class of groups, can remedy the situation; (2) whether some other "hard" problem from combinatorial group theory can be used, instead of the conjugacy search problem, in a public key exchange protocol. Another question that we address here, although somewhat vague, is likely to become a focus of the future research in public key cryptography based on symbolic computation: (3) whether one can efficiently disguise an element of a given group (or a semigroup) by using defining relations.<|reference_end|> | arxiv | @article{shpilrain2004combinatorial,
title={Combinatorial group theory and public key cryptography},
author={Vladimir Shpilrain and Gabriel Zapata},
journal={arXiv preprint arXiv:math/0410068},
year={2004},
archivePrefix={arXiv},
eprint={math/0410068},
primaryClass={math.GR cs.CR}
} | shpilrain2004combinatorial |
arxiv-676719 | math/0410282 | Balanced Boolean functions that can be evaluated so that every input bit is unlikely to be read | <|reference_start|>Balanced Boolean functions that can be evaluated so that every input bit is unlikely to be read: A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random inputs, no input bit is read with probability more than Theta(n^{-1/2} sqrt{log n}). We give a balanced monotone Boolean function for which the corresponding probability is Theta(n^{-1/3} log n). We then show that for any randomized algorithm for evaluating a balanced Boolean function, when the input bits are uniformly random, there is some input bit that is read with probability at least Theta(n^{-1/2}). For balanced monotone Boolean functions, there is some input bit that is read with probability at least Theta(n^{-1/3}).<|reference_end|> | arxiv | @article{benjamini2004balanced,
title={Balanced Boolean functions that can be evaluated so that every input bit
is unlikely to be read},
author={Itai Benjamini, Oded Schramm, David B. Wilson},
journal={Proc. 37th ACM Symposium on Theory of Computing (STOC), pages
244--250, 2005},
year={2004},
doi={10.1145/1060590.1060627},
archivePrefix={arXiv},
eprint={math/0410282},
primaryClass={math.PR cs.CC}
} | benjamini2004balanced |
arxiv-676720 | math/0410317 | On doubly-cyclic convolutional codes | <|reference_start|>On doubly-cyclic convolutional codes: Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of doubly-cyclic CC's. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC's, basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated.This shows that some of them are optimal or near optimal with respect to distance and performance.<|reference_end|> | arxiv | @article{gluesing-luerssen2004on,
title={On doubly-cyclic convolutional codes},
author={Heide Gluesing-Luerssen, Wiland Schmale},
journal={arXiv preprint arXiv:math/0410317},
year={2004},
archivePrefix={arXiv},
eprint={math/0410317},
primaryClass={math.RA cs.IT math.IT}
} | gluesing-luerssen2004on |
arxiv-676721 | math/0410550 | Further developements in finite fibonomial calculus | <|reference_start|>Further developements in finite fibonomial calculus: Primary definitions, notation and general observations of finite fibonomial operator calculus (ffoc) are presented. Kwasniewski's combinatorial interpretation of fibonomial coefficients by the use of fibonacci cobweb poset is given. Some elements of incidence algebra of fibonacci cobweb poset are defined.<|reference_end|> | arxiv | @article{krot2004further,
title={Further developements in finite fibonomial calculus},
author={Ewa Krot},
journal={arXiv preprint arXiv:math/0410550},
year={2004},
archivePrefix={arXiv},
eprint={math/0410550},
primaryClass={math.CO cs.DM}
} | krot2004further |
arxiv-676722 | math/0410574 | A note on comparison of scientific impact expressed by the number of citations in different fields of science | <|reference_start|>A note on comparison of scientific impact expressed by the number of citations in different fields of science: Citation distributions for 1992, 1994, 1996, 1997, 1999, and 2001, which were published in the 2004 report of the National Science Foundation, USA, are analyzed. It is shown that the ratio of the total number of citations of any two broad fields of science remains close to constant over the analyzed years. Based on this observation, normalization of total numbers of citations with respect to the number of citations in mathematics is suggested as a tool for comparing scientific impact expressed by the number of citations in different fields of science.<|reference_end|> | arxiv | @article{podlubny2004a,
title={A note on comparison of scientific impact expressed by the number of
citations in different fields of science},
author={Igor Podlubny},
journal={Scientometrics, Vol.64, no.1, July 2005, pp.95-99. Journal ISSN:
0138-9130 (Paper) 1588-2861 (Online)},
year={2004},
doi={10.1007/s11192-005-0240-0},
archivePrefix={arXiv},
eprint={math/0410574},
primaryClass={math.ST cs.GL physics.soc-ph stat.TH}
} | podlubny2004a |
arxiv-676723 | math/0410580 | Filled Julia sets with empty interior are computable | <|reference_start|>Filled Julia sets with empty interior are computable: We show that if a polynomial filled Julia set has empty interior, then it is computable.<|reference_end|> | arxiv | @article{binder2004filled,
title={Filled Julia sets with empty interior are computable},
author={I. Binder, M. Braverman, M. Yampolsky},
journal={arXiv preprint arXiv:math/0410580},
year={2004},
archivePrefix={arXiv},
eprint={math/0410580},
primaryClass={math.DS cs.CC}
} | binder2004filled |
arxiv-676724 | math/0410593 | The Schreier-Sims algorithm for matrix groups | <|reference_start|>The Schreier-Sims algorithm for matrix groups: This is the report of a project with the aim to make a new implementation of the Schreier-Sims algorithm in GAP, specialized for matrix groups. The standard Schreier-Sims algorithm is described in some detail, followed by descriptions of the probabilistic Schreier-Sims algorithm and the Schreier-Todd-Coxeter-Sims algorithm. Then we discuss our implementation and some optimisations, and finally we report on the performance of our implementation, as compared to the existing implementation in GAP, and we give benchmark results. The conclusion is that our implementation in some cases is faster and consumes much less memory.<|reference_end|> | arxiv | @article{bäärnhielm2004the,
title={The Schreier-Sims algorithm for matrix groups},
author={Henrik B"a"arnhielm},
journal={arXiv preprint arXiv:math/0410593},
year={2004},
archivePrefix={arXiv},
eprint={math/0410593},
primaryClass={math.GR cs.DS}
} | bäärnhielm2004the |
arxiv-676725 | math/0411002 | On umbral extensions of Stirling numbers and Dobinski-like formulas | <|reference_start|>On umbral extensions of Stirling numbers and Dobinski-like formulas: Umbral extensions of the stirling numbers of the second kind are considered and the resulting dobinski-like various formulas including new ones are presented. These extensions naturally encompass the two well known q-extensions. The further consecutive umbral extensions q-stirling numbers are therefore realized here in a two-fold way. The fact that the umbral q-extended dobinski formula may also be interpreted as the average of powers of random variable with the q-poisson distribution singles out the q-extensions which appear to be a kind of singular point in the domain of umbral extensions as expressed by corresponding two observations. Other relevant possibilities are tackled with the paper`s closing down questions and suggestions with respect to other already existing extensions while a brief limited survey of these other type extensions is being delivered. There the newton interpolation formula and divided differences appear helpful and inevitable along with umbra symbolic language in describing properties of general exponential polynomials of touchard and their possible generalizations. Exponential structures or algebraically equivalent prefabs with their exponential formula appear to be also naturally relevant.<|reference_end|> | arxiv | @article{kwasniewski2004on,
title={On umbral extensions of Stirling numbers and Dobinski-like formulas},
author={A. K. Kwasniewski},
journal={Adv. Stud. Contemp. Math., Vol 12, no. 1, (2006) 73-100},
year={2004},
archivePrefix={arXiv},
eprint={math/0411002},
primaryClass={math.CO cs.DM}
} | kwasniewski2004on |
arxiv-676726 | math/0411007 | The First Ascent into the Incidence Algebra of the Fibonacci Cobweb Poset | <|reference_start|>The First Ascent into the Incidence Algebra of the Fibonacci Cobweb Poset: The explicite formulas for m\"{o}biusien function and some other important elements of the incidence algebra are delivered. For that to do one uses kwa\'sniewski's construction of his fibonacci cobweb poset in the plane grid coordinate system.<|reference_end|> | arxiv | @article{krot2004the,
title={The First Ascent into the Incidence Algebra of the Fibonacci Cobweb
Poset},
author={Ewa Krot},
journal={Advanced Studies in Conterporary Mathematics 11 (2005), No. 2,
179-184},
year={2004},
archivePrefix={arXiv},
eprint={math/0411007},
primaryClass={math.CO cs.DM}
} | krot2004the |
arxiv-676727 | math/0411056 | Generators of algebraic curvature tensors based on a (2,1)-symmetry | <|reference_start|>Generators of algebraic curvature tensors based on a (2,1)-symmetry: We consider generators of algebraic curvature tensors R which can be constructed by a Young symmetrization of product tensors U*w or w*U, where U and w are covariant tensors of order 3 and 1. We assume that U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2,1). We show that the set S contains exactly one symmetry class S_0 whose elements U can not play the role of generators of tensors R. The tensors U of all other symmetry classes from S\{S_0} can be used as generators for tensors R. Using Computer Algebra we search for such generators whose coordinate representations are polynomials with a minimal number of summands. For a generic choice of the symmetry class of U we obtain lengths of 8 summands. In special cases these numbers can be reduced to the minimum 4. If this minimum occurs then U admits an index commutation symmetry. Furthermore minimal lengths are possible if U is formed from torsion-free covariant derivatives of alternating 2-tensor fields. We apply ideals and idempotents of group rings C[S_r] of symmetric groups S_r, Young symmetrizers, discrete Fourier transforms and Littlewood-Richardson products. For symbolic calculations we used the Mathematica packages Ricci and PERMS.<|reference_end|> | arxiv | @article{fiedler2004generators,
title={Generators of algebraic curvature tensors based on a (2,1)-symmetry},
author={Bernd Fiedler},
journal={arXiv preprint arXiv:math/0411056},
year={2004},
archivePrefix={arXiv},
eprint={math/0411056},
primaryClass={math.DG cs.SC math.CO}
} | fiedler2004generators |
arxiv-676728 | math/0411107 | First Steps in Algorithmic Fewnomial Theory | <|reference_start|>First Steps in Algorithmic Fewnomial Theory: Fewnomial theory began with explicit bounds -- solely in terms of the number of variables and monomial terms -- on the number of real roots of systems of polynomial equations. Here we take the next logical step of investigating the corresponding existence problem: Let FEAS_R denote the problem of deciding whether a given system of multivariate polynomial equations with integer coefficients has a real root or not. We describe a phase-transition for when m is large enough to make FEAS_R be NP-hard, when restricted to inputs consisting of a single n-variate polynomial with exactly m monomial terms: polynomial-time for m<=n+2 (for any fixed n) and NP-hardness for m<=n+n^{epsilon} (for n varying and any fixed epsilon>0). Because of important connections between FEAS_R and A-discriminants, we then study some new families of A-discriminants whose signs can be decided within polynomial-time. (A-discriminants contain all known resultants as special cases, and the latter objects are central in algorithmic algebraic geometry.) Baker's Theorem from diophantine approximation arises as a key tool. Along the way, we also derive new quantitative bounds on the real zero sets of n-variate (n+2)-nomials.<|reference_end|> | arxiv | @article{bihan2004first,
