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arxiv-676901 | math/0702116 | A Direct Matrix Method for Computing Analytical Jacobians of Discretized Nonlinear Integro-differential Equations | <|reference_start|>A Direct Matrix Method for Computing Analytical Jacobians of Discretized Nonlinear Integro-differential Equations: In this pedagogical article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro-differential equations. The method is based on a formulation of the discretized equations in vector form using only matrix-vector products and component-wise operations. By applying simple matrix-based differentiation rules, the matrix form of the analytical Jacobian can be calculated with little more difficulty than that required when computing derivatives in single-variable calculus. After describing the direct matrix method, we present numerical experiments demonstrating the computational performance of the method, discuss its connection to the Newton-Kantorovich method, and apply it to illustrative 1D and 2D example problems. MATLAB code is provided to demonstrate the low code complexity required by the method.<|reference_end|> | arxiv | @article{chu2007a,
title={A Direct Matrix Method for Computing Analytical Jacobians of Discretized
Nonlinear Integro-differential Equations},
author={Kevin T. Chu},
journal={arXiv preprint arXiv:math/0702116},
year={2007},
doi={10.1016/j.jcp.2009.04.031},
archivePrefix={arXiv},
eprint={math/0702116},
primaryClass={math.NA cs.CE}
} | chu2007a |
arxiv-676902 | math/0702129 | Pebble Game Algorithms and Sparse Graphs | <|reference_start|>Pebble Game Algorithms and Sparse Graphs: A multi-graph $G$ on $n$ vertices is $(k,\ell)$-sparse if every subset of $n'\leq n$ vertices spans at most $kn'- \ell$ edges. $G$ is {\em tight} if, in addition, it has exactly $kn - \ell$ edges. For integer values $k$ and $\ell \in [0, 2k)$, we characterize the $(k,\ell)$-sparse graphs via a family of simple, elegant and efficient algorithms called the $(k,\ell)$-pebble games.<|reference_end|> | arxiv | @article{lee2007pebble,
title={Pebble Game Algorithms and Sparse Graphs},
author={Audrey Lee and Ileana Streinu},
journal={arXiv preprint arXiv:math/0702129},
year={2007},
number={UMass Amherst Computer Science Department TR 07-02},
archivePrefix={arXiv},
eprint={math/0702129},
primaryClass={math.CO cs.CG}
} | lee2007pebble |
arxiv-676903 | math/0702239 | Polyhedral representation conversion up to symmetries | <|reference_start|>Polyhedral representation conversion up to symmetries: We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. We in particular discuss decomposition methods, which reduce the problem to a number of lower dimensional subproblems. These methods have been successfully used by different authors in special contexts. Moreover, we sketch an incremental method, which is a generalization of Fourier-Motzkin elimination, and we give some ideas how symmetry can be exploited using pivots.<|reference_end|> | arxiv | @article{bremner2007polyhedral,
title={Polyhedral representation conversion up to symmetries},
author={David Bremner, Mathieu Dutour Sikiric, Achill Schuermann},
journal={CRM Proceedings & Lecture Notes 48, AMS, 2009, pp. 45-71},
year={2007},
archivePrefix={arXiv},
eprint={math/0702239},
primaryClass={math.MG cs.CG}
} | bremner2007polyhedral |
arxiv-676904 | math/0702301 | Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting | <|reference_start|>Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting: The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection, signal denoising, compressive sensing, and constructive approximation. Of interest are conditions on the model dimension $p$, the sparsity index $s$ (number of non-zero entries in $\beta^*$), and the number of observations $n$ that are necessary and/or sufficient to ensure asymptotically perfect recovery of the sparsity pattern. This paper focuses on the information-theoretic limits of sparsity recovery: in particular, for a noisy linear observation model based on measurement vectors drawn from the standard Gaussian ensemble, we derive both a set of sufficient conditions for asymptotically perfect recovery using the optimal decoder, as well as a set of necessary conditions that any decoder, regardless of its computational complexity, must satisfy for perfect recovery. This analysis of optimal decoding limits complements our previous work (ARXIV: math.ST/0605740) on sharp thresholds for sparsity recovery using the Lasso ($\ell_1$-constrained quadratic programming) with Gaussian measurement ensembles.<|reference_end|> | arxiv | @article{wainwright2007information-theoretic,
title={Information-theoretic limits on sparsity recovery in the
high-dimensional and noisy setting},
author={Martin J. Wainwright},
journal={arXiv preprint arXiv:math/0702301},
year={2007},
archivePrefix={arXiv},
eprint={math/0702301},
primaryClass={math.ST cs.IT math.IT stat.TH}
} | wainwright2007information-theoretic |
arxiv-676905 | math/0702325 | Neighbor selection and hitting probability in small-world graphs | <|reference_start|>Neighbor selection and hitting probability in small-world graphs: Small-world graphs, which combine randomized and structured elements, are seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this type it is possible to route, or navigate, between vertices in few steps even with very little knowledge of the graph itself. In an attempt to understand how such graphs arise we introduce a different criterion for graphs to be navigable in this sense, relating the neighbor selection of a vertex to the hitting probability of routed walks. In several models starting from both discrete and continuous settings, this can be shown to lead to graphs with the desired properties. It also leads directly to an evolutionary model for the creation of similar graphs by the stepwise rewiring of the edges, and we conjecture, supported by simulations, that these too are navigable.<|reference_end|> | arxiv | @article{sandberg2007neighbor,
title={Neighbor selection and hitting probability in small-world graphs},
author={Oskar Sandberg},
journal={Annals of Applied Probability 2008, Vol. 18, No. 5, 1771-1793},
year={2007},
doi={10.1214/07-AAP499},
number={IMS-AAP-AAP499},
archivePrefix={arXiv},
eprint={math/0702325},
primaryClass={math.PR cs.DS}
} | sandberg2007neighbor |
arxiv-676906 | math/0702334 | An Example of Pi^0_3-complete Infinitary Rational Relation | <|reference_start|>An Example of Pi^0_3-complete Infinitary Rational Relation: We give in this paper an example of infinitary rational relation, accepted by a 2-tape B\"{u}chi automaton, which is Pi^0_3-complete in the Borel hierarchy. Moreover the example of infinitary rational relation given in this paper has a very simple structure and can be easily described by its sections.<|reference_end|> | arxiv | @article{finkel2007an,
title={An Example of Pi^0_3-complete Infinitary Rational Relation},
author={Olivier Finkel (LIP)},
journal={arXiv preprint arXiv:math/0702334},
year={2007},
archivePrefix={arXiv},
eprint={math/0702334},
primaryClass={math.LO cs.CC cs.LO}
} | finkel2007an |
arxiv-676907 | math/0702744 | Matrix norms and rapid mixing for spin systems | <|reference_start|>Matrix norms and rapid mixing for spin systems: We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is $\mathbf{0}$ (as in heat bath dynamics). We apply the matrix norm methods to random update and systematic scan Glauber dynamics for coloring various classes of graphs. We give a general method for estimating a norm of a symmetric nonregular matrix. This leads to improved mixing times for any class of graphs which is hereditary and sufficiently sparse including several classes of degree-bounded graphs such as nonregular graphs, trees, planar graphs and graphs with given tree-width and genus.<|reference_end|> | arxiv | @article{dyer2007matrix,
title={Matrix norms and rapid mixing for spin systems},
author={Martin Dyer, Leslie Ann Goldberg, Mark Jerrum},
journal={Annals of Applied Probability 2009, Vol. 19, No. 1, 71-107},
year={2007},
doi={10.1214/08-AAP532},
number={IMS-AAP-AAP532},
archivePrefix={arXiv},
eprint={math/0702744},
primaryClass={math.PR cs.DS}
} | dyer2007matrix |
arxiv-676908 | math/0702804 | The Loss Rank Principle for Model Selection | <|reference_start|>The Loss Rank Principle for Model Selection: We introduce a new principle for model selection in regression and classification. Many regression models are controlled by some smoothness or flexibility or complexity parameter c, e.g. the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polynomials. Let f_D^c be the (best) regressor of complexity c on data D. A more flexible regressor can fit more data D' well than a more rigid one. If something (here small loss) is easy to achieve it's typically worth less. We define the loss rank of f_D^c as the number of other (fictitious) data D' that are fitted better by f_D'^c than D is fitted by f_D^c. We suggest selecting the model complexity c that has minimal loss rank (LoRP). Unlike most penalized maximum likelihood variants (AIC,BIC,MDL), LoRP only depends on the regression function and loss function. It works without a stochastic noise model, and is directly applicable to any non-parametric regressor, like kNN. In this paper we formalize, discuss, and motivate LoRP, study it for specific regression problems, in particular linear ones, and compare it to other model selection schemes.<|reference_end|> | arxiv | @article{hutter2007the,
title={The Loss Rank Principle for Model Selection},
author={Marcus Hutter},
journal={Proc. 20th Annual Conf. on Learning Theory (COLT 2007) pages
589-603},
year={2007},
doi={10.1007/978-3-540-72927-3_42},
archivePrefix={arXiv},
eprint={math/0702804},
primaryClass={math.ST cs.LG stat.ME stat.ML stat.TH}
} | hutter2007the |
arxiv-676909 | math/0702866 | Consumer Profile Identification and Allocation | <|reference_start|>Consumer Profile Identification and Allocation: We propose an easy-to-use methodology to allocate one of the groups which have been previously built from a complete learning data base, to new individuals. The learning data base contains continuous and categorical variables for each individual. The groups (clusters) are built by using only the continuous variables and described with the help of the categorical ones. For the new individuals, only the categorical variables are available, and it is necessary to define a model which computes the probabilities to belong to each of the clusters, by using only the categorical variables. Then this model provides a decision rule to assign the new individuals and gives an efficient tool to decision-makers. This tool is shown to be very efficient for customers allocation in consumer clusters for marketing purposes, for example.<|reference_end|> | arxiv | @article{letrémy2007consumer,
title={Consumer Profile Identification and Allocation},
author={Patrick Letr'emy (SAMOS, CES), Marie Cottrell (SAMOS, CES), Eric
Esposito (RDD GDF), Val'erie Laffite (RDD GDF), Sally Showk (RDD GDF)},
journal={arXiv preprint arXiv:math/0702866},
year={2007},
archivePrefix={arXiv},
eprint={math/0702866},
primaryClass={math.ST cs.NE stat.TH}
} | letrémy2007consumer |
arxiv-676910 | math/0703019 | Reading policies for joins: An asymptotic analysis | <|reference_start|>Reading policies for joins: An asymptotic analysis: Suppose that $m_n$ observations are made from the distribution $\mathbf {R}$ and $n-m_n$ from the distribution $\mathbf {S}$. Associate with each pair, $x$ from $\mathbf {R}$ and $y$ from $\mathbf {S}$, a nonnegative score $\phi(x,y)$. An optimal reading policy is one that yields a sequence $m_n$ that maximizes $\mathbb{E}(M(n))$, the expected sum of the $(n-m_n)m_n$ observed scores, uniformly in $n$. The alternating policy, which switches between the two sources, is the optimal nonadaptive policy. In contrast, the greedy policy, which chooses its source to maximize the expected gain on the next step, is shown to be the optimal policy. Asymptotics are provided for the case where the $\mathbf {R}$ and $\mathbf {S}$ distributions are discrete and $\phi(x,y)=1 or 0$ according as $x=y$ or not (i.e., the observations match). Specifically, an invariance result is proved which guarantees that for a wide class of policies, including the alternating and the greedy, the variable M(n) obeys the same CLT and LIL. A more delicate analysis of the sequence $\mathbb{E}(M(n))$ and the sample paths of M(n), for both alternating and greedy, reveals the slender sense in which the latter policy is asymptotically superior to the former, as well as a sense of equivalence of the two and robustness of the former.<|reference_end|> | arxiv | @article{russo2007reading,
title={Reading policies for joins: An asymptotic analysis},
author={Ralph P. Russo, Nariankadu D. Shyamalkumar},
journal={Annals of Applied Probability 2007, Vol. 17, No. 1, 230-264},
year={2007},
doi={10.1214/105051606000000646},
number={IMS-AAP-AAP404},
archivePrefix={arXiv},
eprint={math/0703019},
primaryClass={math.PR cs.DB}
} | russo2007reading |
arxiv-676911 | math/0703241 | Sofic Trace of a Cellular Automaton | <|reference_start|>Sofic Trace of a Cellular Automaton: The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram, ie the infinite sequence of states of a particular cell of a configuration; in the language of symbolic dynamics one says that it is a factor system. In this paper we study conditions for a sofic subshift to be the trace of a cellular automaton.<|reference_end|> | arxiv | @article{cervelle2007sofic,
title={Sofic Trace of a Cellular Automaton},
author={Julien Cervelle (IGM), Enrico Formenti (I3S), Pierre Guillon (IGM)},
journal={arXiv preprint arXiv:math/0703241},
year={2007},
archivePrefix={arXiv},
eprint={math/0703241},
primaryClass={math.DS cs.CC cs.DM}
} | cervelle2007sofic |
arxiv-676912 | math/0703436 | A parametric representation of totally mixed Nash equilibria | <|reference_start|>A parametric representation of totally mixed Nash equilibria: We compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with pre-fixed structure. Using this representation, we show conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present a symbolic procedure that allows us to describe and estimate the number of isolated totally mixed Nash equilibria of an arbitrary game. Under certain assumptions, the algorithm computes the exact number of these equilibria.<|reference_end|> | arxiv | @article{jeronimo2007a,
title={A parametric representation of totally mixed Nash equilibria},
author={G. Jeronimo, D. Perrucci, J. Sabia},
journal={arXiv preprint arXiv:math/0703436},
year={2007},
archivePrefix={arXiv},
eprint={math/0703436},
primaryClass={math.AG cs.GT}
} | jeronimo2007a |
arxiv-676913 | math/0703575 | Convex Discrete Optimization | <|reference_start|>Convex Discrete Optimization: We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variable dimension. We discuss some of the many applications of this theory including to quadratic programming, matroids, bin packing and cutting-stock problems, vector partitioning and clustering, multiway transportation problems, and privacy and confidential statistical data disclosure. Highlights of our work include a strongly polynomial time algorithm for convex and linear combinatorial optimization over any family presented by a membership oracle when the underlying polytope has few edge-directions; a new theory of so-termed n-fold integer programming, yielding polynomial time solution of important and natural classes of convex and linear integer programming problems in variable dimension; and a complete complexity classification of high dimensional transportation problems, with practical applications to fundamental problems in privacy and confidential statistical data disclosure.<|reference_end|> | arxiv | @article{onn2007convex,
title={Convex Discrete Optimization},
author={Shmuel Onn},
journal={Encyclopedia of Optimization 2009: 513-550},
year={2007},
archivePrefix={arXiv},
eprint={math/0703575},
primaryClass={math.OC cs.CC cs.DM math.CO}
} | onn2007convex |
arxiv-676914 | math/0703656 | Using decision problems in public key cryptography | <|reference_start|>Using decision problems in public key cryptography: There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they are of the following nature: given a property P and the information that there are objects with the property P, find at least one particular object with the property P. So far, no cryptographic protocol based on a search problem in a non-commutative (semi)group has been recognized as secure enough to be a viable alternative to established protocols (such as RSA) based on commutative (semi)groups, although most of these protocols are more efficient than RSA is. In this paper, we suggest to use decision problems from combinatorial group theory as the core of a public key establishment protocol or a public key cryptosystem. By using a popular decision problem, the word problem, we design a cryptosystem with the following features: (1) Bob transmits to Alice an encrypted binary sequence which Alice decrypts correctly with probability "very close" to 1; (2) the adversary, Eve, who is granted arbitrarily high (but fixed) computational speed, cannot positively identify (at least, in theory), by using a "brute force attack", the "1" or "0" bits in Bob's binary sequence. In other words: no matter what computational speed we grant Eve at the outset, there is no guarantee that her "brute force attack" program will give a conclusive answer (or an answer which is correct with overwhelming probability) about any bit in Bob's sequence.<|reference_end|> | arxiv | @article{shpilrain2007using,
