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arxiv-676601 | math/0209332 | Hypercomputation: computing more than the Turing machine | <|reference_start|>Hypercomputation: computing more than the Turing machine: Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation that can compute more than the Turing machine and addresses their implications. In this report, I survey much of the work that has been done on hypercomputation, explaining how such non-classical models fit into the classical theory of computation and comparing their relative powers. I also examine the physical requirements for such machines to be constructible and the kinds of hypercomputation that may be possible within the universe. Finally, I show how the possibility of hypercomputation weakens the impact of Godel's Incompleteness Theorem and Chaitin's discovery of 'randomness' within arithmetic.<|reference_end|> | arxiv | @article{ord2002hypercomputation:,
title={Hypercomputation: computing more than the Turing machine},
author={Toby Ord},
journal={arXiv preprint arXiv:math/0209332},
year={2002},
archivePrefix={arXiv},
eprint={math/0209332},
primaryClass={math.LO cs.OH math-ph math.MP}
} | ord2002hypercomputation: |
arxiv-676602 | math/0209407 | Uniformly distributed sequences of p-adic integers, II | <|reference_start|>Uniformly distributed sequences of p-adic integers, II: The paper describes ergodic (with respect to the Haar measure) functions in the class of all functions, which are defined on (and take values in) the ring of p-adic integers, and which satisfy (at least, locally) Lipschitz condition with coefficient 1. Equiprobable (in particular, measure-preserving) functions of this class are described also. In some cases (and especially for p=2) the descriptions are given by explicit formulae. Some of the results may be viewed as descriptions of ergodic isometric dynamical systems on p-adic unit disk. The study was motivated by the problem of pseudorandom number generation for computer simulation and cryptography. From this view the paper describes nonlinear congruential pseudorandom generators modulo M which produce stricly periodic uniformly distributed sequences modulo M with maximal possible period length (i.e., exactly M). Both the state change function and the output function of these generators could be, e.g., meromorphic functions (in particular, polynomials with rational, but not necessarily integer coefficients, or rational functions), or compositions of arithmetical operations (like addition, multiplication, exponentiation, raising to integer powers, including negative ones) with standard computer operations, such as bitwise logical operations (XOR, OR, AND, etc.). The linear complexity of the produced sequences is also studied.<|reference_end|> | arxiv | @article{anashin2002uniformly,
title={Uniformly distributed sequences of p-adic integers, II},
author={Vladimir Anashin (Faculty for the Information Security, Russian State
University for the Humanities)},
journal={Diskret.Mat., vol. 14 (2002), no. 4. pp. 3--64 (Russian); Discrete
Math. Appl., vol. 12 (2002), no. 6, pp. 527--590 (English translation)},
year={2002},
number={IISIS-02-09-01},
archivePrefix={arXiv},
eprint={math/0209407},
primaryClass={math.NT cs.IT math.DS math.IT}
} | anashin2002uniformly |
arxiv-676603 | math/0210018 | Topological robotics: motion planning in projective spaces | <|reference_start|>Topological robotics: motion planning in projective spaces: We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial position to a final position by a continuous motion in the space. The final goal is to construct an algorithm which will perform this task once the initial and final positions are given. Any such motion planning algorithm will have instabilities, which are caused by topological reasons. A general approach to study instabilities of robot motion was suggested recently by the first named author. With any path-connected topological space X one associates a number TC(X), called the topological complexity of X. This number is of fundamental importance for the motion planning problem: TC(X) determines character of instabilities which have all motion planning algorithms in X. In the present paper we study the topological complexity of real projective spaces. In particular we compute TC(RP^n) for all n<24. Our main result is that (for n distinct from 1, 3, 7) the problem of calculating of TC(RP^n) is equivalent to finding the smallest k such that RP^n can be immersed into the Euclidean space R^{k-1}.<|reference_end|> | arxiv | @article{farber2002topological,
title={Topological robotics: motion planning in projective spaces},
author={Michael Farber, Serge Tabachnikov and Sergey Yuzvinsky},
journal={arXiv preprint arXiv:math/0210018},
year={2002},
archivePrefix={arXiv},
eprint={math/0210018},
primaryClass={math.AT cs.RO math.DG}
} | farber2002topological |
arxiv-676604 | math/0210052 | Criteria for Balance in Abelian Gain Graphs, with Applications to Piecewise-Linear Geometry | <|reference_start|>Criteria for Balance in Abelian Gain Graphs, with Applications to Piecewise-Linear Geometry: A gain graph is a triple (G,h,H), where G is a connected graph with an arbitrary, but fixed, orientation of edges, H is a group, and h is a homomorphism from the free group on the edges of G to H. A gain graph is called balanced if the h-image of each closed walk on G is the identity. Consider a gain graph with abelian gain group having no odd torsion. If there is a basis of the graph's binary cycle space each of whose members can be lifted to a closed walk whose gain is the identity, then the gain graph is balanced, provided that the graph is finite or the group has no nontrivial infinitely 2-divisible elements. We apply this theorem to deduce a result on the projective geometry of piecewise-linear realizations of cell-decompositions of manifolds.<|reference_end|> | arxiv | @article{rybnikov2002criteria,
title={Criteria for Balance in Abelian Gain Graphs, with Applications to
Piecewise-Linear Geometry},
author={Konstantin Rybnikov, Thomas Zaslavsky},
journal={Discrete and Computational Geometry, 34 (2005), no. 2, 251-268.},
year={2002},
archivePrefix={arXiv},
eprint={math/0210052},
primaryClass={math.CO cs.CG cs.DM cs.DS math.AT}
} | rybnikov2002criteria |
arxiv-676605 | math/0210115 | Topological Robotics: Subspace Arrangements and Collision Free Motion Planning | <|reference_start|>Topological Robotics: Subspace Arrangements and Collision Free Motion Planning: We study an elementary problem of the topological robotics: collective motion of a set of $n$ distinct particles which one has to move from an initial configuration to a final configuration, with the requirement that no collisions occur in the process of motion. The ultimate goal is to construct an algorithm which will perform this task once the initial and the final configurations are given. This reduces to a topological problem of finding the topological complexity TC(C_n(\R^m)) of the configutation space C_n(\R^m) of $n$ distinct ordered particles in \R^m. We solve this problem for m=2 (the planar case) and for all odd m, including the case m=3 (particles in the three-dimensional space). We also study a more general motion planning problem in Euclidean space with a hyperplane arrangement as obstacle.<|reference_end|> | arxiv | @article{farber2002topological,
title={Topological Robotics: Subspace Arrangements and Collision Free Motion
Planning},
author={Michael Farber and Sergey Yuzvinsky},
journal={arXiv preprint arXiv:math/0210115},
year={2002},
archivePrefix={arXiv},
eprint={math/0210115},
primaryClass={math.AT cs.RO math.DG}
} | farber2002topological |
arxiv-676606 | math/0210408 | Representations of finite groups on Riemann-Roch spaces | <|reference_start|>Representations of finite groups on Riemann-Roch spaces: We study the action of a finite group on the Riemann-Roch space of certain divisors on a curve. If $G$ is a finite subgroup of the automorphism group of a projective curve $X$ over an algebraically closed field and $D$ is a divisor on $X$ left stable by $G$ then we show the irreducible constituents of the natural representation of $G$ on the Riemann-Roch space $L(D)=L_X(D)$ are of dimension $\leq d$, where $d$ is the size of the smallest $G$-orbit acting on $X$. We give an example to show that this is, in general, sharp (i.e., that dimension $d$ irreducible constituents can occur). Connections with coding theory, in particular to permutation decoding of AG codes, are discussed in the last section. Many examples are included.<|reference_end|> | arxiv | @article{joyner2002representations,
title={Representations of finite groups on Riemann-Roch spaces},
author={David Joyner and Will Traves},
journal={arXiv preprint arXiv:math/0210408},
year={2002},
archivePrefix={arXiv},
eprint={math/0210408},
primaryClass={math.AG cs.IT math.GR math.IT}
} | joyner2002representations |
arxiv-676607 | math/0211040 | On cyclic convolutional codes | <|reference_start|>On cyclic convolutional codes: We investigate the notion of cyclicity for convolutional codes as it has been introduced by Piret and Roos in the seventies. Codes of this type are described as submodules of the module of all vector polynomials in one variable with some additional generalized cyclic structure but also as specific left ideals in a skew polynomial ring. Extending a result of Piret, we show in a purely algebraic setting that these ideals are always principal. This leads to the notion of a generator polynomial just like for cyclic block codes. Similarly a control polynomial can be introduced by considering the right annihilator ideal. An algorithmic procedure is developed which produces unique reduced generator and control polynomials. We also show how basic code properties and a minimal generator matrix can be read off from these objects. A close link between polynomial and vector description of the codes is provided by certain generalized circulant matrices.<|reference_end|> | arxiv | @article{gluesing-luerssen2002on,
title={On cyclic convolutional codes},
author={H. Gluesing-Luerssen and W. Schmale},
journal={arXiv preprint arXiv:math/0211040},
year={2002},
archivePrefix={arXiv},
eprint={math/0211040},
primaryClass={math.RA cs.IT math.CO math.IT}
} | gluesing-luerssen2002on |
arxiv-676608 | math/0211107 | On Near-MDS Elliptic Codes | <|reference_start|>On Near-MDS Elliptic Codes: The main conjecture on maximum distance separable (MDS) codes states that, execpt for some special cases, the maximum length of a q-ary linear MDS code is q+1. This conjecture does not hold true for near maximum distance separable codes because of the existence of q-ary near MDS elliptic codes having length bigger than q+1. An interesting related question is whether a near MDS elliptic code can be extended to a longer near MDS code. Our results are some non-extendability results and an alternative and simpler construction for certain known near MDS elliptic codes.<|reference_end|> | arxiv | @article{giulietti2002on,
title={On Near-MDS Elliptic Codes},
author={Massimo Giulietti},
journal={arXiv preprint arXiv:math/0211107},
year={2002},
archivePrefix={arXiv},
eprint={math/0211107},
primaryClass={math.AG cs.IT math.CO math.IT}
} | giulietti2002on |
arxiv-676609 | math/0211156 | Ideal decompositions and computation of tensor normal forms | <|reference_start|>Ideal decompositions and computation of tensor normal forms: Symmetry properties of r-times covariant tensors T can be described by certain linear subspaces W of the group ring K[S_r] of a symmetric group S_r. If for a class of tensors T such a W is known, the elements of the orthogonal subspace W^{\bot} of W within the dual space of K[S_r] yield linear identities needed for a treatment of the term combination problem for the coordinates of the T. We give the structure of these W for every situation which appears in symbolic tensor calculations by computer. Characterizing idempotents of such W can be determined by means of an ideal decomposition algorithm which works in every semisimple ring up to an isomorphism. Furthermore, we use tools such as the Littlewood-Richardson rule, plethysms and discrete Fourier transforms for S_r to increase the efficience of calculations. All described methods were implemented in a Mathematica package called PERMS.<|reference_end|> | arxiv | @article{fiedler2002ideal,
title={Ideal decompositions and computation of tensor normal forms},
author={B. Fiedler},
journal={Seminaire Lotharingien de Combinatoire, 45 (2001) Article B45g.
