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arxiv-669201 | cond-mat/0202190 | Threshold Disorder as a Source of Diverse and Complex Behavior in Random Nets | <|reference_start|>Threshold Disorder as a Source of Diverse and Complex Behavior in Random Nets: We study the diversity of complex spatio-temporal patterns in the behavior of random synchronous asymmetric neural networks (RSANNs). Special attention is given to the impact of disordered threshold values on limit-cycle diversity and limit-cycle complexity in RSANNs which have `normal' thresholds by default. Surprisingly, RSANNs exhibit only a small repertoire of rather complex limit-cycle patterns when all parameters are fixed. This repertoire of complex patterns is also rather stable with respect to small parameter changes. These two unexpected results may generalize to the study of other complex systems. In order to reach beyond this seemingly-disabling `stable and small' aspect of the limit-cycle repertoire of RSANNs, we have found that if an RSANN has threshold disorder above a critical level, then there is a rapid increase of the size of the repertoire of patterns. The repertoire size initially follows a power-law function of the magnitude of the threshold disorder. As the disorder increases further, the limit-cycle patterns themselves become simpler until at a second critical level most of the limit cycles become simple fixed points. Nonetheless, for moderate changes in the threshold parameters, RSANNs are found to display specific features of behavior desired for rapidly-responding processing systems: accessibility to a large set of complex patterns.<|reference_end|> | arxiv | @article{mcguire2002threshold,
title={Threshold Disorder as a Source of Diverse and Complex Behavior in Random
Nets},
author={Patrick C. McGuire, Henrik Bohr, John W. Clark, Robert Haschke, Chris
Pershing, Johann Rafelski},
journal={Neural Networks,15(10), pp. 1243-1258 (2002)},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0202190},
primaryClass={cond-mat.dis-nn cs.NE q-bio.NC}
} | mcguire2002threshold |
arxiv-669202 | cond-mat/0202383 | Extended Comment on Language Trees and Zipping | <|reference_start|>Extended Comment on Language Trees and Zipping: This is the extended version of a Comment submitted to Physical Review Letters. I first point out the inappropriateness of publishing a Letter unrelated to physics. Next, I give experimental results showing that the technique used in the Letter is 3 times worse and 17 times slower than a simple baseline. And finally, I review the literature, showing that the ideas of the Letter are not novel. I conclude by suggesting that Physical Review Letters should not publish Letters unrelated to physics.<|reference_end|> | arxiv | @article{goodman2002extended,
title={Extended Comment on Language Trees and Zipping},
author={Joshua Goodman},
journal={arXiv preprint arXiv:cond-mat/0202383},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0202383},
primaryClass={cond-mat.stat-mech cs.CL cs.LG}
} | goodman2002extended |
arxiv-669203 | cond-mat/0203227 | Ising Model on Networks with an Arbitrary Distribution of Connections | <|reference_start|>Ising Model on Networks with an Arbitrary Distribution of Connections: We find the exact critical temperature $T_c$ of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution $P(k)$. We observe an anomalous behavior of the magnetization, magnetic susceptibility and specific heat, when $P(k)$ is fat-tailed, or, loosely speaking, when the fourth moment of the distribution diverges in infinite networks. When the second moment becomes divergent, $T_c$ approaches infinity, the phase transition is of infinite order, and size effect is anomalously strong.<|reference_end|> | arxiv | @article{dorogovtsev2002ising,
title={Ising Model on Networks with an Arbitrary Distribution of Connections},
author={S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes},
journal={Phys.Rev.E66:016104,2002},
year={2002},
doi={10.1103/PhysRevE.66.016104},
archivePrefix={arXiv},
eprint={cond-mat/0203227},
primaryClass={cond-mat.stat-mech cs.NI hep-lat hep-th math-ph math.MP nlin.SI physics.class-ph}
} | dorogovtsev2002ising |
arxiv-669204 | cond-mat/0203436 | Entropy estimation of symbol sequences | <|reference_start|>Entropy estimation of symbol sequences: We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our interest is in describing their convergence with sequence length, assuming no limits for the space and time complexities of the compression algorithms. A scaling law is proposed for extrapolation from finite sample lengths. This is applied to sequences of dynamical systems in non-trivial chaotic regimes, a 1-D cellular automaton, and to written English texts.<|reference_end|> | arxiv | @article{schürmann2002entropy,
title={Entropy estimation of symbol sequences},
author={Thomas Sch"urmann and Peter Grassberger},
journal={CHAOS Vol. 6, No. 3 (1996) 414-427},
year={2002},
doi={10.1063/1.166191},
archivePrefix={arXiv},
eprint={cond-mat/0203436},
primaryClass={cond-mat.stat-mech cs.CL cs.IT math.IT physics.data-an stat.ML}
} | schürmann2002entropy |
arxiv-669205 | cond-mat/0203591 | Anticorrelations and subdiffusion in financial systems | <|reference_start|>Anticorrelations and subdiffusion in financial systems: Statistical dynamics of financial systems is investigated, based on a model of a randomly coupled equation system driven by a stochastic Langevin force. Anticorrelations of price returns, and subdiffusion of prices is found from the model, and and compared with those calculated from historical $/EURO exchange rates.<|reference_end|> | arxiv | @article{staliunas2002anticorrelations,
title={Anticorrelations and subdiffusion in financial systems},
author={Kestutis Staliunas},
journal={arXiv preprint arXiv:cond-mat/0203591},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0203591},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CE q-fin.ST}
} | staliunas2002anticorrelations |
arxiv-669206 | cond-mat/0204102 | Accelerated growth of networks | <|reference_start|>Accelerated growth of networks: In many real growing networks the mean number of connections per vertex increases with time. The Internet, the Word Wide Web, collaboration networks, and many others display this behavior. Such a growth can be called {\em accelerated}. We show that this acceleration influences distribution of connections and may determine the structure of a network. We discuss general consequences of the acceleration and demonstrate its features applying simple illustrating examples. In particular, we show that the accelerated growth fairly well explains the structure of the Word Web (the network of interacting words of human language). Also, we use the models of the accelerated growth of networks to describe a wealth condensation transition in evolving societies.<|reference_end|> | arxiv | @article{dorogovtsev2002accelerated,
title={Accelerated growth of networks},
author={S.N. Dorogovtsev, J.F.F. Mendes},
journal={arXiv preprint arXiv:cond-mat/0204102},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0204102},
primaryClass={cond-mat.stat-mech cs.NI}
} | dorogovtsev2002accelerated |