title={Using decision problems in public key cryptography},
author={Vladimir Shpilrain and Gabriel Zapata},
journal={arXiv preprint arXiv:math/0703656},
year={2007},
archivePrefix={arXiv},
eprint={math/0703656},
primaryClass={math.GR cs.CR}
} | shpilrain2007using |
arxiv-676915 | math/0703713 | The logic of message passing | <|reference_start|>The logic of message passing: Message passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message passing. In order to achieve this we introduce the categorical notion of a linear actegory and the related polycategorical notion of a poly-actegory. Not surprisingly the notation used for the term calculus borrows heavily from the (synchronous) pi-calculus. The cut elimination procedure for the system provides an operational semantics.<|reference_end|> | arxiv | @article{cockett2007the,
title={The logic of message passing},
author={J. R. B. Cockett and Craig Pastro},
journal={Science of Computer Programming 74 no.8 (2009) 498-533},
year={2007},
archivePrefix={arXiv},
eprint={math/0703713},
primaryClass={math.CT cs.LO}
} | cockett2007the |
arxiv-676916 | math/0703865 | Solving Triangular Peg Solitaire | <|reference_start|>Solving Triangular Peg Solitaire: We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple solution strategies. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more consecutive jumps by the same peg), and find the shortest solution to the basic game on all triangular boards with up to 55 holes (10 holes on a side).<|reference_end|> | arxiv | @article{bell2007solving,
title={Solving Triangular Peg Solitaire},
author={George I. Bell},
journal={Journal of Integer Sequences, Vol. 11 (2008), Article 08.4.8},
year={2007},
archivePrefix={arXiv},
eprint={math/0703865},
primaryClass={math.CO cs.DM}
} | bell2007solving |
arxiv-676917 | math/0703902 | Connectivity and equilibrium in random games | <|reference_start|>Connectivity and equilibrium in random games: We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random utility tables are assigned to the players. We provide conditions for the structure of the graph under which equilibria are likely to exist and complementary conditions which make the existence of equilibria highly unlikely. Our results have immediate implications for many deterministic graphs and generalize known results for random games on the complete graph. In particular, our results imply that the probability that bounded degree graphs have pure Nash equilibria is exponentially small in the size of the graph and yield a simple algorithm that finds small nonexistence certificates for a large family of graphs. Then we show that in any strongly connected graph of n vertices with expansion $(1+\Omega(1))\log_2(n)$ the distribution of the number of equilibria approaches the Poisson distribution with parameter 1, asymptotically as $n \to +\infty$.<|reference_end|> | arxiv | @article{daskalakis2007connectivity,
title={Connectivity and equilibrium in random games},
author={Constantinos Daskalakis, Alexandros G. Dimakis, Elchanan Mossel},
journal={Annals of Applied Probability 2011, Vol. 21, No. 3, 987-1016},
year={2007},
doi={10.1214/10-AAP715},
number={IMS-AAP-AAP715},
archivePrefix={arXiv},
eprint={math/0703902},
primaryClass={math.PR cs.GT math.CO}
} | daskalakis2007connectivity |
arxiv-676918 | math/0703921 | Sparse Hypergraphs and Pebble Game Algorithms | <|reference_start|>Sparse Hypergraphs and Pebble Game Algorithms: A hypergraph $G=(V,E)$ is $(k,\ell)$-sparse if no subset $V'\subset V$ spans more than $k|V'|-\ell$ hyperedges. We characterize $(k,\ell)$-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lov{\'{a}}sz, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address the problem of finding lower-dimensional representations of sparse hypergraphs, and identify a critical behaviour in terms of the sparsity parameters $k$ and $\ell$. Our constructions extend the pebble games of Lee and Streinu from graphs to hypergraphs.<|reference_end|> | arxiv | @article{streinu2007sparse,
title={Sparse Hypergraphs and Pebble Game Algorithms},
author={Ileana Streinu and Louis Theran},
journal={arXiv preprint arXiv:math/0703921},
year={2007},
archivePrefix={arXiv},
eprint={math/0703921},
primaryClass={math.CO cs.DS}
} | streinu2007sparse |
arxiv-676919 | math/0703927 | On Computing the Distinguishing Numbers of Planar Graphs and Beyond: a Counting Approach | <|reference_start|>On Computing the Distinguishing Numbers of Planar Graphs and Beyond: a Counting Approach: A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest integer k for which G has a distinguishing k-labeling. In this paper, we apply the principle of inclusion-exclusion and develop recursive formulas to count the number of inequivalent distinguishing k-labelings of a graph. Along the way, we prove that the distinguishing number of a planar graph can be computed in time polynomial in the size of the graph.}<|reference_end|> | arxiv | @article{arvind2007on,
title={On Computing the Distinguishing Numbers of Planar Graphs and Beyond: a
Counting Approach},
author={V. Arvind, Christine T. Cheng, Nikhil R. Devanur},
journal={arXiv preprint arXiv:math/0703927},
year={2007},
archivePrefix={arXiv},
eprint={math/0703927},
primaryClass={math.CO cs.DS}
} | arvind2007on |
arxiv-676920 | math/9310227 | A linear construction for certain Kerdock and Preparata codes | <|reference_start|>A linear construction for certain Kerdock and Preparata codes: The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over $\ZZ_4$, the integers $\bmod~4$. The Kerdock and Preparata codes are duals over $\ZZ_4$, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over $\ZZ_4$. This provides a simple definition for these codes and explains why their Hamming weight distributions are dual to each other. First- and second-order Reed-Muller codes are also linear codes over $\ZZ_4$, but Hamming codes in general are not, nor is the Golay code.<|reference_end|> | arxiv | @article{calderbank1993a,
title={A linear construction for certain Kerdock and Preparata codes},
author={A. R. Calderbank, A. Roger Hammons Jr., P. Vijay Kumar, N. J. A.
Sloane, Patrick Sol'e},
journal={Bull. Amer. Math. Soc. (N.S.) 29 (1993) 218-222},
year={1993},
number={Bulletin migration 11/99},
archivePrefix={arXiv},
eprint={math/9310227},
primaryClass={math.CO cs.IT math.IT}
} | calderbank1993a |
arxiv-676921 | math/9409219 | Proving probabilistic correctness statements: the case of Rabin's algorithm for mutual exclusion | <|reference_start|>Proving probabilistic correctness statements: the case of Rabin's algorithm for mutual exclusion: The correctness of most randomized distributed algorithms is expressed by a statement of the form ``some predicate of the executions holds with high probability, regardless of the order in which actions are scheduled''. In this paper, we present a general methodology to prove correctness statements of such randomized algorithms. Specifically, we show how to prove such statements by a series of refinements, which terminate in a statement independent of the schedule. To demonstrate the subtlety of the issues involved in this type of analysis, we focus on Rabin's randomized distributed algorithm for mutual exclusion [Rabin 82]. Surprisingly, it turns out that the algorithm does not maintain one of the requirements of the problem under a certain schedule. In particular, we give a schedule under which a set of processes can suffer lockout for arbitrary long periods.<|reference_end|> | arxiv | @article{saias1994proving,
title={Proving probabilistic correctness statements: the case of Rabin's
algorithm for mutual exclusion},
author={Isaac Saias},
journal={arXiv preprint arXiv:math/9409219},
year={1994},
number={LACES 68Q-94-14},
archivePrefix={arXiv},
eprint={math/9409219},
primaryClass={math.CO cs.CC}
} | saias1994proving |
arxiv-676922 | math/9409220 | Number of faults a system can withstand without repairs | <|reference_start|>Number of faults a system can withstand without repairs: We consider the following scheduling problem. A system is composed of $n$ processors drawn from a pool of $N$. The processors can become faulty while in operation and faulty processors never recover. A report is issued whenever a fault occurs. This report states only the existence of a fault, but does not indicate its location. Based on this report, the scheduler can reconfigure the system and choose another set of $n$ processors. The system operates satisfactorily as long as at most $f$ of the $n$ selected processors are faulty. We exhibit a scheduling strategy allowing the system to operate satisfactorily until approximately $(N/n)f$ faults are reported in the worst case. Our precise bound is tight.<|reference_end|> | arxiv | @article{goemans1994number,
title={Number of faults a system can withstand without repairs},
author={Michel Goemans, Nancy Lynch, Isaac Saias},
journal={arXiv preprint arXiv:math/9409220},
year={1994},
number={LACES 68Q-94-15},
archivePrefix={arXiv},
eprint={math/9409220},
primaryClass={math.CO cs.CC}
} | goemans1994number |
arxiv-676923 | math/9409221 | Proving time bounds for randomized distributed algorithms | <|reference_start|>Proving time bounds for randomized distributed algorithms: A method of analyzing time bounds for randomized distributed algorithms is presented, in the context of a new and general framework for describing and reasoning about randomized algorithms. The method consists of proving auxiliary statements of the form U (t)->(p) U', which means that whenever the algorithm begins in a state in set U, with probability p, it will reach a state in set U' within time t. The power of the method is illustrated by its use in proving a constant upper bound on the expected time for some process to reach its critical region, in Lehmann and Rabin's Dining Philosophers algorithm.<|reference_end|> | arxiv | @article{lynch1994proving,
title={Proving time bounds for randomized distributed algorithms},
author={Nancy Lynch, Isaac Saias, Roberto Segala},
journal={arXiv preprint arXiv:math/9409221},
year={1994},
number={LACES 68Q-94-16},
archivePrefix={arXiv},
eprint={math/9409221},
primaryClass={math.CO cs.CC}
} | lynch1994proving |
arxiv-676924 | math/9409223 | On the minimum latency problem | <|reference_start|>On the minimum latency problem: We are given a set of points $p_1,\ldots , p_n$ and a symmetric distance matrix $(d_{ij})$ giving the distance between $p_i$ and $p_j$. We wish to construct a tour that minimizes $\sum_{i=1}^n \ell(i)$, where $\ell(i)$ is the {\em latency} of $p_i$, defined to be the distance traveled before first visiting $p_i$. This problem is also known in the literature as the {\em deliveryman problem} or the {\em traveling repairman problem}. It arises in a number of applications including disk-head scheduling, and turns out to be surprisingly different from the traveling salesman problem in character. We give exact and approximate solutions to a number of cases, including a constant-factor approximation algorithm whenever the distance matrix satisfies the triangle inequality.<|reference_end|> | arxiv | @article{blum1994on,
title={On the minimum latency problem},
author={Avrim Blum, Prasad Chalasani, Don Coppersmith, Bill Pulleyblank,
Prabhakar Raghavan, Madhu Sudan},
journal={arXiv preprint arXiv:math/9409223},
year={1994},
number={LACES 68Q-94-18},
archivePrefix={arXiv},
eprint={math/9409223},
primaryClass={math.CO cs.CC}
} | blum1994on |
arxiv-676925 | math/9409224 | An on-line algorithm for improving performance in navigation | <|reference_start|>An on-line algorithm for improving performance in navigation: Recent papers have shown optimally-competitive on-line strategies for a robot traveling from a point $s$ to a point $t$ in certain unknown geometric environments. We consider the question: Having gained some partial information about the scene on its first trip from $s$ to $t$, can the robot improve its performance on subsequent trips it might make? This is a type of on-line problem where a strategy must exploit {\em partial information \/} about the future (e.g., about obstacles that lie ahead). For scenes with axis-parallel rectangular obstacles where the Euclidean distance between $s$ and $t$ is $n$, we present a deterministic algorithm whose {\em average\/} trip length after $k$ trips, $k \leq n$, is $O(\rootnbyk)$ times the length of the shortest $s$-$t$ path in the scene. We also show that this is the best a deterministic strategy can do. This algorithm can be thought of as performing an optimal tradeoff between search effort and the goodness of the path found. We improve this algorithm so that for {\em every\/} $i \leq n$, the robot's $i$th trip length is $O(\rootnbyi)$ times the shortest $s$-$t$ path length. A key idea of the paper is that a {\em tree\/} structure can be defined in the scene, where the nodes are portions of certain obstacles and the edges are ``short'' paths from a node to its children. The core of our algorithms is an on-line strategy for traversing this tree optimally.<|reference_end|> | arxiv | @article{blum1994an,
title={An on-line algorithm for improving performance in navigation},
author={Avrim Blum, Prasad Chalasani},
journal={arXiv preprint arXiv:math/9409224},
year={1994},
number={LACES 68Q-94-19},
archivePrefix={arXiv},
eprint={math/9409224},
primaryClass={math.CO cs.CC}
} | blum1994an |
arxiv-676926 | math/9409225 | The complexity of approximating PSPACE-Complete problems for hierarchical specifications | <|reference_start|>The complexity of approximating PSPACE-Complete problems for hierarchical specifications: We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient approximation algorithms is characterized, for several standard graph theoretic and combinatorial problems. We present polynomial time approximation algorithms for several standard PSPACE-hard problems considered in the literature. In contrast, we show that unless P = PSPACE, there is no polynomial time epsilon-approximation for any epsilon>0, for several other problems, when the instances are specified hierarchically. We present polynomial time approximation algorithms for the following problems when the graphs are specified hierarchically: {minimum vertex cover}, {maximum 3SAT}, {weighted max cut}, {minimum maximal matching}, {bounded degree maximum independent set} In contrast, we show that unless P = PSPACE, there is no polynomial time epsilon-approximation for any epsilon>0, for the following problems when the instances are specified hierarchically: {the number of true gates in a monotone acyclic circuit when all input values are specified} and {the optimal value of the objective function of a linear program} It is also shown that unless P = PSPACE, a performance guarantee of less than 2 cannot be obtained in polynomial time for the following problems when the instances are specified hierarchically: {high degree subgraph}, {k-vertex connected subgraph}, and {k-edge connected subgraph}<|reference_end|> | arxiv | @article{marathe1994the,
title={The complexity of approximating PSPACE-Complete problems for
hierarchical specifications},
author={Madhav V. Marathe, Harry B. Hunt III, S. S. Ravi},
journal={arXiv preprint arXiv:math/9409225},
year={1994},
number={LACES 68Q-94-21},
archivePrefix={arXiv},
eprint={math/9409225},
primaryClass={math.CO cs.CC}
} | marathe1994the |
arxiv-676927 | math/9409226 | Geometry based heuristics for unit disk graphs | <|reference_start|>Geometry based heuristics for unit disk graphs: Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a competitive ratio of 6 for unit disk graphs. Our heuristics do not need a geometric representation of unit disk graphs. Geometric representations are used only in establishing the performance guarantees of the heuristics. Several of our approximation algorithms can be extended to intersection graphs of circles of arbitrary radii in the plane, intersection graphs of regular polygons, and to intersection graphs of higher dimensional regular objects.<|reference_end|> | arxiv | @article{marathe1994geometry,
title={Geometry based heuristics for unit disk graphs},
author={Madhav V. Marathe, H. Breu, Harry B. Hunt III, S. S. Ravi, Daniel J.