http://www.mat.univie.ac.at/~slc/wpapers/s45fiedler.html},
year={2002},
archivePrefix={arXiv},
eprint={math/0211156},
primaryClass={math.CO cs.SC math.DG}
} | fiedler2002ideal |
arxiv-676610 | math/0211267 | On alternative approach for verifiable secret sharing | <|reference_start|>On alternative approach for verifiable secret sharing: Secret sharing allows split/distributed control over the secret (e.g. master key). Verifiable secret sharing (VSS) is the secret sharing extended by verification capacity. Usually verification comes at the price. We propose "free lunch", the approach that allows to overcome this inconvenience.<|reference_end|> | arxiv | @article{kulesza2002on,
title={On alternative approach for verifiable secret sharing},
author={Kamil Kulesza, Zbigniew Kotulski, Joseph Pieprzyk},
journal={arXiv preprint arXiv:math/0211267},
year={2002},
archivePrefix={arXiv},
eprint={math/0211267},
primaryClass={math.CO cs.CR cs.DM}
} | kulesza2002on |
arxiv-676611 | math/0211269 | On ASGS framework: general requirements and an example of implementation | <|reference_start|>On ASGS framework: general requirements and an example of implementation: In the paper we propose general framework for Automatic Secret Generation and Sharing (ASGS) that should be independent of underlying secret sharing scheme. ASGS allows to prevent the dealer from knowing the secret or even to eliminate him at all. Two situations are discussed. First concerns simultaneous generation and sharing of the random, prior nonexistent secret. Such a secret remains unknown until it is reconstructed. Next, we propose the framework for automatic sharing of a known secret. In this case the dealer does not know the secret and the secret owner does not know the shares. We present opportunities for joining ASGS with other extended capabilities, with special emphasize on PVSS and proactive secret sharing. Finally, we illustrate framework with practical implementation. Keywords: cryptography, secret sharing, data security, extended capabilities, extended key verification protocol<|reference_end|> | arxiv | @article{kulesza2002on,
title={On ASGS framework: general requirements and an example of implementation},
author={Kamil Kulesza, Zbigniew Kotulski},
journal={arXiv preprint arXiv:math/0211269},
year={2002},
archivePrefix={arXiv},
eprint={math/0211269},
primaryClass={math.CO cs.CR cs.DM cs.IT math.IT}
} | kulesza2002on |
arxiv-676612 | math/0211307 | On the multiresolution structure of Internet traffic traces | <|reference_start|>On the multiresolution structure of Internet traffic traces: Internet traffic on a network link can be modeled as a stochastic process. After detecting and quantifying the properties of this process, using statistical tools, a series of mathematical models is developed, culminating in one that is able to generate ``traffic'' that exhibits --as a key feature-- the same difference in behavior for different time scales, as observed in real traffic, and is moreover indistinguishable from real traffic by other statistical tests as well. Tools inspired from the models are then used to determine and calibrate the type of activity taking place in each of the time scales. Surprisingly, the above procedure does not require any detailed information originating from either the network dynamics, or the decomposition of the total traffic into its constituent user connections, but rather only the compliance of these connections to very weak conditions.<|reference_end|> | arxiv | @article{drakakis2002on,
title={On the multiresolution structure of Internet traffic traces},
author={Konstantinos Drakakis, Dragan Radulovic},
journal={arXiv preprint arXiv:math/0211307},
year={2002},
doi={10.1117/12.475274},
archivePrefix={arXiv},
eprint={math/0211307},
primaryClass={math.PR cs.NI}
} | drakakis2002on |
arxiv-676613 | math/0211317 | On graph coloring check-digit method | <|reference_start|>On graph coloring check-digit method: We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the result is outlined. Next, graph coloring based check-digit scheme is proposed. We use quantitative result derived, to show, that feasibility of the proposed scheme increases with size of the number which digits are checked, and overall probability of digits errors.<|reference_end|> | arxiv | @article{kulesza2002on,
title={On graph coloring check-digit method},
author={Kamil Kulesza, Zbigniew Kotulski},
journal={arXiv preprint arXiv:math/0211317},
year={2002},
archivePrefix={arXiv},
eprint={math/0211317},
primaryClass={math.CO cs.CR cs.DM cs.DS}
} | kulesza2002on |
arxiv-676614 | math/0211344 | Algebraic methods for computing smallest enclosing and circumscribing cylinders of simplices | <|reference_start|>Algebraic methods for computing smallest enclosing and circumscribing cylinders of simplices: We provide an algebraic framework to compute smallest enclosing and smallest circumscribing cylinders of simplices in Euclidean space $\E^n$. Explicitly, the computation of a smallest enclosing cylinder in $\mathbb{E}^3$ is reduced to the computation of a smallest circumscribing cylinder. We improve existing polynomial formulations to compute the locally extreme circumscribing cylinders in $\E^3$ and exhibit subclasses of simplices where the algebraic degrees can be further reduced. Moreover, we generalize these efficient formulations to the $n$-dimensional case and provide bounds on the number of local extrema. Using elementary invariant theory, we prove structural results on the direction vectors of any locally extreme circumscribing cylinder for regular simplices.<|reference_end|> | arxiv | @article{brandenberg2002algebraic,
title={Algebraic methods for computing smallest enclosing and circumscribing
cylinders of simplices},
author={R. Brandenberg (Technische Universitaet Muenchen), T. Theobald
(Technische Universitaet Muenchen)},
journal={arXiv preprint arXiv:math/0211344},
year={2002},
archivePrefix={arXiv},
eprint={math/0211344},
primaryClass={math.OC cs.CG}
} | brandenberg2002algebraic |
arxiv-676615 | math/0212038 | A Goppa-like bound on the trellis state complexity of algebraic geometric codes | <|reference_start|>A Goppa-like bound on the trellis state complexity of algebraic geometric codes: For a linear code $\cC$ of length $n$ and dimension $k$, Wolf noticed that the trellis state complexity $s(\cC)$ of $\cC$ is upper bounded by $w(\cC):=\min(k,n-k)$. In this paper we point out some new lower bounds for $s(\cC)$. In particular, if $\cC$ is an Algebraic Geometric code, then $s(\cC)\geq w(\cC)-(g-a)$, where $g$ is the genus of the underlying curve and $a$ is the abundance of the code.<|reference_end|> | arxiv | @article{munuera2002a,
title={A Goppa-like bound on the trellis state complexity of algebraic
geometric codes},
author={Carlos Munuera and Fernando Torres},
journal={arXiv preprint arXiv:math/0212038},
year={2002},
archivePrefix={arXiv},
eprint={math/0212038},
primaryClass={math.AG cs.IT math.IT}
} | munuera2002a |
arxiv-676616 | math/0212044 | Toric ideals, real toric varieties, and the algebraic moment map | <|reference_start|>Toric ideals, real toric varieties, and the algebraic moment map: This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties and the algebraic moment map. In particular, we explain the relation between linear precision and the algebraic moment map. This builds on the introduction to toric varieties by David Cox: What is a Toric Variety? at http://www.cs.amherst.edu/~dac/lectures/tutorial.ps<|reference_end|> | arxiv | @article{sottile2002toric,
title={Toric ideals, real toric varieties, and the algebraic moment map},
author={Frank Sottile},
journal={in Topics in Algebraic Geometry and Geometric Modeling, Contemp.
Math., 334, 2003., pp.225-240},
year={2002},
archivePrefix={arXiv},
eprint={math/0212044},
primaryClass={math.AG cs.CG}
} | sottile2002toric |
arxiv-676617 | math/0212212 | Coverage control for mobile sensing networks | <|reference_start|>Coverage control for mobile sensing networks: This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.<|reference_end|> | arxiv | @article{cortes2002coverage,
title={Coverage control for mobile sensing networks},
author={J. Cortes, S. Martinez, T. Karatas, F. Bullo},
journal={IEEE Transactions on Robotics and Automation 20 (2) (2004),
243-255},
year={2002},
archivePrefix={arXiv},
eprint={math/0212212},
primaryClass={math.OC cs.IT math.IT}
} | cortes2002coverage |
arxiv-676618 | math/0212278 | Determination of the structure of algebraic curvature tensors by means of Young symmetrizers | <|reference_start|>Determination of the structure of algebraic curvature tensors by means of Young symmetrizers: For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins that every algebraic curvature tensor has a structure which is very similar to that of the above Osserman curvature tensors. We verify our results by means of the Littlewood-Richardson rule and plethysms. For certain symbolic calculations we used the Mathematica packages MathTensor, Ricci and PERMS.<|reference_end|> | arxiv | @article{fiedler2002determination,
title={Determination of the structure of algebraic curvature tensors by means
of Young symmetrizers},
author={B. Fiedler},
journal={Seminaire Lotharingien de Combinatoire, 48 (2003) Article B48d},
year={2002},
archivePrefix={arXiv},
eprint={math/0212278},
primaryClass={math.CO cs.SC math.DG}
} | fiedler2002determination |
arxiv-676619 | math/0301042 | On the symmetry classes of the first covariant derivatives of tensor fields | <|reference_start|>On the symmetry classes of the first covariant derivatives of tensor fields: We show that the symmetry classes of torsion-free covariant derivatives $\nabla T$ of r-times covariant tensor fields T can be characterized by Littlewood-Richardson products $\sigma [1]$ where $\sigma$ is a representation of the symmetric group $S_r$ which is connected with the symmetry class of T. If $\sigma = [\lambda]$ is irreducible then $\sigma [1]$ has a multiplicity free reduction $[\lambda][1] = \sum [\mu]$ and all primitive idempotents belonging to that sum can be calculated from a generating idempotent e of the symmetry class of T by means of the irreducible characters or of a discrete Fourier transform of $S_{r+1}$. We apply these facts to derivatives $\nabla S$, $\nabla A$ of symmetric or alternating tensor fields. The symmetry classes of the differences $\nabla S - sym(\nabla S)$ and $\nabla A - alt(\nabla A)$ are characterized by Young frames (r, 1) and (2, 1^{r-1}), respectively. However, while the symmetry class of $\nabla A - alt(\nabla A)$ can be generated by Young symmetrizers of (2, 1^{r-1}), no Young symmetrizer of (r, 1) generates the symmetry class of $\nabla S - sym(\nabla S)$. Furthermore we show in the case r = 2 that $\nabla S - sym(\nabla S)$ and $\nabla A - alt(\nabla A)$ can be applied in generator formulas of algebraic covariant derivative curvature tensors. For certain symbolic calculations we used the Mathematica packages Ricci and PERMS.<|reference_end|> | arxiv | @article{fiedler2003on,
title={On the symmetry classes of the first covariant derivatives of tensor
fields},
author={B. Fiedler},
journal={Seminaire Lotharingien de Combinatoire, 49 (2003) Article B49f},
year={2003},
archivePrefix={arXiv},
eprint={math/0301042},
primaryClass={math.CO cs.SC math.DG}
} | fiedler2003on |
arxiv-676620 | math/0301135 | Grassmannian Frames with Applications to Coding and Communication | <|reference_start|>Grassmannian Frames with Applications to Coding and Communication: For a given class ${\cal F}$ of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation $|< f_k,f_l >|$ among all frames $\{f_k\}_{k \in {\cal I}} \in {\cal F}$. We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These bounds yield a simple condition under which Grassmannian frames coincide with uniform tight frames. We exploit connections to graph theory, equiangular line sets, and coding theory in order to derive explicit constructions of Grassmannian frames. Our findings extend recent results on uniform tight frames. We then introduce infinite-dimensional Grassmannian frames and analyze their connection to uniform tight frames for frames which are generated by group-like unitary systems. We derive an example of a Grassmannian Gabor frame by using connections to sphere packing theory. Finally we discuss the application of Grassmannian frames to wireless communication and to multiple description coding.<|reference_end|> | arxiv | @article{strohmer2003grassmannian,
title={Grassmannian Frames with Applications to Coding and Communication},
author={Thomas Strohmer and Robert Heath},
journal={arXiv preprint arXiv:math/0301135},
year={2003},
archivePrefix={arXiv},
eprint={math/0301135},
primaryClass={math.FA cs.IT math.IT}
} | strohmer2003grassmannian |
arxiv-676621 | math/0301211 | Binary trees and fibred categories | <|reference_start|>Binary trees and fibred categories: We develop a purely set-theoretic formalism for binary trees and binary graphs. We define a category of binary automata, and display it as a fibred category over the category of binary graphs. We also relate the notion of binary graphs to transition systems, which arise in the theory of concurrent computing.<|reference_end|> | arxiv | @article{raghavendra2003binary,
title={Binary trees and fibred categories},
author={N. Raghavendra},
journal={arXiv preprint arXiv:math/0301211},
year={2003},
archivePrefix={arXiv},
eprint={math/0301211},
primaryClass={math.CO cs.DM math.CT}
} | raghavendra2003binary |
arxiv-676622 | math/0301268 | Improving Search Algorithms by Using Intelligent Coordinates | <|reference_start|>Improving Search Algorithms by Using Intelligent Coordinates: We consider the problem of designing a set of computational agents so that as they all pursue their self-interests a global function G of the collective system is optimized. Three factors govern the quality of such design. The first relates to conventional exploration-exploitation search algorithms for finding the maxima of such a global function, e.g., simulated annealing. Game-theoretic algorithms instead are related to the second of those factors, and the third is related to techniques from the field of machine learning. Here we demonstrate how to exploit all three factors by modifying the search algorithm's exploration stage so that rather than by random sampling, each coordinate of the underlying search space is controlled by an associated machine-learning-based ``player'' engaged in a non-cooperative game. Experiments demonstrate that this modification improves SA by up to an order of magnitude for bin-packing and for a model of an economic process run over an underlying network. These experiments also reveal novel small worlds phenomena.<|reference_end|> | arxiv | @article{wolpert2003improving,
title={Improving Search Algorithms by Using Intelligent Coordinates},
author={David Wolpert, Kagan Tumer and Esfandiar Bandari},
journal={arXiv preprint arXiv:math/0301268},
year={2003},
doi={10.1103/PhysRevE.69.017701},