title={First Steps in Algorithmic Fewnomial Theory},
author={Frederic Bihan, J. Maurice Rojas, Casey E. Stella},
journal={arXiv preprint arXiv:math/0411107},
year={2004},
archivePrefix={arXiv},
eprint={math/0411107},
primaryClass={math.AG cs.CC math.AC}
} | bihan2004first |
arxiv-676729 | math/0411128 | Why Delannoy numbers? | <|reference_start|>Why Delannoy numbers?: This article is not a research paper, but a little note on the history of combinatorics: We present here a tentative short biography of Henri Delannoy, and a survey of his most notable works. This answers to the question raised in the title, as these works are related to lattice paths enumeration, to the so-called Delannoy numbers, and were the first general way to solve Ballot-like problems. These numbers appear in probabilistic game theory, alignments of DNA sequences, tiling problems, temporal representation models, analysis of algorithms and combinatorial structures.<|reference_end|> | arxiv | @article{banderier2004why,
title={Why Delannoy numbers?},
author={Cyril Banderier (LIPN), Sylviane Schwer (LIPN)},
journal={Journal of Statistical Planning and Inference 135, 1 (11/2005)
40-54},
year={2004},
doi={10.1016/j.jspi.2005.02.004},
archivePrefix={arXiv},
eprint={math/0411128},
primaryClass={math.CO cs.DS cs.GT math.HO math.PR math.ST q-bio.GN stat.TH}
} | banderier2004why |
arxiv-676730 | math/0411138 | Generating Functions For Kernels of Digraphs (Enumeration & Asymptotics for Nim Games) | <|reference_start|>Generating Functions For Kernels of Digraphs (Enumeration & Asymptotics for Nim Games): In this article, we study directed graphs (digraphs) with a coloring constraint due to Von Neumann and related to Nim-type games. This is equivalent to the notion of kernels of digraphs, which appears in numerous fields of research such as game theory, complexity theory, artificial intelligence (default logic, argumentation in multi-agent systems), 0-1 laws in monadic second order logic, combinatorics (perfect graphs)... Kernels of digraphs lead to numerous difficult questions (in the sense of NP-completeness, #P-completeness). However, we show here that it is possible to use a generating function approach to get new informations: we use technique of symbolic and analytic combinatorics (generating functions and their singularities) in order to get exact and asymptotic results, e.g. for the existence of a kernel in a circuit or in a unicircuit digraph. This is a first step toward a generatingfunctionology treatment of kernels, while using, e.g., an approach "a la Wright". Our method could be applied to more general "local coloring constraints" in decomposable combinatorial structures.<|reference_end|> | arxiv | @article{banderier2004generating,
title={Generating Functions For Kernels of Digraphs (Enumeration & Asymptotics
for Nim Games)},
author={Cyril Banderier (LIPN), Jean-Marie Le Bars (LIPN, GREYC), Vlady
Ravelomanana (LIPN)},
journal={Proceedings of FPSAC'04 (2004) 91-105},
year={2004},
archivePrefix={arXiv},
eprint={math/0411138},
primaryClass={math.CO cs.DM cs.DS cs.GT math.PR}
} | banderier2004generating |
arxiv-676731 | math/0411145 | Information on some recent applications of umbral extensions to discrete mathematics | <|reference_start|>Information on some recent applications of umbral extensions to discrete mathematics: At the first part of the paper we show how specific umbral extensions of the Stirling numbers of the second kind result in new type of Dobinski-like formulas. In the second part among others one recovers how and why Ward solution of uncountable family of extended difference calculus nonhomogeneous equations extends to Ward-Appell polynomials case . Illustrative specifications to q-calculus case and fibonomial calculus case are made explicit due to the usage of the so called upside down notation for objects of extended finite operator calculus .<|reference_end|> | arxiv | @article{kwasniewski2004information,
title={Information on some recent applications of umbral extensions to discrete
mathematics},
author={A.K.Kwasniewski},
journal={Review Bulletin of Calcutta Mathematical Society Vol. 13 (2005)
1-10},
year={2004},
archivePrefix={arXiv},
eprint={math/0411145},
primaryClass={math.CO cs.DM}
} | kwasniewski2004information |
arxiv-676732 | math/0411239 | Very well-covered graphs with log-concave independence polynomials | <|reference_start|>Very well-covered graphs with log-concave independence polynomials: If for any $k$ the $k$-th coefficient of a polynomial $I(G;x)$ is equal to the number of stable sets of cardinality $k$ in the graph $G$, then it is called the independence polynomial of $G$ (Gutman and Harary, 1983). Alavi, Malde, Schwenk and Erdos (1987) conjectured that $I(G;x)$ is unimodal, whenever $G$ is a forest, while Brown, Dilcher and Nowakowski (2000) conjectured that $I(G;x)$ is unimodal for any well-covered graph G. Michael and Traves (2003) showed that the assertion is false for well-covered graphs with $a(G)$ > 3 ($a(G)$ is the size of a maximum stable set of the graph $G$), while for very well-covered graphs the conjecture is still open. In this paper we give support to both conjectures by demonstrating that if $a(G)$ < 4, or $G$ belongs to ${K_{1,n}, P_{n}: n > 0}$, then $I(G*;x)$ is log-concave, and, hence, unimodal (where $G*$ is the very well-covered graph obtained from $G$ by appending a single pendant edge to each vertex).<|reference_end|> | arxiv | @article{levit2004very,
title={Very well-covered graphs with log-concave independence polynomials},
author={Vadim E. Levit and Eugen Mandrescu},
journal={arXiv preprint arXiv:math/0411239},
year={2004},
archivePrefix={arXiv},
eprint={math/0411239},
primaryClass={math.CO cs.DM}
} | levit2004very |
arxiv-676733 | math/0411250 | Generating functions for generating trees | <|reference_start|>Generating functions for generating trees: Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumeration sequences (sometimes, to explicit formulae as well) and provide efficient random generation algorithms. We investigate the links between the structural properties of the rewriting rules defining such trees and the rationality, algebraicity, or transcendence of the corresponding generating function.<|reference_end|> | arxiv | @article{banderier2004generating,
title={Generating functions for generating trees},
author={Cyril Banderier (LIPN, ALGO UR-R), Philippe Flajolet (ALGO UR-R),
Daniele Gardy (PRISM), Mireille Bousquet-Melou (LABRI), Alain Denise (LRI),
Dominique Gouyou-Beauchamps (LRI)},
journal={Discrete Mathematics 246 (1-3) (2002) 29-55},
year={2004},
doi={10.1016/S0012-365X(01)00250-3},
archivePrefix={arXiv},
eprint={math/0411250},
primaryClass={math.CO cs.DM cs.DS}
} | banderier2004generating |
arxiv-676734 | math/0411356 | Characterization and enumeration of toroidal K_3,3-subdivision-free graphs | <|reference_start|>Characterization and enumeration of toroidal K_3,3-subdivision-free graphs: We describe the structure of 2-connected non-planar toroidal graphs with no K_{3,3}-subdivisions, using an appropriate substitution of planar networks into the edges of certain graphs called toroidal cores. The structural result is based on a refinement of the algorithmic results for graphs containing a fixed K_5-subdivision in [A. Gagarin and W. Kocay, "Embedding graphs containing K_5-subdivisions'', Ars Combin. 64 (2002), 33-49]. It allows to recognize these graphs in linear-time and makes possible to enumerate labelled 2-connected toroidal graphs containing no K_{3,3}-subdivisions and having minimum vertex degree two or three by using an approach similar to [A. Gagarin, G. Labelle, and P. Leroux, "Counting labelled projective-planar graphs without a K_{3,3}-subdivision", submitted, arXiv:math.CO/0406140, (2004)].<|reference_end|> | arxiv | @article{gagarin2004characterization,
title={Characterization and enumeration of toroidal K_{3,3}-subdivision-free
graphs},
author={Andrei Gagarin, Gilbert Labelle, Pierre Leroux (LaCIM, Universite du
Quebec a Montreal)},
journal={Discrete Math. 307 (2007), no. 23, pp. 2993-3005},
year={2004},
doi={10.1016/j.disc.2007.03.083},
archivePrefix={arXiv},
eprint={math/0411356},
primaryClass={math.CO cs.DM}
} | gagarin2004characterization |
arxiv-676735 | math/0411378 | Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log? | <|reference_start|>Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?: The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize this issue by asking whether the discrete log problem (DLOG) has the same difficulty for all curves over a given finite field with the same order. We prove that this is essentially true by showing polynomial time random reducibility of DLOG among such curves, assuming the Generalized Riemann Hypothesis (GRH). We do so by constructing certain expander graphs, similar to Ramanujan graphs, with elliptic curves as nodes and low degree isogenies as edges. The result is obtained from the rapid mixing of random walks on this graph. Our proof works only for curves with (nearly) the same endomorphism rings. Without this technical restriction such a DLOG equivalence might be false; however, in practice the restriction may be moot, because all known polynomial time techniques for constructing equal order curves produce only curves with nearly equal endomorphism rings.<|reference_end|> | arxiv | @article{jao2004do,
title={Do All Elliptic Curves of the Same Order Have the Same Difficulty of
Discrete Log?},
author={David Jao, Stephen D. Miller, Ramarathnam Venkatesan},
journal={Advances in Cryptology -- Asiacrypt 2005, LNCS 3788, pp. 21-40.},
year={2004},
doi={10.1007/11593447_2},
archivePrefix={arXiv},
eprint={math/0411378},
primaryClass={math.NT cs.CC cs.CR math.AG math.CO}
} | jao2004do |
arxiv-676736 | math/0411488 | The obstructions for toroidal graphs with no $K_3,3$'s | <|reference_start|>The obstructions for toroidal graphs with no $K_3,3$'s: Forbidden minors and subdivisions for toroidal graphs are numerous. We consider the toroidal graphs with no $K_{3,3}$-subdivisions that coincide with the toroidal graphs with no $K_{3,3}$-minors. These graphs admit a unique decomposition into planar components and have short lists of obstructions. We provide the complete lists of four forbidden minors and eleven forbidden subdivisions for the toroidal graphs with no $K_{3,3}$'s and prove that the lists are sufficient.<|reference_end|> | arxiv | @article{gagarin2004the,
title={The obstructions for toroidal graphs with no $K_{3,3}$'s},
author={Andrei Gagarin, Wendy Myrvold, and John Chambers},
journal={Discrete Math. 309 (2009), no. 11, pp. 3625-3631},
year={2004},
doi={10.1016/j.disc.2007.12.075},
archivePrefix={arXiv},
eprint={math/0411488},
primaryClass={math.CO cs.DM}
} | gagarin2004the |
arxiv-676737 | math/0411515 | Fast Non-Parametric Bayesian Inference on Infinite Trees | <|reference_start|>Fast Non-Parametric Bayesian Inference on Infinite Trees: Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A Bayesian would assign a data-independent prior probability to "subdivide", which leads to a prior over infinite(ly many) trees. We derive an exact, fast, and simple inference algorithm for such a prior, for the data evidence, the predictive distribution, the effective model dimension, and other quantities.<|reference_end|> | arxiv | @article{hutter2004fast,
title={Fast Non-Parametric Bayesian Inference on Infinite Trees},