Rosenkrantz},
journal={arXiv preprint arXiv:math/9409226},
year={1994},
number={LACES 68Q-94-22},
archivePrefix={arXiv},
eprint={math/9409226},
primaryClass={math.CO cs.CC}
} | marathe1994geometry |
arxiv-676928 | math/9410208 | Three-dimensional alpha shapes | <|reference_start|>Three-dimensional alpha shapes: Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in $\Real^3$. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter $\alpha \in \Real$ controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size $n$ in time $O(n^2)$, worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.<|reference_end|> | arxiv | @article{edelsbrunner1994three-dimensional,
title={Three-dimensional alpha shapes},
author={Herbert Edelsbrunner, Ernst M"ucke},
journal={arXiv preprint arXiv:math/9410208},
year={1994},
number={LACES 52B-94-25},
archivePrefix={arXiv},
eprint={math/9410208},
primaryClass={math.CO cs.CC math.MG}
} | edelsbrunner1994three-dimensional |
arxiv-676929 | math/9410209 | Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms | <|reference_start|>Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms: This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.<|reference_end|> | arxiv | @article{edelsbrunner1994simulation,
title={Simulation of simplicity: a technique to cope with degenerate cases in
geometric algorithms},
author={Herbert Edelsbrunner, Ernst M"ucke},
journal={arXiv preprint arXiv:math/9410209},
year={1994},
number={LACES 68Q-94-24},
archivePrefix={arXiv},
eprint={math/9410209},
primaryClass={math.CO cs.CC}
} | edelsbrunner1994simulation |
arxiv-676930 | math/9411219 | Lower bounds for identifying subset members with subset queries | <|reference_start|>Lower bounds for identifying subset members with subset queries: An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs in areas such as fault detection, multiaccess communications, optimal search, blood testing and chromosome mapping. Consider the two stage algorithm for solving a group testing problem. In the first stage a predetermined set of queries are asked in parallel and in the second stage, $P$ is determined by testing individual objects. Let $n=\cardof{\cO}$. Suppose that $P$ is generated by independently adding each $x\in \cO$ to $P$ with probability $p/n$. Let $q_1$ ($q_2$) be the number of queries asked in the first (second) stage of this algorithm. We show that if $q_1=o(\log(n)\log(n)/\log\log(n))$, then $\Exp(q_2) = n^{1-o(1)}$, while there exist algorithms with $q_1 = O(\log(n)\log(n)/\log\log(n))$ and $\Exp(q_2) = o(1)$. The proof involves a relaxation technique which can be used with arbitrary distributions. The best previously known bound is $q_1+\Exp(q_2) = \Omega(p\log(n))$. For general group testing algorithms, our results imply that if the average number of queries over the course of $n^\gamma$ ($\gamma>0$) independent experiments is $O(n^{1-\epsilon})$, then with high probability $\Omega(\log(n)\log(n)/\log\log(n))$ non-singleton subsets are queried. This settles a conjecture of Bill Bruno and David Torney and has important consequences for the use of group testing in screening DNA libraries and other applications where it is more cost effective to use non-adaptive algorithms and/or too expensive to prepare a subset $Q$ for its first test.<|reference_end|> | arxiv | @article{knill1994lower,
title={Lower bounds for identifying subset members with subset queries},
author={Emanuel Knill},
journal={arXiv preprint arXiv:math/9411219},
year={1994},
number={LACES 68Q-94-23},
archivePrefix={arXiv},
eprint={math/9411219},
primaryClass={math.CO cs.CC}
} | knill1994lower |
arxiv-676931 | math/9411222 | The complexity of broadcasting in bounded-degree networks | <|reference_start|>The complexity of broadcasting in bounded-degree networks: Broadcasting concerns the dissemination of a message originating at one node of a network to all other nodes. This task is accomplished by placing a series of calls over the communication lines of the network between neighboring nodes, where each call requires a unit of time and a call can involve only two nodes. We show that for bounded-degree networks determining the minimum broadcast time from an originating node remains NP-complete.<|reference_end|> | arxiv | @article{dinneen1994the,
title={The complexity of broadcasting in bounded-degree networks},
author={Michael J. Dinneen},
journal={arXiv preprint arXiv:math/9411222},
year={1994},
number={LACES 68Q-94-31},
archivePrefix={arXiv},
eprint={math/9411222},
primaryClass={math.CO cs.CC}
} | dinneen1994the |
arxiv-676932 | math/9411235 | McColm conjecture | <|reference_start|>McColm conjecture: Gregory McColm conjectured that positive elementary inductions are bounded in a class K of finite structures if every (FO + LFP) formula is equivalent to a first-order formula in K. Here (FO + LFP) is the extension of first-order logic with the least fixed point operator. We disprove the conjecture. Our main results are two model-theoretic constructions, one deterministic and the other randomized, each of which refutes McColm's conjecture.<|reference_end|> | arxiv | @article{gurevich1994mccolm,
title={McColm conjecture},
author={Yuri Gurevich, Neil Immerman, Saharon Shelah},
journal={Symposium on Logic in Computer Science (1994), 10--19},
year={1994},
number={Shelah [GISh:525]},
archivePrefix={arXiv},
eprint={math/9411235},
primaryClass={math.LO cs.LO}
} | gurevich1994mccolm |
arxiv-676933 | math/9411236 | On finite rigid structures | <|reference_start|>On finite rigid structures: The main result of this paper is a probabilistic construction of finite rigid structures. It yields a finitely axiomatizable class of finite rigid structures where no L^omega_{infty, omega} formula with counting quantifiers defines a linear order.<|reference_end|> | arxiv | @article{gurevich1994on,
title={On finite rigid structures},
author={Yuri Gurevich, Saharon Shelah},
journal={J. Symbolic Logic 61 (1996), 549--562},
year={1994},
number={Shelah [GuSh:526]},
archivePrefix={arXiv},
eprint={math/9411236},
primaryClass={math.LO cs.LO}
} | gurevich1994on |
arxiv-676934 | math/9504213 | Path optimization and near-greedy analysis for graph partitioning: an empirical study | <|reference_start|>Path optimization and near-greedy analysis for graph partitioning: an empirical study: This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the min_quotient_cut problem. We present the results of computational comparisons between this technique and the Kernighan-Lin algorithm, the simulated annealing algorithm, the FLOW-lagorithm the multilevel algorithm, and teh recent 0.878-approximation algorithm. The experiments were conducted on two classes of graphs that have become standard for such tests: random and random geometric. They show that for both classes of inputs and both variations of the problem, the new heuristic is competitive with the other algorithms and holds an advantage for min_quotient_cut when applied to very large, sparse geometric graphs. In the last part of the paper, we describe an approach to analyzing graph partitioning algorithms from the statistical point of view. Every partitioning of a graph is viewed as a result achieved by a "near gready" partitioning algorithm. The experiments show that for "good" partitionings, the number of non-greedy steps needed to obtain them is quite small; moreover, it is "statistically" smaller for better partitionings. This led us to conjecture that there exists an "optimal" distribution of the non-greedy steps that characterize the classes of graphs that we studied.<|reference_end|> | arxiv | @article{berry1995path,
title={Path optimization and near-greedy analysis for graph partitioning: an
empirical study},
author={Jonathan Berry, Mark Goldberg},
journal={arXiv preprint arXiv:math/9504213},
year={1995},
number={LACES 68Q-95-25},
archivePrefix={arXiv},
eprint={math/9504213},
primaryClass={math.CO cs.CC}
} | berry1995path |
arxiv-676935 | math/9508218 | An analysis of Bennett's pebble game | <|reference_start|>An analysis of Bennett's pebble game: Bennett's pebble game was introduced to obtain better time/space tradeoffs in the simulation of standard Turing machines by reversible ones. So far only upper bounds for the tradeoff based on the pebble game have been published. Here we give a recursion for the time optimal solution of the pebble game given a space bound. We analyze the recursion to obtain an explicit asymptotic expression for the best time-space product.<|reference_end|> | arxiv | @article{knill1995an,
title={An analysis of Bennett's pebble game},
author={Emanuel Knill},
journal={arXiv preprint arXiv:math/9508218},
year={1995},
number={LACES 68Q-95-31},
archivePrefix={arXiv},
eprint={math/9508218},
primaryClass={math.CO cs.CC}
} | knill1995an |
arxiv-676936 | math/9508219 | New results on binary linear codes | <|reference_start|>New results on binary linear codes: This research announcement describes in very rough terms methods and a computer language under development, which can be used to prove the nonexistence of binary linear codes. Over a hundred new results have been obtained by the author. For example, there is no [29,11,10] code. The proof of this is roughly outlined.<|reference_end|> | arxiv | @article{jaffe1995new,
title={New results on binary linear codes},
author={David B. Jaffe},
journal={arXiv preprint arXiv:math/9508219},
year={1995},
number={LACES 94B-95-32},
archivePrefix={arXiv},
eprint={math/9508219},
primaryClass={math.CO cs.IT math.IT}
} | jaffe1995new |
arxiv-676937 | math/9610221 | Extensions and Corrections for: ``A Convex Geometric Approach to Counting the Roots of a Polynomial System'' | <|reference_start|>Extensions and Corrections for: ``A Convex Geometric Approach to Counting the Roots of a Polynomial System'': This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.<|reference_end|> | arxiv | @article{rojas1996extensions,
title={Extensions and Corrections for: ``A Convex Geometric Approach to
Counting the Roots of a Polynomial System''},
author={J. Maurice Rojas},
journal={arXiv preprint arXiv:math/9610221},
year={1996},
number={MSRI 1996-075},
archivePrefix={arXiv},
eprint={math/9610221},
primaryClass={math.AG cs.DS}
} | rojas1996extensions |
arxiv-676938 | math/9702221 | Some New Applications of Toric Geometry | <|reference_start|>Some New Applications of Toric Geometry: This paper reexamines univariate reduction from a toric geometric point of view. We begin by constructing a binomial variant of the $u$-resultant and then retailor the generalized characteristic polynomial to fully exploit sparsity in the monomial structure of any given polynomial system. We thus obtain a fast new algorithm for univariate reduction and a better understanding of the underlying projections. As a corollary, we show that a refinement of Hilbert's Tenth Problem is decidable within single-exponential time. We also show how certain multisymmetric functions of the roots of polynomial systems can be calculated with sparse resultants.<|reference_end|> | arxiv | @article{rojas1997some,
title={Some New Applications of Toric Geometry},
author={J. Maurice Rojas},
journal={arXiv preprint arXiv:math/9702221},
year={1997},
number={MSRI 1997-016},
archivePrefix={arXiv},
eprint={math/9702221},
primaryClass={math.AG cs.DS}
} | rojas1997some |
arxiv-676939 | math/9702222 | Toric Generalized Characteristic Polynomials | <|reference_start|>Toric Generalized Characteristic Polynomials: We illustrate an efficient new method for handling polynomial systems with degenerate solution sets. In particular, a corollary of our techniques is a new algorithm to find an isolated point in every excess component of the zero set (over an algebraically closed field) of any $n$ by $n$ system of polynomial equations. Since we use the sparse resultant, we thus obtain complexity bounds (for converting any input polynomial system into a multilinear factorization problem) which are close to cubic in the degree of the underlying variety -- significantly better than previous bounds which were pseudo-polynomial in the classical B\'ezout bound. By carefully taking into account the underlying toric geometry, we are also able to improve the reliability of certain sparse resultant based algorithms for polynomial system solving.<|reference_end|> | arxiv | @article{rojas1997toric,
title={Toric Generalized Characteristic Polynomials},
author={J. Maurice Rojas},
journal={arXiv preprint arXiv:math/9702222},
year={1997},
number={MSRI 1997-017},
archivePrefix={arXiv},
eprint={math/9702222},
primaryClass={math.AG cs.DS}
} | rojas1997toric |
arxiv-676940 | math/9704218 | A simple polynomial time algorithm to approximate the permanent within a simply exponential factor | <|reference_start|>A simple polynomial time algorithm to approximate the permanent within a simply exponential factor: We present a simple randomized polynomial time algorithm to approximate the mixed discriminant of $n$ positive semidefinite $n \times n$ matrices within a factor $2^{O(n)}$. Consequently, the algorithm allows us to approximate in randomized polynomial time the permanent of a given $n \times n$ non-negative matrix within a factor $2^{O(n)}$. When applied to approximating the permanent, the algorithm turns out to be a simple modification of the well-known Godsil-Gutman estimator.<|reference_end|> | arxiv | @article{barvinok1997a,
title={A simple polynomial time algorithm to approximate the permanent within a
simply exponential factor},
author={Alexander Barvinok},
journal={arXiv preprint arXiv:math/9704218},
year={1997},
number={MSRI 1997-031, formerly math.LA/9704218},
archivePrefix={arXiv},
eprint={math/9704218},
primaryClass={math.RA cs.DS}
} | barvinok1997a |
arxiv-676941 | math/9705225 | Choiceless polynomial time | <|reference_start|>Choiceless polynomial time: Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured the negative answer. The problem motivated a quest for stronger and stronger PTime logics. All these logics avoid arbitrary choice. Here we attempt to capture the choiceless fragment of PTime. Our computation model is a version of abstract state machines (formerly called evolving algebras). The idea is to replace arbitrary choice with parallel execution. The resulting logic is more expressive than other PTime logics in the literature. A more difficult theorem shows that the logic does not capture all PTime.<|reference_end|> | arxiv | @article{blass1997choiceless,
title={Choiceless polynomial time},
author={Andreas Blass, Yuri Gurevich, Saharon Shelah},
journal={arXiv preprint arXiv:math/9705225},