archivePrefix={arXiv},
eprint={math/0301268},
primaryClass={math.OC cond-mat.stat-mech cs.MA nlin.AO}
} | wolpert2003improving |
arxiv-676623 | math/0301274 | On the existence of a new family of Diophantine equations for $\bf \Omega$ | <|reference_start|>On the existence of a new family of Diophantine equations for $\bf \Omega$: We show how to determine the $k$-th bit of Chaitin's algorithmically random real number $\Omega$ by solving $k$ instances of the halting problem. From this we then reduce the problem of determining the $k$-th bit of $\Omega$ to determining whether a certain Diophantine equation with two parameters, $k$ and $N$, has solutions for an odd or an even number of values of $N$. We also demonstrate two further examples of $\Omega$ in number theory: an exponential Diophantine equation with a parameter $k$ which has an odd number of solutions iff the $k$-th bit of $\Omega$ is 1, and a polynomial of positive integer variables and a parameter $k$ that takes on an odd number of positive values iff the $k$-th bit of $\Omega$ is 1.<|reference_end|> | arxiv | @article{ord2003on,
title={On the existence of a new family of Diophantine equations for $\bf
\Omega$},
author={Toby Ord and Tien D. Kieu},
journal={Fundamenta Informaticae 56 (2003) 273--284},
year={2003},
archivePrefix={arXiv},
eprint={math/0301274},
primaryClass={math.NT cs.CC quant-ph}
} | ord2003on |
arxiv-676624 | math/0302043 | Extended visual cryptography systems | <|reference_start|>Extended visual cryptography systems: Visual cryptography schemes have been introduced in 1994 by Naor and Shamir. Their idea was to encode a secret image into $n$ shadow images and to give exactly one such shadow image to each member of a group $P$ of $n$ persons. Whereas most work in recent years has been done concerning the problem of qualified and forbidden subsets of $P$ or the question of contrast optimizing, in this paper we study extended visual cryptography schemes, i.e. shared secret systems where any subset of $P$ shares its own secret.<|reference_end|> | arxiv | @article{klein2003extended,
title={Extended visual cryptography systems},
author={Andreas Klein and Markus Wessler},
journal={arXiv preprint arXiv:math/0302043},
year={2003},
archivePrefix={arXiv},
eprint={math/0302043},
primaryClass={math.CO cs.IT math.IT}
} | klein2003extended |
arxiv-676625 | math/0302132 | Computing Symmetrized Weight Enumerators for Lifted Quadratic Residue Codes | <|reference_start|>Computing Symmetrized Weight Enumerators for Lifted Quadratic Residue Codes: The paper describes a method to determine symmetrized weight enumerators of $p^m$-linear codes based on the notion of a disjoint weight enumerator. Symmetrized weight enumerators are given for the lifted quadratic residue codes of length 24 modulo $2^m$ and modulo $3^m$, for any positive $m$.<|reference_end|> | arxiv | @article{duursma2003computing,
title={Computing Symmetrized Weight Enumerators for Lifted Quadratic Residue
Codes},
author={I.M. Duursma, M. Greferath},
journal={arXiv preprint arXiv:math/0302132},
year={2003},
archivePrefix={arXiv},
eprint={math/0302132},
primaryClass={math.CO cs.IT math.IT}
} | duursma2003computing |
arxiv-676626 | math/0302154 | Twisted Klein curves modulo 2 | <|reference_start|>Twisted Klein curves modulo 2: We give an explicit description of all 168 quartic curves over the field of two elements that are isomorphic to the Klein curve over an algebraic extension. Some of the curves have been known for their small class number, others for attaining the maximal number of rational points.<|reference_end|> | arxiv | @article{duursma2003twisted,
title={Twisted Klein curves modulo 2},
author={I.M. Duursma},
journal={arXiv preprint arXiv:math/0302154},
year={2003},
archivePrefix={arXiv},
eprint={math/0302154},
primaryClass={math.NT cs.IT math.AG math.IT}
} | duursma2003twisted |
arxiv-676627 | math/0302172 | Results on zeta functions for codes | <|reference_start|>Results on zeta functions for codes: We give a new and short proof of the Mallows-Sloane upper bound for self-dual codes. We formulate a version of Greene's theorem for normalized weight enumerators. We relate normalized rank-generating polynomials to two-variable zeta functions. And we show that a self-dual code has the Clifford property, but that the same property does not hold in general for formally self-dual codes.<|reference_end|> | arxiv | @article{duursma2003results,
title={Results on zeta functions for codes},
author={I.M. Duursma},
journal={arXiv preprint arXiv:math/0302172},
year={2003},
archivePrefix={arXiv},
eprint={math/0302172},
primaryClass={math.CO cs.IT math.IT math.NT}
} | duursma2003results |
arxiv-676628 | math/0302303 | Cubefree binary words avoiding long squares | <|reference_start|>Cubefree binary words avoiding long squares: Entringer, Jackson, and Schatz conjectured in 1974 that every infinite cubefree binary word contains arbitrarily long squares. In this paper we show this conjecture is false: there exist infinite cubefree binary words avoiding all squares xx with |x| >= 4, and the number 4 is best possible. However, the Entringer-Jackson-Schatz conjecture is true if "cubefree" is replaced with "overlap-free".<|reference_end|> | arxiv | @article{rampersad2003cubefree,
title={Cubefree binary words avoiding long squares},
author={Narad Rampersad, Jeffrey Shallit, Ming-wei Wang},
journal={arXiv preprint arXiv:math/0302303},
year={2003},
archivePrefix={arXiv},
eprint={math/0302303},
primaryClass={math.CO cs.DM}
} | rampersad2003cubefree |
arxiv-676629 | math/0302315 | Memory Efficient Arithmetic | <|reference_start|>Memory Efficient Arithmetic: In this paper we give an algorithm for computing the mth base-b digit (m=1 is the least significant digit) of an integer n (actually, it finds sharp approximations to n/b^m mod 1), where n is defined as the last number in a sequence of integers s1,s2,...,sL=n, where s1=0, s2=1, and each successive si is either the sum, product, or difference of two previous sj's in the sequence. In many cases, the algorithm will find this mth digit using far less memory than it takes to write down all the base-b digits of n, while the number of bit operations will grow only slighly worse than linear in the number of digits. One consequence of this result is that the mth base-10 digit of 2^t can be found using O(t^{2/3} log^C t) bits of storage (for some C>0), and O(t log^C t) bit operations. The algorithm is also highly parallelizable, and an M-fold reduction in running time can be achieved using M processors, although the memory required will then grow by a factor of M.<|reference_end|> | arxiv | @article{croot2003memory,
title={Memory Efficient Arithmetic},
author={Ernie Croot},
journal={arXiv preprint arXiv:math/0302315},
year={2003},
archivePrefix={arXiv},
eprint={math/0302315},
primaryClass={math.NT cs.DS}
} | croot2003memory |
arxiv-676630 | math/0303104 | Bounding the trellis state complexity of algebraic geometric codes | <|reference_start|>Bounding the trellis state complexity of algebraic geometric codes: Let C be an algebraic geometric code of dimension k and length n constructed on a curve X over $F_q$. Let s(C) be the state complexity of C and set w(C):=min{k,n-k}, the Wolf upper bound on s(C). We introduce a numerical function R that depends on the gonality sequence of X and show that s(C)\geq w(C)-R(2g-2), where g is the genus of X. As a matter of fact, R(2g-2)\leq g-(\gamma_2-2) with \gamma_2 being the gonality over F_q of X, and thus in particular we have that s(C)\geq w(C)-g+\gamma_2-2.<|reference_end|> | arxiv | @article{munuera2003bounding,
title={Bounding the trellis state complexity of algebraic geometric codes},
author={Carlos Munuera and Fernando Torres},
journal={arXiv preprint arXiv:math/0303104},
year={2003},
archivePrefix={arXiv},
eprint={math/0303104},
primaryClass={math.AG cs.IT math.IT}
} | munuera2003bounding |
arxiv-676631 | math/0303254 | Strongly MDS Convolutional Codes | <|reference_start|>Strongly MDS Convolutional Codes: MDS convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper we introduce a class of MDS convolutional codes whose column distances reach the generalized Singleton bound at the earliest possible instant. We call these codes strongly MDS convolutional codes. It is shown that these codes can decode a maximum number of errors per time interval when compared with other convolutional codes of the same rate and degree. These codes have also a maximum or near maximum distance profile. A code has a maximum distance profile if and only if the dual code has this property.<|reference_end|> | arxiv | @article{gluesing-luerssen2003strongly,
title={Strongly MDS Convolutional Codes},
author={Heide Gluesing-Luerssen, Joachim Rosenthal and Roxana Smarandache},
journal={arXiv preprint arXiv:math/0303254},
year={2003},
archivePrefix={arXiv},
eprint={math/0303254},
primaryClass={math.RA cs.IT math.IT math.OC}
} | gluesing-luerssen2003strongly |
arxiv-676632 | math/0303386 | Generic properties of Whitehead's Algorithm and isomorphism rigidity of random one-relator groups | <|reference_start|>Generic properties of Whitehead's Algorithm and isomorphism rigidity of random one-relator groups: We prove that Whitehead's algorithm for solving the automorphism problem in a fixed free group $F_k$ has strongly linear time generic-case complexity. This is done by showing that the ``hard'' part of the algorithm terminates in linear time on an exponentially generic set of input pairs. We then apply these results to one-relator groups. We obtain a Mostow-type isomorphism rigidity result for random one-relator groups: If two such groups are isomorphic then their Cayley graphs on the \emph{given generating sets} are isometric. Although no nontrivial examples were previously known, we prove that one-relator groups are generically \emph{complete} groups, that is, they have trivial center and trivial outer automorphism group. We also prove that the stabilizers of generic elements of $F_k$ in $Aut(F_k)$ are cyclic groups generated by inner automorphisms and that $Aut(F_k)$-orbits are uniformly small in the sense of their growth entropy. We further prove that the number $I_k(n)$ of \emph{isomorphism types} of $k$-generator one-relator groups with defining relators of length $n$ satisfies \[ \frac{c_1}{n} (2k-1)^n \le I_k(n)\le \frac{c_2}{n} (2k-1)^n, \] where $c_1=c_1(k)>0, c_2=c_2(k)>0$ are some constants independent of $n$. Thus $I_k(n)$ grows in essentially the same manner as the number of cyclic words of length $n$.<|reference_end|> | arxiv | @article{kapovich2003generic,
title={Generic properties of Whitehead's Algorithm and isomorphism rigidity of
random one-relator groups},
author={Ilya Kapovich, Paul Schupp and Vladimir Shpilrain},
journal={arXiv preprint arXiv:math/0303386},
year={2003},
archivePrefix={arXiv},
eprint={math/0303386},
primaryClass={math.GR cs.CC math.GT}
} | kapovich2003generic |
arxiv-676633 | math/0304095 | Polynomial versus Exponential Growth in Repetition-Free Binary Words | <|reference_start|>Polynomial versus Exponential Growth in Repetition-Free Binary Words: It is known that the number of overlap-free binary words of length n grows polynomially, while the number of cubefree binary words grows exponentially. We show that the dividing line between polynomial and exponential growth is 7/3. More precisely, there are only polynomially many binary words of length n that avoid 7/3-powers, but there are exponentially many binary words of length n that avoid (7/3+)-powers. This answers an open question of Kobayashi from 1986.<|reference_end|> | arxiv | @article{karhumaki2003polynomial,
title={Polynomial versus Exponential Growth in Repetition-Free Binary Words},
author={Juhani Karhumaki and Jeffrey Shallit},
journal={arXiv preprint arXiv:math/0304095},
year={2003},
archivePrefix={arXiv},
eprint={math/0304095},
primaryClass={math.CO cs.DM}
} | karhumaki2003polynomial |
arxiv-676634 | math/0304100 | A Direct Ultrametric Approach to Additive Complexity and the Shub-Smale Tau Conjecture | <|reference_start|>A Direct Ultrametric Approach to Additive Complexity and the Shub-Smale Tau Conjecture: The Shub-Smale Tau Conjecture is a hypothesis relating the number of integral roots of a polynomial f in one variable and the Straight-Line Program (SLP) complexity of f. A consequence of the truth of this conjecture is that, for the Blum-Shub-Smale model over the complex numbers, P differs from NP. We prove two weak versions of the Tau Conjecture and in so doing show that the Tau Conjecture follows from an even more plausible hypothesis. Our results follow from a new p-adic analogue of earlier work relating real algebraic geometry to additive complexity. For instance, we can show that a nonzero univariate polynomial of additive complexity s can have no more than 15+s^3(s+1)(7.5)^s s! =O(e^{s\log s}) roots in the 2-adic rational numbers Q_2, thus dramatically improving an earlier result of the author. This immediately implies the same bound on the number of ordinary rational roots, whereas the best previous upper bound via earlier techniques from real algebraic geometry was a quantity in Omega((22.6)^{s^2}). This paper presents another step in the author's program of establishing an algorithmic arithmetic version of fewnomial theory.<|reference_end|> | arxiv | @article{rojas2003a,
title={A Direct Ultrametric Approach to Additive Complexity and the Shub-Smale
Tau Conjecture},
author={J. Maurice Rojas},
journal={arXiv preprint arXiv:math/0304100},
year={2003},
archivePrefix={arXiv},
eprint={math/0304100},
primaryClass={math.NT cs.CC}
} | rojas2003a |
arxiv-676635 | math/0304192 | On reconstructing n-point configurations from the distribution of distances or areas | <|reference_start|>On reconstructing n-point configurations from the distribution of distances or areas: One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this distribution. After giving some counterexamples, we prove that this is the case for the vast majority of configurations. In the second part of the paper, the distribution of areas of sub-triangles is used for characterizing point configurations. Again it turns out that most configurations are reconstructible from the distribution of areas, though there are counterexamples.<|reference_end|> | arxiv | @article{boutin2003on,
title={On reconstructing n-point configurations from the distribution of
distances or areas},
author={Mireille Boutin, Gregor Kemper},
journal={arXiv preprint arXiv:math/0304192},
year={2003},
archivePrefix={arXiv},
eprint={math/0304192},
primaryClass={math.AC cs.CV cs.SC}
} | boutin2003on |
arxiv-676636 | math/0304283 | Whitehead method and Genetic Algorithms | <|reference_start|>Whitehead method and Genetic Algorithms: In this paper we discuss a genetic version (GWA) of the Whitehead's algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisingly fast and outperforms the standard Whitehead's algorithm in free groups of rank >= 5. Experimenting with GWA we collected an interesting numerical data that clarifies the time-complexity of the Whitehead's Problem in general. These experiments led us to several mathematical conjectures. If confirmed they will shed light on hidden mechanisms of Whitehead Method and geometry of automorphic orbits in free groups.<|reference_end|> | arxiv | @article{miasnikov2003whitehead,