author={Marcus Hutter},
journal={Proc. 10th International Conf. on Artificial Intelligence and
Statistics (AISTATS-2005) 144-151},
year={2004},
number={IDSIA-24-04},
archivePrefix={arXiv},
eprint={math/0411515},
primaryClass={math.ST cs.LG math.PR stat.TH}
} | hutter2004fast |
arxiv-676738 | math/0411644 | The conjugacy search problem in public key cryptography: unnecessary and insufficient | <|reference_start|>The conjugacy search problem in public key cryptography: unnecessary and insufficient: The conjugacy search problem in a group G is the problem of recovering an x in G from given g in G and h=x^{-1}gx. This problem is in the core of several recently suggested public key exchange protocols, most notably the one due to Anshel, Anshel, and Goldfeld, and the one due to Ko, Lee at al. In this note, we make two observations that seem to have eluded most people's attention. The first observation is that solving the conjugacy search problem is not necessary for an adversary to get the common secret key in the Ko-Lee protocol. It is sufficient to solve an apparently easier problem of finding x, y in G such that h=ygx for given g, h in G. Another observation is that solving the conjugacy search problem is not sufficient for an adversary to get the common secret key in the Anshel-Anshel-Goldfeld protocol.<|reference_end|> | arxiv | @article{shpilrain2004the,
title={The conjugacy search problem in public key cryptography: unnecessary and
insufficient},
author={Vladimir Shpilrain and Alexander Ushakov},
journal={arXiv preprint arXiv:math/0411644},
year={2004},
archivePrefix={arXiv},
eprint={math/0411644},
primaryClass={math.GR cs.CR}
} | shpilrain2004the |
arxiv-676739 | math/0412233 | Extended finite operator calculus as an example of algebraization of analysis | <|reference_start|>Extended finite operator calculus as an example of algebraization of analysis: A wardian calculus of sequences started almost seventy years ago constitutes the general scheme for extensions of the classical umbral operator calculus considered by many afterwards . At the same time this calculus is an example of the algebraization of the analysis here restricted to the algebra of formal series. This is a review article based on the recent first author contributions. As the survey article it is supplemented by the short indicatory glossaries of notation and terms used by prominent contributors to the domain.<|reference_end|> | arxiv | @article{kwasniewski2004extended,
title={Extended finite operator calculus as an example of algebraization of
analysis},
author={A.K.Kwasniewski, E.Borak},
journal={arXiv preprint arXiv:math/0412233},
year={2004},
archivePrefix={arXiv},
eprint={math/0412233},
primaryClass={math.CO cs.DM}
} | kwasniewski2004extended |
arxiv-676740 | math/0501388 | Efficiently Detecting Torsion Points and Subtori | <|reference_start|>Efficiently Detecting Torsion Points and Subtori: Suppose X is the complex zero set of a finite collection of polynomials in Z[x_1,...,x_n]. We show that deciding whether X contains a point all of whose coordinates are d_th roots of unity can be done within NP^NP (relative to the sparse encoding), under a plausible assumption on primes in arithmetic progression. In particular, our hypothesis can still hold even under certain failures of the Generalized Riemann Hypothesis, such as the presence of Siegel-Landau zeroes. Furthermore, we give a similar (but UNconditional) complexity upper bound for n=1. Finally, letting T be any algebraic subgroup of (C^*)^n we show that deciding whether X contains T is coNP-complete (relative to an even more efficient encoding),unconditionally. We thus obtain new non-trivial families of multivariate polynomial systems where deciding the existence of complex roots can be done unconditionally in the polynomial hierarchy -- a family of complexity classes lying between PSPACE and P, intimately connected with the P=?NP Problem. We also discuss a connection to Laurent's solution of Chabauty's Conjecture from arithmetic geometry.<|reference_end|> | arxiv | @article{rojas2005efficiently,
title={Efficiently Detecting Torsion Points and Subtori},
author={J. Maurice Rojas},
journal={arXiv preprint arXiv:math/0501388},
year={2005},
archivePrefix={arXiv},
eprint={math/0501388},
primaryClass={math.AG cs.CC math.NT}
} | rojas2005efficiently |
arxiv-676741 | math/0502024 | The maximum entropy state | <|reference_start|>The maximum entropy state: We give an algorithm for calculating the maximum entropy state as the least fixed point of a Scott continuous mapping on the domain of classical states in their Bayesian order.<|reference_end|> | arxiv | @article{martin2005the,
title={The maximum entropy state},
author={Keye Martin},
journal={arXiv preprint arXiv:math/0502024},
year={2005},
archivePrefix={arXiv},
eprint={math/0502024},
primaryClass={math.PR cs.LO math-ph math.MP quant-ph}
} | martin2005the |
arxiv-676742 | math/0502172 | An hybrid system approach to nonlinear optimal control problems | <|reference_start|>An hybrid system approach to nonlinear optimal control problems: We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced by piecewise affine approximations which allow an analytical resolution. The sequence of affine models then forms a sequence of states of a hybrid automaton. Given a sequence of states, we introduce an hybrid approximation of the nonlinear controllable domain and propose a new algorithm computing a controllable, piecewise convex approximation. The same way the nonlinear optimal control problem is replaced by an hybrid piecewise affine one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce the global structure of the hybrid optimal control steering the system to the target.<|reference_end|> | arxiv | @article{dumas2005an,
title={An hybrid system approach to nonlinear optimal control problems},
author={Jean-Guillaume Luc Dumas (LJK), Aude Rondepierre (MIP)},
journal={arXiv preprint arXiv:math/0502172},
year={2005},
archivePrefix={arXiv},
eprint={math/0502172},
primaryClass={math.OC cs.SC}
} | dumas2005an |
arxiv-676743 | math/0502232 | Individual displacements in hashing with coalesced chains | <|reference_start|>Individual displacements in hashing with coalesced chains: We study the asymptotic distribution of the displacements in hashing with coalesced chains, for both late-insertion and early-insertion. Asymptotic formulas for means and variances follow. The method uses Poissonization and some stochastic calculus.<|reference_end|> | arxiv | @article{janson2005individual,
title={Individual displacements in hashing with coalesced chains},
author={Svante Janson},
journal={arXiv preprint arXiv:math/0502232},
year={2005},
number={U.U.D.M. 2005:4},
archivePrefix={arXiv},
eprint={math/0502232},
primaryClass={math.PR cs.DS}
} | janson2005individual |
arxiv-676744 | math/0502315 | Strong Asymptotic Assertions for Discrete MDL in Regression and Classification | <|reference_start|>Strong Asymptotic Assertions for Discrete MDL in Regression and Classification: We study the properties of the MDL (or maximum penalized complexity) estimator for Regression and Classification, where the underlying model class is countable. We show in particular a finite bound on the Hellinger losses under the only assumption that there is a "true" model contained in the class. This implies almost sure convergence of the predictive distribution to the true one at a fast rate. It corresponds to Solomonoff's central theorem of universal induction, however with a bound that is exponentially larger.<|reference_end|> | arxiv | @article{poland2005strong,
title={Strong Asymptotic Assertions for Discrete MDL in Regression and
Classification},
author={Jan Poland and Marcus Hutter},
journal={Proc. 14th Dutch-Belgium Conf. on Machine Learning (Benelearn
2005) 67-72},
year={2005},
number={IDSIA-02-05},
archivePrefix={arXiv},
eprint={math/0502315},
primaryClass={math.ST cs.AI cs.IT cs.LG math.IT math.PR stat.TH}
} | poland2005strong |
arxiv-676745 | math/0502327 | Decoding by Linear Programming | <|reference_start|>Decoding by Linear Programming: This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector $f \in \R^n$ from corrupted measurements $y = A f + e$. Here, $A$ is an $m$ by $n$ (coding) matrix and $e$ is an arbitrary and unknown vector of errors. Is it possible to recover $f$ exactly from the data $y$? We prove that under suitable conditions on the coding matrix $A$, the input $f$ is the unique solution to the $\ell_1$-minimization problem ($\|x\|_{\ell_1} := \sum_i |x_i|$) $$ \min_{g \in \R^n} \| y - Ag \|_{\ell_1} $$ provided that the support of the vector of errors is not too large, $\|e\|_{\ell_0} := |\{i : e_i \neq 0\}| \le \rho \cdot m$ for some $\rho > 0$. In short, $f$ can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; $f$ is recovered exactly even in situations where a significant fraction of the output is corrupted.<|reference_end|> | arxiv | @article{candes2005decoding,
title={Decoding by Linear Programming},
author={Emmanuel Candes, Terence Tao},
journal={arXiv preprint arXiv:math/0502327},
year={2005},
archivePrefix={arXiv},
eprint={math/0502327},
primaryClass={math.MG cs.CR}
} | candes2005decoding |
arxiv-676746 | math/0502354 | On computational complexity of Siegel Julia sets | <|reference_start|>On computational complexity of Siegel Julia sets: It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.<|reference_end|> | arxiv | @article{binder2005on,
title={On computational complexity of Siegel Julia sets},
author={I. Binder, M. Braverman, M. Yampolsky},
journal={arXiv preprint arXiv:math/0502354},
year={2005},
doi={10.1007/s00220-006-1546-3},
archivePrefix={arXiv},
eprint={math/0502354},
primaryClass={math.DS cs.CC}
} | binder2005on |
arxiv-676747 | math/0503210 | An Introduction to Finite Fibonomial Calculus | <|reference_start|>An Introduction to Finite Fibonomial Calculus: This is an indicatory presentation of main definitions and theorems of fibonomial calculus which is a special case of psi-extented rota's finite operator calculus.<|reference_end|> | arxiv | @article{krot2005an,
title={An Introduction to Finite Fibonomial Calculus},
author={Ewa Krot},
journal={CEJM, 2(5) 2004, 754-766},
year={2005},
archivePrefix={arXiv},
eprint={math/0503210},
primaryClass={math.CO cs.DM}
} | krot2005an |
arxiv-676748 | math/0503286 | Cobweb posets as noncommutative prefabs | <|reference_start|>Cobweb posets as noncommutative prefabs: A class of new type graded infinite posets with minimal element are considered. These so called cobweb posets introduced recently by the present author provide a wide range of new noncommutative prefab combinatorial schema with characteristic graded subposets as primes. The schema are defined here via relaxing commutativity and associativity requirements imposed on the composition of prefabs by the fathers of this fertile concept. The construction and the very first basic properties of cobweb prefabs are pointed out in what follows. An another single valued commutative amd associative composision is also considered.<|reference_end|> | arxiv | @article{kwasniewski2005cobweb,
title={Cobweb posets as noncommutative prefabs},
author={A.K.Kwasniewski},
journal={Adv. Stud. Contemp. Math. vol. 14 (1) 2007. pp. 37-47},
year={2005},
archivePrefix={arXiv},
eprint={math/0503286},
primaryClass={math.CO cs.DM}
} | kwasniewski2005cobweb |
arxiv-676749 | math/0503295 | Characterization of the Fibonacci Cobweb Poset as oDAG | <|reference_start|>Characterization of the Fibonacci Cobweb Poset as oDAG: The characterization of fibonacci cobweb poset as d.a.g. and o.d.a.g. is given. The dim 2 poset such that its hasse diagram coincide with digraf of fibonacci cobweb poset is constructed.<|reference_end|> | arxiv | @article{krot2005characterization,