year={1997},
number={Shelah [BGSh:533]},
archivePrefix={arXiv},
eprint={math/9705225},
primaryClass={math.LO cs.LO}
} | blass1997choiceless |
arxiv-676942 | math/9801152 | On the classifiability of cellular automata | <|reference_start|>On the classifiability of cellular automata: Based on computer simulations Wolfram presented in several papers conjectured classifications of cellular automata into 4 types. He distinguishes the 4 classes of cellular automata by the evolution of the pattern generated by applying a cellular automaton to a finite input. Wolfram's qualitative classification is based on the examination of a large number of simulations. In addition to this classification based on the rate of growth, he conjectured a similar classification according to the eventual pattern. We consider here one formalization of his rate of growth suggestion. After completing our major results (based only on Wolfram's work), we investigated other contributions to the area and we report the relation of some of them to our discoveries.<|reference_end|> | arxiv | @article{baldwin1998on,
title={On the classifiability of cellular automata},
author={John T. Baldwin, Saharon Shelah},
journal={arXiv preprint arXiv:math/9801152},
year={1998},
number={Shelah [BlSh:623]},
archivePrefix={arXiv},
eprint={math/9801152},
primaryClass={math.LO cs.NE}
} | baldwin1998on |
arxiv-676943 | math/9807179 | Polynomial time logic: Inability to express | <|reference_start|>Polynomial time logic: Inability to express: Here we deal with the logic of [GuSh 533], which tries to capture polynomial time (for finite models). There it is proved that the logic cannot say much on models with equality only. Here we prove that it cannot say much on models for which we expect it cannot say much, like random enough graphs. This is the result of having a general criterion.<|reference_end|> | arxiv | @article{shelah1998polynomial,
title={Polynomial time logic: Inability to express},
author={Saharon Shelah},
journal={arXiv preprint arXiv:math/9807179},
year={1998},
number={Shelah [Sh:634]},
archivePrefix={arXiv},
eprint={math/9807179},
primaryClass={math.LO cs.LO}
} | shelah1998polynomial |
arxiv-676944 | math/9809009 | Uncomputably Large Integral Points on Algebraic Plane Curves? | <|reference_start|>Uncomputably Large Integral Points on Algebraic Plane Curves?: We show that the decidability of an amplification of Hilbert's Tenth Problem in three variables implies the existence of uncomputably large integral points on certain algebraic curves. We obtain this as a corollary of a new positive complexity result: the Diophantine prefixes EAE and EEAE are generically decidable. This means, taking the former prefix as an example, that we give a precise geometric classification of those polynomials f in Z[v,x,y] for which the question... ``Does there exists a v in N such that for all x in N, there exists a y in N with f(v,x,y)=0?'' ...may be undecidable, and we show that this set of polynomials is quite small in a rigourous sense. (The decidability of EAE was previously an open question.) The analogous result for the prefix EEAE is even stronger. We thus obtain a connection between the decidability of certain Diophantine problems, height bounds for points on curves, and the geometry of certain complex surfaces and 3-folds.<|reference_end|> | arxiv | @article{rojas1998uncomputably,
title={Uncomputably Large Integral Points on Algebraic Plane Curves?},
author={J. Maurice Rojas},
journal={arXiv preprint arXiv:math/9809009},
year={1998},
archivePrefix={arXiv},
eprint={math/9809009},
primaryClass={math.NT cs.CC cs.SC math.AG math.LO}
} | rojas1998uncomputably |
arxiv-676945 | math/9809071 | Solving Degenerate Sparse Polynomial Systems Faster | <|reference_start|>Solving Degenerate Sparse Polynomial Systems Faster: Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in every irreducible component of the zero set Z of F. Our techniques allow us to sharpen and lower prior complexity bounds for this problem by fully taking into account the monomial term structure. As a corollary of our development we also obtain new explicit formulae for the exact number of isolated roots of F and the intersection multiplicity of the positive-dimensional part of Z. Finally, we present a combinatorial construction of non-degenerate polynomial systems, with specified monomial term structure and maximally many isolated roots, which may be of independent interest.<|reference_end|> | arxiv | @article{rojas1998solving,
title={Solving Degenerate Sparse Polynomial Systems Faster},
author={J. Maurice Rojas},
journal={arXiv preprint arXiv:math/9809071},
year={1998},
archivePrefix={arXiv},
eprint={math/9809071},
primaryClass={math.AG cs.CC cs.NA math.NA}
} | rojas1998solving |
arxiv-676946 | math/9809201 | On quantification with a finite universe | <|reference_start|>On quantification with a finite universe: We consider a finite universe U (more exactly - a family U of them) and second order quantifiers Q_K, where for each U this means quantifying over a family of n(K)-place relations closed under permuting U. We define some natural orders and shed some light on the classification problem of those quantifiers.<|reference_end|> | arxiv | @article{shelah1998on,
title={On quantification with a finite universe},
author={Saharon Shelah},
journal={arXiv preprint arXiv:math/9809201},
year={1998},
number={Shelah [Sh:639]},
archivePrefix={arXiv},
eprint={math/9809201},
primaryClass={math.LO cs.CC cs.LO}
} | shelah1998on |
arxiv-676947 | math/9810022 | Active Libraries: Rethinking the roles of compilers and libraries | <|reference_start|>Active Libraries: Rethinking the roles of compilers and libraries: We describe Active Libraries, which take an active role in compilation. Unlike traditional libraries which are passive collections of functions and objects, Active Libraries may generate components, specialize algorithms, optimize code, configure and tune themselves for a target machine, and describe themselves to tools (such as profilers and debuggers) in an intelligible way. Several such libraries are described, as are implementation technologies.<|reference_end|> | arxiv | @article{veldhuizen1998active,
title={Active Libraries: Rethinking the roles of compilers and libraries},
author={Todd L. Veldhuizen and Dennis Gannon},
journal={arXiv preprint arXiv:math/9810022},
year={1998},
number={formerly math.SC/9810022},
archivePrefix={arXiv},
eprint={math/9810022},
primaryClass={math.NA cs.PL}
} | veldhuizen1998active |
arxiv-676948 | math/9901074 | Differential interactive games: The short-term predictions | <|reference_start|>Differential interactive games: The short-term predictions: Procedures of the short-term predictions for processes in general 2-person differential interactive games are proposed. Their effectiveness is discussed.<|reference_end|> | arxiv | @article{juriev1999differential,
title={Differential interactive games: The short-term predictions},
author={Denis V. Juriev},
journal={arXiv preprint arXiv:math/9901074},
year={1999},
archivePrefix={arXiv},
eprint={math/9901074},
primaryClass={math.HO cs.HC}
} | juriev1999differential |
arxiv-676949 | math/9902043 | The Average-Case Area of Heilbronn-Type Triangles | <|reference_start|>The Average-Case Area of Heilbronn-Type Triangles: From among $ {n \choose 3}$ triangles with vertices chosen from $n$ points in the unit square, let $T$ be the one with the smallest area, and let $A$ be the area of $T$. Heilbronn's triangle problem asks for the maximum value assumed by $A$ over all choices of $n$ points. We consider the average-case: If the $n$ points are chosen independently and at random (with a uniform distribution), then there exist positive constants $c$ and $C$ such that $c/n^3 < \mu_n < C/n^3$ for all large enough values of $n$, where $\mu_n$ is the expectation of $A$. Moreover, $c/n^3 < A < C/n^3$, with probability close to one. Our proof uses the incompressibility method based on Kolmogorov complexity; it actually determines the area of the smallest triangle for an arrangement in ``general position.''<|reference_end|> | arxiv | @article{jiang1999the,
title={The Average-Case Area of Heilbronn-Type Triangles},
author={Tao Jiang (UCR), Ming Li (UCSB), Paul Vitanyi (CWI and U Amsterdam)},
journal={T. Jiang, M. Li, and P. Vitanyi, The average-case area of
Heilbronn-type triangles, Random Structures and Algorithms, 20:2(2002),
206-219},
year={1999},
archivePrefix={arXiv},
eprint={math/9902043},
primaryClass={math.CO cs.CG cs.DM math.LO math.MG math.PR}
} | jiang1999the |
arxiv-676950 | math/9902151 | Homotopy invariants of higher dimensional categories and concurrency in computer science | <|reference_start|>Homotopy invariants of higher dimensional categories and concurrency in computer science: The strict globular $\omega$-categories formalize the execution paths of a parallel automaton and the homotopies between them. One associates to such (and any) $\omega$-category $\C$ three homology theories. The first one is called the globular homology. It contains the oriented loops of $\C$. The two other ones are called the negative (resp. positive) corner homology. They contain in a certain manner the branching areas of execution paths or negative corners (resp. the merging areas of execution paths or positive corners) of $\C$. Two natural linear maps called the negative (resp. the positive) Hurewicz morphism from the globular homology to the negative (resp. positive) corner homology are constructed. We explain the reason why these constructions allow to reinterprete some geometric problems coming from computer science.<|reference_end|> | arxiv | @article{gaucher1999homotopy,
title={Homotopy invariants of higher dimensional categories and concurrency in
computer science},
author={Philippe Gaucher},
journal={Mathematical Structure in Computer Science 10 (2000), no. 4,
p.481-524},
year={1999},
doi={10.1017/S0960129500003182},
archivePrefix={arXiv},
eprint={math/9902151},
primaryClass={math.CT cs.OH math.AT}
} | gaucher1999homotopy |
arxiv-676951 | math/9905046 | Duality between Multidimensional Convolutional Codes and Systems | <|reference_start|>Duality between Multidimensional Convolutional Codes and Systems: Multidimensional convolutional codes generalize (one dimensional) convolutional codes and they correspond under a natural duality to multidimensional systems widely studied in the systems literature.<|reference_end|> | arxiv | @article{gluesing-luerssen1999duality,
title={Duality between Multidimensional Convolutional Codes and Systems},
author={Heide Gluesing-Luerssen, Joachim Rosenthal and Paul Weiner},
journal={arXiv preprint arXiv:math/9905046},
year={1999},
archivePrefix={arXiv},
eprint={math/9905046},
primaryClass={math.OC cs.IT math.AC math.AG math.IT}
} | gluesing-luerssen1999duality |
arxiv-676952 | math/9905155 | An Implementation of the Bestvina-Handel Algorithm for Surface Homeomorphisms | <|reference_start|>An Implementation of the Bestvina-Handel Algorithm for Surface Homeomorphisms: Bestvina and Handel have found an effective algorithm that determines whether a given homeomorphism of an orientable, possibly punctured surface is pseudo-Anosov. We present a software package in Java that realizes this algorithm for surfaces with one puncture. Moreover, the package allows the user to define homeomorphisms in terms of Dehn twists, and in the pseudo-Anosov case it generates images of train tracks in the sense of Bestvina-Handel.<|reference_end|> | arxiv | @article{brinkmann1999an,
title={An Implementation of the Bestvina-Handel Algorithm for Surface
Homeomorphisms},
author={Peter Brinkmann},
journal={Experimental Mathematics 9:2, 2000, 235-240},
year={1999},
archivePrefix={arXiv},
eprint={math/9905155},
primaryClass={math.GR cs.MS math.GT}
} | brinkmann1999an |
arxiv-676953 | math/9905165 | Perception games, the image understanding and interpretational geometry | <|reference_start|>Perception games, the image understanding and interpretational geometry: The interactive game theoretical approach to the description of perception processes is proposed. The subject is treated formally in terms of a new class of the verbalizable interactive games which are called the perception games. An application of the previously elaborated formalism of dialogues and verbalizable interactive games to the visual perception allows to combine the linguistic (such as formal grammars), psycholinguistic and (interactive) game theoretical methods for analysis of the image understanding by a human that may be also useful for the elaboration of computer vision systems. By the way the interactive game theoretical aspects of interpretational geometries are clarified.<|reference_end|> | arxiv | @article{juriev1999perception,
title={Perception games, the image understanding and interpretational geometry},
author={Denis V. Juriev},
journal={arXiv preprint arXiv:math/9905165},
year={1999},
archivePrefix={arXiv},
eprint={math/9905165},
primaryClass={math.HO cs.CV}
} | juriev1999perception |
arxiv-676954 | math/9909163 | Coding Theory and Uniform Distributions | <|reference_start|>Coding Theory and Uniform Distributions: In the present paper we introduce and study finite point subsets of a special kind, called optimum distributions, in the n-dimensional unit cube. Such distributions are closely related with known (delta,s,n)-nets of low discrepancy. It turns out that optimum distributions have a rich combinatorial structure. Namely, we show that optimum distributions can be characterized completely as maximum distance separable codes with respect to a non-Hamming metric. Weight spectra of such codes can be evaluated precisely. We also consider linear codes and distributions and study their general properties including the duality with respect to a suitable inner product. The corresponding generalized MacWilliams identities for weight enumerators are briefly discussed. Broad classes of linear maximum distance separable codes and linear optimum distributions are explicitely constructed in the paper by the Hermite interpolations over finite fields.<|reference_end|> | arxiv | @article{skriganov1999coding,
title={Coding Theory and Uniform Distributions},
author={M. M. Skriganov},
journal={arXiv preprint arXiv:math/9909163},
year={1999},
archivePrefix={arXiv},
eprint={math/9909163},
primaryClass={math.CO cs.IT math.IT math.NT}
} | skriganov1999coding |