title={Whitehead method and Genetic Algorithms},
author={Alexei D. Miasnikov, Alexei G. Myasnikov},
journal={arXiv preprint arXiv:math/0304283},
year={2003},
archivePrefix={arXiv},
eprint={math/0304283},
primaryClass={math.GR cs.NE cs.SC}
} | miasnikov2003whitehead |
arxiv-676637 | math/0304292 | The Ubiquity of Order Domains for the Construction of Error Control Codes | <|reference_start|>The Ubiquity of Order Domains for the Construction of Error Control Codes: The order domains are a class of commutative rings introduced by H{\o}holdt, van Lint, and Pellikaan to simplify the theory of error control codes using ideas from algebraic geometry. The definition is largely motivated by the structures utilized in the Berlekamp-Massey-Sakata (BMS) decoding algorithm, with Feng-Rao majority voting for unknown syndromes, applied to one-point geometric Goppa codes constructed from curves. However, order domains are much more general, and O'Sullivan has shown that the BMS algorithm can be applied to decode all codes constructed from order domains by a suitable generalization of Goppa's procedure for curves. In this article we will first discuss the connection between order domains and valuations on function fields over a finite field. Under some mild conditions, we will see that a general projective variety over a finite field has projective models which can be used to construct order domains and Goppa-type codes for which the BMS algorithm is applicable. We will then give a slightly different interpretation of Geil and Pellikaan's extrinsic characterization of order domains via the theory of Gr\"obner bases, and show that their results are related to the existence of toric deformations of varieties. To illustrate the potential usefulness of these observations, we present a series of new explicit examples of order domains associated to varieties with many rational points over finite fields: Hermitian hypersurfaces, Grassmannians, and flag varieties.<|reference_end|> | arxiv | @article{little2003the,
title={The Ubiquity of Order Domains for the Construction of Error Control
Codes},
author={John B. Little},
journal={Advances in Mathematics of Communications 1 (2007), 151-171},
year={2003},
archivePrefix={arXiv},
eprint={math/0304292},
primaryClass={math.AC cs.IT math.AG math.IT math.RA}
} | little2003the |
arxiv-676638 | math/0304305 | Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture | <|reference_start|>Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture: The Andrews-Curtis conjecture states that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of the elementary Nielsen transformations and conjugations. In this paper we describe all balanced presentations of the trivial group on two generators and with the total length of relators <= 12. We show that all these presentations satisfy the Andrews-Curtis conjecture.<|reference_end|> | arxiv | @article{miasnikov2003balanced,
title={Balanced presentations of the trivial group on two generators and the
Andrews-Curtis conjecture},
author={Alexei D. Miasnikov, Alexei G. Myasnikov},
journal={In W.Kantor and A.Seress,editors, Groups and Computation III,
volume 23, (2001) 257-263, Berlin},
year={2003},
archivePrefix={arXiv},
eprint={math/0304305},
primaryClass={math.GR cs.SC}
} | miasnikov2003balanced |
arxiv-676639 | math/0304306 | Genetic algorithms and the Andrews-Curtis conjecture | <|reference_start|>Genetic algorithms and the Andrews-Curtis conjecture: The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be transformed into the trivial presentation by a finite sequence of "elementary transformations" which are Nielsen transformations together with an arbitrary conjugation of a relator. It is believed that the Andrews-Curtis conjecture is false; however, not so many possible counterexamples are known. It is not a trivial matter to verify whether the conjecture holds for a given balanced presentation or not. The purpose of this paper is to describe some non-deterministic methods, called Genetic Algorithms, designed to test the validity of the Andrews-Curtis conjecture. Using such algorithm we have been able to prove that all known (to us) balanced presentations of the trivial group where the total length of the relators is at most 12 satisfy the conjecture. In particular, the Andrews-Curtis conjecture holds for the presentation <x,y|x y x = y x y, x^2 = y^3> which was one of the well known potential counterexamples.<|reference_end|> | arxiv | @article{miasnikov2003genetic,
title={Genetic algorithms and the Andrews-Curtis conjecture},
author={Alexei D. Miasnikov},
journal={International Journal of Algebra and Computation, Vol. 9 No. 6,
(1999) 671-686},
year={2003},
archivePrefix={arXiv},
eprint={math/0304306},
primaryClass={math.GR cs.NE cs.SC}
} | miasnikov2003genetic |
arxiv-676640 | math/0304346 | The envelope of lines meeting a fixed line that are tangent to two spheres | <|reference_start|>The envelope of lines meeting a fixed line that are tangent to two spheres: We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also meet the given line. All such configurations are degenerate. The path to this result involves the interplay of some beautiful and intricate geometry of real surfaces in 3-space, complex algebraic geometry, explicit computation and graphics.<|reference_end|> | arxiv | @article{megyesi2003the,
title={The envelope of lines meeting a fixed line that are tangent to two
spheres},
author={G'abor Megyesi (UMIST) and Frank Sottile (Texas A&M University)},
journal={Discrete and Computational Geometry, 33, Number 4, (2005)
617--644.},
year={2003},
archivePrefix={arXiv},
eprint={math/0304346},
primaryClass={math.AG cs.CG math.MG}
} | megyesi2003the |
arxiv-676641 | math/0304476 | Simultaneous avoidance of large squares and fractional powers in infinite binary words | <|reference_start|>Simultaneous avoidance of large squares and fractional powers in infinite binary words: In 1976, Dekking showed that there exists an infinite binary word that contains neither squares yy with y >= 4 nor cubes xxx. We show that `cube' can be replaced by any fractional power > 5/2. We also consider the analogous problem where `4' is replaced by any integer. This results in an interesting and subtle hierarchy.<|reference_end|> | arxiv | @article{shallit2003simultaneous,
title={Simultaneous avoidance of large squares and fractional powers in
infinite binary words},
author={Jeffrey Shallit},
journal={arXiv preprint arXiv:math/0304476},
year={2003},
archivePrefix={arXiv},
eprint={math/0304476},
primaryClass={math.CO cs.DM}
} | shallit2003simultaneous |
arxiv-676642 | math/0305121 | Robust Estimators under the Imprecise Dirichlet Model | <|reference_start|>Robust Estimators under the Imprecise Dirichlet Model: Walley's Imprecise Dirichlet Model (IDM) for categorical data overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or intervals. The main objective of this work is to derive exact, conservative, and approximate, robust and credible interval estimates under the IDM for a large class of statistical estimators, including the entropy and mutual information.<|reference_end|> | arxiv | @article{hutter2003robust,
title={Robust Estimators under the Imprecise Dirichlet Model},
author={Marcus Hutter},
journal={Proc. 3rd International Symposium on Imprecise Probabilities and
Their Application (ISIPTA-2003), pages 274-289},
year={2003},
number={IDSIA-03-03},
archivePrefix={arXiv},
eprint={math/0305121},
primaryClass={math.PR cs.IT cs.LG math.IT math.ST stat.TH}
} | hutter2003robust |
arxiv-676643 | math/0305135 | Distance bounds for convolutional codes and some optimal codes | <|reference_start|>Distance bounds for convolutional codes and some optimal codes: After a discussion of the Griesmer and Heller bound for the distance of a convolutional code we present several codes with various parameters, over various fields, and meeting the given distance bounds. Moreover, the Griesmer bound is used for deriving a lower bound for the field size of an MDS convolutional code and examples are presented showing that, in most cases, the lower bound is tight. Most of the examples in this paper are cyclic convolutional codes in a generalized sense as it has been introduced in the seventies. A brief introduction to this promising type of cyclicity is given at the end of the paper in order to make the examples more transparent.<|reference_end|> | arxiv | @article{gluesing-luerssen2003distance,
title={Distance bounds for convolutional codes and some optimal codes},
author={Heide Gluesing-Luerssen and Wiland Schmale},
journal={arXiv preprint arXiv:math/0305135},
year={2003},
archivePrefix={arXiv},
eprint={math/0305135},
primaryClass={math.RA cs.IT math.IT math.OC}
} | gluesing-luerssen2003distance |
arxiv-676644 | math/0305308 | Numerical Analogues of Aronson's Sequence | <|reference_start|>Numerical Analogues of Aronson's Sequence: Aronson's sequence 1, 4, 11, 16, ... is defined by the English sentence ``t is the first, fourth, eleventh, sixteenth, ... letter of this sentence.'' This paper introduces some numerical analogues, such as: a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition ``n is a member of the sequence if and only if a(n) is odd.'' This sequence can also be characterized by its ``square'', the sequence a^(2)(n) = a(a(n)), which equals 2n+3 for n >= 1. There are many generalizations of this sequence, some of which are new, while others throw new light on previously known sequences.<|reference_end|> | arxiv | @article{cloitre2003numerical,
title={Numerical Analogues of Aronson's Sequence},
author={Benoit Cloitre, N. J. A. Sloane, Matthew J. Vandermast},
journal={J. Integer Sequences, 6 (2003), #03.2.2},
year={2003},
archivePrefix={arXiv},
eprint={math/0305308},
primaryClass={math.NT cs.IT math.IT}
} | cloitre2003numerical |
arxiv-676645 | math/0306081 | Avoiding large squares in infinite binary words | <|reference_start|>Avoiding large squares in infinite binary words: We consider three aspects of avoiding large squares in infinite binary words. First, we construct an infinite binary word avoiding both cubes xxx and squares yy with |y| >= 4; our construction is somewhat simpler than the original construction of Dekking. Second, we construct an infinite binary word avoiding all squares except 00, 11, and 0101; our construction is somewhat simpler than the original construction of Fraenkel and Simpson. In both cases, we also show how to modify our construction to obtain exponentially many words of length n with the given avoidance properties. Finally, we answer an open question of Prodinger and Urbanek from 1979 by demonstrating the existence of two infinite binary words, each avoiding arbitrarily large squares, such that their perfect shuffle has arbitrarily large squares.<|reference_end|> | arxiv | @article{rampersad2003avoiding,
title={Avoiding large squares in infinite binary words},
author={Narad Rampersad, Jeffrey Shallit, and Ming-wei Wang},
journal={arXiv preprint arXiv:math/0306081},
year={2003},
archivePrefix={arXiv},
eprint={math/0306081},
primaryClass={math.CO cs.DM}
} | rampersad2003avoiding |
arxiv-676646 | math/0306354 | Coding and tiling of Julia sets for subhyperbolic rational maps | <|reference_start|>Coding and tiling of Julia sets for subhyperbolic rational maps: Let $f:\hat{C}\to\hat{C}$ be a subhyperbolic rational map of degree $d$. We construct a set of coding maps $Cod(f)=\{\pi_r:\Sigma\to J\}_r$ of the Julia set $J$ by geometric coding trees, where the parameter $r$ ranges over mappings from a certain tree to the Riemann sphere. Using the universal covering space $\phi:\tilde S\to S$ for the corresponding orbifold, we lift the inverse of $f$ to an iterated function system $I=(g_i)_{i=1,2,...,d}$. For the purpose of studying the structure of $Cod(f)$, we generalize Kenyon and Lagarias-Wang's results : If the attractor $K$ of $I$ has positive measure, then $K$ tiles $\phi^{-1}(J)$, and the multiplicity of $\pi_r$ is well-defined. Moreover, we see that the equivalence relation induced by $\pi_r$ is described by a finite directed graph, and give a necessary and sufficient condition for two coding maps $\pi_r$ and $\pi_{r'}$ to be equal.<|reference_end|> | arxiv | @article{kameyama2003coding,
title={Coding and tiling of Julia sets for subhyperbolic rational maps},
author={Atsushi Kameyama},
journal={arXiv preprint arXiv:math/0306354},
year={2003},
archivePrefix={arXiv},
eprint={math/0306354},
primaryClass={math.DS cs.IT math.IT}
} | kameyama2003coding |
arxiv-676647 | math/0306395 | Sur la non-linearite des fonctions booleennes | <|reference_start|>Sur la non-linearite des fonctions booleennes: Boolean functions on the space $F_{2}^m$ are not only important in the theory of error-correcting codes, but also in cryptography, where they occur in private key systems. In these two cases, the nonlinearity of these function is a main concept. In this article, I show that the spectral amplitude of boolean functions, which is linked to their nonlinearity, is of the order of $2^{m/2}\sqrt{m}$ in mean, whereas its range is bounded by $2^{m/2}$ and $2^m$. Moreover I examine a conjecture of Patterson and Wiedemann saying that the minimum of this spectral amplitude is as close as desired to $2^{m/2}$. I also study a weaker conjecture about the moments of order 4 of their Fourier transform. This article is inspired by works of Salem, Zygmund, Kahane and others about the related problem of real polynomials with random coefficients.<|reference_end|> | arxiv | @article{rodier2003sur,
title={Sur la non-linearite des fonctions booleennes},
author={Francois Rodier},
journal={arXiv preprint arXiv:math/0306395},
year={2003},
doi={10.4064/aa115-1-1},
archivePrefix={arXiv},
eprint={math/0306395},
primaryClass={math.NT cs.IT math.IT}
} | rodier2003sur |
arxiv-676648 | math/0306401 | The number of transversals to line segments in R^3 | <|reference_start|>The number of transversals to line segments in R^3: We completely describe the structure of the connected components of transversals to a collection of n line segments in R^3. We show that n>2 arbitrary line segments in R^3 admit 0, 1, ..., n or infinitely many line transversals. In the latter case, the transversals form up to n connected components.<|reference_end|> | arxiv | @article{brönnimann2003the,
title={The number of transversals to line segments in R^3},
author={Herv'e Br"onnimann, Hazel Everett, Sylvain Lazard, Frank Sottile,
and Sue Whitesides},
journal={Discrete and Computational Geometry, Volume 34, Number 3, (2005),
381--390.},
year={2003},
archivePrefix={arXiv},
eprint={math/0306401},
primaryClass={math.MG cs.CG}
} | brönnimann2003the |