title={Characterization of the Fibonacci Cobweb Poset as oDAG},
author={Ewa Krot},
journal={arXiv preprint arXiv:math/0503295},
year={2005},
archivePrefix={arXiv},
eprint={math/0503295},
primaryClass={math.CO cs.DM}
} | krot2005characterization |
arxiv-676750 | math/0503453 | Weakly complete axiomatization of exogenous quantum propositional logic | <|reference_start|>Weakly complete axiomatization of exogenous quantum propositional logic: A weakly complete finitary axiomatization for EQPL (exogenous quantum propositional logic) is presented. The proof is carried out using a non trivial extension of the Fagin-Halpern-Megiddo technique together with three Henkin style completions.<|reference_end|> | arxiv | @article{mateus2005weakly,
title={Weakly complete axiomatization of exogenous quantum propositional logic},
author={P. Mateus and A. Sernadas (CLC, Dep Math, IST, Lisbon, Portugal)},
journal={arXiv preprint arXiv:math/0503453},
year={2005},
doi={10.1016/j.ic.2006.02.001},
archivePrefix={arXiv},
eprint={math/0503453},
primaryClass={math.LO cs.LO quant-ph}
} | mateus2005weakly |
arxiv-676751 | math/0503503 | Noise stability of functions with low influences: invariance and optimality | <|reference_start|>Noise stability of functions with low influences: invariance and optimality: In this paper we study functions with low influences on product probability spaces. The analysis of boolean functions with low influences has become a central problem in discrete Fourier analysis. It is motivated by fundamental questions arising from the construction of probabilistically checkable proofs in theoretical computer science and from problems in the theory of social choice in economics. We prove an invariance principle for multilinear polynomials with low influences and bounded degree; it shows that under mild conditions the distribution of such polynomials is essentially invariant for all product spaces. Ours is one of the very few known non-linear invariance principles. It has the advantage that its proof is simple and that the error bounds are explicit. We also show that the assumption of bounded degree can be eliminated if the polynomials are slightly ``smoothed''; this extension is essential for our applications to ``noise stability''-type problems. In particular, as applications of the invariance principle we prove two conjectures: the ``Majority Is Stablest'' conjecture from theoretical computer science, which was the original motivation for this work, and the ``It Ain't Over Till It's Over'' conjecture from social choice theory.<|reference_end|> | arxiv | @article{mossel2005noise,
title={Noise stability of functions with low influences: invariance and
optimality},
author={Elchanan Mossel and Ryan O'Donnell and Krzysztof Oleszkiewicz},
journal={arXiv preprint arXiv:math/0503503},
year={2005},
archivePrefix={arXiv},
eprint={math/0503503},
primaryClass={math.PR cs.CC math.CO}
} | mossel2005noise |
arxiv-676752 | math/0504037 | Modelling Linear Logic Without Units (Preliminary Results) | <|reference_start|>Modelling Linear Logic Without Units (Preliminary Results): We describe a notion of categorical model for unitless fragments of (multiplicative) linear logic. The basic definition uses promonoidal categories, and we also give an equivalent elementary axiomatisation.<|reference_end|> | arxiv | @article{houston2005modelling,
title={Modelling Linear Logic Without Units (Preliminary Results)},
author={Robin Houston, Dominic Hughes and Andrea Schalk},
journal={arXiv preprint arXiv:math/0504037},
year={2005},
archivePrefix={arXiv},
eprint={math/0504037},
primaryClass={math.CT cs.LO math.LO}
} | houston2005modelling |
arxiv-676753 | math/0504378 | A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood is Hard | <|reference_start|>A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood is Hard: Maximum likelihood is one of the most widely used techniques to infer evolutionary histories. Although it is thought to be intractable, a proof of its hardness has been lacking. Here, we give a short proof that computing the maximum likelihood tree is NP-hard by exploiting a connection between likelihood and parsimony observed by Tuffley and Steel.<|reference_end|> | arxiv | @article{roch2005a,
title={A Short Proof that Phylogenetic Tree Reconstruction by Maximum
Likelihood is Hard},
author={S. Roch},
journal={arXiv preprint arXiv:math/0504378},
year={2005},
archivePrefix={arXiv},
eprint={math/0504378},
primaryClass={math.PR cs.CC cs.CE math.ST q-bio.PE stat.TH}
} | roch2005a |
arxiv-676754 | math/0504522 | On the Classification of All Self-Dual Additive Codes over GF(4) of Length up to 12 | <|reference_start|>On the Classification of All Self-Dual Additive Codes over GF(4) of Length up to 12: We consider additive codes over GF(4) that are self-dual with respect to the Hermitian trace inner product. Such codes have a well-known interpretation as quantum codes and correspond to isotropic systems. It has also been shown that these codes can be represented as graphs, and that two codes are equivalent if and only if the corresponding graphs are equivalent with respect to local complementation and graph isomorphism. We use these facts to classify all codes of length up to 12, where previously only all codes of length up to 9 were known. We also classify all extremal Type II codes of length 14. Finally, we find that the smallest Type I and Type II codes with trivial automorphism group have length 9 and 12, respectively.<|reference_end|> | arxiv | @article{danielsen2005on,
title={On the Classification of All Self-Dual Additive Codes over GF(4) of
Length up to 12},
author={Lars Eirik Danielsen (1), Matthew G. Parker (1) ((1) University of
Bergen)},
journal={Journal of Combinatorial Theory, Series A 113(7), pp. 1351-1367,
2006},
year={2005},
doi={10.1016/j.jcta.2005.12.004},
archivePrefix={arXiv},
eprint={math/0504522},
primaryClass={math.CO cs.IT math.IT}
} | danielsen2005on |
arxiv-676755 | math/0505418 | Internalising modified realisability in constructive type theory | <|reference_start|>Internalising modified realisability in constructive type theory: A modified realisability interpretation of infinitary logic is formalised and proved sound in constructive type theory (CTT). The logic considered subsumes first order logic. The interpretation makes it possible to extract programs with simplified types and to incorporate and reason about them in CTT.<|reference_end|> | arxiv | @article{palmgren2005internalising,
title={Internalising modified realisability in constructive type theory},
author={Erik Palmgren},
journal={Logical Methods in Computer Science, Volume 1, Issue 2 (October 5,
2005) lmcs:2266},
year={2005},
doi={10.2168/LMCS-1(2:2)2005},
archivePrefix={arXiv},
eprint={math/0505418},
primaryClass={math.LO cs.LO}
} | palmgren2005internalising |
arxiv-676756 | math/0505487 | Thompson's group and public key cryptography | <|reference_start|>Thompson's group and public key cryptography: Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al. exploited the conjugacy search problem in groups, which is a ramification of the discrete logarithm problem. However, it is a prevalent opinion now that the conjugacy search problem alone is unlikely to provide sufficient level of security no matter what particular group is chosen as a platform. In this paper we employ another problem (we call it the decomposition problem), which is more general than the conjugacy search problem, and we suggest to use R. Thompson's group as a platform. This group is well known in many areas of mathematics, including algebra, geometry, and analysis. It also has several properties that make it fit for cryptographic purposes. In particular, we show here that the word problem in Thompson's group is solvable in almost linear time.<|reference_end|> | arxiv | @article{shpilrain2005thompson's,
title={Thompson's group and public key cryptography},
author={Vladimir Shpilrain and Alexander Ushakov},
journal={arXiv preprint arXiv:math/0505487},
year={2005},
archivePrefix={arXiv},
eprint={math/0505487},
primaryClass={math.GR cs.CR}
} | shpilrain2005thompson's |
arxiv-676757 | math/0505617 | On computational complexity of Riemann mapping | <|reference_start|>On computational complexity of Riemann mapping: In this paper we consider the computational complexity of uniformizing a domain with a given computable boundary. We give nontrivial upper and lower bounds in two settings: when the approximation of boundary is given either as a list of pixels, or by a Turing Machine.<|reference_end|> | arxiv | @article{binder2005on,
title={On computational complexity of Riemann mapping},
author={Ilia Binder, Mark Braverman, Michael Yampolsky},
journal={arXiv preprint arXiv:math/0505617},
year={2005},
archivePrefix={arXiv},
eprint={math/0505617},
primaryClass={math.CV cs.CC}
} | binder2005on |
arxiv-676758 | math/0506082 | Discrete differential geometry of proteins: a new method for encoding three-dimensional structures of proteins | <|reference_start|>Discrete differential geometry of proteins: a new method for encoding three-dimensional structures of proteins: In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method is the correspondence between protein-folding and ``integration''. A protein is approximated by a folded tetrahedron sequence. And the binary code of a protein is obtained as the ``second derivative'' of the shape of the folded tetrahedron sequence. With this method at hand, we can extract static structural information of a protein from its gene. And we can describe the distribution of three-dimensional structures of proteins without any subjective hierarchical classification.<|reference_end|> | arxiv | @article{morikawa2005discrete,
title={Discrete differential geometry of proteins: a new method for encoding
three-dimensional structures of proteins},
author={Naoto Morikawa},
journal={arXiv preprint arXiv:math/0506082},
year={2005},
archivePrefix={arXiv},
eprint={math/0506082},
primaryClass={math.CO cs.DM math.MG q-bio.GN}
} | morikawa2005discrete |
arxiv-676759 | math/0506180 | Constructions in public-key cryptography over matrix groups | <|reference_start|>Constructions in public-key cryptography over matrix groups: The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new homomorphic public-key cryptosystem. They rely on difficulty of the conjugacy and membership problems for subgroups of a given group. To support these and other known cryptographic schemes we present a general technique to produce a family of instances being matrix groups (over finite commutative rings) which play a role for these schemes similar to the groups $Z\_n^*$ in the existing cryptographic constructions like RSA or discrete logarithm.<|reference_end|> | arxiv | @article{grigoriev2005constructions,
title={Constructions in public-key cryptography over matrix groups},
author={Dimitri Grigoriev (IRMAR), Ilia Ponomarenko},
journal={arXiv preprint arXiv:math/0506180},
year={2005},
number={2005-19},
archivePrefix={arXiv},
eprint={math/0506180},
primaryClass={math.GR cs.CR math-ph math.MP}
} | grigoriev2005constructions |