arxiv-676955 | math/9910062 | Efficient sphere-covering and converse measure concentration via generalized coding theorems | <|reference_start|>Efficient sphere-covering and converse measure concentration via generalized coding theorems: Suppose A is a finite set equipped with a probability measure P and let M be a ``mass'' function on A. We give a probabilistic characterization of the most efficient way in which A^n can be almost-covered using spheres of a fixed radius. An almost-covering is a subset C_n of A^n, such that the union of the spheres centered at the points of C_n has probability close to one with respect to the product measure P^n. An efficient covering is one with small mass M^n(C_n); n is typically large. With different choices for M and the geometry on A our results give various corollaries as special cases, including Shannon's data compression theorem, a version of Stein's lemma (in hypothesis testing), and a new converse to some measure concentration inequalities on discrete spaces. Under mild conditions, we generalize our results to abstract spaces and non-product measures.<|reference_end|> | arxiv | @article{kontoyiannis1999efficient,
title={Efficient sphere-covering and converse measure concentration via
generalized coding theorems},
author={Ioannis Kontoyiannis},
journal={arXiv preprint arXiv:math/9910062},
year={1999},
archivePrefix={arXiv},
eprint={math/9910062},
primaryClass={math.PR cs.IT math.FA math.IT}
} | kontoyiannis1999efficient |
arxiv-676956 | math/9910149 | Rational points, genus and asymptotic behaviour in reduced algebraic curves over finite fields | <|reference_start|>Rational points, genus and asymptotic behaviour in reduced algebraic curves over finite fields: The number A(q) shows the asymptotic behaviour of the quotient of the number of rational points over the genus of non-singular absolutely irreducible curves over a finite field Fq. Research on bounds for A(q) is closely connected with the so-called asymptotic main problem in Coding Theory. In this paper, we study some generalizations of this number for non-irreducible curves, their connection with A(q) and its application in Coding Theory.<|reference_end|> | arxiv | @article{farran1999rational,
title={Rational points, genus and asymptotic behaviour in reduced algebraic
curves over finite fields},
author={J. I. Farran},
journal={arXiv preprint arXiv:math/9910149},
year={1999},
number={AGT-34},
archivePrefix={arXiv},
eprint={math/9910149},
primaryClass={math.AG cs.IT math.IT math.NT}
} | farran1999rational |
arxiv-676957 | math/9910151 | Decoding Algebraic Geometry codes by a key equation | <|reference_start|>Decoding Algebraic Geometry codes by a key equation: A new effective decoding algorithm is presented for arbitrary algebraic-geometric codes on the basis of solving a generalized key equation with the majority coset scheme of Duursma. It is an improvement of Ehrhard's algorithm, since the method corrects up to the half of the Goppa distance with complexity order O(n**2.81), and with no further assumption on the degree of the divisor G.<|reference_end|> | arxiv | @article{farran1999decoding,
title={Decoding Algebraic Geometry codes by a key equation},
author={J. I. Farran},
journal={arXiv preprint arXiv:math/9910151},
year={1999},
number={AGT-63},
archivePrefix={arXiv},
eprint={math/9910151},
primaryClass={math.AG cs.IT math.IT math.NA}
} | farran1999decoding |
arxiv-676958 | math/9910155 | Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models | <|reference_start|>Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models: We present an algorithm to compute the Weierstrass semigroup at a point P together with functions for each value in the semigroup, provided P is the only branch at infinity of a singular plane model for the curve. As a byproduct, the method also provides us with a basis for the spaces L(mP) and the computation of the Feng-Rao distance for the corresponding array of geometric Goppa codes. A general computation of the Feng-Rao distance is also obtained. Everything can be applied to the decoding problem by using the majority scheme of Feng and Rao.<|reference_end|> | arxiv | @article{campillo1999computing,
title={Computing Weierstrass semigroups and the Feng-Rao distance from singular
plane models},
author={A. Campillo and J. I. Farran},
journal={arXiv preprint arXiv:math/9910155},
year={1999},
number={AGT-58},
archivePrefix={arXiv},
eprint={math/9910155},
primaryClass={math.AG cs.IT math.IT math.NA}
} | campillo1999computing |
arxiv-676959 | math/9910175 | Polynomial method in coding and information theory | <|reference_start|>Polynomial method in coding and information theory: Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the applicability of the method was extended to cover a wider range of problems in coding and information theory. In this paper we present a general framework for the method which includes previous results as particular cases. We explain how this generalization leads to new asymptotic bounds on the performance of codes in binary-input memoryless channels and the Gaussian channel, which improve the results of Shannon et al. of 1959-67, and to a number of other results in combinatorial coding theory.<|reference_end|> | arxiv | @article{ashikhmin1999polynomial,
title={Polynomial method in coding and information theory},
author={A. Ashikhmin, A. Barg, S. Litsyn},
journal={arXiv preprint arXiv:math/9910175},
year={1999},
archivePrefix={arXiv},
eprint={math/9910175},
primaryClass={math.CO cs.IT math.IT}
} | ashikhmin1999polynomial |
arxiv-676960 | math/9910185 | Geometric Thickness of Complete Graphs | <|reference_start|>Geometric Thickness of Complete Graphs: We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straight-line edges and assign each edge to a layer so that no two edges on the same layer cross. The geometric thickness lies between two previously studied quantities, the (graph-theoretical) thickness and the book thickness. We investigate the geometric thickness of the family of complete graphs, K_n. We show that the geometric thickness of K_n lies between ceiling((n/5.646) + 0.342) and ceiling(n/4), and we give exact values of the geometric thickness of K_n for n <= 12 and n in {15,16}. We also consider the geometric thickness of the family of complete bipartite graphs. In particular, we show that, unlike the case of complete graphs, there are complete bipartite graphs with arbitrarily large numbers of vertices for which the geometric thickness coincides with the standard graph-theoretical thickness.<|reference_end|> | arxiv | @article{dillencourt1999geometric,
title={Geometric Thickness of Complete Graphs},
author={Michael B. Dillencourt and David Eppstein and Daniel S. Hirschberg},
journal={J. Graph Algorithms & Applications 4(3):5-17, 2000},
year={1999},
archivePrefix={arXiv},
eprint={math/9910185},
primaryClass={math.CO cs.DM}
} | dillencourt1999geometric |
arxiv-676961 | math/9911025 | On the parameters of Algebraic Geometry codes related to Arf semigroups | <|reference_start|>On the parameters of Algebraic Geometry codes related to Arf semigroups: In this paper we compute the order (or Feng-Rao) bound on the minimum distance of one-point algebraic geometry codes, when the Weierstrass semigroup at the point Q is an Arf semigroup. The results developed to that purpose also provide the dimension of the improved geometric Goppa codes related to those.<|reference_end|> | arxiv | @article{campillo1999on,
title={On the parameters of Algebraic Geometry codes related to Arf semigroups},
author={A. Campillo, J. I. Farran and C. Munuera},
journal={arXiv preprint arXiv:math/9911025},
year={1999},
number={AGT-83},
archivePrefix={arXiv},
eprint={math/9911025},
primaryClass={math.NT cs.IT math.AG math.IT}
} | campillo1999on |
arxiv-676962 | math/9912059 | Combinatorics of branchings in higher dimensional automata | <|reference_start|>Combinatorics of branchings in higher dimensional automata: We explore the combinatorial properties of the branching areas of execution paths in higher dimensional automata. Mathematically, this means that we investigate the combinatorics of the negative corner (or branching) homology of a globular $\omega$-category and the combinatorics of a new homology theory called the reduced branching homology. The latter is the homology of the quotient of the branching complex by the sub-complex generated by its thin elements. Conjecturally it coincides with the non reduced theory for higher dimensional automata, that is $\omega$-categories freely generated by precubical sets. As application, we calculate the branching homology of some $\omega$-categories and we give some invariance results for the reduced branching homology. We only treat the branching side. The merging side, that is the case of merging areas of execution paths is similar and can be easily deduced from the branching side.<|reference_end|> | arxiv | @article{gaucher1999combinatorics,
title={Combinatorics of branchings in higher dimensional automata},
author={Philippe Gaucher},
journal={Theory and Applications of Categories, Vol. 8, 2001, No. 12, pp
324-376},
year={1999},
archivePrefix={arXiv},
eprint={math/9912059},
primaryClass={math.CT cs.OH math.AT}
} | gaucher1999combinatorics |
arxiv-676963 | nlin/0001057 | Numerical Replication of Computer Simulations: Some Pitfalls and How To Avoid Them | <|reference_start|>Numerical Replication of Computer Simulations: Some Pitfalls and How To Avoid Them: A computer simulation, such as a genetic algorithm, that uses IEEE standard floating-point arithmetic may not produce exactly the same results in two different runs, even if it is rerun on the same computer with the same input and random number seeds. Researchers should not simply assume that the results from one run replicate those from another but should verify this by actually comparing the data. However, researchers who are aware of this pitfall can reliably replicate simulations, in practice. This paper discusses the problem and suggests solutions.<|reference_end|> | arxiv | @article{belding2000numerical,
title={Numerical Replication of Computer Simulations: Some Pitfalls and How To
Avoid Them},
author={Theodore C. Belding},
journal={arXiv preprint arXiv:nlin/0001057},
year={2000},
archivePrefix={arXiv},
eprint={nlin/0001057},
primaryClass={nlin.AO cs.NE}
} | belding2000numerical |
arxiv-676964 | nlin/0002040 | The dynamics of iterated transportation simulations | <|reference_start|>The dynamics of iterated transportation simulations: Iterating between a router and a traffic micro-simulation is an increasibly accepted method for doing traffic assignment. This paper, after pointing out that the analytical theory of simulation-based assignment to-date is insufficient for some practical cases, presents results of simulation studies from a real world study. Specifically, we look into the issues of uniqueness, variability, and robustness and validation. Regarding uniqueness, despite some cautionary notes from a theoretical point of view, we find no indication of ``meta-stable'' states for the iterations. Variability however is considerable. By variability we mean the variation of the simulation of a given plan set by just changing the random seed. We show then results from three different micro-simulations under the same iteration scenario in order to test for the robustness of the results under different implementations. We find the results encouraging, also when comparing to reality and with a traditional assignment result. Keywords: dynamic traffic assignment (DTA); traffic micro-simulation; TRANSIMS; large-scale simulations; urban planning<|reference_end|> | arxiv | @article{nagel2000the,
title={The dynamics of iterated transportation simulations},
author={Kai Nagel, Marcus Rickert, Patrice M. Simon, Martin Pieck},
journal={arXiv preprint arXiv:nlin/0002040},
year={2000},
archivePrefix={arXiv},
eprint={nlin/0002040},
primaryClass={nlin.AO cs.CE}
} | nagel2000the |
arxiv-676965 | nlin/0004007 | A Century of Controvery Over the Foundations of Mathematics II | <|reference_start|>A Century of Controvery Over the Foundations of Mathematics II: Transcript of G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The notion of randomness is taken from physics and applied to pure mathematics in order to shed light on the incompleteness phenomenon discovered by K. Godel.<|reference_end|> | arxiv | @article{chaitin2000a,
title={A Century of Controvery Over the Foundations of Mathematics II},
author={G.J. Chaitin (IBM Research)},
journal={arXiv preprint arXiv:nlin/0004007},
year={2000},
archivePrefix={arXiv},
eprint={nlin/0004007},
primaryClass={nlin.CD cs.CC math.HO}
} | chaitin2000a |
arxiv-676966 | nlin/0006025 | Information Bottlenecks, Causal States, and Statistical Relevance Bases: How to Represent Relevant Information in Memoryless Transduction | <|reference_start|>Information Bottlenecks, Causal States, and Statistical Relevance Bases: How to Represent Relevant Information in Memoryless Transduction: Discovering relevant, but possibly hidden, variables is a key step in constructing useful and predictive theories about the natural world. This brief note explains the connections between three approaches to this problem: the recently introduced information-bottleneck method, the computational mechanics approach to inferring optimal models, and Salmon's statistical relevance basis.<|reference_end|> | arxiv | @article{shalizi2000information,
title={Information Bottlenecks, Causal States, and Statistical Relevance Bases:
How to Represent Relevant Information in Memoryless Transduction},
author={Cosma Rohilla Shalizi and James P. Crutchfield (Santa Fe Institute)},
journal={Advances in Complex Systems, vol. 5, pp. 91--95 (2002)},
year={2000},
doi={10.1142/S0219525902000481},
archivePrefix={arXiv},
eprint={nlin/0006025},
primaryClass={nlin.AO cond-mat.dis-nn cs.LG physics.data-an}
} | shalizi2000information |
arxiv-676967 | nlin/0102026 | Parity Problem With A Cellular Automaton Solution | <|reference_start|>Parity Problem With A Cellular Automaton Solution: The parity of a bit string of length $N$ is a global quantity that can be efficiently compute using a global counter in ${O} (N)$ time. But is it possible to find the parity using cellular automata with a set of local rule tables without using any global counter? Here, we report a way to solve this problem using a number of $r=1$ binary, uniform, parallel and deterministic cellular automata applied in succession for a total of ${O} (N^2)$ time.<|reference_end|> | arxiv | @article{lee2001parity,
title={Parity Problem With A Cellular Automaton Solution},
author={K. M. Lee, Hao Xu and H. F. Chau},