arxiv-676649 | math/0307064 | The Number of Hierarchical Orderings | <|reference_start|>The Number of Hierarchical Orderings: An ordered set-partition (or preferential arrangement) of n labeled elements represents a single ``hierarchy''; these are enumerated by the ordered Bell numbers. In this note we determine the number of ``hierarchical orderings'' or ``societies'', where the n elements are first partitioned into m <= n subsets and a hierarchy is specified for each subset. We also consider the unlabeled case, where the ordered Bell numbers are replaced by the composition numbers. If there is only a single hierarchy, we show that the average rank of an element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the unlabeled case.<|reference_end|> | arxiv | @article{sloane2003the,
title={The Number of Hierarchical Orderings},
author={N. J. A. Sloane, Thomas Wieder},
journal={Order, 21 (2004), 83-89},
year={2003},
archivePrefix={arXiv},
eprint={math/0307064},
primaryClass={math.CO cs.IT math.IT}
} | sloane2003the |
arxiv-676650 | math/0307196 | Convolutional Codes with Maximum Distance Profile | <|reference_start|>Convolutional Codes with Maximum Distance Profile: Maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible distance from each other relative to any other convolutional code of the same rate and degree. In this paper we use methods from systems theory to characterize maximum distance profile codes algebraically. Tha main result shows that maximum distance profile codes form a generic set inside the variety which parametrizes the set of convolutional codes of a fixed rate and a fixed degree.<|reference_end|> | arxiv | @article{hutchinson2003convolutional,
title={Convolutional Codes with Maximum Distance Profile},
author={R. Hutchinson, J. Rosenthal, R. Smarandache},
journal={arXiv preprint arXiv:math/0307196},
year={2003},
archivePrefix={arXiv},
eprint={math/0307196},
primaryClass={math.OC cs.IT math.IT math.RA}
} | hutchinson2003convolutional |
arxiv-676651 | math/0308046 | Still better nonlinear codes from modular curves | <|reference_start|>Still better nonlinear codes from modular curves: We give a new construction of nonlinear error-correcting codes over suitable finite fields k from the geometry of modular curves with many rational points over k, combining two recent improvements on Goppa's construction. The resulting codes are asymptotically the best currently known.<|reference_end|> | arxiv | @article{elkies2003still,
title={Still better nonlinear codes from modular curves},
author={Noam D. Elkies},
journal={arXiv preprint arXiv:math/0308046},
year={2003},
archivePrefix={arXiv},
eprint={math/0308046},
primaryClass={math.NT cs.IT math.AG math.IT}
} | elkies2003still |
arxiv-676652 | math/0308110 | Sphere packing bounds in the Grassmann and Stiefel manifolds | <|reference_start|>Sphere packing bounds in the Grassmann and Stiefel manifolds: Applying the Riemann geometric machinery of volume estimates in terms of curvature, bounds for the minimal distance of packings/codes in the Grassmann and Stiefel manifolds will be derived and analyzed. In the context of space-time block codes this leads to a monotonically increasing minimal distance lower bound as a function of the block length. This advocates large block lengths for the code design.<|reference_end|> | arxiv | @article{henkel2003sphere,
title={Sphere packing bounds in the Grassmann and Stiefel manifolds},
author={Oliver Henkel},
journal={IEEE Transactions on Information Theory, vol 51, no 10, (2005),
3445-3456},
year={2003},
doi={10.1109/TIT.2005.855594},
archivePrefix={arXiv},
eprint={math/0308110},
primaryClass={math.MG cs.IT math.IT}
} | henkel2003sphere |
arxiv-676653 | math/0308153 | Mathematics and Logic as Information Compression by Multiple Alignment, Unification and Search | <|reference_start|>Mathematics and Logic as Information Compression by Multiple Alignment, Unification and Search: This article introduces the conjecture that "mathematics, logic and related disciplines may usefully be understood as information compression (IC) by 'multiple alignment', 'unification' and 'search' (ICMAUS)". As a preparation for the two main sections of the article, concepts of information and information compression are reviewed. Related areas of research are also described including IC in brains and nervous systems, and IC in relation to inductive inference, Minimum Length Encoding and probabilistic reasoning. The ICMAUS concepts and a computer model in which they are embodied are briefly described. The first of the two main sections describes how many of the commonly-used forms and structures in mathematics, logic and related disciplines (such as theoretical linguistics and computer programming) may be seen as devices for IC. In some cases, these forms and structures may be interpreted in terms of the ICMAUS framework. The second main section describes a selection of examples where processes of calculation and inference in mathematics, logic and related disciplines may be understood as IC. In many cases, these examples may be understood more specifically in terms of the ICMAUS concepts.<|reference_end|> | arxiv | @article{wolff2003mathematics,
title={Mathematics and Logic as Information Compression by Multiple Alignment,
Unification and Search},
author={J Gerard Wolff},
journal={arXiv preprint arXiv:math/0308153},
year={2003},
archivePrefix={arXiv},
eprint={math/0308153},
primaryClass={math.GM cs.AI math.LO}
} | wolff2003mathematics |
arxiv-676654 | math/0309081 | Asymmetric binary covering codes | <|reference_start|>Asymmetric binary covering codes: An asymmetric binary covering code of length n and radius R is a subset C of the n-cube Q_n such that every vector x in Q_n can be obtained from some vector c in C by changing at most R 1's of c to 0's, where R is as small as possible. K^+(n,R) is defined as the smallest size of such a code. We show K^+(n,R) is of order 2^n/n^R for constant R, using an asymmetric sphere-covering bound and probabilistic methods. We show K^+(n,n-R')=R'+1 for constant coradius R' iff n>=R'(R'+1)/2. These two results are extended to near-constant R and R', respectively. Various bounds on K^+ are given in terms of the total number of 0's or 1's in a minimal code. The dimension of a minimal asymmetric linear binary code ([n,R]^+ code) is determined to be min(0,n-R). We conclude by discussing open problems and techniques to compute explicit values for K^+, giving a table of best known bounds.<|reference_end|> | arxiv | @article{cooper2003asymmetric,
title={Asymmetric binary covering codes},
author={Joshua N. Cooper, Robert B. Ellis, and Andrew B. Kahng},
journal={J. Combin. Theory Ser. A 100 (2002), no. 2, 232--249},
year={2003},
archivePrefix={arXiv},
eprint={math/0309081},
primaryClass={math.CO cs.IT math.IT}
} | cooper2003asymmetric |
arxiv-676655 | math/0309083 | Convex Combinatorial Optimization | <|reference_start|>Convex Combinatorial Optimization: We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.<|reference_end|> | arxiv | @article{onn2003convex,
title={Convex Combinatorial Optimization},
author={Shmuel Onn and Uriel G. Rothblum},
journal={Discrete and Computational Geometry, 32:549--566, 2004},
year={2003},
archivePrefix={arXiv},
eprint={math/0309083},
primaryClass={math.CO cs.DM math.OC}
} | onn2003convex |
arxiv-676656 | math/0309120 | An invariant of finitary codes with finite expected square root coding length | <|reference_start|>An invariant of finitary codes with finite expected square root coding length: Let $p$ and $q$ be probability vectors with the same entropy $h$. Denote by $B(p)$ the Bernoulli shift indexed by $\Z$ with marginal distribution $p$. Suppose that $\phi$ is a measure preserving homomorphism from $B(p)$ to $B(q)$. We prove that if the coding length of $\phi$ has a finite 1/2 moment, then $\sigma_p^2=\sigma_q^2$, where $\sigma_p^2=\sum_i p_i(-\log p_i-h)^2$ is the {\dof informational variance} of $p$. In this result, which sharpens a theorem of Parry (1979), the 1/2 moment cannot be replaced by a lower moment. On the other hand, for any $\theta<1$, we exhibit probability vectors $p$ and $q$ that are not permutations of each other, such that there exists a finitary isomorphism $\Phi$ from $B(p)$ to $B(q)$ where the coding lengths of $\Phi$ and of its inverse have a finite $\theta$ moment. We also present an extension to ergodic Markov chains.<|reference_end|> | arxiv | @article{harvey2003an,
title={An invariant of finitary codes with finite expected square root coding
length},
author={Nate Harvey, Yuval Peres (UC Berkeley)},
journal={arXiv preprint arXiv:math/0309120},
year={2003},
archivePrefix={arXiv},
eprint={math/0309120},
primaryClass={math.PR cs.IT math.IT}
} | harvey2003an |
arxiv-676657 | math/0309123 | Error Correcting Codes on Algebraic Surfaces | <|reference_start|>Error Correcting Codes on Algebraic Surfaces: Error correcting codes are defined and important parameters for a code are explained. Parameters of new codes constructed on algebraic surfaces are studied. In particular, codes resulting from blowing up points in $\proj^2$ are briefly studied, then codes resulting from ruled surfaces are covered. Codes resulting from ruled surfaces over curves of genus 0 are completely analyzed, and some codes are discovered that are better than direct product Reed Solomon codes of similar length. Ruled surfaces over genus 1 curves are also studied, but not all classes are completely analyzed. However, in this case a family of codes are found that are comparable in performance to the direct product code of a Reed Solomon code and a Goppa code. Some further work is done on surfaces from higher genus curves, but there remains much work to be done in this direction to understand fully the resulting codes. Codes resulting from blowing points on surfaces are also studied, obtaining necessary parameters for constructing infinite families of such codes. Also included is a paper giving explicit formulas for curves with more \field{q}-rational points than were previously known for certain combinations of field size and genus. Some upper bounds are now known to be optimal from these examples.<|reference_end|> | arxiv | @article{lomont2003error,
title={Error Correcting Codes on Algebraic Surfaces},
author={Chris Lomont},
journal={arXiv preprint arXiv:math/0309123},
year={2003},
archivePrefix={arXiv},
eprint={math/0309123},
primaryClass={math.NT cs.IT math.AG math.IT}
} | lomont2003error |
arxiv-676658 | math/0309285 | An Algorithm for Optimal Partitioning of Data on an Interval | <|reference_start|>An Algorithm for Optimal Partitioning of Data on an Interval: Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large space of partitions of $N$ data points in time $O(N^2)$. The algorithm is guaranteed to find the exact global optimum, automatically determines the model order (the number of segments), has a convenient real-time mode, can be extended to higher dimensional data spaces, and solves a surprising variety of problems in signal detection and characterization, density estimation, cluster analysis and classification.<|reference_end|> | arxiv | @article{jackson2003an,
title={An Algorithm for Optimal Partitioning of Data on an Interval},
author={Brad Jackson, Jeffrey D. Scargle, David Barnes, Sundararajan Arabhi,
Alina Alt, Peter Gioumousis, Elyus Gwin, Paungkaew Sangtrakulcharoen, Linda
Tan, and Tun Tao Tsai},
journal={arXiv preprint arXiv:math/0309285},
year={2003},
doi={10.1109/LSP.2001.838216},
archivePrefix={arXiv},
eprint={math/0309285},
primaryClass={math.NA astro-ph cs.CE cs.DS cs.IT math.CO math.IT}
} | jackson2003an |
arxiv-676659 | math/0309347 | Nowhere-Zero Flow Polynomials | <|reference_start|>Nowhere-Zero Flow Polynomials: In this article we introduce the flow polynomial of a digraph and use it to study nowhere-zero flows from a commutative algebraic perspective. Using Hilbert's Nullstellensatz, we establish a relation between nowhere-zero flows and dual flows. For planar graphs this gives a relation between nowhere-zero flows and flows of their planar duals. It also yields an appealing proof that every bridgeless triangulated graph has a nowhere-zero four-flow.<|reference_end|> | arxiv | @article{onn2003nowhere-zero,
title={Nowhere-Zero Flow Polynomials},
author={Shmuel Onn},
journal={Journal of Combinatorial Theory Series A, 108:205--215, 2004},
year={2003},
archivePrefix={arXiv},
eprint={math/0309347},
primaryClass={math.CO cs.DM math.AC}
} | onn2003nowhere-zero |
arxiv-676660 | math/0309389 | Approximate Squaring | <|reference_start|>Approximate Squaring: We study the ``approximate squaring'' map f(x) := x ceiling(x) and its behavior when iterated. We conjecture that if f is repeatedly applied to a rational number r = l/d > 1 then eventually an integer will be reached. We prove this when d=2, and provide evidence that it is true in general by giving an upper bound on the density of the ``exceptional set'' of numbers which fail to reach an integer. We give similar results for a p-adic analogue of f, when the exceptional set is nonempty, and for iterating the ``approximate multiplication'' map f_r(x) := r ceiling(x) where r is a fixed rational number.<|reference_end|> | arxiv | @article{lagarias2003approximate,
title={Approximate Squaring},
author={J. C. Lagarias, N. J. A. Sloane},
journal={Experimental Math. 13 (2004), 113--128.},
year={2003},
archivePrefix={arXiv},
eprint={math/0309389},
primaryClass={math.NT cs.IT math.IT}
} | lagarias2003approximate |
arxiv-676661 | math/0309425 | Algebraic Aspects of Multiple Zeta Values | <|reference_start|>Algebraic Aspects of Multiple Zeta Values: Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves "coding" the multiple zeta values by monomials in two noncommuting variables x and y. Multiple zeta values can then be thought of as defining a map \zeta: H^0 -> R, where H^0 is the graded rational vector space generated by the "admissible words" of the noncommutative polynomial algebra Q<x,y>. Now H^0 admits two (commutative) products making \zeta a homomorphism: the shuffle product and the "harmonic" product. The latter makes H^0 a subalgebra of the algebra QSym of quasi-symmetric functions. We also discuss some results about multiple zeta values that can be stated in terms of derivations and cyclic derivations of Q<x,y>, and define an action of the Hopf algebra QSym on Q<x,y> that appears useful. Finally, we apply the algebraic approach to finite partial sums of multiple zeta value series.<|reference_end|> | arxiv | @article{hoffman2003algebraic,
title={Algebraic Aspects of Multiple Zeta Values},
author={Michael E. Hoffman},
journal={in Zeta Functions, Topology and Quantum Physics (T. Aoki et. al.,
eds.), Springer, 2005, pp. 51-74},
year={2003},
archivePrefix={arXiv},
eprint={math/0309425},
primaryClass={math.QA cs.IT math.IT math.NT}
} | hoffman2003algebraic |