arxiv-676760 | math/0506475 | Foundations of real analysis and computability theory in non-Aristotelian finitary logic | <|reference_start|>Foundations of real analysis and computability theory in non-Aristotelian finitary logic: This paper outlines new paradigms for real analysis and computability theory in the recently proposed non-Aristotelian finitary logic (NAFL). Constructive real analysis in NAFL (NRA) is accomplished by a translation of diagrammatic concepts from Euclidean geometry into an extension (NPAR) of the NAFL version of Peano Arithmetic (NPA). Such a translation is possible because NPA proves the existence of every infinite proper class of natural numbers that is definable in the language of NPA. Infinite sets are not permitted in NPAR and quantification over proper classes is banned; hence Cantor's diagonal argument cannot be legally formulated in NRA, and there is no `cardinality' for any collection (`super-class') of real numbers. Many of the useful aspects of classical real analysis, such as, the calculus of Newton and Leibniz, are justifiable in NRA. But the paradoxes, such as, Zeno's paradoxes of motion and the Banach-Tarski paradox, are resolved because NRA admits only closed super-classes of real numbers; in particular, open/semi-open intervals of real numbers are not permitted. The NAFL version of computability theory (NCT) rejects Turing's argument for the undecidability of the halting problem and permits hypercomputation. Important potential applications of NCT are in the areas of quantum and autonomic computing.<|reference_end|> | arxiv | @article{srinivasan2005foundations,
title={Foundations of real analysis and computability theory in
non-Aristotelian finitary logic},
author={Radhakrishnan Srinivasan, H. P. Raghunandan},
journal={arXiv preprint arXiv:math/0506475},
year={2005},
archivePrefix={arXiv},
eprint={math/0506475},
primaryClass={math.LO cs.LO math.GM}
} | srinivasan2005foundations |
arxiv-676761 | math/0506538 | Edit Distance between Unlabeled Ordered Trees | <|reference_start|>Edit Distance between Unlabeled Ordered Trees: There exists a bijection between one stack sortable permutations --permutations which avoid the pattern 231-- and planar trees. We define an edit distance between permutations which is coherent with the standard edit distance between trees. This one-to-one correspondence yields a polynomial algorithm for the subpermutation problem for $(231)$ avoiding permutations. Moreover, we obtain the generating function of the edit distance between ordered trees and some special ones. For the general case we show that the mean edit distance between a planar tree and all other planar trees is at least $n/ln(n)$. Some results can be extended to labeled trees considering colored Dyck paths or equivalently colored one stack sortable permutations.<|reference_end|> | arxiv | @article{micheli2005edit,
title={Edit Distance between Unlabeled Ordered Trees},
author={Anne Micheli (LIAFA), Dominique Rossin (LIAFA)},
journal={arXiv preprint arXiv:math/0506538},
year={2005},
archivePrefix={arXiv},
eprint={math/0506538},
primaryClass={math.CO cs.DM}
} | micheli2005edit |
arxiv-676762 | math/0506553 | Introduction to Cirquent Calculus and Abstract Resource Semantics | <|reference_start|>Introduction to Cirquent Calculus and Abstract Resource Semantics: This paper introduces a refinement of the sequent calculus approach called cirquent calculus. While in Gentzen-style proof trees sibling (or cousin, etc.) sequents are disjoint sequences of formulas, in cirquent calculus they are permitted to share elements. Explicitly allowing or disallowing shared resources and thus taking to a more subtle level the resource-awareness intuitions underlying substructural logics, cirquent calculus offers much greater flexibility and power than sequent calculus does. A need for substantially new deductive tools came with the birth of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) - the semantically constructed formal theory of computational resources, which has stubbornly resisted any axiomatization attempts within the framework of traditional syntactic approaches. Cirquent calculus breaks the ice. Removing contraction from the full collection of its rules yields a sound and complete system for the basic fragment CL5 of computability logic. Doing the same in sequent calculus, on the other hand, throws out the baby with the bath water, resulting in the strictly weaker affine logic. An implied claim of computability logic is that it is CL5 rather than affine logic that adequately materializes the resource philosophy traditionally associated with the latter. To strengthen this claim, the paper further introduces an abstract resource semantics and shows the soundness and completeness of CL5 with respect to it.<|reference_end|> | arxiv | @article{japaridze2005introduction,
title={Introduction to Cirquent Calculus and Abstract Resource Semantics},
author={Giorgi Japaridze},
journal={Journal of Logic and Computation 16 (2006), pp. 489-532},
year={2005},
doi={10.1093/logcom/exl005},
archivePrefix={arXiv},
eprint={math/0506553},
primaryClass={math.LO cs.LO}
} | japaridze2005introduction |
arxiv-676763 | math/0507032 | Transitive Hall sets | <|reference_start|>Transitive Hall sets: We give the definition of Lazard and Hall sets in the context of transitive factorizations of free monoids. The equivalence of the two properties is proved. This allows to build new effective bases of free partially commutative Lie algebras. The commutation graphs for which such sets exist are completely characterized and we explicit, in this context, the classical PBW rewriting process.<|reference_end|> | arxiv | @article{duchamp2005transitive,
title={Transitive Hall sets},
author={G'erard Henry Edmond Duchamp (LIPN), Jean-Gabriel Luque (IGM),
Marianne Deboysson-Flouret (LIH)},
journal={arXiv preprint arXiv:math/0507032},
year={2005},
archivePrefix={arXiv},
eprint={math/0507032},
primaryClass={math.CO cs.DM}
} | duchamp2005transitive |
arxiv-676764 | math/0507041 | The conjugacy problem and related problems in lattice-ordered groups | <|reference_start|>The conjugacy problem and related problems in lattice-ordered groups: We study, from a constructive computational point of view, the techniques used to solve the conjugacy problem in the "generic" lattice-ordered group Aut(R) of order automorphisms of the real line. We use these techniques in order to show that for each choice of parameters f,g in Aut(R), the equation xfx=g is effectively solvable in Aut(R).<|reference_end|> | arxiv | @article{holland2005the,
title={The conjugacy problem and related problems in lattice-ordered groups},
author={W. Charles Holland and Boaz Tsaban},
journal={International Journal of Algebra and Computation 15 (2005),
395-404},
year={2005},
doi={10.1142/S0218196705002232},
archivePrefix={arXiv},
eprint={math/0507041},
primaryClass={math.GR cs.CC math.GN}
} | holland2005the |
arxiv-676765 | math/0507235 | Analyticity of Entropy Rate of Hidden Markov Chains | <|reference_start|>Analyticity of Entropy Rate of Hidden Markov Chains: We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions the hidden Markov chain {\em itself} varies analytically, in a strong sense, as a function of the underlying Markov chain parameters.<|reference_end|> | arxiv | @article{han2005analyticity,
title={Analyticity of Entropy Rate of Hidden Markov Chains},
author={Guangyue Han, Brian Marcus},
journal={arXiv preprint arXiv:math/0507235},
year={2005},
archivePrefix={arXiv},
eprint={math/0507235},
primaryClass={math.PR cs.IT math.IT}
} | han2005analyticity |
arxiv-676766 | math/0507410 | Methods for the construction of generators of algebraic curvature tensors | <|reference_start|>Methods for the construction of generators of algebraic curvature tensors: We demonstrate the use of several tools from Algebraic Combinatorics such as Young tableaux, symmetry operators, the Littlewood-Richardson rule and discrete Fourier transforms of symmetric groups in investigations of algebraic curvature tensors.<|reference_end|> | arxiv | @article{fiedler2005methods,
title={Methods for the construction of generators of algebraic curvature
tensors},
author={Bernd Fiedler},
journal={arXiv preprint arXiv:math/0507410},
year={2005},
archivePrefix={arXiv},
eprint={math/0507410},
primaryClass={math.CO cs.SC math.DG}
} | fiedler2005methods |
arxiv-676767 | math/0508171 | Matrices of Forests and the Analysis of Digraphs | <|reference_start|>Matrices of Forests and the Analysis of Digraphs: The matrices of spanning rooted forests are studied as a tool for analysing the structure of digraphs and measuring their characteristics. The problems of revealing the basis bicomponents, measuring vertex proximity, and ranking from preference relations / sports competitions are considered. It is shown that the vertex accessibility measure based on spanning forests has a number of desirable properties. An interpretation for the normalized matrix of out-forests in terms of information dissemination is given. Keywords: Laplacian matrix, spanning forest, matrix-forest theorem, proximity measure, bicomponent, ranking, incomplete tournament, paired comparisons<|reference_end|> | arxiv | @article{chebotarev2005matrices,
title={Matrices of Forests and the Analysis of Digraphs},
author={Pavel Chebotarev and Rafig Agaev},
journal={arXiv preprint arXiv:math/0508171},
year={2005},
archivePrefix={arXiv},
eprint={math/0508171},
primaryClass={math.CO cs.CV cs.NI}
} | chebotarev2005matrices |
arxiv-676768 | math/0508183 | On a Duality between Metrics and $\Sigma$-Proximities | <|reference_start|>On a Duality between Metrics and $\Sigma$-Proximities: : In studies of discrete structures, functions are frequently used that express proximity, but are not metrics. We consider a class of such functions that is characterized by a normalization condition and an inequality that plays the same role as the triangle inequality does for metrics. We show that the introduced functions, named $\Sigma$-proximities, are in a definite sense dual to metrics: there exists a natural one-to-one correspondence between metrics and $\Sigma$-proximities defined on the same finite set; in contrast to metrics, $\Sigma$-proximities measure {\it comparative} proximity; the closer the objects, the greater the $\Sigma$-proximity; diagonal entries of the $\Sigma$-proximity matrix characterize the ``centrality'' of elements. The results are extended to arbitrary infinite sets.<|reference_end|> | arxiv | @article{chebotarev2005on,
title={On a Duality between Metrics and $\Sigma$-Proximities},
author={P. Yu. Chebotarev and E. V. Shamis},
journal={Automation and Remote Control 59 (1998) 608--612},
year={2005},
archivePrefix={arXiv},
eprint={math/0508183},
primaryClass={math.MG cs.DS math.CO}
} | chebotarev2005on |
arxiv-676769 | math/0508199 | Extending Utility Representations of Partial Orders | <|reference_start|>Extending Utility Representations of Partial Orders: The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em separably increasing}. Explicit formulas are given for a class of extensions which involves an arbitrary bounded increasing function. Similar results are obtained for monotone functions that represent strict partial orders on arbitrary abstract sets X. The special case where P is a Pareto subset is considered.<|reference_end|> | arxiv | @article{chebotarev2005extending,
title={Extending Utility Representations of Partial Orders},
author={Pavel Chebotarev},
journal={In: Constructing and Applying Objective Functions. Lecture Notes
in Economics and Math. Systems, Vol.510, Springer, 2002, P. 63-74},
year={2005},
doi={10.1007/978-3-642-56038-5_4},
archivePrefix={arXiv},
eprint={math/0508199},
primaryClass={math.OC cs.DS math.FA}
} | chebotarev2005extending |
arxiv-676770 | math/0508212 | The Symmetric Traveling Salesman Problem | <|reference_start|>The Symmetric Traveling Salesman Problem: Let M be an nXn symetric matrix, n, even, T, an upper bound for T_OPT, an optimal tour, sigma_T, the smaller-valued perfect matching obtained from alternate edges of T expressed as a product of 2-cycles. Applying the modified Floyd-Warshall algorithm to (sigma_T)^-1M^-, we construct acceptable and 2-circuit cycles some sets of which may yield circuits that can be patched into tours. We obtain necessary and sufficient conditions for a set, S, of cycles to yield circuits that may be patched into a tour.Assume that the following (Condition A)is valid: If (sigma_T)s = T*, |T*|<T, then all cycles of s have values less than |T| - |sigma_T|.Let SFWOPT),S(OPT)be the respective sets of cycles yielding T_FWOPT, T_OPT. Given Condition(A), using F-W, we can always obtain S(FWOPT). Using Condition A but not F-W, S_OPT is always obtainable from a subset of the cycles obtained.<|reference_end|> | arxiv | @article{kleiman2005the,