arxiv-669207 | cond-mat/0204111 | Principles of statistical mechanics of random networks | <|reference_start|>Principles of statistical mechanics of random networks: We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilibrium uncorrelated networks, fat-tailed degree distributions may exist only starting from some critical average number of connections of a vertex, in a phase with a condensate of edges.<|reference_end|> | arxiv | @article{dorogovtsev2002principles,
title={Principles of statistical mechanics of random networks},
author={S.N. Dorogovtsev, J.F.F. Mendes, A.N. Samukhin},
journal={Nucl.Phys. B666 (2003) 396-416},
year={2002},
doi={10.1016/S0550-3213(03)00504-2},
archivePrefix={arXiv},
eprint={cond-mat/0204111},
primaryClass={cond-mat.stat-mech cs.NI hep-lat hep-th math-ph math.MP nlin.AO}
} | dorogovtsev2002principles |
arxiv-669208 | cond-mat/0204181 | Local Search in Unstructured Networks | <|reference_start|>Local Search in Unstructured Networks: We review a number of message-passing algorithms that can be used to search through power-law networks. Most of these algorithms are meant to be improvements for peer-to-peer file sharing systems, and some may also shed some light on how unstructured social networks with certain topologies might function relatively efficiently with local information. Like the networks that they are designed for, these algorithms are completely decentralized, and they exploit the power-law link distribution in the node degree. We demonstrate that some of these search algorithms can work well on real Gnutella networks, scale sub-linearly with the number of nodes, and may help reduce the network search traffic that tends to cripple such networks.<|reference_end|> | arxiv | @article{adamic2002local,
title={Local Search in Unstructured Networks},
author={Lada A. Adamic, Rajan M. Lukose, Bernardo A. Huberman},
journal={arXiv preprint arXiv:cond-mat/0204181},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0204181},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.NI}
} | adamic2002local |
arxiv-669209 | cond-mat/0205034 | Phase Transition in a Random Fragmentation Problem with Applications to Computer Science | <|reference_start|>Phase Transition in a Random Fragmentation Problem with Applications to Computer Science: We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x_0. The process stops when all the fragments have sizes smaller than x_0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m=m_c. For m<m_c, the fluctuations are Gaussian where as for m>m_c they are anomalously large and non-Gaussian. We apply this general result to analyze two different search algorithms in computer science.<|reference_end|> | arxiv | @article{dean2002phase,
title={Phase Transition in a Random Fragmentation Problem with Applications to
Computer Science},
author={David S. Dean and Satya N. Majumdar},
journal={J. Phys. A. 35, L501 (2002)},
year={2002},
doi={10.1088/0305-4470/35/32/101},
archivePrefix={arXiv},
eprint={cond-mat/0205034},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.DS math.PR}
} | dean2002phase |
arxiv-669210 | cond-mat/0205336 | Exact Solution of a Drop-push Model for Percolation | <|reference_start|>Exact Solution of a Drop-push Model for Percolation: Motivated by a computer science algorithm known as `linear probing with hashing' we study a new type of percolation model whose basic features include a sequential `dropping' of particles on a substrate followed by their transport via a `pushing' mechanism. Our exact solution in one dimension shows that, unlike the ordinary random percolation model, the drop-push model has nontrivial spatial correlations generated by the dynamics itself. The critical exponents in the drop-push model are also different from that of the ordinary percolation. The relevance of our results to computer science is pointed out.<|reference_end|> | arxiv | @article{majumdar2002exact,
title={Exact Solution of a Drop-push Model for Percolation},
author={Satya N. Majumdar and David S. Dean},
journal={Phys. Rev. Lett., 89, 115701 (2002)},
year={2002},
doi={10.1103/PhysRevLett.89.115701},
archivePrefix={arXiv},
eprint={cond-mat/0205336},
primaryClass={cond-mat.stat-mech cs.DS math.PR}
} | majumdar2002exact |
arxiv-669211 | cond-mat/0206084 | Internet topology at the router and autonomous system level | <|reference_start|>Internet topology at the router and autonomous system level: We present a statistical analysis of different metrics characterizing the topological properties of Internet maps, collected at two different resolution scales: the router and the autonomous system level. The metrics we consider allow us to confirm the presence of scale-free signatures in several statistical distributions, as well as to show in a quantitative way the hierarchical nature of the Internet. Our findings are relevant for the development of more accurate Internet topology generators, which should include, along with the scale-free properties of the connectivity distribution, the hierarchical signatures unveiled in the present work.<|reference_end|> | arxiv | @article{vazquez2002internet,
title={Internet topology at the router and autonomous system level},
author={A. Vazquez, R. Pastor-Satorras, and A. Vespignani},
journal={arXiv preprint arXiv:cond-mat/0206084},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0206084},
primaryClass={cond-mat.dis-nn cs.NI}
} | vazquez2002internet |
arxiv-669212 | cond-mat/0206410 | Optimal network topologies for local search with congestion | <|reference_start|>Optimal network topologies for local search with congestion: The problem of searchability in decentralized complex networks is of great importance in computer science, economy and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and obtain expressions for the average search cost--written in terms of the search algorithm and the topological properties of the network--both in presence and abscence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: star-like configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when the number of parallel searches is large.<|reference_end|> | arxiv | @article{guimera2002optimal,
title={Optimal network topologies for local search with congestion},
author={R. Guimera, A. Arenas, A. Diaz-Guilera, F. Vega-Redondo, A. Cabrales},
journal={Phys. Rev. Lett. 89, 248701 (2002)},
year={2002},
doi={10.1103/PhysRevLett.89.248701},
archivePrefix={arXiv},
eprint={cond-mat/0206410},
primaryClass={cond-mat.dis-nn cs.NI}
} | guimera2002optimal |
arxiv-669213 | cond-mat/0207035 | Computational complexity arising from degree correlations in networks | <|reference_start|>Computational complexity arising from degree correlations in networks: We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of finding minimal vertex covers on these graphs, we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks. This results in a higher complexity of the network in a computational sense: Simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case, whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization.<|reference_end|> | arxiv | @article{vazquez2002computational,
title={Computational complexity arising from degree correlations in networks},
author={Alexei Vazquez and Martin Weigt},
journal={Phys. Rev. E 67, 027101 (2003)},
year={2002},
doi={10.1103/PhysRevE.67.027101},
archivePrefix={arXiv},
eprint={cond-mat/0207035},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC}
} | vazquez2002computational |