arxiv-676662 | math/0310020 | Generators of algebraic covariant derivative curvature tensors and Young symmetrizers | <|reference_start|>Generators of algebraic covariant derivative curvature tensors and Young symmetrizers: We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1),(2 1)}. Each of the partitions (2), (3) and (1 1) describes exactly one symmetry class, whereas the partition (2 1) characterizes an infinite set S of irreducible symmetry classes. This 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'. Foundation of our investigations is a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins about a Young symmetrizer that generates the symmetry class of algebraic covariant derivative curvature tensors. Furthermore we apply ideals and idempotents in group rings C[Sr], the Littlewood-Richardson rule and discrete Fourier transforms for symmetric groups Sr. For certain symbolic calculations we used the Mathematica packages Ricci and PERMS.<|reference_end|> | arxiv | @article{fiedler2003generators,
title={Generators of algebraic covariant derivative curvature tensors and Young
symmetrizers},
author={B. Fiedler},
journal={In: Leading-Edge Computer Science, S. Shannon (ed.), Nova Science
Publishers, Inc. New York, 2006. pp. 219-239. ISBN: 1-59454-526-X},
year={2003},
archivePrefix={arXiv},
eprint={math/0310020},
primaryClass={math.CO cs.SC math.DG}
} | fiedler2003generators |
arxiv-676663 | math/0310109 | Shortest paths in the Tower of Hanoi graph and finite automata | <|reference_start|>Shortest paths in the Tower of Hanoi graph and finite automata: We present efficient algorithms for constructing a shortest path between two states in the Tower of Hanoi graph, and for computing the length of the shortest path. The key element is a finite-state machine which decides, after examining on the average only 63/38 of the largest discs, whether the largest disc will be moved once or twice. This solves a problem raised by Andreas Hinz, and results in a better understanding of how the shortest path is determined. Our algorithm for computing the length of the shortest path is typically about twice as fast as the existing algorithm. We also use our results to give a new derivation of the average distance 466/885 between two random points on the Sierpinski gasket of unit side.<|reference_end|> | arxiv | @article{romik2003shortest,
title={Shortest paths in the Tower of Hanoi graph and finite automata},
author={Dan Romik},
journal={arXiv preprint arXiv:math/0310109},
year={2003},
archivePrefix={arXiv},
eprint={math/0310109},
primaryClass={math.CO cs.DM math.PR}
} | romik2003shortest |
arxiv-676664 | math/0310144 | A Generalization of Repetition Threshold | <|reference_start|>A Generalization of Repetition Threshold: Brandenburg and (implicitly) Dejean introduced the concept of repetition threshold: the smallest real number alpha such that there exists an infinite word over a k-letter alphabet that avoids beta-powers for all beta>alpha. We generalize this concept to include the lengths of the avoided words. We give some conjectures supported by numerical evidence and prove one of these conjectures.<|reference_end|> | arxiv | @article{ilie2003a,
title={A Generalization of Repetition Threshold},
author={Lucian Ilie, Jeffrey Shallit},
journal={arXiv preprint arXiv:math/0310144},
year={2003},
archivePrefix={arXiv},
eprint={math/0310144},
primaryClass={math.CO cs.DM}
} | ilie2003a |
arxiv-676665 | math/0310148 | Convolutional Codes of Goppa Type | <|reference_start|>Convolutional Codes of Goppa Type: A new kind of Convolutional Codes generalizing Goppa Codes is proposed. This provides a systematic method for constructing convolutional codes with prefixed properties. In particular, examples of Maximum-Distance Separable (MDS) convolutional codes are obtained.<|reference_end|> | arxiv | @article{perez2003convolutional,
title={Convolutional Codes of Goppa Type},
author={J.A. Dominguez Perez, J.M. Mu~noz Porras, G. Serrano Sotelo},
journal={AAECC, 15 (2004), 51-61},
year={2003},
archivePrefix={arXiv},
eprint={math/0310148},
primaryClass={math.OC cs.IT math.AG math.IT}
} | perez2003convolutional |
arxiv-676666 | math/0310149 | Convolutional Goppa Codes | <|reference_start|>Convolutional Goppa Codes: We define Convolutional Goppa Codes over algebraic curves and construct their corresponding dual codes. Examples over the projective line and over elliptic curves are described, obtaining in particular some Maximum-Distance Separable (MDS) convolutional codes.<|reference_end|> | arxiv | @article{porras2003convolutional,
title={Convolutional Goppa Codes},
author={J.M. Mu~noz Porras, J.A. Dominguez Perez, J.I. Iglesias Curto, G.
Serrano Sotelo},
journal={arXiv preprint arXiv:math/0310149},
year={2003},
doi={10.1109/TIT.2005.860447},
archivePrefix={arXiv},
eprint={math/0310149},
primaryClass={math.OC cs.IT math.AG math.IT}
} | porras2003convolutional |
arxiv-676667 | math/0310175 | Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products | <|reference_start|>Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products: The present paper extends generalized morphisms of relations into the realm of Monoidal Fuzzy Logics by first proving and then using relational inequalities over pseudo-associative BK-products (compositions) of relations in these logics. In 1977 Bandler and Kohout introduced generalized homomorphism, proteromorphism, amphimorphism, forward and backward compatibility of relations, and non-associative and pseudo-associative products (compositions) of relations into crisp (non-fuzzy Boolean) theory of relations. This was generalized later by Kohout to relations based on fuzzy Basic Logic systems (BL) of H\'ajek and also for relational systems based on left-continuous t-norms. The present paper is based on monoidal logics, hence it subsumes as special cases the theories of generalized morphisms (etc.) based on the following systems of logics: BL systems (which include the well known Goedel, product logic systems; Lukasiewicz logic and its extension to MV-algebras related to quantum logics), intuitionistic logics and linear logics.<|reference_end|> | arxiv | @article{kohout2003defining,
title={Defining Homomorphisms and Other Generalized Morphisms of Fuzzy
Relations in Monoidal Fuzzy Logics by Means of BK-Products},
author={Ladislav J. Kohout},
journal={arXiv preprint arXiv:math/0310175},
year={2003},
archivePrefix={arXiv},
eprint={math/0310175},
primaryClass={math.LO cs.LO math-ph math.MP math.QA}
} | kohout2003defining |
arxiv-676668 | math/0310193 | The Satisfiability Threshold of Random 3-SAT Is at Least 352 | <|reference_start|>The Satisfiability Threshold of Random 3-SAT Is at Least 352: We prove that a random 3-SAT instance with clause-to-variable density less than 3.52 is satisfiable with high probability. The proof comes through an algorithm which selects (and sets) a variable depending on its degree and that of its complement.<|reference_end|> | arxiv | @article{hajiaghayi2003the,
title={The Satisfiability Threshold of Random 3-SAT Is at Least 3.52},
author={MohammadTaghi Hajiaghayi and Gregory B. Sorkin},
journal={arXiv preprint arXiv:math/0310193},
year={2003},
archivePrefix={arXiv},
eprint={math/0310193},
primaryClass={math.CO cs.DM math.PR}
} | hajiaghayi2003the |
arxiv-676669 | math/0310232 | Monotone properties of random geometric graphs have sharp thresholds | <|reference_start|>Monotone properties of random geometric graphs have sharp thresholds: Random geometric graphs result from taking $n$ uniformly distributed points in the unit cube, $[0,1]^d$, and connecting two points if their Euclidean distance is at most $r$, for some prescribed $r$. We show that monotone properties for this class of graphs have sharp thresholds by reducing the problem to bounding the bottleneck matching on two sets of $n$ points distributed uniformly in $[0,1]^d$. We present upper bounds on the threshold width, and show that our bound is sharp for $d=1$ and at most a sublogarithmic factor away for $d\ge2$. Interestingly, the threshold width is much sharper for random geometric graphs than for Bernoulli random graphs. Further, a random geometric graph is shown to be a subgraph, with high probability, of another independently drawn random geometric graph with a slightly larger radius; this property is shown to have no analogue for Bernoulli random graphs.<|reference_end|> | arxiv | @article{goel2003monotone,
title={Monotone properties of random geometric graphs have sharp thresholds},
author={Ashish Goel, Sanatan Rai, Bhaskar Krishnamachari},
journal={Annals of Applied Probability 2005, Vol. 15, No. 4, 2535-2552},
year={2003},
doi={10.1214/105051605000000575},
number={IMS-AAP-AAP0122},
archivePrefix={arXiv},
eprint={math/0310232},
primaryClass={math.PR cond-mat.stat-mech cs.DM math.CO}
} | goel2003monotone |
arxiv-676670 | math/0310385 | De Bruijn Cycles for Covering Codes | <|reference_start|>De Bruijn Cycles for Covering Codes: A de Bruijn covering code is a q-ary string S so that every q-ary string is at most R symbol changes from some n-word appearing consecutively in S. We introduce these codes and prove that they can have length close to the smallest possible covering code. The proof employs tools from field theory, probability, and linear algebra. We also prove a number of ``spectral'' results on de Bruijn covering codes. Included is a table of the best known bounds on the lengths of small binary de Bruijn covering codes, up to R=11 and n=13, followed by several open questions in this area.<|reference_end|> | arxiv | @article{chung2003de,
title={De Bruijn Cycles for Covering Codes},
author={Fan Chung and Joshua N. Cooper},
journal={arXiv preprint arXiv:math/0310385},
year={2003},
archivePrefix={arXiv},
eprint={math/0310385},
primaryClass={math.CO cs.IT math.IT}
} | chung2003de |
arxiv-676671 | math/0311004 | Which Point Configurations are Determined by the Distribution of their Pairwise Distances? | <|reference_start|>Which Point Configurations are Determined by the Distribution of their Pairwise Distances?: In a previous paper we showed that, for any $n \ge m+2$, most sets of $n$ points in $\RR^m$ are determined (up to rotations, reflections, translations and relabeling of the points) by the distribution of their pairwise distances. But there are some exceptional point configurations which are not reconstructible from the distribution of distances in the above sense. In this paper, we present a reconstructibility test with running time $O(n^{11})$. The cases of orientation preserving rigid motions (rotations and translations) and scalings are also discussed.<|reference_end|> | arxiv | @article{boutin2003which,
title={Which Point Configurations are Determined by the Distribution of their
Pairwise Distances?},
author={Mireille Boutin, Gregor Kemper},
journal={arXiv preprint arXiv:math/0311004},
year={2003},
archivePrefix={arXiv},
eprint={math/0311004},
primaryClass={math.MG cs.CV math.AC math.AG}
} | boutin2003which |
arxiv-676672 | math/0311046 | Codes and Invariant Theory | <|reference_start|>Codes and Invariant Theory: The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and modules. The proof of the theorem uses a categorical approach, and will be the subject of a forthcoming book. However, the theorem can be stated and applied without using category theory, and we illustrate it here by applying it to generalized doubly-even codes over fields of characteristic 2, doubly-even codes over the integers modulo a power of 2, and self-dual codes over the noncommutative ring $\F_q + \F_q u$, where $u^2 = 0$..<|reference_end|> | arxiv | @article{nebe2003codes,
title={Codes and Invariant Theory},
author={Gabriele Nebe, E.M. Rains, N.J.A. Sloane},
journal={arXiv preprint arXiv:math/0311046},
year={2003},
archivePrefix={arXiv},
eprint={math/0311046},
primaryClass={math.NT cs.IT math.IT}
} | nebe2003codes |
arxiv-676673 | math/0311047 | Assessing security of some group based cryptosystems | <|reference_start|>Assessing security of some group based cryptosystems: One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem (sometimes erroneously called just the conjugacy problem): given two elements a, b of a group G and the information that a^x=b for some x \in G, find at least one particular element x like that. Here a^x stands for xax^{-1}. The computational difficulty of this problem in some particular groups has been used in several group based cryptosystems. Recently, a few preprints have been in circulation that suggested various "neighbourhood search" type heuristic attacks on the conjugacy search problem. The goal of the present survey is to stress a (probably well known) fact that these heuristic attacks alone are not a threat to the security of a cryptosystem, and, more importantly, to suggest a more credible approach to assessing security of group based cryptosystems. Such an approach should be necessarily based on the concept of the average case complexity (or expected running time) of an algorithm. These arguments support the following conclusion: although it is generally feasible to base the security of a cryptosystem on the difficulty of the conjugacy search problem, the group G itself (the "platform") has to be chosen very carefully. In particular, experimental as well as theoretical evidence collected so far makes it appear likely that braid groups are not a good choice for the platform. We also reflect on possible replacements.<|reference_end|> | arxiv | @article{shpilrain2003assessing,
title={Assessing security of some group based cryptosystems},
author={Vladimir Shpilrain},
journal={arXiv preprint arXiv:math/0311047},
year={2003},
archivePrefix={arXiv},
eprint={math/0311047},
primaryClass={math.GR cs.CC cs.CR}
} | shpilrain2003assessing |
arxiv-676674 | math/0311129 | Cayley-Bacharach and evaluation codes on complete intersections | <|reference_start|>Cayley-Bacharach and evaluation codes on complete intersections: In recent work, J. Hansen uses cohomological methods to find a lower bound for the minimum distance of an evaluation code determined by a reduced complete intersection in the projective plane. In this paper, we generalize Hansen's results from P^2 to P^m; we also show that the hypotheses in Hansen's work may be weakened. The proof is succinct and follows by combining the Cayley-Bacharach theorem and bounds on evaluation codes obtained from reduced zero-schemes.<|reference_end|> | arxiv | @article{gold2003cayley-bacharach,
title={Cayley-Bacharach and evaluation codes on complete intersections},
author={Leah Gold, John Little, Hal Schenck},
journal={J. Pure Applied Algebra 196 (2005) 91-99},
year={2003},
archivePrefix={arXiv},
eprint={math/0311129},
primaryClass={math.AG cs.IT math.AC math.IT}
} | gold2003cayley-bacharach |
arxiv-676675 | math/0311228 | Transforming triangulations on non planar-surfaces | <|reference_start|>Transforming triangulations on non planar-surfaces: We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder.<|reference_end|> | arxiv | @article{cortes2003transforming,
title={Transforming triangulations on non planar-surfaces},
author={C. Cortes, C. I. Grima, F. Hurtado, A. Marquez, F. Santos, and J.