journal={arXiv preprint arXiv:nlin/0102026},
year={2001},
doi={10.1103/PhysRevE.64.026702},
archivePrefix={arXiv},
eprint={nlin/0102026},
primaryClass={nlin.CG cond-mat.stat-mech cs.CC nlin.AO}
} | lee2001parity |
arxiv-676968 | nlin/0103057 | Finding The Sign Of A Function Value By Binary Cellular Automaton | <|reference_start|>Finding The Sign Of A Function Value By Binary Cellular Automaton: Given a continuous function $f(x)$, suppose that the sign of $f$ only has finitely many discontinuous points in the interval $[0,1]$. We show how to use a sequence of one dimensional deterministic binary cellular automata to determine the sign of $f(\rho)$ where $\rho$ is the (number) density of 1s in an arbitrarily given bit string of finite length provided that $f$ satisfies certain technical conditions.<|reference_end|> | arxiv | @article{chau2001finding,
title={Finding The Sign Of A Function Value By Binary Cellular Automaton},
author={H. F. Chau, H. Xu, K. M. Lee, L. W. Siu and K. K. Yan},
journal={arXiv preprint arXiv:nlin/0103057},
year={2001},
doi={10.1142/S0129183102003929},
archivePrefix={arXiv},
eprint={nlin/0103057},
primaryClass={nlin.CG cond-mat cs.CC}
} | chau2001finding |
arxiv-676969 | nlin/0109001 | Complex Philosophy | <|reference_start|>Complex Philosophy: We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing regularities in nature. We define absolute being (observer independent, infinite) and relative being (observer dependent, finite), and notice the differences between them. We draw issues on relative causality and absolute causality among abstraction levels. We also make reflections on determinism. We reject the search for any absolute truth (because of their infinity), and promote the idea that all comprehensible truths are relative, since they were created in finite contexts. This leads us to suggest to search the less-incompleteness of ideas and contexts instead of their truths.<|reference_end|> | arxiv | @article{gershenson2001complex,
title={Complex Philosophy},
author={Carlos Gershenson},
journal={arXiv preprint arXiv:nlin/0109001},
year={2001},
archivePrefix={arXiv},
eprint={nlin/0109001},
primaryClass={nlin.AO cs.CC}
} | gershenson2001complex |
arxiv-676970 | nlin/0109019 | Olfactory search at high Reynolds number | <|reference_start|>Olfactory search at high Reynolds number: Locating the source of odor in a turbulent environment - a common behavior for living organisms - is non-trivial because of the random nature of mixing. Here we analyze the statistical physics aspects of the problem and propose an efficient strategy for olfactory search which can work in turbulent plumes. The algorithm combines the maximum likelihood inference of the source position with an active search. Our approach provides the theoretical basis for the design of olfactory robots and the quantitative tools for the analysis of the observed olfactory search behavior of living creatures (e.g. odor modulated optomotor anemotaxis of moth)<|reference_end|> | arxiv | @article{balkovsky2001olfactory,
title={Olfactory search at high Reynolds number},
author={Eugene Balkovsky, Boris I. Shraiman},
journal={arXiv preprint arXiv:nlin/0109019},
year={2001},
doi={10.1073/pnas.192393499},
archivePrefix={arXiv},
eprint={nlin/0109019},
primaryClass={nlin.CD cs.RO nlin.AO physics.bio-ph}
} | balkovsky2001olfactory |
arxiv-676971 | nlin/0202038 | On model selection and the disability of neural networks to decompose tasks | <|reference_start|>On model selection and the disability of neural networks to decompose tasks: A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry point of view, that allows to calculate these correlations. In practise, this describes how one response is unlearned while another is trained. Concerning conventional feed-forward neural networks we find that they generically introduce strong correlations, are predisposed to forgetting, and inappropriate for task decomposition. Perspectives to solve these problems are discussed.<|reference_end|> | arxiv | @article{toussaint2002on,
title={On model selection and the disability of neural networks to decompose
tasks},
author={Marc Toussaint},
journal={Proceedings of the International Joint Conference on Neural
Networks (IJCNN 2002), 245-250.},
year={2002},
archivePrefix={arXiv},
eprint={nlin/0202038},
primaryClass={nlin.AO cond-mat.dis-nn cs.NE}
} | toussaint2002on |
arxiv-676972 | nlin/0202039 | A neural model for multi-expert architectures | <|reference_start|>A neural model for multi-expert architectures: We present a generalization of conventional artificial neural networks that allows for a functional equivalence to multi-expert systems. The new model provides an architectural freedom going beyond existing multi-expert models and an integrative formalism to compare and combine various techniques of learning. (We consider gradient, EM, reinforcement, and unsupervised learning.) Its uniform representation aims at a simple genetic encoding and evolutionary structure optimization of multi-expert systems. This paper contains a detailed description of the model and learning rules, empirically validates its functionality, and discusses future perspectives.<|reference_end|> | arxiv | @article{toussaint2002a,
title={A neural model for multi-expert architectures},
author={Marc Toussaint},
journal={Proceedings of the International Joint Conference on Neural
Networks (IJCNN 2002), 2755-2760.},
year={2002},
archivePrefix={arXiv},
eprint={nlin/0202039},
primaryClass={nlin.AO cond-mat.dis-nn cs.NE}
} | toussaint2002a |
arxiv-676973 | nlin/0204038 | Neutrality: A Necessity for Self-Adaptation | <|reference_start|>Neutrality: A Necessity for Self-Adaptation: Self-adaptation is used in all main paradigms of evolutionary computation to increase efficiency. We claim that the basis of self-adaptation is the use of neutrality. In the absence of external control neutrality allows a variation of the search distribution without the risk of fitness loss.<|reference_end|> | arxiv | @article{toussaint2002neutrality:,
title={Neutrality: A Necessity for Self-Adaptation},
author={Marc Toussaint and Christian Igel},
journal={Proceedings of the Congress on Evolutionary Computation (CEC
2002), 1354-1359.},
year={2002},
archivePrefix={arXiv},
eprint={nlin/0204038},
primaryClass={nlin.AO cs.NE q-bio}
} | toussaint2002neutrality: |
arxiv-676974 | nlin/0207032 | Modulo Three Problem With A Cellular Automaton Solution | <|reference_start|>Modulo Three Problem With A Cellular Automaton Solution: An important global property of a bit string is the number of ones in it. It has been found that the parity (odd or even) of this number can be found by a sequence of deterministic, translational invariant cellular automata with parallel update in succession for a total of O(N^2) time. In this paper, we discover a way to check if this number is divisible by three using the same kind of cellular automata in O(N^3) time. We also speculate that the method described here could be generalized to check if it is divisible by four and other positive integers.<|reference_end|> | arxiv | @article{xu2002modulo,
title={Modulo Three Problem With A Cellular Automaton Solution},
author={Hao Xu, K. M. Lee and H. F. Chau},
journal={arXiv preprint arXiv:nlin/0207032},
year={2002},
doi={10.1142/S0129183103004450},
archivePrefix={arXiv},
eprint={nlin/0207032},
primaryClass={nlin.CG cs.CC}
} | xu2002modulo |
arxiv-676975 | nlin/0210041 | Simple Model for the Dynamics of Correlations in the Evolution of Economic Entities Under Varying Economic Conditions | <|reference_start|>Simple Model for the Dynamics of Correlations in the Evolution of Economic Entities Under Varying Economic Conditions: From some observations on economic behaviors, in particular changing economic conditions with time and space, we develop a very simple model for the evolution of economic entities within a geographical type of framework. We raise a few questions and attempt to investigate whether some of them can be tackled by our model. Several cases of interest are reported. It is found that the model even in its simple forms can lead to a large variety of situations, including: delocalization and cycles, but also pre-chaotic behavior.<|reference_end|> | arxiv | @article{ausloos2002simple,
title={Simple Model for the Dynamics of Correlations in the Evolution of
Economic Entities Under Varying Economic Conditions},
author={Marcel Ausloos (Univ. de Liege), Paulette Clippe (Univ. de Liege) and
Andrzej Pekalski (University of Wroclaw)},
journal={Physica A 324 (2003) 330-337},
year={2002},
doi={10.1016/S0378-4371(02)01844-7},
archivePrefix={arXiv},
eprint={nlin/0210041},
primaryClass={nlin.AO cond-mat.stat-mech cs.CE physics.soc-ph}
} | ausloos2002simple |
arxiv-676976 | nlin/0211010 | Evolution and anti-evolution in a minimal stock market model | <|reference_start|>Evolution and anti-evolution in a minimal stock market model: We present a novel microscopic stock market model consisting of a large number of random agents modeling traders in a market. Each agent is characterized by a set of parameters that serve to make iterated predictions of two successive returns. The future price is determined according to the offer and the demand of all agents. The system evolves by redistributing the capital among the agents in each trading cycle. Without noise the dynamics of this system is nearly regular and thereby fails to reproduce the stochastic return fluctuations observed in real markets. However, when in each cycle a small amount of noise is introduced we find the typical features of real financial time series like fat-tails of the return distribution and large temporal correlations in the volatility without significant correlations in the price returns. Introducing the noise by an evolutionary process leads to different scalings of the return distributions that depend on the definition of fitness. Because our realistic model has only very few parameters, and the results appear to be robust with respect to the noise level and the number of agents we expect that our framework may serve as new paradigm for modeling self generated return fluctuations in markets.<|reference_end|> | arxiv | @article{rothenstein2002evolution,
title={Evolution and anti-evolution in a minimal stock market model},
author={R. Rothenstein and K. Pawelzik},
journal={Physica A 326, 534-543(2003)},
year={2002},
doi={10.1016/S0378-4371(03)00396-0},
archivePrefix={arXiv},
eprint={nlin/0211010},
primaryClass={nlin.AO cond-mat.stat-mech cs.MA q-fin.TR}
} | rothenstein2002evolution |
arxiv-676977 | nlin/0211013 | A Spin Glass Model of Human Logic Systems | <|reference_start|>A Spin Glass Model of Human Logic Systems: In this paper, we discuss different models for human logic systems and describe a game with nature. G\"odel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking. These classical logic networks are then coupled using rules that depend on whether two networks contain axioms or anti-axioms. The social lattice of axiom based logic networks is then placed with the environment network in a game including entropy as a cost factor. The classical logical networks are then replaced with ``preference axioms'' to the role of fuzzy logic.<|reference_end|> | arxiv | @article{shafee2002a,
title={A Spin Glass Model of Human Logic Systems},
author={Fariel Shafee},
journal={arXiv preprint arXiv:nlin/0211013},
year={2002},
archivePrefix={arXiv},
eprint={nlin/0211013},
primaryClass={nlin.AO cond-mat.dis-nn cs.MA}
} | shafee2002a |
arxiv-676978 | nlin/0211024 | Exploring the cooperative regimes in a model of agents without memory or "tags": indirect reciprocity vs selfish incentives | <|reference_start|>Exploring the cooperative regimes in a model of agents without memory or "tags": indirect reciprocity vs selfish incentives: The self-organization in cooperative regimes in a simple mean-field version of a model based on "selfish" agents which play the Prisoner's Dilemma (PD) game is studied. The agents have no memory and use strategies not based on direct reciprocity nor 'tags'. Two variables are assigned to each agent $i$ at time $t$, measuring its capital $C(i;t)$ and its probability of cooperation $p(i;t)$. At each time step $t$ a pair of agents interact by playing the PD game. These 2 agents update their probability of cooperation $p(i)$ as follows: they compare the profits they made in this interaction $\delta C(i;t)$ with an estimator $\epsilon(i;t)$ and, if $\delta C(i;t) \ge \epsilon(i;t)$, agent $i$ increases its $p(i;t)$ while if $\delta C(i;t) < \epsilon(i;t)$ the agent decreases $p(i;t)$. The 4!=24 different cases produced by permuting the four Prisoner's Dilemma canonical payoffs 3, 0, 1, and 5 - corresponding,respectively, to $R$ (reward), $S$ (sucker's payoff), $T$ (temptation to defect) and $P$ (punishment) - are analyzed. It turns out that for all these 24 possibilities, after a transient,the system self-organizes into a stationary state with average equilibrium probability of cooperation $\bar{p}_\infty$ = constant $ > 0$.Depending on the payoff matrix, there are different equilibrium states characterized by their average probability of cooperation and average equilibrium per-capita-income ($\bar{p}_\infty,\bar{\delta C}_\infty$).<|reference_end|> | arxiv | @article{fort2002exploring,
title={Exploring the cooperative regimes in a model of agents without memory or
"tags": indirect reciprocity vs. selfish incentives},
author={H. Fort},
journal={Physica A326 (2003) 286-298},
year={2002},
doi={10.1016/S0378-4371(03)00263-2},
archivePrefix={arXiv},
eprint={nlin/0211024},
primaryClass={nlin.AO cond-mat cs.CE hep-lat nlin.CG physics.soc-ph}
} | fort2002exploring |
arxiv-676979 | nlin/0212001 | A Generalization of Chaitin's Halting Probability \Omega and Halting Self-Similar Sets | <|reference_start|>A Generalization of Chaitin's Halting Probability \Omega and Halting Self-Similar Sets: We generalize the concept of randomness in an infinite binary sequence in order to characterize the degree of randomness by a real number D>0. Chaitin's halting probability \Omega is generalized to \Omega^D whose degree of randomness is precisely D. On the basis of this generalization, we consider the degree of randomness of each point in Euclidean space through its base-two expansion. It is then shown that the maximum value of such a degree of randomness provides the Hausdorff dimension of a self-similar set that is computable in a certain sense. The class of such self-similar sets includes familiar fractal sets such as the Cantor set, von Koch curve, and Sierpinski gasket. Knowledge of the property of \Omega^D allows us to show that the self-similar subset of [0,1] defined by the halting set of a universal algorithm has a Hausdorff dimension of one.<|reference_end|> | arxiv | @article{tadaki2002a,