arxiv-669214 | cond-mat/0207140 | Alternative solutions to diluted p-spin models and XORSAT problems | <|reference_start|>Alternative solutions to diluted p-spin models and XORSAT problems: We derive analytical solutions for p-spin models with finite connectivity at zero temperature. These models are the statistical mechanics equivalent of p-XORSAT problems in theoretical computer science. We give a full characterization of the phase diagram: location of the phase transitions (static and dynamic), together with a description of the clustering phenomenon taking place in configurational space. We use two alternative methods: the cavity approach and a rigorous derivation.<|reference_end|> | arxiv | @article{mezard2002alternative,
title={Alternative solutions to diluted p-spin models and XORSAT problems},
author={M. Mezard, F. Ricci-Tersenghi and R. Zecchina},
journal={J. Stat. Phys. 111, 505 (2003)},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0207140},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.DM}
} | mezard2002alternative |
arxiv-669215 | cond-mat/0208414 | Winner-Relaxing Self-Organizing Maps | <|reference_start|>Winner-Relaxing Self-Organizing Maps: A new family of self-organizing maps, the Winner-Relaxing Kohonen Algorithm, is introduced as a generalization of a variant given by Kohonen in 1991. The magnification behaviour is calculated analytically. For the original variant a magnification exponent of 4/7 is derived; the generalized version allows to steer the magnification in the wide range from exponent 1/2 to 1 in the one-dimensional case, thus provides optimal mapping in the sense of information theory. The Winner Relaxing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.<|reference_end|> | arxiv | @article{claussen2002winner-relaxing,
title={Winner-Relaxing Self-Organizing Maps},
author={Jens Christian Claussen (Theoretical Physics, University Kiel)},
journal={Neural Computation 17 (5), 996-1009 (2005)},
year={2002},
doi={10.1162/0899766053491922},
archivePrefix={arXiv},
eprint={cond-mat/0208414},
primaryClass={cond-mat.dis-nn cs.NE nlin.AO q-bio.NC}
} | claussen2002winner-relaxing |
arxiv-669216 | cond-mat/0208460 | Coloring random graphs | <|reference_start|>Coloring random graphs: We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on $q$, we find the precise value of the critical average connectivity $c_q$. Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms.<|reference_end|> | arxiv | @article{mulet2002coloring,
title={Coloring random graphs},
author={R. Mulet, A. Pagnani, M. Weigt, R. Zecchina},
journal={Phys. Rev. Lett. 89, 268701 (2002)},
year={2002},
doi={10.1103/PhysRevLett.89.268701},
archivePrefix={arXiv},
eprint={cond-mat/0208460},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.CC}
} | mulet2002coloring |
arxiv-669217 | cond-mat/0208488 | On the Prospects of Chaos Aware Traffic Modeling | <|reference_start|>On the Prospects of Chaos Aware Traffic Modeling: In this paper the chaotic properties of the TCP congestion avoidance mechanism are investigated. The analysis focuses on the origin of the complex behavior appearing in deterministic TCP/IP networks. From the traffic modeling point of view the understanding of the mechanism generating chaos is essential, since present models are unable to cope with this phenomena. Using the basic tools of chaos theory in our study, the main characteristics of chaotic dynamics are revealed. The dynamics of packet loss events is studied by a simple symbolic description. The cellular structure of the phase space of congestion windows is shown. This implies periodic behavior for large time scales. Chaotic behavior in short time scales and periodicity for larger times makes it necessary to develop models that account for both. Thus a simple model that describes the congestion window dynamics according to fluid equations, but handles the packet loss events separately is introduced. This model can reproduce the basic features observed in realistic packet level simulations.<|reference_end|> | arxiv | @article{fekete2002on,
title={On the Prospects of Chaos Aware Traffic Modeling},
author={A. Fekete, M. Marodi, G. Vattay},
journal={arXiv preprint arXiv:cond-mat/0208488},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0208488},
primaryClass={cond-mat.dis-nn cs.NI nlin.CD}
} | fekete2002on |
arxiv-669218 | cond-mat/0209111 | Approaches to Network Classification | <|reference_start|>Approaches to Network Classification: We introduce a novel approach to description of networks/graphs. It is based on an analogue physical model which is dynamically evolved. This evolution depends on the connectivity matrix and readily brings out many qualitative features of the graph.<|reference_end|> | arxiv | @article{gudkov2002approaches,
title={Approaches to Network Classification},
author={Vladimir Gudkov, Joseph E. Johnson and Shmuel Nussinov},
journal={arXiv preprint arXiv:cond-mat/0209111},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0209111},
primaryClass={cond-mat.stat-mech cs.DM hep-ph math.CO physics.comp-ph}
} | gudkov2002approaches |
arxiv-669219 | cond-mat/0209112 | Graph equivalence and characterization via a continuous evolution of a physical analog | <|reference_start|>Graph equivalence and characterization via a continuous evolution of a physical analog: A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto ``physical'' models - namely $n$ simplexes in $n-1$ dimensions - is applied to the graph equivalence problem. It is shown to solve this long standing problem in polynomial, short, time.<|reference_end|> | arxiv | @article{gudkov2002graph,
title={Graph equivalence and characterization via a continuous evolution of a
physical analog},
author={Vladimir Gudkov and Shmuel Nussinov},
journal={arXiv preprint arXiv:cond-mat/0209112},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0209112},
primaryClass={cond-mat.stat-mech cs.DM hep-ph math.CO physics.comp-ph}
} | gudkov2002graph |
arxiv-669220 | cond-mat/0209419 | A Novel Approach Applied to the Largest Clique Problem | <|reference_start|>A Novel Approach Applied to the Largest Clique Problem: A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we apply it to the NP complete problem of finding the largest perfect clique within a graph $G$.<|reference_end|> | arxiv | @article{gudkov2002a,
title={A Novel Approach Applied to the Largest Clique Problem},
author={Vladimir Gudkov, Shmuel Nussinov and Zohar Nussinov},
journal={arXiv preprint arXiv:cond-mat/0209419},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0209419},
primaryClass={cond-mat cs.DM math.CO physics.comp-ph}
} | gudkov2002a |
arxiv-669221 | cond-mat/0211605 | Evolution of Cooperation in a Spatial Prisoner's Dilemma | <|reference_start|>Evolution of Cooperation in a Spatial Prisoner's Dilemma: We investigate the spatial distribution and the global frequency of agents who can either cooperate or defect. The agent interaction is described by a deterministic, non-iterated prisoner's dilemma game, further each agent only locally interacts with his neighbors. Based on a detailed analysis of the local payoff structures we derive critical conditions for the invasion or the spatial coexistence of cooperators and defectors. These results are concluded in a phase diagram that allows to identify five regimes, each characterized by a distinct spatiotemporal dynamics and a corresponding final spatial structure. In addition to the complete invasion of defectors, we find coexistence regimes with either a majority of cooperators in large spatial domains, or a minority of cooperators organized in small non-stationary domains or in small clusters. The analysis further allowed a verification of computer simulation results by Nowak and May (1993). Eventually, we present simulation results of a true 5-person game on a lattice. This modification leads to non-uniform spatial interactions that may even enhance the effect of cooperation. Keywords: Prisoner's dilemma; cooperation; spatial 5-person game<|reference_end|> | arxiv | @article{schweitzer2002evolution,