title={The Symmetric Traveling Salesman Problem},
author={Howard Kleiman},
journal={arXiv preprint arXiv:math/0508212},
year={2005},
archivePrefix={arXiv},
eprint={math/0508212},
primaryClass={math.CO cs.DS}
} | kleiman2005the |
arxiv-676771 | math/0508319 | Combinations and Mixtures of Optimal Policies in Unichain Markov Decision Processes are Optimal | <|reference_start|>Combinations and Mixtures of Optimal Policies in Unichain Markov Decision Processes are Optimal: We show that combinations of optimal (stationary) policies in unichain Markov decision processes are optimal. That is, let M be a unichain Markov decision process with state space S, action space A and policies \pi_j^*: S -> A (1\leq j\leq n) with optimal average infinite horizon reward. Then any combination \pi of these policies, where for each state i in S there is a j such that \pi(i)=\pi_j^*(i), is optimal as well. Furthermore, we prove that any mixture of optimal policies, where at each visit in a state i an arbitrary action \pi_j^*(i) of an optimal policy is chosen, yields optimal average reward, too.<|reference_end|> | arxiv | @article{ortner2005combinations,
title={Combinations and Mixtures of Optimal Policies in Unichain Markov
Decision Processes are Optimal},
author={Ronald Ortner},
journal={arXiv preprint arXiv:math/0508319},
year={2005},
archivePrefix={arXiv},
eprint={math/0508319},
primaryClass={math.CO cs.DM cs.LG math.OC math.PR}
} | ortner2005combinations |
arxiv-676772 | math/0508320 | Embeddability of Arrangements of Pseudocircles into the Sphere | <|reference_start|>Embeddability of Arrangements of Pseudocircles into the Sphere: An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart, Ortner 2004) so-called *intersection schemes* were introduced. Building up on results about the latter, we first clarify the notion of embedding of an arrangement. Once this is done it is shown how the embeddability of an arrangement depends on the embeddability of its subarrangements. The main result presented is that an arrangement of pseudocircles can be embedded into the sphere if and only if all of its subarrangements of four pseudocircles are embeddable into the sphere as well.<|reference_end|> | arxiv | @article{ortner2005embeddability,
title={Embeddability of Arrangements of Pseudocircles into the Sphere},
author={Ronald Ortner},
journal={arXiv preprint arXiv:math/0508320},
year={2005},
archivePrefix={arXiv},
eprint={math/0508320},
primaryClass={math.CO cs.CG math.GT}
} | ortner2005embeddability |
arxiv-676773 | math/0508350 | Toward accurate polynomial evaluation in rounded arithmetic | <|reference_start|>Toward accurate polynomial evaluation in rounded arithmetic: Given a multivariate real (or complex) polynomial $p$ and a domain $\cal D$, we would like to decide whether an algorithm exists to evaluate $p(x)$ accurately for all $x \in {\cal D}$ using rounded real (or complex) arithmetic. Here ``accurately'' means with relative error less than 1, i.e., with some correct leading digits. The answer depends on the model of rounded arithmetic: We assume that for any arithmetic operator $op(a,b)$, for example $a+b$ or $a \cdot b$, its computed value is $op(a,b) \cdot (1 + \delta)$, where $| \delta |$ is bounded by some constant $\epsilon$ where $0 < \epsilon \ll 1$, but $\delta$ is otherwise arbitrary. This model is the traditional one used to analyze the accuracy of floating point algorithms.Our ultimate goal is to establish a decision procedure that, for any $p$ and $\cal D$, either exhibits an accurate algorithm or proves that none exists. In contrast to the case where numbers are stored and manipulated as finite bit strings (e.g., as floating point numbers or rational numbers) we show that some polynomials $p$ are impossible to evaluate accurately. The existence of an accurate algorithm will depend not just on $p$ and $\cal D$, but on which arithmetic operators and which constants are are available and whether branching is permitted. Toward this goal, we present necessary conditions on $p$ for it to be accurately evaluable on open real or complex domains ${\cal D}$. We also give sufficient conditions, and describe progress toward a complete decision procedure. We do present a complete decision procedure for homogeneous polynomials $p$ with integer coefficients, ${\cal D} = \C^n$, and using only the arithmetic operations $+$, $-$ and $\cdot$.<|reference_end|> | arxiv | @article{demmel2005toward,
title={Toward accurate polynomial evaluation in rounded arithmetic},
author={James Demmel, Ioana Dumitriu, Olga Holtz},
journal={in Foundations of Computational Mathematics: Santander 2005 (L.
Pardo et al, eds.) Cambridge University Press, 2006, pp. 36-105},
year={2005},
archivePrefix={arXiv},
eprint={math/0508350},
primaryClass={math.NA cs.CC}
} | demmel2005toward |
arxiv-676774 | math/0508533 | On the cascade rollback synchronization | <|reference_start|>On the cascade rollback synchronization: We consider a cascade model of $N$ different processors performing a distributed parallel simulation. The main goal of the study is to show that the long-time dynamics of the system has a cluster behavior. To attack this problem we combine two methods: stochastic comparison and Foster-Lyapunov functions.<|reference_end|> | arxiv | @article{manita2005on,
title={On the cascade rollback synchronization},
author={Anatoli Manita and Francois Simonot},
journal={arXiv preprint arXiv:math/0508533},
year={2005},
archivePrefix={arXiv},
eprint={math/0508533},
primaryClass={math.PR cs.DC}
} | manita2005on |
arxiv-676775 | math/0509004 | Counting unlabelled toroidal graphs with no K33-subdivisions | <|reference_start|>Counting unlabelled toroidal graphs with no K33-subdivisions: We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of core graphs. Using structure theorems for toroidal and projective-planar graphs containing no K33-subdivisions, we apply these techniques to obtain their unlabelled enumeration.<|reference_end|> | arxiv | @article{gagarin2005counting,
title={Counting unlabelled toroidal graphs with no K33-subdivisions},
author={Andrei Gagarin, Gilbert Labelle, Pierre Leroux (LaCIM, Universite du
Quebec a Montreal)},
journal={Adv. in Appl. Math. 39 (2007), no. 1, pp. 51-75},
year={2005},
doi={10.1016/j.aam.2006.05.006},
archivePrefix={arXiv},
eprint={math/0509004},
primaryClass={math.CO cs.DM}
} | gagarin2005counting |
arxiv-676776 | math/0509248 | Deterministic modal Bayesian Logic: derive the Bayesian within the modal logic T | <|reference_start|>Deterministic modal Bayesian Logic: derive the Bayesian within the modal logic T: In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of logical independence is also defined within the logic itself. This logic is shown to be non trivial and is not reduced to classical propositions. A model is constructed for the logic. Completeness results are proved. It is shown that any unconditioned probability can be extended to the whole logic DmBL. The Bayesian is then recovered from the probabilistic DmBL. At last, it is shown why DmBL is compliant with Lewis triviality.<|reference_end|> | arxiv | @article{dambreville2005deterministic,
title={Deterministic modal Bayesian Logic: derive the Bayesian within the modal
logic T},
author={Frederic Dambreville (DGA/CEP/GIP/SRO)},
journal={arXiv preprint arXiv:math/0509248},
year={2005},
archivePrefix={arXiv},
eprint={math/0509248},
primaryClass={math.LO cs.LO math.PR}
} | dambreville2005deterministic |
arxiv-676777 | math/0509325 | On $Z_2^k$-Dual Binary Codes | <|reference_start|>On $Z_2^k$-Dual Binary Codes: A new generalization of the Gray map is introduced. The new generalization $\Phi: Z_{2^k}^n \to Z_{2}^{2^{k-1}n}$ is connected with the known generalized Gray map $\phi$ in the following way: if we take two dual linear $Z_{2^k}$-codes and construct binary codes from them using the generalizations $\phi$ and $\Phi$ of the Gray map, then the weight enumerators of the binary codes obtained will satisfy the MacWilliams identity. The classes of $Z_{2^k}$-linear Hadamard codes and co-$Z_{2^k}$-linear extended 1-perfect codes are described, where co-$Z_{2^k}$-linearity means that the code can be obtained from a linear $Z_{2^k}$-code with the help of the new generalized Gray map. Keywords: Gray map, Hadamard codes, MacWilliams identity, perfect codes, $Z_{2^k}$-linearity<|reference_end|> | arxiv | @article{krotov2005on,
title={On $Z_{2^k}$-Dual Binary Codes},
author={Denis Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)},
journal={IEEE Trans. Inf. Theory 53(4) 2007, 1532-1537},
year={2005},
doi={10.1109/TIT.2007.892787},
archivePrefix={arXiv},
eprint={math/0509325},
primaryClass={math.CO cs.IT math.IT}
} | krotov2005on |
arxiv-676778 | math/0509358 | On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4 | <|reference_start|>On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4: A subset $S$ of $\{0,1,...,2t-1\}^n$ is called a $t$-fold MDS code if every line in each of $n$ base directions contains exactly $t$ elements of $S$. The adjacency graph of a $t$-fold MDS code is not connected if and only if the characteristic function of the code is the repetition-free sum of the characteristic functions of $t$-fold MDS codes of smaller lengths. In the case $t=2$, the theory has the following application. The union of two disjoint $(n,4^{n-1},2)$ MDS codes in $\{0,1,2,3\}^n$ is a double-MDS-code. If the adjacency graph of the double-MDS-code is not connected, then the double-code can be decomposed into double-MDS-codes of smaller lengths. If the graph has more than two connected components, then the MDS codes are also decomposable. The result has an interpretation as a test for reducibility of $n$-quasigroups of order 4. Keywords: MDS codes, n-quasigroups, decomposability, reducibility, frequency hypercubes, latin hypercubes<|reference_end|> | arxiv | @article{krotov2005on,
title={On decomposability of 4-ary distance 2 MDS codes, double-codes, and
n-quasigroups of order 4},
author={Denis Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)},
journal={Discrete Math. 308(15) 2008, 3322-3334},
year={2005},
doi={10.1016/j.disc.2007.06.038},
archivePrefix={arXiv},
eprint={math/0509358},
primaryClass={math.CO cs.IT math.IT}
} | krotov2005on |
arxiv-676779 | math/0509478 | Simultaneous Diagonal Flips in Plane Triangulations | <|reference_start|>Simultaneous Diagonal Flips in Plane Triangulations: Simultaneous diagonal flips in plane triangulations are investigated. It is proved that every $n$-vertex triangulation with at least six vertices has a simultaneous flip into a 4-connected triangulation, and that it can be computed in O(n) time. It follows that every triangulation has a simultaneous flip into a Hamiltonian triangulation. This result is used to prove that for any two $n$-vertex triangulations, there exists a sequence of $O(\log n)$ simultaneous flips to transform one into the other. The total number of edges flipped in this sequence is O(n). The maximum size of a simultaneous flip is then studied. It is proved that every triangulation has a simultaneous flip of at least ${1/3}(n-2)$ edges. On the other hand, every simultaneous flip has at most $n-2$ edges, and there exist triangulations with a maximum simultaneous flip of ${6/7}(n-2)$ edges.<|reference_end|> | arxiv | @article{bose2005simultaneous,
title={Simultaneous Diagonal Flips in Plane Triangulations},
author={Prosenjit Bose, Jurek Czyzowicz, Zhicheng Gao, Pat Morin, David R.