Valenzuela},
journal={SIAM J. Discrete Math. 24:3 (2010), 821-840},
year={2003},
doi={10.1137/070697987},
archivePrefix={arXiv},
eprint={math/0311228},
primaryClass={math.MG cs.CG}
} | cortes2003transforming |
arxiv-676676 | math/0311289 | Complete Weight Enumerators of Generalized Doubly-Even Self-Dual Codes | <|reference_start|>Complete Weight Enumerators of Generalized Doubly-Even Self-Dual Codes: For any q which is a power of 2 we describe a finite subgroup of the group of invertible complex q by q matrices under which the complete weight enumerators of generalized doubly-even self-dual codes over the field with q elements are invariant. An explicit description of the invariant ring and some applications to extremality of such codes are obtained in the case q=4.<|reference_end|> | arxiv | @article{nebe2003complete,
title={Complete Weight Enumerators of Generalized Doubly-Even Self-Dual Codes},
author={Gabriele Nebe, H.-G. Quebbemann, E. M. Rains, N. J. A. Sloane},
journal={Finite Fields Applic. 10 (2004), 540-550},
year={2003},
archivePrefix={arXiv},
eprint={math/0311289},
primaryClass={math.NT cs.IT math.IT}
} | nebe2003complete |
arxiv-676677 | math/0311319 | Modular and p-adic cyclic codes | <|reference_start|>Modular and p-adic cyclic codes: This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo p^a and over the p-adic numbers, where p is a prime not dividing n. An especially interesting example is the 2-adic cyclic code of length 7 with generator polynomial X^3 + lambda X^2 + (lambda - 1) X - 1, where lambda satisfies lambda^2 - lambda + 2 =0. This is the 2-adic generalization of both the binary Hamming code and the quaternary octacode (the latter being equivalent to the Nordstrom-Robinson code). Other examples include the 2-adic Golay code of length 24 and the 3-adic Golay code of length 12.<|reference_end|> | arxiv | @article{calderbank2003modular,
title={Modular and p-adic cyclic codes},
author={A. R. Calderbank, N. J. A. Sloane},
journal={Designs, Codes and Cryptography, Vol. 6 (1995), 21-35},
year={2003},
archivePrefix={arXiv},
eprint={math/0311319},
primaryClass={math.CO cs.IT math.IT}
} | calderbank2003modular |
arxiv-676678 | math/0312092 | On the Parameters of Convolutional Codes with Cyclic Structure | <|reference_start|>On the Parameters of Convolutional Codes with Cyclic Structure: In this paper convolutional codes with cyclic structure will be investigated. These codes can be understood as left principal ideals in a suitable skew-polynomial ring. It has been shown in [3] that only certain combinations of the parameters (field size, length, dimension, and Forney indices) can occur for cyclic codes. We will investigate whether all these combinations can indeed be realized by a suitable cyclic code and, if so, how to construct such a code. A complete characterization and construction will be given for minimal cyclic codes. It is derived from a detailed investigation of the units in the skew-polynomial ring.<|reference_end|> | arxiv | @article{gluesing-luerssen2003on,
title={On the Parameters of Convolutional Codes with Cyclic Structure},
author={Heide Gluesing-Luerssen and Barbara Langfeld},
journal={arXiv preprint arXiv:math/0312092},
year={2003},
archivePrefix={arXiv},
eprint={math/0312092},
primaryClass={math.RA cs.IT math.CO math.IT}
} | gluesing-luerssen2003on |
arxiv-676679 | math/0312171 | Short formulas for algebraic covariant derivative curvature tensors via Algebraic Combinatorics | <|reference_start|>Short formulas for algebraic covariant derivative curvature tensors via Algebraic Combinatorics: We consider generators of algebraic covariant derivative curvature tensors R' which can be constructed by a Young symmetrization of product tensors W*U or U*W, where W and U are covariant tensors of order 2 and 3. W is a symmetric or alternating tensor whereas U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2,1). 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 16 or 20 summands if W is symmetric or skew-symmetric, respectively. In special cases these numbers can be reduced to the minima 12 or 10. If these minima occur then U admits an index commutation symmetry. Furthermore minimal lengths are possible if U is formed from torsion-free covariant derivatives of symmetric or alternating 2-tensor fields. Foundation of our investigations is a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins about a Young symmetrizer that generates the symmetry class of algebraic covariant derivative curvature tensors. Furthermore we apply ideals and idempotents in group rings C[S_r] and discrete Fourier transforms for symmetric groups S_r. For symbolic calculations we used the Mathematica packages Ricci and PERMS.<|reference_end|> | arxiv | @article{fiedler2003short,
title={Short formulas for algebraic covariant derivative curvature tensors via
Algebraic Combinatorics},
author={Bernd Fiedler},
journal={arXiv preprint arXiv:math/0312171},
year={2003},
archivePrefix={arXiv},
eprint={math/0312171},
primaryClass={math.CO cs.SC math.DG}
} | fiedler2003short |
arxiv-676680 | math/0312397 | On Simple Characterisations of Sheffer psi- polynomials and Related Propositions of the Calculus of Sequences | <|reference_start|>On Simple Characterisations of Sheffer psi- polynomials and Related Propositions of the Calculus of Sequences: A calculus of sequences started in 1936 opened the way for future extensions of umbral calculus in its finite operator form. Because of historically established notation we call it the psi-calculus.It appears in parts to be almost automatic extension of the standard classical finite operator calculus.<|reference_end|> | arxiv | @article{kwasniewski2003on,
title={On Simple Characterisations of Sheffer psi- polynomials and Related
Propositions of the Calculus of Sequences},
author={A. K. Kwasniewski},
journal={Bull. Soc. Sci. Lett. Lodz Ser. Rech. Deform. 52, Ser. Rech.
Deform. 36 (2002) pp.45-65},
year={2003},
archivePrefix={arXiv},
eprint={math/0312397},
primaryClass={math.CO cs.DM}
} | kwasniewski2003on |
arxiv-676681 | math/0312422 | \Sigma\Pi-polycategories, additive linear logic, and process semantics | <|reference_start|>\Sigma\Pi-polycategories, additive linear logic, and process semantics: We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multi-channel concurrent processes. The polycategorical model induced by this process semantics is shown to be equivalent to the free polycategory based on the syntax (i.e., it is full and faithfully complete). This establishes that the additive fragment of linear logic provides a semantics of concurrent processes. Another property of this semantics is that it gives a canonical representation of proofs in additive linear logic. This arXived version omits Section 1.7.1: "Circuit diagrams for polycategories" as the Xy-pic diagrams would not compile due to lack of memory. For a complete version see "http://www.cpsc.ucalgary.ca/~pastroc/".<|reference_end|> | arxiv | @article{pastro2003\sigma\pi-polycategories,,
title={\Sigma\Pi-polycategories, additive linear logic, and process semantics},
author={C. A. Pastro},
journal={arXiv preprint arXiv:math/0312422},
year={2003},
number={Master's thesis, University of Calgary, 2004},
archivePrefix={arXiv},
eprint={math/0312422},
primaryClass={math.CT cs.LO math.LO}
} | pastro2003\sigma\pi-polycategories, |
arxiv-676682 | math/0401045 | Unitary Space Time Constellation Analysis: An Upper Bound for the Diversity | <|reference_start|>Unitary Space Time Constellation Analysis: An Upper Bound for the Diversity: The diversity product and the diversity sum are two very important parameters for a good-performing unitary space time constellation. A basic question is what the maximal diversity product (or sum) is. In this paper we are going to derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension $n$ and any size $m$ using packing techniques on the compact Lie group U(n).<|reference_end|> | arxiv | @article{han2004unitary,
title={Unitary Space Time Constellation Analysis: An Upper Bound for the
Diversity},
author={Guangyue Han, Joachim Rosenthal},
journal={arXiv preprint arXiv:math/0401045},
year={2004},
archivePrefix={arXiv},
eprint={math/0401045},
primaryClass={math.CO cs.IT math.IT}
} | han2004unitary |
arxiv-676683 | math/0401083 | On extended umbral calculus, oscillator-like algebras and Generalized Clifford Algebra | <|reference_start|>On extended umbral calculus, oscillator-like algebras and Generalized Clifford Algebra: Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized Clifford algebras also in the context of azimuthal quantization of angular momentum which was interpreted afterwards as the finite dimensional quantum mechanics .<|reference_end|> | arxiv | @article{kwasniewski2004on,
title={On extended umbral calculus, oscillator-like algebras and Generalized
Clifford Algebra},
author={A.K.Kwasniewski},
journal={Advances in Applied Clifford Algebras 11 No2 267-279 (2001)},
year={2004},
archivePrefix={arXiv},
eprint={math/0401083},
primaryClass={math.QA cs.DM}
} | kwasniewski2004on |
arxiv-676684 | math/0401157 | Generalized PSK in Space Time Coding | <|reference_start|>Generalized PSK in Space Time Coding: A wireless communication system using multiple antennas promises reliable transmission under Rayleigh flat fading assumptions. Design criteria and practical schemes have been presented for both coherent and non-coherent communication channels. In this paper we generalize one dimensional phase shift keying (PSK) signals and introduce space time constellations from generalized phase shift keying (GPSK) signals based on the complex and real orthogonal designs. The resulting space time constellations reallocate the energy for each transmitting antenna and feature good diversity products, consequently their performances are better than some of the existing comparable codes. Moreover since the maximum likelihood (ML) decoding of our proposed codes can be decomposed to one dimensional PSK signal demodulation, the ML decoding of our codes can be implemented in a very efficient way.<|reference_end|> | arxiv | @article{han2004generalized,
title={Generalized PSK in Space Time Coding},
author={Guangyue Han},
journal={arXiv preprint arXiv:math/0401157},
year={2004},
doi={10.1109/TCOMM.2005.847166},
archivePrefix={arXiv},
eprint={math/0401157},
primaryClass={math.CO cs.IT math.IT math.OC}
} | han2004generalized |
arxiv-676685 | math/0401279 | Backward Optimized Orthogonal Matching Pursuit | <|reference_start|>Backward Optimized Orthogonal Matching Pursuit: A recursive approach for shrinking coefficients of an atomic decomposition is proposed. The corresponding algorithm evolves so as to provide at each iteration a) the orthogonal projection of a signal onto a reduced subspace and b) the index of the coefficient to be disregarded in order to construct a coarser approximation minimizing the norm of the residual error.<|reference_end|> | arxiv | @article{andrle2004backward,
title={Backward Optimized Orthogonal Matching Pursuit},
author={M. Andrle, L. Rebollo-Neira, E. Sagianos},
journal={arXiv preprint arXiv:math/0401279},
year={2004},
doi={10.1109/LSP.2004.833503},
archivePrefix={arXiv},
eprint={math/0401279},
primaryClass={math.GM cs.IT math.IT}
} | andrle2004backward |
arxiv-676686 | math/0402078 | Towards psi-extension of Rota`s Finite Operator Calculus | <|reference_start|>Towards psi-extension of Rota`s Finite Operator Calculus: A class of extended umbral calculi in operator form is presented. Extensions of all basic theorems of classical Finite Operator Calculus are shown to hold. The impossibility of straightforward extending of quantum q-plane formulation of the q-umbral caculus to the general psi-calculus case is demonstrated.<|reference_end|> | arxiv | @article{kwasniewski2004towards,
title={Towards psi-extension of Rota`s Finite Operator Calculus},
author={A. K. Kwasniewski},
journal={Reports on Mathematical Physics Vol. 48 No 3 (2001) : 305-342},
year={2004},
doi={10.1016/S0034-4877(01)80092-6},
archivePrefix={arXiv},
eprint={math/0402078},
primaryClass={math.CO cs.DM}
} | kwasniewski2004towards |
arxiv-676687 | math/0402125 | Poisson, Dobinski, Rota and coherent states | <|reference_start|>Poisson, Dobinski, Rota and coherent states: New q- Dobinski formula might also be interpreted as the average of specific q-powers of random variable X with the usual Poisson distribution.<|reference_end|> | arxiv | @article{kwasniewski2004poisson,,
title={Poisson, Dobinski, Rota and coherent states},
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)
17-19},
year={2004},
archivePrefix={arXiv},
eprint={math/0402125},
primaryClass={math.CO cs.DM}
} | kwasniewski2004poisson, |
arxiv-676688 | math/0402254 | q-Poisson, q-Dobinski, q-Rota and q-coherent states | <|reference_start|>q-Poisson, q-Dobinski, q-Rota and q-coherent states: q- Dobinski formula may be interpreted as the average of powers of a random variable X_q with the q- Poisson distribution.<|reference_end|> | arxiv | @article{kwasniewski2004q-poisson,,
title={q-Poisson, q-Dobinski, q-Rota and q-coherent states},
author={A. K.Kwasniewski},
journal={Proc. Jangjeon Math. Soc. Vol. 7 (2), 2004 pp. 95-98},
year={2004},
archivePrefix={arXiv},
eprint={math/0402254},
primaryClass={math.CO cs.DM}
} | kwasniewski2004q-poisson, |
arxiv-676689 | math/0402291 | Information on Combinatorial Interpretation of Fibonomial Coefficients | <|reference_start|>Information on Combinatorial Interpretation of Fibonomial Coefficients: Fibonomial coefficients count the number of specific finite birth self-similar subposets of an infinite non-tree poset naturally related to the Fibonacci tree of rabbits growth process.<|reference_end|> | arxiv | @article{kwasniewski2004information,
title={Information on Combinatorial Interpretation of Fibonomial Coefficients},
author={A. K. Kwasniewski},
journal={Bull. Soc. Sci. Lett. Lodz Ser. Rech. Deform. 53, Ser.