title={Evolution of Cooperation in a Spatial Prisoner's Dilemma},
author={Frank Schweitzer, Laxmidhar Behera, Heinz Muehlenbein},
journal={arXiv preprint arXiv:cond-mat/0211605},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0211605},
primaryClass={cond-mat.stat-mech cs.GT nlin.CG}
} | schweitzer2002evolution |
arxiv-669222 | cond-mat/0212451 | Constraint Satisfaction by Survey Propagation | <|reference_start|>Constraint Satisfaction by Survey Propagation: Survey Propagation is an algorithm designed for solving typical instances of random constraint satisfiability problems. It has been successfully tested on random 3-SAT and random $G(n,\frac{c}{n})$ graph 3-coloring, in the hard region of the parameter space. Here we provide a generic formalism which applies to a wide class of discrete Constraint Satisfaction Problems.<|reference_end|> | arxiv | @article{braunstein2002constraint,
title={Constraint Satisfaction by Survey Propagation},
author={A. Braunstein, M. Mezard, M. Weigt and R. Zecchina},
journal={Advances in Neural Information Processing Systems. Vol 9. Oxford
University Press; 2005. 424},
year={2002},
archivePrefix={arXiv},
eprint={cond-mat/0212451},
primaryClass={cond-mat.dis-nn cs.CC}
} | braunstein2002constraint |
arxiv-669223 | cond-mat/0301035 | Scaling and Universality in Continuous Length Combinatorial Optimization | <|reference_start|>Scaling and Universality in Continuous Length Combinatorial Optimization: We consider combinatorial optimization problems defined over random ensembles, and study how solution cost increases when the optimal solution undergoes a small perturbation delta. For the minimum spanning tree, the increase in cost scales as delta^2; for the mean-field and Euclidean minimum matching and traveling salesman problems in dimension d>=2, the increase scales as delta^3; this is observed in Monte Carlo simulations in d=2,3,4 and in theoretical analysis of a mean-field model. We speculate that the scaling exponent could serve to classify combinatorial optimization problems into a small number of distinct categories, similar to universality classes in statistical physics.<|reference_end|> | arxiv | @article{aldous2003scaling,
title={Scaling and Universality in Continuous Length Combinatorial Optimization},
author={David Aldous and Allon G. Percus},
journal={arXiv preprint arXiv:cond-mat/0301035},
year={2003},
doi={10.1073/pnas.1635191100},
number={LA-UR-02-7322},
archivePrefix={arXiv},
eprint={cond-mat/0301035},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.DM}
} | aldous2003scaling |
arxiv-669224 | cond-mat/0301271 | Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms | <|reference_start|>Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms: Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random satisfiability problems. We find two different dynamical regimes, depending on the number of constraints per variable: For low constraintness, the problems are solved efficiently, i.e. in linear time. For higher constraintness, the solution times become exponential. We observe that the dynamical behavior is characterized by a fast equilibration and fluctuations around this equilibrium. If the algorithm runs long enough, an exponentially rare fluctuation towards a solution appears.<|reference_end|> | arxiv | @article{barthel2003solving,
title={Solving satisfiability problems by fluctuations: The dynamics of
stochastic local search algorithms},
author={Wolfgang Barthel, Alexander K. Hartmann, and Martin Weigt},
journal={Phys. Rev. E 67, 066104 (2003)},
year={2003},
doi={10.1103/PhysRevE.67.066104},
archivePrefix={arXiv},
eprint={cond-mat/0301271},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.CC}
} | barthel2003solving |
arxiv-669225 | cond-mat/0301272 | Relaxation and Metastability in the RandomWalkSAT search procedure | <|reference_start|>Relaxation and Metastability in the RandomWalkSAT search procedure: An analysis of the average properties of a local search resolution procedure for the satisfaction of random Boolean constraints is presented. Depending on the ratio alpha of constraints per variable, resolution takes a time T_res growing linearly (T_res \sim tau(alpha) N, alpha < alpha_d) or exponentially (T_res \sim exp(N zeta(alpha)), alpha > alpha_d) with the size N of the instance. The relaxation time tau(alpha) in the linear phase is calculated through a systematic expansion scheme based on a quantum formulation of the evolution operator. For alpha > alpha_d, the system is trapped in some metastable state, and resolution occurs from escape from this state through crossing of a large barrier. An annealed calculation of the height zeta(alpha) of this barrier is proposed. The polynomial/exponentiel cross-over alpha_d is not related to the onset of clustering among solutions.<|reference_end|> | arxiv | @article{semerjian2003relaxation,
title={Relaxation and Metastability in the RandomWalkSAT search procedure},
author={Guilhem Semerjian, Remi Monasson},
journal={Phys. Rev. E 67, 066103 (2003)},
year={2003},
doi={10.1103/PhysRevE.67.066103},
number={LPT-ENS 02/66},
archivePrefix={arXiv},
eprint={cond-mat/0301272},
primaryClass={cond-mat cs.CC}
} | semerjian2003relaxation |
arxiv-669226 | cond-mat/0301307 | Nonextensive statistical mechanics and economics | <|reference_start|>Nonextensive statistical mechanics and economics: Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous success in describing, among others, the particular stationary state corresponding to thermal equilibrium. There are, however, vast classes of complex systems which accomodate quite badly, or even not at all, within the BG formalism. Such dynamical systems exhibit, in one way or another, nonergodic aspects. In order to be able to theoretically study at least some of these systems, a formalism was proposed 14 years ago, which is sometimes referred to as nonextensive statistical mechanics. We briefly introduce this formalism, its foundations and applications. Furthermore, we provide some bridging to important economical phenomena, such as option pricing, return and volume distributions observed in the financial markets, and the fascinating and ubiquitous concept of risk aversion. One may summarize the whole approach by saying that BG statistical mechanics is based on the entropy $S_{BG}=-k \sum_i p_i \ln p_i$, and typically provides {\it exponential laws} for describing stationary states and basic time-dependent phenomena, while nonextensive statistical mechanics is instead based on the entropic form $S_q=k(1-\sum_ip_i^q)/(q-1)$ (with $S_1=S_{BG}$), and typically provides, for the same type of description, (asymptotic) {\it power laws}.<|reference_end|> | arxiv | @article{tsallis2003nonextensive,
title={Nonextensive statistical mechanics and economics},