Wood},
journal={J. Graph Theory 54(4):307-330, 2007},
year={2005},
doi={10.1002/jgt.20214},
archivePrefix={arXiv},
eprint={math/0509478},
primaryClass={math.CO cs.CG}
} | bose2005simultaneous |
arxiv-676780 | math/0509523 | Permutation Polynomials modulo m | <|reference_start|>Permutation Polynomials modulo m: This paper mainly studies problems about so called "permutation polynomials modulo $m$", polynomials with integer coefficients that can induce bijections over Z_m={0,...,m-1}. The necessary and sufficient conditions of permutation polynomials are given, and the number of all permutation polynomials of given degree and the number induced bijections are estimated. A method is proposed to determine all equivalent polynomials from the induced polynomial function, which can be used to determine all equivalent polynomials that induce a given bijection. A few problems have not been solved yet in this paper and left for open study. Note: After finishing the first draft, we noticed that some results obtained in this paper can be proved in other ways (see Remark 2). In this case, this work gives different and independent proofs of related results.<|reference_end|> | arxiv | @article{li2005permutation,
title={Permutation Polynomials modulo m},
author={Shujun Li},
journal={arXiv preprint arXiv:math/0509523},
year={2005},
archivePrefix={arXiv},
eprint={math/0509523},
primaryClass={math.NT cs.CR}
} | li2005permutation |
arxiv-676781 | math/0509575 | Evolutionary Trees and the Ising Model on the Bethe Lattice: a Proof of Steel's Conjecture | <|reference_start|>Evolutionary Trees and the Ising Model on the Bethe Lattice: a Proof of Steel's Conjecture: A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct the leaf-labelled tree. It is well known that in order to reconstruct a tree on $n$ leaves, sample sequences of length $\Omega(\log n)$ are needed. It was conjectured by M. Steel that for the CFN/Ising evolutionary model, if the mutation probability on all edges of the tree is less than $p^{\ast} = (\sqrt{2}-1)/2^{3/2}$, then the tree can be recovered from sequences of length $O(\log n)$. The value $p^{\ast}$ is given by the transition point for the extremality of the free Gibbs measure for the Ising model on the binary tree. Steel's conjecture was proven by the second author in the special case where the tree is "balanced." The second author also proved that if all edges have mutation probability larger than $p^{\ast}$ then the length needed is $n^{\Omega(1)}$. Here we show that Steel's conjecture holds true for general trees by giving a reconstruction algorithm that recovers the tree from $O(\log n)$-length sequences when the mutation probabilities are discretized and less than $p^\ast$. Our proof and results demonstrate that extremality of the free Gibbs measure on the infinite binary tree, which has been studied before in probability, statistical physics and computer science, determines how distinguishable are Gibbs measures on finite binary trees.<|reference_end|> | arxiv | @article{daskalakis2005evolutionary,
title={Evolutionary Trees and the Ising Model on the Bethe Lattice: a Proof of
Steel's Conjecture},
author={Constantinos Daskalakis, Elchanan Mossel, Sebastien Roch},
journal={arXiv preprint arXiv:math/0509575},
year={2005},
archivePrefix={arXiv},
eprint={math/0509575},
primaryClass={math.PR cs.CE cs.DS math.CA math.CO math.ST q-bio.PE stat.TH}
} | daskalakis2005evolutionary |
arxiv-676782 | math/0509620 | On diameter perfect constant-weight ternary codes | <|reference_start|>On diameter perfect constant-weight ternary codes: From cosets of binary Hamming codes we construct diameter perfect constant-weight ternary codes with weight $n-1$ (where $n$ is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before. Keywords: constant-weight codes, ternary codes, perfect codes, diameter perfect codes, perfect matchings, Preparata codes<|reference_end|> | arxiv | @article{krotov2005on,
title={On diameter perfect constant-weight ternary codes},
author={Denis Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)},
journal={Discrete Math. 308(14) 2008, 3104-3114},
year={2005},
doi={10.1016/j.disc.2007.08.037},
archivePrefix={arXiv},
eprint={math/0509620},
primaryClass={math.CO cs.IT math.IT}
} | krotov2005on |
arxiv-676783 | math/0510013 | Network Kriging | <|reference_start|>Network Kriging: Network service providers and customers are often concerned with aggregate performance measures that span multiple network paths. Unfortunately, forming such network-wide measures can be difficult, due to the issues of scale involved. In particular, the number of paths grows too rapidly with the number of endpoints to make exhaustive measurement practical. As a result, it is of interest to explore the feasibility of methods that dramatically reduce the number of paths measured in such situations while maintaining acceptable accuracy. We cast the problem as one of statistical prediction--in the spirit of the so-called `kriging' problem in spatial statistics--and show that end-to-end network properties may be accurately predicted in many cases using a surprisingly small set of carefully chosen paths. More precisely, we formulate a general framework for the prediction problem, propose a class of linear predictors for standard quantities of interest (e.g., averages, totals, differences) and show that linear algebraic methods of subset selection may be used to effectively choose which paths to measure. We characterize the performance of the resulting methods, both analytically and numerically. The success of our methods derives from the low effective rank of routing matrices as encountered in practice, which appears to be a new observation in its own right with potentially broad implications on network measurement generally.<|reference_end|> | arxiv | @article{chua2005network,
title={Network Kriging},
author={David B. Chua, Eric D. Kolaczyk and Mark Crovella},
journal={arXiv preprint arXiv:math/0510013},
year={2005},
archivePrefix={arXiv},
eprint={math/0510013},
primaryClass={math.ST cs.NI stat.TH}
} | chua2005network |
arxiv-676784 | math/0510027 | Prefab posets` Whitney numbers | <|reference_start|>Prefab posets` Whitney numbers: We introduce a natural partial order in structurally natural finite subsets the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling-like numbers` triangular array are then calculated and the explicit formula for them is provided. Next - in the second construction - we endow the set sums of prefabiants with such an another partial order that their their bell like numbers include fibonacci triad sequences introduced recently by the present author in order to extend famous relation between binomial newton coefficients and fibonacci numbers onto the infinity of their relatives among which there are also the fibonacci triad sequences and binomial-like coefficients (incidence coefficients included).<|reference_end|> | arxiv | @article{kwasniewski2005prefab,
title={Prefab posets` Whitney numbers},
author={A. K. Kwasniewski},
journal={Bull. Soc. Sci. Lett. Lodz, vol 60, (2005). 25-33},
year={2005},
archivePrefix={arXiv},
eprint={math/0510027},
primaryClass={math.CO cs.DM}
} | kwasniewski2005prefab |
arxiv-676785 | math/0510263 | Cubic Partial Cubes from Simplicial Arrangements | <|reference_start|>Cubic Partial Cubes from Simplicial Arrangements: We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.<|reference_end|> | arxiv | @article{eppstein2005cubic,
title={Cubic Partial Cubes from Simplicial Arrangements},
author={David Eppstein},
journal={Electronic J. Combinatorics 13(1, R79):1\^a?"14, Sep 2006},
year={2005},
archivePrefix={arXiv},
eprint={math/0510263},
primaryClass={math.CO cs.CG math.MG}
} | eppstein2005cubic |
arxiv-676786 | math/0510264 | Gowers Uniformity, Influence of Variables, and PCPs | <|reference_start|>Gowers Uniformity, Influence of Variables, and PCPs: Gowers introduced, for d\geq 1, the notion of dimension-d uniformity U^d(f) of a function f: G -> \C, where G is a finite abelian group and \C are the complex numbers. Roughly speaking, if U^d(f) is small, then f has certain "pseudorandomness" properties. We prove the following property of functions with large U^d(f). Write G=G_1 x >... x G_n as a product of groups. If a bounded balanced function f:G_1 x ... x G_n -> \C is such that U^{d} (f) > epsilon, then one of the coordinates of f has influence at least epsilon/2^{O(d)}. The Gowers inner product of a collection of functions is a related notion of pseudorandomness. We prove that if a collection of bounded functions has large Gowers inner product, and at least one function in the collection is balanced, then there is a variable that has high influence for at least four of the functions in the collection. Finally, we relate the acceptance probability of the "hypergraph long-code test" proposed by Samorodnitsky and Trevisan to the Gowers inner product of the functions being tested and we deduce applications to the construction of Probabilistically Checkable Proofs and to hardness of approximation.<|reference_end|> | arxiv | @article{samorodnitsky2005gowers,
title={Gowers Uniformity, Influence of Variables, and PCPs},
author={Alex Samorodnitsky and Luca Trevisan},
journal={arXiv preprint arXiv:math/0510264},
year={2005},
archivePrefix={arXiv},
eprint={math/0510264},
primaryClass={math.CO cs.CC}
} | samorodnitsky2005gowers |
arxiv-676787 | math/0510276 | An algorithmic and a geometric characterization of Coarsening At Random | <|reference_start|>An algorithmic and a geometric characterization of Coarsening At Random: We show that the class of conditional distributions satisfying the coarsening at Random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects generalizing the notion of partition of a set. However, the complexity of a given CAR mechanism can be large: the maximal "height" of the needed multicovers can be exponential in the number of points in the sample space. The results stem from a geometric interpretation of the set of CAR distributions as a convex polytope and a characterization of its extreme points. The hierarchy of CAR models defined in this way could be useful in parsimonious statistical modelling of CAR mechanisms, though the results also raise doubts in applied work as to the meaningfulness of the CAR assumption in its full generality.<|reference_end|> | arxiv | @article{gill2005an,
title={An algorithmic and a geometric characterization of Coarsening At Random},
author={Richard D. Gill (Leiden University), Peter D. Grunwald (CWI Amsterdam)},
journal={The Annals of Statistics 2008, Vol. 36, No. 5, 2409-2422},
year={2005},
doi={10.1214/07-AOS532},
number={See also 0811.0683 (duplicate submission)},
archivePrefix={arXiv},
eprint={math/0510276},
primaryClass={math.ST cs.AI stat.ME stat.TH}
} | gill2005an |
arxiv-676788 | math/0510304 | Stationary or static space-times and Young tableaux | <|reference_start|>Stationary or static space-times and Young tableaux: Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors \theta with an irreducible (2,1)-symmetry. In differential geometry examples of curvature formulas are known which contain generators on the basis of S or A realized by differentiable tensor fields in a natural way. We show that certain curvature formulas for stationary or static space-times contain such differentiable realizations of generators based on \theta. The tensor \theta is connected with the timelike Killing vector field of the space-time. \theta lies in a special symmetry class from the infinite family of irreducible (2,1)-symmetry classes. We determine characteristics of this class. In particular, this class allows a maximal reduction of the length of the curvature formulas. We use a projection formalism by Vladimirov, Young symmetrizers and Littlewood-Richardson products. Computer calculations were carried out by means of the packages Ricci and PERMS.<|reference_end|> | arxiv | @article{fiedler2005stationary,
title={Stationary or static space-times and Young tableaux},
author={Bernd Fiedler},
journal={J.Phys.Conf.Ser.30:152-162,2006},
year={2005},
doi={10.1088/1742-6596/30/1/018},
archivePrefix={arXiv},
eprint={math/0510304},
primaryClass={math.DG cs.SC gr-qc math.CO}
} | fiedler2005stationary |
arxiv-676789 | math/0510520 | Counting Solutions to Binomial Complete Intersections | <|reference_start|>Counting Solutions to Binomial Complete Intersections: We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is #P-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors.<|reference_end|> | arxiv | @article{cattani2005counting,
title={Counting Solutions to Binomial Complete Intersections},
author={Eduardo Cattani and Alicia Dickenstein},
journal={arXiv preprint arXiv:math/0510520},
year={2005},
archivePrefix={arXiv},
eprint={math/0510520},
primaryClass={math.AC cs.CC math.CO}
} | cattani2005counting |