Rech.Deform. 42 (2002) pp.39-41},
year={2004},
archivePrefix={arXiv},
eprint={math/0402291},
primaryClass={math.CO cs.DM}
} | kwasniewski2004information |
arxiv-676690 | math/0402344 | More on combinatorial interpretation of the fibonomial coefficients | <|reference_start|>More on combinatorial interpretation of the fibonomial coefficients: Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via characteristic matrix of the corresponding partial order relation . Relevance of the proposal to more general unification treatment is indicated.<|reference_end|> | arxiv | @article{kwasniewski2004more,
title={More on combinatorial interpretation of the fibonomial coefficients},
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. 44 (2004)
23-38},
year={2004},
archivePrefix={arXiv},
eprint={math/0402344},
primaryClass={math.CO cs.DM}
} | kwasniewski2004more |
arxiv-676691 | math/0402346 | Applications of Lefschetz numbers in control theory | <|reference_start|>Applications of Lefschetz numbers in control theory: We develop some applications of techniques of the Lefschetz coincidence theory in control theory. The topics are existence of equilibria and their robustness, controllability and its robustness.<|reference_end|> | arxiv | @article{saveliev2004applications,
title={Applications of Lefschetz numbers in control theory},
author={Peter Saveliev},
journal={arXiv preprint arXiv:math/0402346},
year={2004},
archivePrefix={arXiv},
eprint={math/0402346},
primaryClass={math.OC cs.SY math.AT}
} | saveliev2004applications |
arxiv-676692 | math/0403017 | Combinatorial interpretation of the recurrence relation for fibonomial coefficients | <|reference_start|>Combinatorial interpretation of the recurrence relation for fibonomial coefficients: Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with quite an exhaustive context where apart from plane grid coordinate system used several figures illustrate the exposition of statements and the derivation of the recurrence itself.<|reference_end|> | arxiv | @article{kwasniewski2004combinatorial,
title={Combinatorial interpretation of the recurrence relation for fibonomial
coefficients},
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. 44 (2004)
pp. 23-38},
year={2004},
archivePrefix={arXiv},
eprint={math/0403017},
primaryClass={math.CO cs.DM}
} | kwasniewski2004combinatorial |
arxiv-676693 | math/0403054 | $\psi$-Poisson, $q$-Cigler, $\psi$-Dobinski, $\psi$-Rota and $\psi$-coherent states | <|reference_start|>$\psi$-Poisson, $q$-Cigler, $\psi$-Dobinski, $\psi$-Rota and $\psi$-coherent states: Cigler simple derivation of usual and extended Dobinski formula is recalled and it is noted that both may be interpreted as averages of powers of random variables with the corresponding usual or extended Poisson distributions. In parallel more general formulas of extended operator umbral calculi origin are revealed . The formulas encompass both earlier cases as very specific ones.<|reference_end|> | arxiv | @article{kwasniewski2004$\psi$-poisson,,
title={$\psi$-Poisson, $q$-Cigler, $\psi$-Dobinski, $\psi$-Rota and
$\psi$-coherent states},
author={A. K. Kwasniewski},
journal={Proc. Jangjeon Math. Soc. Vol. 7 (2), 2004 pp. 95-98},
year={2004},
archivePrefix={arXiv},
eprint={math/0403054},
primaryClass={math.CO cs.DM}
} | kwasniewski2004$\psi$-poisson, |
arxiv-676694 | math/0403107 | Cauchy type identities and corresponding fermatian matrices via non-comuting variables of extended finite operator calculus | <|reference_start|>Cauchy type identities and corresponding fermatian matrices via non-comuting variables of extended finite operator calculus: New family of extended Cauchy type identities is found and related Fermat type matrices are provided ready for applications in extended scope. This is achieved due to the use specifically non-commuting variables of extended finite operator calculus introduced by the author few years ago.<|reference_end|> | arxiv | @article{kwasniewski2004cauchy,
title={Cauchy type identities and corresponding fermatian matrices via
non-comuting variables of extended finite operator calculus},
author={A. KL. Kwasniewski},
journal={Proc. Jangjeon Math. Soc. Vol 8 (2005) no. 2. pp.191-196},
year={2004},
archivePrefix={arXiv},
eprint={math/0403107},
primaryClass={math.CO cs.DM}
} | kwasniewski2004cauchy |
arxiv-676695 | math/0403123 | Pascal like matrices - an accessible factory of one source identities and resulting applications | <|reference_start|>Pascal like matrices - an accessible factory of one source identities and resulting applications: The extension of pascalian like matrices depending on a variable from any field of zero characteristics are shown at work for the first time. Their properties appear to be one source factory of identities and resulting foreseen applications<|reference_end|> | arxiv | @article{kwasniewski2004pascal,
title={Pascal like matrices - an accessible factory of one source identities
and resulting applications},
author={A. K. Kwasniewski},
journal={Adv. Stud. Contemp. Math. 10 (2005) No. 2, pp. 111-120},
year={2004},
archivePrefix={arXiv},
eprint={math/0403123},
primaryClass={math.CO cs.DM}
} | kwasniewski2004pascal |
arxiv-676696 | math/0403139 | First contact remarks on umbra difference calculus references streams | <|reference_start|>First contact remarks on umbra difference calculus references streams: The reference links to the modern classical umbral calculus before that known as blissardian symbolic method are numerous. Rota founded and then extended finite operator calculus has links to references which are plenty numerous. The references via links to the difference q calculus umbra way treaded or without even referring to umbra are giant numerous. These reference links now result in counting in thousands the relevant papers . The purpose of the present attempt is to offer one of the keys to enter the world of those thousands of references.<|reference_end|> | arxiv | @article{kwasniewski2004first,
title={First contact remarks on umbra difference calculus references streams},
author={A.K.Kwasniewski},
journal={Bull. Soc. Sci. Lett. Lodz, 60, (2005) pp. 17-25 ArXiv:
math.CO/0403139},
year={2004},
archivePrefix={arXiv},
eprint={math/0403139},
primaryClass={math.CO cs.DM}
} | kwasniewski2004first |
arxiv-676697 | math/0403548 | Remarks on codes from modular curves: MAGMA applications | <|reference_start|>Remarks on codes from modular curves: MAGMA applications: Expository paper discussing AG or Goppa codes arising from curves, first from an abstract general perspective then turning to concrete examples associated to modular curves. We will try to explain these extremely technical ideas using a special case at a level to a typical graduate student with some background in modular forms, number theory, group theory, and algebraic geometry. Many examples using MAGMA are included.<|reference_end|> | arxiv | @article{joyner2004remarks,
title={Remarks on codes from modular curves: MAGMA applications},
author={David Joyner and Salahoddin Shokranian},
journal={Algebr. Geom. Topol. 12 (2012) 2259-2286},
year={2004},
doi={10.2140/agt.2012.12.2259},
archivePrefix={arXiv},
eprint={math/0403548},
primaryClass={math.NT cs.IT math.AG math.IT}
} | joyner2004remarks |
arxiv-676698 | math/0404076 | Probabilistic Solutions of Equations in the Braid Group | <|reference_start|>Probabilistic Solutions of Equations in the Braid Group: Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability. Moreover, with a significant probability, the solution will be the first in the list. This gives a probabilistic solution to: The conjugacy problem, the group membership problem, the shortest representation of an element, and other combinatorial group-theoretic problems in random subgroups of the braid group. We use a memory-based extension of the standard length-based approach, which in principle can be applied to any group admitting an efficient, reasonably behaving length function.<|reference_end|> | arxiv | @article{garber2004probabilistic,
title={Probabilistic Solutions of Equations in the Braid Group},
author={D. Garber, S. Kaplan, M. Teicher, B. Tsaban and U. Vishne},
journal={Advances in Applied Mathematics 35 (2005), 323--334},
year={2004},
doi={10.1016/j.aam.2005.03.002},
archivePrefix={arXiv},
eprint={math/0404076},
primaryClass={math.GR cs.CR math.GT}
} | garber2004probabilistic |
arxiv-676699 | math/0404158 | A note on mobiusien function and mobiusien inversion formula of fibonacci cobweb poset | <|reference_start|>A note on mobiusien function and mobiusien inversion formula of fibonacci cobweb poset: The explicit formula for mobiusien function of fibonacci cobweb poset P is given for the first time by the use of definition of P in plane grid coordinate system.<|reference_end|> | arxiv | @article{krot2004a,
title={A note on mobiusien function and mobiusien inversion formula of
fibonacci cobweb poset},
author={Ewa Krot},
journal={Bulletin de la Societe des Sciences et des Lettres de Lodz (54),
Serie: Recherches sur les Deformations Vol. 44 (2004), 39-44},
year={2004},
archivePrefix={arXiv},
eprint={math/0404158},
primaryClass={math.CO cs.DM}
} | krot2004a |
arxiv-676700 | math/0404325 | Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes | <|reference_start|>Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes: Given positive integers $n$ and $d$, let $A_2(n,d)$ denote the maximum size of a binary code of length $n$ and minimum distance $d$. The well-known Gilbert-Varshamov bound asserts that $A_2(n,d) \geq 2^n/V(n,d-1)$, where $V(n,d) = \sum_{i=0}^{d} {n \choose i}$ is the volume of a Hamming sphere of radius $d$. We show that, in fact, there exists a positive constant $c$ such that $$ A_2(n,d) \geq c \frac{2^n}{V(n,d-1)} \log_2 V(n,d-1) $$ whenever $d/n \le 0.499$. The result follows by recasting the Gilbert- Varshamov bound into a graph-theoretic framework and using the fact that the corresponding graph is locally sparse. Generalizations and extensions of this result are briefly discussed.<|reference_end|> | arxiv | @article{jiang2004asymptotic,
title={Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of
Binary Codes},
author={Tao Jiang and Alexander Vardy},
journal={IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 50, No. 8, pp.
1655-1664, August 2004
(http://www.ieeexplore.ieee.org/iel5/18/29198/01317112.pdf)},
year={2004},
doi={10.1109/TIT.2004.831751},
archivePrefix={arXiv},
eprint={math/0404325},
primaryClass={math.CO cs.IT math.AC math.IT}
} | jiang2004asymptotic |
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