author={Constantino Tsallis, Celia Anteneodo, Lisa Borland and Roberto Osorio},
journal={Physica A 324, 89 (2003).},
year={2003},
doi={10.1016/S0378-4371(03)00042-6},
archivePrefix={arXiv},
eprint={cond-mat/0301307},
primaryClass={cond-mat.stat-mech cs.CE q-fin.ST}
} | tsallis2003nonextensive |
arxiv-669227 | cond-mat/0301459 | Collectives for the Optimal Combination of Imperfect Objects | <|reference_start|>Collectives for the Optimal Combination of Imperfect Objects: In this letter we summarize some recent theoretical work on the design of collectives, i.e., of systems containing many agents, each of which can be viewed as trying to maximize an associated private utility, where there is also a world utility rating the behavior of that overall system that the designer of the collective wishes to optimize. We then apply algorithms based on that work on a recently suggested testbed for such optimization problems (Challet & Johnson, PRL, vol 89, 028701 2002). This is the problem of finding the combination of imperfect nano-scale objects that results in the best aggregate object. We present experimental results showing that these algorithms outperform conventional methods by more than an order of magnitude in this domain.<|reference_end|> | arxiv | @article{tumer2003collectives,
title={Collectives for the Optimal Combination of Imperfect Objects},
author={Kagan Tumer and David Wolpert},
journal={arXiv preprint arXiv:cond-mat/0301459},
year={2003},
archivePrefix={arXiv},
eprint={cond-mat/0301459},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.MA nlin.AO}
} | tumer2003collectives |
arxiv-669228 | cond-mat/0302050 | Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations | <|reference_start|>Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations: In a parallel discrete-event simulation (PDES) scheme, tasks are distributed among processing elements (PEs), whose progress is controlled by a synchronization scheme. For lattice systems with short-range interactions, the progress of the conservative PDES scheme is governed by the Kardar-Parisi-Zhang equation from the theory of non-equilibrium surface growth. Although the simulated (virtual) times of the PEs progress at a nonzero rate, their standard deviation (spread) diverges with the number of PEs, hindering efficient data collection. We show that weak random interactions among the PEs can make this spread nondivergent. The PEs then progress at a nonzero, near-uniform rate without requiring global synchronizations.<|reference_end|> | arxiv | @article{korniss2003suppressing,
title={Suppressing Roughness of Virtual Times in Parallel Discrete-Event
Simulations},
author={G. Korniss, M.A. Novotny, H. Guclu, Z. Toroczkai, and P.A. Rikvold},
journal={Science 299, 677 (2003)},
year={2003},
doi={10.1126/science.1079382},
archivePrefix={arXiv},
eprint={cond-mat/0302050},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.DC physics.comp-ph}
} | korniss2003suppressing |
arxiv-669229 | cond-mat/0302536 | Phase Diagram for the Constrained Integer Partitioning Problem | <|reference_start|>Phase Diagram for the Constrained Integer Partitioning Problem: We consider the problem of partitioning $n$ integers into two subsets of given cardinalities such that the discrepancy, the absolute value of the difference of their sums, is minimized. The integers are i.i.d. random variables chosen uniformly from the set $\{1,...,M\}$. We study how the typical behavior of the optimal partition depends on $n,M$ and the bias $s$, the difference between the cardinalities of the two subsets in the partition. In particular, we rigorously establish this typical behavior as a function of the two parameters $\kappa:=n^{-1}\log_2M$ and $b:=|s|/n$ by proving the existence of three distinct ``phases'' in the $\kappa b$-plane, characterized by the value of the discrepancy and the number of optimal solutions: a ``perfect phase'' with exponentially many optimal solutions with discrepancy 0 or 1; a ``hard phase'' with minimal discrepancy of order $Me^{-\Theta(n)}$; and a ``sorted phase'' with an unique optimal partition of order $Mn$, obtained by putting the $(s+n)/2$ smallest integers in one subset. Our phase diagram covers all but a relatively small region in the $\kappa b$-plane. We also show that the three phases can be alternatively characterized by the number of basis solutions of the associated linear programming problem, and by the fraction of these basis solutions whose $\pm 1$-valued components form optimal integer partitions of the subproblem with the corresponding weights. We show in particular that this fraction is one in the sorted phase, and exponentially small in both the perfect and hard phases, and strictly exponentially smaller in the hard phase than in the perfect phase. Open problems are discussed, and numerical experiments are presented.<|reference_end|> | arxiv | @article{borgs2003phase,
title={Phase Diagram for the Constrained Integer Partitioning Problem},
author={C. Borgs, J.T. Chayes, S. Mertens and B. Pittel},
journal={arXiv preprint arXiv:cond-mat/0302536},
year={2003},
archivePrefix={arXiv},
eprint={cond-mat/0302536},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC math.PR}
} | borgs2003phase |
arxiv-669230 | cond-mat/0303089 | Multiplicative point process as a model of trading activity | <|reference_start|>Multiplicative point process as a model of trading activity: Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spectral density S(f) scaling as a power of the frequency f. Furthermore, we analyze the relation between the power-law correlations and the origin of the power-law probability distribution of the signal intensity. We introduce a stochastic multiplicative model for the time intervals between point events and analyze the statistical properties of the signal analytically and numerically. Such model system exhibits power-law spectral density S(f)~1/f**beta for various values of beta, including beta=1/2, 1 and 3/2. Explicit expressions for the power spectra in the low frequency limit and for the distribution density of the interevent time are obtained. The counting statistics of the events is analyzed analytically and numerically, as well. The specific interest of our analysis is related with the financial markets, where long-range correlations of price fluctuations largely depend on the number of transactions. We analyze the spectral density and counting statistics of the number of transactions. The model reproduces spectral properties of the real markets and explains the mechanism of power-law distribution of trading activity. The study provides evidence that the statistical properties of the financial markets are enclosed in the statistics of the time interval between trades. A multiplicative point process serves as a consistent model generating this statistics.<|reference_end|> | arxiv | @article{gontis2003multiplicative,
title={Multiplicative point process as a model of trading activity},
author={Vygintas Gontis and Bronislovas Kaulakys},
journal={Gontis V., Kaulakys B., Physica A 343 (2004) 505-514},
year={2003},
doi={10.1016/j.physa.2004.05.080},
archivePrefix={arXiv},
eprint={cond-mat/0303089},
primaryClass={cond-mat.stat-mech cs.CE math.SP nlin.AO nlin.CD q-fin.TR}
} | gontis2003multiplicative |