arxiv-676790 | math/0510521 | On surrogate loss functions and $f$-divergences | <|reference_start|>On surrogate loss functions and $f$-divergences: The goal of binary classification is to estimate a discriminant function $\gamma$ from observations of covariate vectors and corresponding binary labels. We consider an elaboration of this problem in which the covariates are not available directly but are transformed by a dimensionality-reducing quantizer $Q$. We present conditions on loss functions such that empirical risk minimization yields Bayes consistency when both the discriminant function and the quantizer are estimated. These conditions are stated in terms of a general correspondence between loss functions and a class of functionals known as Ali-Silvey or $f$-divergence functionals. Whereas this correspondence was established by Blackwell [Proc. 2nd Berkeley Symp. Probab. Statist. 1 (1951) 93--102. Univ. California Press, Berkeley] for the 0--1 loss, we extend the correspondence to the broader class of surrogate loss functions that play a key role in the general theory of Bayes consistency for binary classification. Our result makes it possible to pick out the (strict) subset of surrogate loss functions that yield Bayes consistency for joint estimation of the discriminant function and the quantizer.<|reference_end|> | arxiv | @article{nguyen2005on,
title={On surrogate loss functions and $f$-divergences},
author={XuanLong Nguyen, Martin J. Wainwright, Michael I. Jordan},
journal={Annals of Statistics 2009, Vol. 37, No. 2, 876-904},
year={2005},
doi={10.1214/08-AOS595},
number={IMS-AOS-AOS595},
archivePrefix={arXiv},
eprint={math/0510521},
primaryClass={math.ST cs.IT math.IT stat.TH}
} | nguyen2005on |
arxiv-676791 | math/0510573 | Fast Monte-Carlo Low Rank Approximations for Matrices | <|reference_start|>Fast Monte-Carlo Low Rank Approximations for Matrices: In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time consuming for very large m and n. We present here a Monte Carlo algorithm for iteratively computing a k-rank approximation to the data consisting of mxn matrix A. Each iteration involves the reading of O(k) of columns or rows of A. The complexity of our algorithm is O(kmn). Our algorithm, distinguished from other known algorithms, guarantees that each iteration is a better k-rank approximation than the previous iteration. We believe that this algorithm will have many applications in data mining, data storage and data analysis.<|reference_end|> | arxiv | @article{friedland2005fast,
title={Fast Monte-Carlo Low Rank Approximations for Matrices},
author={Shmuel Friedland, Mostafa Kaveh, Amir Niknejad, Hossein Zare},
journal={arXiv preprint arXiv:math/0510573},
year={2005},
archivePrefix={arXiv},
eprint={math/0510573},
primaryClass={math.NA cs.DS}
} | friedland2005fast |
arxiv-676792 | math/0511343 | Random regular graphs of non-constant degree: Concentration of the chromatic number | <|reference_start|>Random regular graphs of non-constant degree: Concentration of the chromatic number: In this work we show that with high probability the chromatic number of a graph sampled from the random regular graph model $\Gnd$ for $d=o(n^{1/5})$ is concentrated in two consecutive values, thus extending a previous result of Achlioptas and Moore. This concentration phenomena is very similar to that of the binomial random graph model $\Gnp$ with $p=\frac{d}{n}$. Our proof is largely based on ideas of Alon and Krivelevich who proved this two-point concentration result for $\Gnp$ for $p=n^{-\delta}$ where $\delta>1/2$. The main tool used to derive such a result is a careful analysis of the distribution of edges in $\Gnd$, relying both on the switching technique and on bounding the probability of exponentially small events in the configuration model.<|reference_end|> | arxiv | @article{ben-shimon2005random,
title={Random regular graphs of non-constant degree: Concentration of the
chromatic number},
author={Sonny Ben-Shimon and Michael Krivelevich},
journal={Discrete Mathematics, 309(12):4149--4161, 2009},
year={2005},
doi={10.1016/j.disc.2008.12.014},
archivePrefix={arXiv},
eprint={math/0511343},
primaryClass={math.CO cs.DM math.PR}
} | ben-shimon2005random |
arxiv-676793 | math/0512110 | Computably Based Locally Compact Spaces | <|reference_start|>Computably Based Locally Compact Spaces: ASD (Abstract Stone Duality) is a re-axiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambda-calculus. In this paper, this is shown to be equivalent to a notion of computable basis for locally compact sober spaces or locales, involving a family of open subspaces and accompanying family of compact ones. This generalises Smyth's effectively given domains and Jung's strong proximity lattices. Part of the data for a basis is the inclusion relation of compact subspaces within open ones, which is formulated in locale theory as the way-below relation on a continuous lattice. The finitary properties of this relation are characterised here, including the Wilker condition for the cover of a compact space by two open ones. The real line is used as a running example, being closely related to Scott's domain of intervals. ASD does not use the category of sets, but the full subcategory of overt discrete objects plays this role; it is an arithmetic universe (pretopos with lists). In particular, we use this subcategory to translate computable bases for classical spaces into objects in the ASD calculus.<|reference_end|> | arxiv | @article{taylor2005computably,
title={Computably Based Locally Compact Spaces},
author={Paul Taylor},
journal={Logical Methods in Computer Science, Volume 2, Issue 1 (March 7,
2006) lmcs:2255},
year={2005},
doi={10.2168/LMCS-2(1:1)2006},
archivePrefix={arXiv},
eprint={math/0512110},
primaryClass={math.GN cs.LO math.CT}
} | taylor2005computably |
arxiv-676794 | math/0512140 | A new key exchange protocol based on the decomposition problem | <|reference_start|>A new key exchange protocol based on the decomposition problem: In this paper we present a new key establishment protocol based on the decomposition problem in non-commutative groups which is: given two elements $w, w_1$ of the platform group $G$ and two subgroups $A, B \subseteq G$ (not necessarily distinct), find elements $a \in A, b \in B$ such that $w_1 = a w b$. Here we introduce two new ideas that improve the security of key establishment protocols based on the decomposition problem. In particular, we conceal (i.e., do not publish explicitly) one of the subgroups $A, B$, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a given finitely generated subgroup.<|reference_end|> | arxiv | @article{shpilrain2005a,
title={A new key exchange protocol based on the decomposition problem},
author={Vladimir Shpilrain and Alexander Ushakov},
journal={arXiv preprint arXiv:math/0512140},
year={2005},
archivePrefix={arXiv},
eprint={math/0512140},
primaryClass={math.GR cs.CR}
} | shpilrain2005a |
arxiv-676795 | math/0512263 | Metric and probabilistic information associated with Fredholm integral equations of the first kind | <|reference_start|>Metric and probabilistic information associated with Fredholm integral equations of the first kind: The problem of evaluating the information associated with Fredholm integral equations of the first kind, when the integral operator is self-adjoint and compact, is considered here. The data function is assumed to be perturbed gently by an additive noise so that it still belongs to the range of the operator. First we estimate upper and lower bounds for the epsilon-capacity (and then for the metric information), and explicit computations in some specific cases are given; then the problem is reformulated from a probabilistic viewpoint and use is made of the probabilistic information theory. The results obtained by these two approaches are then compared.<|reference_end|> | arxiv | @article{de micheli2005metric,
title={Metric and probabilistic information associated with Fredholm integral
equations of the first kind},
author={Enrico De Micheli, Giovanni Alberto Viano},
journal={J. Integral Equations Appl. 14 (2002), 283-310},
year={2005},
archivePrefix={arXiv},
eprint={math/0512263},
primaryClass={math.CA cs.IT math.IT}
} | de micheli2005metric |
arxiv-676796 | math/0512578 | On cobweb posets and their combinatorially admissible sequences | <|reference_start|>On cobweb posets and their combinatorially admissible sequences: The main purpose of this article is to pose three problems which are easy to be formulated in an elementary way. These problems which are specifically important also for the new class of partially ordered sets seem to be not yet solved.<|reference_end|> | arxiv | @article{kwasniewski2005on,
title={On cobweb posets and their combinatorially admissible sequences},
author={A. K. Kwasniewski},
journal={Adv. Studies Contemp. Math. Vol. 18 No 1, 2009 17-32},
year={2005},
archivePrefix={arXiv},
eprint={math/0512578},
primaryClass={math.CO cs.DM}
} | kwasniewski2005on |
arxiv-676797 | math/0601487 | Constructing pairing-friendly elliptic curves with embedding degree 10 | <|reference_start|>Constructing pairing-friendly elliptic curves with embedding degree 10: We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham. We show that our framework incorporates existing constructions for k = 3, 4, 6, and 12, and we give evidence that the method is unlikely to produce infinite families of curves with embedding degree k > 12.<|reference_end|> | arxiv | @article{freeman2006constructing,
title={Constructing pairing-friendly elliptic curves with embedding degree 10},
author={David Freeman},
journal={arXiv preprint arXiv:math/0601487},
year={2006},
archivePrefix={arXiv},
eprint={math/0601487},
primaryClass={math.NT cs.CR}
} | freeman2006constructing |
arxiv-676798 | math/0601624 | Asymptotics of Bernoulli random walks, bridges, excursions and meanders with a given number of peaks | <|reference_start|>Asymptotics of Bernoulli random walks, bridges, excursions and meanders with a given number of peaks: A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being $+1$ or -1, equally likely. The other families cited in the title are Bernoulli random walks under various conditionings. A peak in a trajectory is a local maximum. In this paper, we condition the families of trajectories to have a given number of peaks. We show that, asymptotically, the main effect of setting the number of peaks is to change the order of magnitude of the trajectories. The counting process of the peaks, that encodes the repartition of the peaks in the trajectories, is also studied. It is shown that suitably normalized, it converges to a Brownian bridge which is independent of the limiting trajectory. Applications in terms of plane trees and parallelogram polyominoes are also provided.<|reference_end|> | arxiv | @article{labarbe2006asymptotics,
title={Asymptotics of Bernoulli random walks, bridges, excursions and meanders
with a given number of peaks},
author={Jean-Maxime Labarbe (LM-Versailles), Jean-Franc{c}ois Marckert
(LaBRI)},
journal={arXiv preprint arXiv:math/0601624},
year={2006},
archivePrefix={arXiv},
eprint={math/0601624},
primaryClass={math.PR cs.DM}
} | labarbe2006asymptotics |
arxiv-676799 | math/0601755 | Graph and Union of Graphs Compositions | <|reference_start|>Graph and Union of Graphs Compositions: Knopfmacher et all [1] was introduced the graph compositions` notion. In this note we add to these a new construction of tree-like graphs where nodes are graphs themselves. The first examples of these tree-like compositions, a corresponding theorem and resulting conclusions are provided.<|reference_end|> | arxiv | @article{bajguz2006graph,
title={Graph and Union of Graphs Compositions},
author={Wieslaw Bajguz},
journal={arXiv preprint arXiv:math/0601755},
year={2006},
archivePrefix={arXiv},
eprint={math/0601755},
primaryClass={math.CO cs.DM}
} | bajguz2006graph |
arxiv-676800 | math/0602053 | Towards a Definition of an Algorithm | <|reference_start|>Towards a Definition of an Algorithm: We define an algorithm to be the set of programs that implement or express that algorithm. The set of all programs is partitioned into equivalence classes. Two programs are equivalent if they are essentially the same program. The set of equivalence classes forms the category of algorithms. Although the set of programs does not even form a category, the set of algorithms form a category with extra structure. The conditions we give that describe when two programs are essentially the same turn out to be coherence relations that enrich the category of algorithms with extra structure. Universal properties of the category of algorithms are proved.<|reference_end|> | arxiv | @article{yanofsky2006towards,
title={Towards a Definition of an Algorithm},
author={Noson S. Yanofsky},
journal={Journal of Logic and Computation 2010;},
year={2006},
archivePrefix={arXiv},
eprint={math/0602053},
primaryClass={math.LO cs.LO math.CT}
} | yanofsky2006towards |
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