title={A Generalization of Chaitin's Halting Probability \Omega and Halting
Self-Similar Sets},
author={Kohtaro Tadaki},
journal={Hokkaido Mathematical Journal, Vol. 31, No. 1, February 2002,
219-253},
year={2002},
doi={10.14492/hokmj/1350911778},
archivePrefix={arXiv},
eprint={nlin/0212001},
primaryClass={nlin.CD cs.CC}
} | tadaki2002a |
arxiv-676980 | nlin/0212030 | The structure of evolutionary exploration: On crossover, buildings blocks and Estimation-Of-Distribution Algorithms | <|reference_start|>The structure of evolutionary exploration: On crossover, buildings blocks and Estimation-Of-Distribution Algorithms: The notion of building blocks can be related to the structure of the offspring probability distribution: loci of which variability is strongly correlated constitute a building block. We call this correlated exploration. With this background we analyze the structure of the offspring probability distribution, or exploration distribution, for a GA with mutation only, a crossover GA, and an Estimation-Of-Distribution Algorithm (EDA). The results allow a precise characterization of the structure of the crossover exploration distribution. Essentially, the crossover operator destroys mutual information between loci by transforming it into entropy; it does the inverse of correlated exploration. In contrast, the objective of EDAs is to model the mutual information between loci in the fitness distribution and thereby they induce correlated exploration.<|reference_end|> | arxiv | @article{toussaint2002the,
title={The structure of evolutionary exploration: On crossover, buildings
blocks and Estimation-Of-Distribution Algorithms},
author={Marc Toussaint},
journal={arXiv preprint arXiv:nlin/0212030},
year={2002},
archivePrefix={arXiv},
eprint={nlin/0212030},
primaryClass={nlin.AO cs.NE q-bio}
} | toussaint2002the |
arxiv-676981 | nlin/0303016 | Algorithmic Chaos | <|reference_start|>Algorithmic Chaos: Many physical theories like chaos theory are fundamentally concerned with the conceptual tension between determinism and randomness. Kolmogorov complexity can express randomness in determinism and gives an approach to formulate chaotic behavior.<|reference_end|> | arxiv | @article{vitanyi2003algorithmic,
title={Algorithmic Chaos},
author={Paul Vitanyi (CWI and University of Amsterdam)},
journal={arXiv preprint arXiv:nlin/0303016},
year={2003},
archivePrefix={arXiv},
eprint={nlin/0303016},
primaryClass={nlin.CD cs.CC math.DS}
} | vitanyi2003algorithmic |
arxiv-676982 | nlin/0303020 | When Can we Call a System Self-organizing? | <|reference_start|>When Can we Call a System Self-organizing?: We do not attempt to provide yet another definition of selforganization, but explore the conditions under which we can model a system as self-organizing. These involve the dynamics of entropy, and the purpose, aspects, and description level chosen by an observer. We show how, changing the level or "graining" of description, the same system can appear selforganizing or self-disorganizing. We discuss ontological issues we face when studying self-organizing systems, and analyse when designing and controlling artificial self-organizing systems is useful. We conclude that self-organization is a way of observing systems, not an absolute class of systems.<|reference_end|> | arxiv | @article{gershenson2003when,
title={When Can we Call a System Self-organizing?},
author={Carlos Gershenson and Francis Heylighen},
journal={In Banzhaf, W, T. Christaller, P. Dittrich, J. T. Kim, and J.
Ziegler, Advances in Artificial Life, 7th European Conference, ECAL 2003,
Dortmund, Germany, pp. 606-614. LNAI 2801. Springer.},
year={2003},
archivePrefix={arXiv},
eprint={nlin/0303020},
primaryClass={nlin.AO cond-mat.dis-nn cond-mat.stat-mech cs.CC}
} | gershenson2003when |
arxiv-676983 | nlin/0303021 | Contextual Random Boolean Networks | <|reference_start|>Contextual Random Boolean Networks: We propose the use of Deterministic Generalized Asynchronous Random Boolean Networks [Gershenson, 2002] as models of contextual deterministic discrete dynamical systems. We show that changes in the context have drastic effects on the global properties of the same networks, namely the average number of attractors and the average percentage of states in attractors. We introduce the situation where we lack knowledge on the context as a more realistic model for contextual dynamical systems. We notice that this makes the network non-deterministic in a specific way, namely introducing a non-Kolmogorovian quantum-like structure for the modelling of the network [Aerts, 1986]. In this case, for example, a state of the network has the potentiality (probability) of collapsing into different attractors, depending on the specific form of lack of knowledge on the context.<|reference_end|> | arxiv | @article{gershenson2003contextual,
title={Contextual Random Boolean Networks},
author={Carlos Gershenson, Jan Broekaert, and Diederik Aerts},
journal={In Banzhaf, W, T. Christaller, P. Dittrich, J. T. Kim, and J.
Ziegler, Advances in Artificial Life, 7th European Conference, ECAL 2003,
Dortmund, Germany, pp. 615-624. LNAI 2801. Springer.},
year={2003},
archivePrefix={arXiv},
eprint={nlin/0303021},
primaryClass={nlin.AO cond-mat.dis-nn cs.CC nlin.CG}
} | gershenson2003contextual |
arxiv-676984 | nlin/0304006 | Determining possible avenues of approach using ANTS | <|reference_start|>Determining possible avenues of approach using ANTS: Threat assessment is an important part of level 3 data fusion. Here we study a subproblem of this, worst-case risk assessment. Inspired by agent-based models used for simulation of trail formation for urban planning, we use ant colony optimization (ANTS) to determine possible avenues of approach for the enemy, given a situation picture. One way of determining such avenues would be to calculate the ``potential field'' caused by placing sources at possible goals for the enemy. This requires postulating a functional form for the potential, and also takes long time. Here we instead seek a method for quickly obtaining an effective potential. ANTS, which has previously been used to obtain approximate solutions to various optimization problems, is well suited for this. The output of our method describes possible avenues of approach for the enemy, i.e, areas where we should be prepared for attack. (The algorithm can also be run ``reversed'' to instead get areas of opportunity for our forces to exploit.) Using real geographical data, we found that our method gives a fast and reliable way of determining such avenues. Our method can be used in a computer-based command and control system to replace the first step of human intelligence analysis.<|reference_end|> | arxiv | @article{svenson2003determining,
title={Determining possible avenues of approach using ANTS},
author={Pontus Svenson and Hedvig Sidenbladh},
journal={Proc 6th Int Conf Information Fusion, Cairns, p 1110 (2003)},
year={2003},
archivePrefix={arXiv},
eprint={nlin/0304006},
primaryClass={nlin.AO cs.AI}
} | svenson2003determining |
arxiv-676985 | nlin/0306055 | A Model for Prejudiced Learning in Noisy Environments | <|reference_start|>A Model for Prejudiced Learning in Noisy Environments: Based on the heuristics that maintaining presumptions can be beneficial in uncertain environments, we propose a set of basic axioms for learning systems to incorporate the concept of prejudice. The simplest, memoryless model of a deterministic learning rule obeying the axioms is constructed, and shown to be equivalent to the logistic map. The system's performance is analysed in an environment in which it is subject to external randomness, weighing learning defectiveness against stability gained. The corresponding random dynamical system with inhomogeneous, additive noise is studied, and shown to exhibit the phenomena of noise induced stability and stochastic bifurcations. The overall results allow for the interpretation that prejudice in uncertain environments entails a considerable portion of stubbornness as a secondary phenomenon.<|reference_end|> | arxiv | @article{schmidt2003a,
title={A Model for Prejudiced Learning in Noisy Environments},
author={Andreas U. Schmidt},
journal={Applied Mathematics and Computation, vol. 168, no. 1 (2005)
354-379},
year={2003},
doi={10.1016/j.amc.2004.09.003},
archivePrefix={arXiv},
eprint={nlin/0306055},
primaryClass={nlin.AO cs.LG}
} | schmidt2003a |
arxiv-676986 | nlin/0309033 | The Interactive Minority Game: a Web-based investigation of human market interactions | <|reference_start|>The Interactive Minority Game: a Web-based investigation of human market interactions: The unprecedented access offered by the World Wide Web brings with it the potential to gather huge amounts of data on human activities. Here we exploit this by using a toy model of financial markets, the Minority Game (MG), to investigate human speculative trading behaviour and information capacity. Hundreds of individuals have played a total of tens of thousands of game turns against computer-controlled agents in the Web-based_Interactive Minority Game_. The analytical understanding of the MG permits fine-tuning of the market situations encountered, allowing for investigation of human behaviour in a variety of controlled environments. In particular, our results indicate a transition in players' decision-making, as the markets become more difficult, between deductive behaviour making use of short-term trends in the market, and highly repetitive behaviour that ignores entirely the market history, yet outperforms random decision-making. PACS: 02.50.Le; 89.65.Gh; 89.70.+c Keywords: Decision theory and game theory; Economics and financial markets; Information theory<|reference_end|> | arxiv | @article{laureti2003the,
title={The Interactive Minority Game: a Web-based investigation of human market
interactions},
author={Paolo Laureti, Peter Ruch, Joseph Wakeling and Yi-Cheng Zhang},
journal={Physica A 331 (2004) 651-659},
year={2003},
doi={10.1016/j.physa.2003.07.002},
archivePrefix={arXiv},
eprint={nlin/0309033},
primaryClass={nlin.AO cond-mat.stat-mech cs.HC physics.soc-ph}
} | laureti2003the |
arxiv-676987 | nlin/0309039 | Self-organizing Traffic Control: First Results | <|reference_start|>Self-organizing Traffic Control: First Results: We developed a virtual laboratory for traffic control where agents use different strategies in order to self-organize on the road. We present our first results where we compare the performance and behaviour promoted by environmental constrains and five different simple strategies: three inspired in flocking behaviour, one selfish, and one inspired in the minority game. Experiments are presented for comparing the strategies. Different issues are discussed, such as the important role of environmental constrains and the emergence of traffic lanes.<|reference_end|> | arxiv | @article{gershenson2003self-organizing,
title={Self-organizing Traffic Control: First Results},
author={Carlos Gershenson},
journal={arXiv preprint arXiv:nlin/0309039},
year={2003},
archivePrefix={arXiv},
eprint={nlin/0309039},
primaryClass={nlin.AO cs.MA}
} | gershenson2003self-organizing |
arxiv-676988 | nlin/0311008 | Phase Transitions in Random Boolean Networks with Different Updating Schemes | <|reference_start|>Phase Transitions in Random Boolean Networks with Different Updating Schemes: In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown that the statistical properties of Random Boolean networks change considerable according to the updating scheme. We study with computer simulations sensitivity to initial conditions as a measure of order/chaos. We find that independently of their updating scheme, all network types have very similar phase transitions, namely when the average number of connections of nodes is between one and three. This critical value depends more on the size of the network than on the updating scheme.<|reference_end|> | arxiv | @article{gershenson2003phase,
title={Phase Transitions in Random Boolean Networks with Different Updating
Schemes},
author={Carlos Gershenson},
journal={arXiv preprint arXiv:nlin/0311008},
year={2003},
archivePrefix={arXiv},
eprint={nlin/0311008},
primaryClass={nlin.AO cond-mat.stat-mech cs.CC nlin.CG q-bio.QM}
} | gershenson2003phase |
arxiv-676989 | nlin/0312056 | Shannon information, LMC complexity and Renyi entropies: a straightforward approach | <|reference_start|>Shannon information, LMC complexity and Renyi entropies: a straightforward approach: The LMC complexity, an indicator of complexity based on a probabilistic description, is revisited. A straightforward approach allows us to establish the time evolution of this indicator in a near-equilibrium situation and gives us a new insight for interpreting the LMC complexity for a general non equilibrium system. Its relationship with the Renyi entropies is also explained. One of the advantages of this indicator is that its calculation does not require a considerable computational effort in many cases of physical and biological interest.<|reference_end|> | arxiv | @article{lopez-ruiz2003shannon,
title={Shannon information, LMC complexity and Renyi entropies: a
straightforward approach},
author={Ricardo Lopez-Ruiz},
journal={arXiv preprint arXiv:nlin/0312056},
year={2003},
archivePrefix={arXiv},
eprint={nlin/0312056},
primaryClass={nlin.AO cond-mat.stat-mech cs.IT math.IT nlin.CD physics.comp-ph q-bio.QM}
} | lopez-ruiz2003shannon |
arxiv-676990 | nlin/0402006 | Updating Schemes in Random Boolean Networks: Do They Really Matter? | <|reference_start|>Updating Schemes in Random Boolean Networks: Do They Really Matter?: In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the complexity reduction related to different updating schemes. We also report that all updating schemes yield very similar critical stability values, meaning that the "edge of chaos" does not depend much on the updating scheme. After discussion, we conclude that synchonous RBNs are justifiable theoretical models of biological networks.<|reference_end|> | arxiv | @article{gershenson2004updating,
title={Updating Schemes in Random Boolean Networks: Do They Really Matter?},
author={Carlos Gershenson},
journal={In Pollack, J., M. Bedau, P. Husbands, T. Ikegami, and R. A.