arxiv-669231 | cond-mat/0304132 | Causalities of the Taiwan Stock Market | <|reference_start|>Causalities of the Taiwan Stock Market: Volatility, fitting with first order Landau expansion, stationarity, and causality of the Taiwan stock market (TAIEX) are investigated based on daily records. Instead of consensuses that consider stock market index change as a random time series we propose the market change as a dual time series consists of the index and the corresponding volume. Therefore, causalities between these two time series are investigated.<|reference_end|> | arxiv | @article{ting2003causalities,
title={Causalities of the Taiwan Stock Market},
author={Juhi-Lian Julian Ting},
journal={Physica A 324, 285-295 (2003)},
year={2003},
doi={10.1016/S0378-4371(02)01842-3},
number={almost Bali 2002, Physica A 2003},
archivePrefix={arXiv},
eprint={cond-mat/0304132},
primaryClass={cond-mat.stat-mech cs.CE q-fin.ST}
} | ting2003causalities |
arxiv-669232 | cond-mat/0305097 | Traveling Front Solutions to Directed Diffusion Limited Aggregation, Digital Search Trees and the Lempel-Ziv Data Compression Algorithm | <|reference_start|>Traveling Front Solutions to Directed Diffusion Limited Aggregation, Digital Search Trees and the Lempel-Ziv Data Compression Algorithm: We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion limited aggregation models on a Cayley tree. We point out that some aspects of these models are closely connected to two different problems in computer science, namely the digital search tree problem in data structures and the Lempel-Ziv algorithm for data compression. The statistics of the number of particles studied here is related to the statistics of height in digital search trees which, in turn, is related to the statistics of the length of the longest word formed by the Lempel-Ziv algorithm. Implications of our results to these computer science problems are pointed out.<|reference_end|> | arxiv | @article{majumdar2003traveling,
title={Traveling Front Solutions to Directed Diffusion Limited Aggregation,
Digital Search Trees and the Lempel-Ziv Data Compression Algorithm},
author={Satya N. Majumdar},
journal={Phys. Rev. E 68, 026103 (2003)},
year={2003},
doi={10.1103/PhysRevE.68.026103},
archivePrefix={arXiv},
eprint={cond-mat/0305097},
primaryClass={cond-mat.stat-mech cs.DS}
} | majumdar2003traveling |
arxiv-669233 | cond-mat/0305508 | Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other | <|reference_start|>Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other: A method of modeling data with gaps by a sequence of curves has been developed. The new method is a generalization of iterative construction of singular expansion of matrices with gaps. Under discussion are three versions of the method featuring clear physical interpretation: linear - modeling the data by a sequence of linear manifolds of small dimension; quasilinear - constructing "principal curves: (or "principal surfaces"), univalently projected on the linear principal components; essentially non-linear - based on constructing "principal curves": (principal strings and beams) employing the variation principle; the iteration implementation of this method is close to Kohonen self-organizing maps. The derived dependencies are extrapolated by Carleman's formulas. The method is interpreted as a construction of neural network conveyor designed to solve the following problems: to fill gaps in data; to repair data - to correct initial data values in such a way as to make the constructed models work best; to construct a calculator to fill gaps in the data line fed to the input.<|reference_end|> | arxiv | @article{gorban2003neural,
title={Neural network modeling of data with gaps: method of principal curves,
Carleman's formula, and other},
author={A. N.Gorban, A. A. Rossiev, D. C. Wunsch II},
journal={arXiv preprint arXiv:cond-mat/0305508},
year={2003},
archivePrefix={arXiv},
eprint={cond-mat/0305508},
primaryClass={cond-mat.dis-nn cs.NE physics.data-an}
} | gorban2003neural |
arxiv-669234 | cond-mat/0305527 | Back-propagation of accuracy | <|reference_start|>Back-propagation of accuracy: In this paper we solve the problem: how to determine maximal allowable errors, possible for signals and parameters of each element of a network proceeding from the condition that the vector of output signals of the network should be calculated with given accuracy? "Back-propagation of accuracy" is developed to solve this problem. The calculation of allowable errors for each element of network by back-propagation of accuracy is surprisingly similar to a back-propagation of error, because it is the backward signals motion, but at the same time it is very different because the new rules of signals transformation in the passing back through the elements are different. The method allows us to formulate the requirements to the accuracy of calculations and to the realization of technical devices, if the requirements to the accuracy of output signals of the network are known.<|reference_end|> | arxiv | @article{senashova2003back-propagation,
title={Back-propagation of accuracy},
author={M.Yu. Senashova, A.N. Gorban, D. C. Wunsch II},
journal={Proceedings of International Conference on Neural Networks
(ICNN'97), 1997, pp. 1998-2001 vol.3},
year={2003},
doi={10.1109/ICNN.1997.614206},
archivePrefix={arXiv},
eprint={cond-mat/0305527},
primaryClass={cond-mat.dis-nn cs.NA cs.NE math.NA}
} | senashova2003back-propagation |
arxiv-669235 | cond-mat/0305575 | Software systems as complex networks: structure, function, and evolvability of software collaboration graphs | <|reference_start|>Software systems as complex networks: structure, function, and evolvability of software collaboration graphs: Software systems emerge from mere keystrokes to form intricate functional networks connecting many collaborating modules, objects, classes, methods, and subroutines. Building on recent advances in the study of complex networks, I have examined software collaboration graphs contained within several open-source software systems, and have found them to reveal scale-free, small-world networks similar to those identified in other technological, sociological, and biological systems. I present several measures of these network topologies, and discuss their relationship to software engineering practices. I also present a simple model of software system evolution based on refactoring processes which captures some of the salient features of the observed systems. Some implications of object-oriented design for questions about network robustness, evolvability, degeneracy, and organization are discussed in the wake of these findings.<|reference_end|> | arxiv | @article{myers2003software,
title={Software systems as complex networks: structure, function, and
evolvability of software collaboration graphs},
author={C. R. Myers},
journal={Phys. Rev. E 68, 046116 (2003)},
year={2003},
doi={10.1103/PhysRevE.68.046116},
archivePrefix={arXiv},
eprint={cond-mat/0305575},
primaryClass={cond-mat.stat-mech cs.SE}
} | myers2003software |
arxiv-669236 | cond-mat/0305582 | On the Tomography of Networks and Multicast Trees | <|reference_start|>On the Tomography of Networks and Multicast Trees: In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific network node consists of two regimes. The first is characterized by rapid growth, and the second decays exponentially. We also show that the nodes degree distribution at each layer is a power law with an exponential cut-off. We obtain similar results for the layers surrounding the root of multicast trees cut from such networks, as well as the Internet. All of our results were obtained both analytically and on empirical Interenet data.<|reference_end|> | arxiv | @article{cohen2003on,
title={On the Tomography of Networks and Multicast Trees},
author={R. Cohen, D. Dolev, S. Havlin, T. Kalisky, O. Mokryn and Y. Shavitt},
journal={arXiv preprint arXiv:cond-mat/0305582},
year={2003},
doi={10.1103/PhysRevE.74.066108},
number={TR2002-49 HUJI (2002)},
archivePrefix={arXiv},
eprint={cond-mat/0305582},
primaryClass={cond-mat cond-mat.dis-nn cs.NI}
} | cohen2003on |
arxiv-669237 | cond-mat/0305681 | Seven clusters in genomic triplet distributions | <|reference_start|>Seven clusters in genomic triplet distributions: In several recent papers new gene-detection algorithms were proposed for detecting protein-coding regions without requiring learning dataset of already known genes. The fact that unsupervised gene-detection is possible closely connected to existence of a cluster structure in oligomer frequency distributions. In this paper we study cluster structure of several genomes in the space of their triplet frequencies, using pure data exploration strategy. Several complete genomic sequences were analyzed, using visualization of tables of triplet frequencies in a sliding window. The distribution of 64-dimensional vectors of triplet frequencies displays a well-detectable cluster structure. The structure was found to consist of seven clusters, corresponding to protein-coding information in three possible phases in one of the two complementary strands and in the non-coding regions with high accuracy (higher than 90% on the nucleotide level). Visualizing and understanding the structure allows to analyze effectively performance of different gene-prediction tools. Since the method does not require extraction of ORFs, it can be applied even for unassembled genomes. The information content of the triplet distributions and the validity of the mean-field models are analysed.<|reference_end|> | arxiv | @article{gorban2003seven,
title={Seven clusters in genomic triplet distributions},
author={A. N. Gorban, A. Yu. Zinovyev, T. G. Popova},
journal={In Silico Biology, 3 (2003), 0039, 471-482},
year={2003},
archivePrefix={arXiv},
eprint={cond-mat/0305681},
primaryClass={cond-mat.dis-nn cs.CV physics.bio-ph physics.data-an q-bio.GN}
} | gorban2003seven |
arxiv-669238 | cond-mat/0306222 | Update statistics in conservative parallel discrete event simulations of asynchronous systems | <|reference_start|>Update statistics in conservative parallel discrete event simulations of asynchronous systems: We model the performance of an ideal closed chain of L processing elements that work in parallel in an asynchronous manner. Their state updates follow a generic conservative algorithm. The conservative update rule determines the growth of a virtual time surface. The physics of this growth is reflected in the utilization (the fraction of working processors) and in the interface width. We show that it is possible to nake an explicit connection between the utilization and the macroscopic structure of the virtual time interface. We exploit this connection to derive the theoretical probability distribution of updates in the system within an approximate model. It follows that the theoretical lower bound for the computational speed-up is s=(L+1)/4 for L>3. Our approach uses simple statistics to count distinct surface configuration classes consistent with the model growth rule. It enables one to compute analytically microscopic properties of an interface, which are unavailable by continuum methods.<|reference_end|> | arxiv | @article{kolakowska2003update,
title={Update statistics in conservative parallel discrete event simulations of
asynchronous systems},
author={A. Kolakowska, M. A. Novotny and Per Arne Rikvold},
journal={Phys. Rev. E 68, 046705 (2003)},
year={2003},
doi={10.1103/PhysRevE.68.046705},
archivePrefix={arXiv},
eprint={cond-mat/0306222},
primaryClass={cond-mat cs.DC}
} | kolakowska2003update |
arxiv-669239 | cond-mat/0306509 | Bug propagation and debugging in asymmetric software structures | <|reference_start|>Bug propagation and debugging in asymmetric software structures: Software dependence networks are shown to be scale-free and asymmetric. We then study how software components are affected by the failure of one of them, and the inverse problem of locating the faulty component. Software at all levels is fragile with respect to the failure of a random single component. Locating a faulty component is easy if the failures only affect their nearest neighbors, while it is hard if the failures propagate further.<|reference_end|> | arxiv | @article{challet2003bug,
title={Bug propagation and debugging in asymmetric software structures},
author={Damien Challet and Andrea Lombardoni},
journal={arXiv preprint arXiv:cond-mat/0306509},
year={2003},
doi={10.1103/PhysRevE.70.046109},
archivePrefix={arXiv},
eprint={cond-mat/0306509},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.SE}
} | challet2003bug |
arxiv-669240 | cond-mat/0306511 | Closed source versus open source in a model of software bug dynamics | <|reference_start|>Closed source versus open source in a model of software bug dynamics: We introduce a simple microscopic description of software bug dynamics where users, programmers and a maintainer interact through a given program, with a particular emphasis on bug creation, detection and fixing. When the program is written from scratch, the first phase of development is characterized by a fast decline of the number of bugs, followed by a slow phase where most bugs have been fixed, hence, are hard to find. Releasing immediately bug fixes speeds up the debugging process, which substantiates bazaar open-source methodology. We provide a mathematical analysis that supports our numerical simulations. Finally, we apply our model to Linux history and determine the existence of a lower bound to the quality of its programmers.<|reference_end|> | arxiv | @article{challet2003closed,
title={Closed source versus open source in a model of software bug dynamics},
author={Damien Challet and Yann Le Du},
journal={arXiv preprint arXiv:cond-mat/0306511},
year={2003},
archivePrefix={arXiv},
eprint={cond-mat/0306511},
primaryClass={cond-mat.stat-mech cs.SE}
} | challet2003closed |
arxiv-669241 | cond-mat/0306609 | Signatures of small-world and scale-free properties in large computer programs | <|reference_start|>Signatures of small-world and scale-free properties in large computer programs: A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the ``information flow'' within the program. We show that, (1) due to its growth in time this network displays a scale-free feature in that the probability of the number of links at a node obeys a power-law distribution, and (2) as a result of performance optimization of the program the network has a small-world structure. We believe that these features are generic for large computer programs. Our work extends the previous studies on growing networks, which have mostly been for physical networks, to the domain of computer software.<|reference_end|> | arxiv | @article{de moura2003signatures,
title={Signatures of small-world and scale-free properties in large computer
programs},