Watson (eds.) Artificial Life IX, Proceedings of the Ninth International
Conference on the Simulation and Synthesis of Living Systems. pp. 238-243.
MIT Press. 2004},
year={2004},
archivePrefix={arXiv},
eprint={nlin/0402006},
primaryClass={nlin.AO cond-mat.other cs.CC nlin.CG q-bio.MN q-bio.OT q-bio.QM}
} | gershenson2004updating |
arxiv-676991 | nlin/0402046 | Spontaneous Emergence of Complex Optimal Networks through Evolutionary Adaptation | <|reference_start|>Spontaneous Emergence of Complex Optimal Networks through Evolutionary Adaptation: An important feature of many complex systems, both natural and artificial, is the structure and organization of their interaction networks with interesting properties. Here we present a theory of self-organization by evolutionary adaptation in which we show how the structure and organization of a network is related to the survival, or in general the performance, objectives of the system. We propose that a complex system optimizes its network structure in order to maximize its overall survival fitness which is composed of short-term and long-term survival components. These in turn depend on three critical measures of the network, namely, efficiency, robustness and cost, and the environmental selection pressure. Using a graph theoretical case study, we show that when efficiency is paramount the "Star" topology emerges and when robustness is important the "Circle" topology is found. When efficiency and robustness requirements are both important to varying degrees, other classes of networks such as the "Hub" emerge. Our assumptions and results are consistent with observations across a wide variety of applications.<|reference_end|> | arxiv | @article{venkatasubramanian2004spontaneous,
title={Spontaneous Emergence of Complex Optimal Networks through Evolutionary
Adaptation},
author={Venkat Venkatasubramanian, Santhoji Katare, Priyan R. Patkar, and
Fangping Mu},
journal={arXiv preprint arXiv:nlin/0402046},
year={2004},
archivePrefix={arXiv},
eprint={nlin/0402046},
primaryClass={nlin.AO cond-mat.stat-mech cs.MA nlin.CG q-bio.QM}
} | venkatasubramanian2004spontaneous |
arxiv-676992 | nlin/0404004 | Protocol Requirements for Self-organizing Artifacts: Towards an Ambient Intelligence | <|reference_start|>Protocol Requirements for Self-organizing Artifacts: Towards an Ambient Intelligence: We discuss which properties common-use artifacts should have to collaborate without human intervention. We conceive how devices, such as mobile phones, PDAs, and home appliances, could be seamlessly integrated to provide an "ambient intelligence" that responds to the user's desires without requiring explicit programming or commands. While the hardware and software technology to build such systems already exists, as yet there is no standard protocol that can learn new meanings. We propose the first steps in the development of such a protocol, which would need to be adaptive, extensible, and open to the community, while promoting self-organization. We argue that devices, interacting through "game-like" moves, can learn to agree about how to communicate, with whom to cooperate, and how to delegate and coordinate specialized tasks. Thus, they may evolve a distributed cognition or collective intelligence capable of tackling complex tasks.<|reference_end|> | arxiv | @article{gershenson2004protocol,
title={Protocol Requirements for Self-organizing Artifacts: Towards an Ambient
Intelligence},
author={Carlos Gershenson and Francis Heylighen (Vrije Universiteit Brussel)},
journal={Minai, A., Braha, D., and Bar-Yam, Y., editors, Unifying Themes in
Complex Systems, volume V, pages 136-143. Springer, Berlin Heidelberg, 2011},
year={2004},
doi={10.1007/978-3-642-17635-7_17},
number={VUB AI Lab Memo 04-04},
archivePrefix={arXiv},
eprint={nlin/0404004},
primaryClass={nlin.AO cs.AI}
} | gershenson2004protocol |
arxiv-676993 | nlin/0404032 | Metrics for more than two points at once | <|reference_start|>Metrics for more than two points at once: The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the triangle inequality, to concern arbitrary numbers of points. Such a measure of how separated the points within a collection are can be bootstrapped, to measure "how separated" from each other are two (or more) collections. The measure presented here also allows fractional membership of an element in a collection. This means it directly concerns measures of ``how spread out" a probability distribution over a space is. When such a measure is bootstrapped to compare two collections, it allows us to measure how separated two probability distributions are, or more generally, how separated a distribution of distributions is.<|reference_end|> | arxiv | @article{wolpert2004metrics,
title={Metrics for more than two points at once},
author={David H. Wolpert},
journal={arXiv preprint arXiv:nlin/0404032},
year={2004},
archivePrefix={arXiv},
eprint={nlin/0404032},
primaryClass={nlin.AO cond-mat.other cs.LG math.GM}
} | wolpert2004metrics |
arxiv-676994 | nlin/0405038 | When Chaos Meets Computers | <|reference_start|>When Chaos Meets Computers: This paper focuses on an interesting phenomenon when chaos meets computers. It is found that digital computers are absolutely incapable of showing true long-time dynamics of some chaotic systems, including the tent map, the Bernoulli shift map and their analogues, even in a high-precision floating-point arithmetic. Although the results cannot directly generalized to most chaotic systems, the risk of using digital computers to numerically study continuous dynamical systems is shown clearly. As a result, we reach the old saying that "it is impossible to do everything with computers only".<|reference_end|> | arxiv | @article{li2004when,
title={When Chaos Meets Computers},
author={Shujun Li},
journal={arXiv preprint arXiv:nlin/0405038},
year={2004},
archivePrefix={arXiv},
eprint={nlin/0405038},
primaryClass={nlin.CD cs.NA}
} | li2004when |
arxiv-676995 | nlin/0407032 | Application of Artificial Neural Network in Jitter Analysis of Dispersion-Managed Communication System | <|reference_start|>Application of Artificial Neural Network in Jitter Analysis of Dispersion-Managed Communication System: Artificial Neural Network (ANN) is used as numerical methode in solving modified Nonlinear Schroedinger (NLS) equation with Dispersion Managed System (DMS) for jitter analysis. We take the optical axis z and the time t as input, and then some relevant values such as the change of position and the center frequency of the pulse, and further the mean square time of incoming pulse which are needed for jitter analysis. It shows that ANN yields numerical solutions which are adaptive with respect to the numerical errors and also verifies the previous numerical results using conventional numerical method. Our result indicates that DMS can minimize the timing jitter induced by some amplifiers.<|reference_end|> | arxiv | @article{zen2004application,
title={Application of Artificial Neural Network in Jitter Analysis of
Dispersion-Managed Communication System},
author={F.P. Zen, B.E. Gunara, W. Hidayat, Z.A. Thalib, H. Zainuddin, J.
Aminuddin},
journal={arXiv preprint arXiv:nlin/0407032},
year={2004},
archivePrefix={arXiv},
eprint={nlin/0407032},
primaryClass={nlin.PS cs.AI cs.NA}
} | zen2004application |
arxiv-676996 | nlin/0407052 | Breaking a chaos-noise-based secure communication scheme | <|reference_start|>Breaking a chaos-noise-based secure communication scheme: This paper studies the security of a secure communication scheme based on two discrete-time intermittently-chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) the key space can be remarkably reduced; 2) the decryption is insensitive to the mismatch of the secret key; 3) the key-generation process is insecure against known/chosen-plaintext attacks. The first two defects mean that the scheme is not secure enough against brute-force attacks, and the third one means that an attacker can easily break the cryptosystem by approximately estimating the secret key once he has a chance to access a fragment of the generated keystream. Yet it remains to be clarified if intermittent chaos could be used for designing secure chaotic cryptosystems.<|reference_end|> | arxiv | @article{li2004breaking,
title={Breaking a chaos-noise-based secure communication scheme},
author={Shujun Li, Gonzalo 'Alvarez, Guanrong Chen and Xuanqin Mou},
journal={Chaos, vol. 15, no. 1, art. no. 013703, March 2005},
year={2004},
doi={10.1063/1.1856711},
archivePrefix={arXiv},
eprint={nlin/0407052},
primaryClass={nlin.CD cs.CR}
} | li2004breaking |
arxiv-676997 | nlin/0407062 | Construction of Single-valued Solutions for Nonintegrable Systems with the Help of the Painleve Test | <|reference_start|>Construction of Single-valued Solutions for Nonintegrable Systems with the Help of the Painleve Test: The Painleve test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the elliptic solutions we transform an initial nonlinear differential equation in a nonlinear algebraic system in parameters of the Laurent-series solutions of the initial equation. The number of unknowns in the obtained nonlinear system does not depend on number of arbitrary coefficients of the used first order equation. In this paper we describe the corresponding algorithm, which has been realized in REDUCE and Maple.<|reference_end|> | arxiv | @article{vernov2004construction,
title={Construction of Single-valued Solutions for Nonintegrable Systems with
the Help of the Painleve Test},
author={S. Yu. Vernov (Skobeltsyn Institute of Nuclear Physics of Moscow State
University)},
journal={arXiv preprint arXiv:nlin/0407062},
year={2004},
archivePrefix={arXiv},
eprint={nlin/0407062},
primaryClass={nlin.SI astro-ph.SR cs.MS math-ph math.DS math.MP}
} | vernov2004construction |
arxiv-676998 | nlin/0408006 | Introduction to Random Boolean Networks | <|reference_start|>Introduction to Random Boolean Networks: The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study their generic properties. Like this, RBNs have been used for exploring the configurations where life could emerge. The fact that RBNs are a generalization of cellular automata makes their research a very important topic. The tutorial, intended for a broad audience, presents the state of the art in RBNs, spanning over several lines of research carried out by different groups. We focus on research done within artificial life, as we cannot exhaust the abundant research done over the decades related to RBNs.<|reference_end|> | arxiv | @article{gershenson2004introduction,
title={Introduction to Random Boolean Networks},
author={Carlos Gershenson},
journal={In Bedau, M., P. Husbands, T. Hutton, S. Kumar, and H. Suzuki
(eds.) Workshop and Tutorial Proceedings, Ninth International Conference on
the Simulation and Synthesis of Living Systems (ALife IX). pp. 160-173. 2004},
year={2004},
archivePrefix={arXiv},
eprint={nlin/0408006},
primaryClass={nlin.AO cond-mat.stat-mech cs.CC nlin.CG q-bio.MN q-bio.QM}
} | gershenson2004introduction |
arxiv-676999 | nlin/0408007 | Entropy Maximization as a Holistic Design Principle for Complex Optimal Networks and the Emergence of Power Laws | <|reference_start|>Entropy Maximization as a Holistic Design Principle for Complex Optimal Networks and the Emergence of Power Laws: We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that the underlying organizing principle is to meet an overall performance target for wide-ranging operating or environmental conditions. This design or survival requirement of reliable performance under uncertainty leads, via the maximum entropy principle, to the emergence of a power law vertex degree distribution. The theory also predicts exponential or Poisson degree distributions depending on network redundancy, thus explaining all three regimes as different manifestations of a common underlying phenomenon within a unified theoretical framework.<|reference_end|> | arxiv | @article{venkatasubramanian2004entropy,
title={Entropy Maximization as a Holistic Design Principle for Complex Optimal
Networks and the Emergence of Power Laws},
author={Venkat Venkatasubramanian, Dimitris N. Politis and Priyan R. Patkar},
journal={arXiv preprint arXiv:nlin/0408007},
year={2004},
archivePrefix={arXiv},
eprint={nlin/0408007},
primaryClass={nlin.AO cond-mat.stat-mech cs.IT math.IT q-bio.QM}
} | venkatasubramanian2004entropy |
arxiv-677000 | nlin/0408039 | Stability and Diversity in Collective Adaptation | <|reference_start|>Stability and Diversity in Collective Adaptation: We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by information flux between agents, giving a novel view of collective adaptation.<|reference_end|> | arxiv | @article{sato2004stability,
title={Stability and Diversity in Collective Adaptation},
author={Yuzuru Sato, Eizo Akiyama, James P. Crutchfield},
journal={arXiv preprint arXiv:nlin/0408039},
year={2004},
doi={10.1016/j.physd.2005.06.031},
number={Santa Fe Institute Working Paper 04-08-025},
archivePrefix={arXiv},
eprint={nlin/0408039},
primaryClass={nlin.AO cs.LG math.DS nlin.CD stat.ML}
} | sato2004stability |
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