author={Alessandro P. S. de Moura, Ying-Cheng Lai, and Adilson E. Motter},
journal={Phys. Rev. E 68, 017102 (2003)},
year={2003},
doi={10.1103/PhysRevE.68.017102},
archivePrefix={arXiv},
eprint={cond-mat/0306609},
primaryClass={cond-mat.dis-nn cs.GL}
} | de moura2003signatures |
arxiv-669242 | cond-mat/0307058 | Finite size scaling approach to dynamic storage allocation problem | <|reference_start|>Finite size scaling approach to dynamic storage allocation problem: It is demonstrated how dynamic storage allocation algorithms can be analyzed in terms of finite size scaling. The method is illustrated in the three simple cases of the it first-fit, next-fit and it best-fit algorithms, and the system works at full capacity. The analysis is done from two different points of view - running speed and employed memory. In both cases, and for all algorithms, it is shown that a simple scaling function exists and the relevant exponents are calculated. The method can be applied on similar problems as well.<|reference_end|> | arxiv | @article{seyed-allaei2003finite,
title={Finite size scaling approach to dynamic storage allocation problem},
author={Hamed Seyed-allaei},
journal={Physica A: Statistical Mechanics and its Applications, Volume 327,
Issues 3-4, 15 September 2003, Pages 563-569},
year={2003},
doi={10.1016/S0378-4371(03)00509-0},
archivePrefix={arXiv},
eprint={cond-mat/0307058},
primaryClass={cond-mat.stat-mech cs.DS}
} | seyed-allaei2003finite |
arxiv-669243 | cond-mat/0307083 | Generation of Explicit Knowledge from Empirical Data through Pruning of Trainable Neural Networks | <|reference_start|>Generation of Explicit Knowledge from Empirical Data through Pruning of Trainable Neural Networks: This paper presents a generalized technology of extraction of explicit knowledge from data. The main ideas are 1) maximal reduction of network complexity (not only removal of neurons or synapses, but removal all the unnecessary elements and signals and reduction of the complexity of elements), 2) using of adjustable and flexible pruning process (the pruning sequence shouldn't be predetermined - the user should have a possibility to prune network on his own way in order to achieve a desired network structure for the purpose of extraction of rules of desired type and form), and 3) extraction of rules not in predetermined but any desired form. Some considerations and notes about network architecture and training process and applicability of currently developed pruning techniques and rule extraction algorithms are discussed. This technology, being developed by us for more than 10 years, allowed us to create dozens of knowledge-based expert systems. In this paper we present a generalized three-step technology of extraction of explicit knowledge from empirical data.<|reference_end|> | arxiv | @article{gorban2003generation,
title={Generation of Explicit Knowledge from Empirical Data through Pruning of
Trainable Neural Networks},
author={A. N. Gorban, Eu. M. Mirkes, V. G. Tsaregorodtsev},
journal={arXiv preprint arXiv:cond-mat/0307083},
year={2003},
archivePrefix={arXiv},
eprint={cond-mat/0307083},
primaryClass={cond-mat cs.NE physics.data-an}
} | gorban2003generation |
arxiv-669244 | cond-mat/0307201 | Punctuated Equilibrium in Software Evolution | <|reference_start|>Punctuated Equilibrium in Software Evolution: The approach based on paradigm of self-organized criticality proposed for experimental investigation and theoretical modelling of software evolution. The dynamics of modifications studied for three free, open source programs Mozilla, Free-BSD and Emacs using the data from version control systems. Scaling laws typical for the self-organization criticality found. The model of software evolution presenting the natural selection principle is proposed. The results of numerical and analytical investigation of the model are presented. They are in a good agreement with the data collected for the real-world software.<|reference_end|> | arxiv | @article{gorshenev2003punctuated,
title={Punctuated Equilibrium in Software Evolution},
author={A. A. Gorshenev (1), Yu. M. Pis'mak (1) ((1) Department of Theoretical
Physics State University of Saint-Petersburg, Saint-Petersburg, Russia)},
journal={arXiv preprint arXiv:cond-mat/0307201},
year={2003},
doi={10.1103/PhysRevE.70.067103},
archivePrefix={arXiv},
eprint={cond-mat/0307201},
primaryClass={cond-mat.stat-mech cs.SE}
} | gorshenev2003punctuated |
arxiv-669245 | cond-mat/0307630 | Product Distribution Field Theory | <|reference_start|>Product Distribution Field Theory: This paper presents a novel way to approximate a distribution governing a system of coupled particles with a product of independent distributions. The approach is an extension of mean field theory that allows the independent distributions to live in a different space from the system, and thereby capture statistical dependencies in that system. It also allows different Hamiltonians for each independent distribution, to facilitate Monte Carlo estimation of those distributions. The approach leads to a novel energy-minimization algorithm in which each coordinate Monte Carlo estimates an associated spectrum, and then independently sets its state by sampling a Boltzmann distribution across that spectrum. It can also be used for high-dimensional numerical integration, (constrained) combinatorial optimization, and adaptive distributed control. This approach also provides a simple, physics-based derivation of the powerful approximate energy-minimization algorithms semi-formally derived in \cite{wowh00, wotu02c, wolp03a}. In addition it suggests many improvements to those algorithms, and motivates a new (bounded rationality) game theory equilibrium concept.<|reference_end|> | arxiv | @article{wolpert2003product,
title={Product Distribution Field Theory},
author={David H. Wolpert},
journal={arXiv preprint arXiv:cond-mat/0307630},
year={2003},
archivePrefix={arXiv},
eprint={cond-mat/0307630},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.MA nlin.AO}
} | wolpert2003product |
arxiv-669246 | cond-mat/0308147 | Instability of one-step replica-symmetry-broken phase in satisfiability problems | <|reference_start|>Instability of one-step replica-symmetry-broken phase in satisfiability problems: We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two random combinatorial problems: k-XORSAT and k-SAT. We present a general method for establishing the stability of these solutions with respect to further steps of replica-symmetry breaking. Our approach extends the ideas of [A.Montanari and F. Ricci-Tersenghi, Eur.Phys.J. B 33, 339 (2003)] to more general combinatorial problems. It turns out that 1RSB is always unstable at sufficiently small clauses density alpha or high energy. In particular, the recent 1RSB solution to 3-SAT is unstable at zero energy for alpha< alpha_m, with alpha_m\approx 4.153. On the other hand, the SAT-UNSAT phase transition seems to be correctly described within 1RSB.<|reference_end|> | arxiv | @article{montanari2003instability,
title={Instability of one-step replica-symmetry-broken phase in satisfiability
problems},
author={Andrea Montanari, Giorgio Parisi and Federico Ricci-Tersenghi},
journal={J. Phys. A 37, 2073 (2004)},
year={2003},
doi={10.1088/0305-4470/37/6/008},
archivePrefix={arXiv},
eprint={cond-mat/0308147},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC}
} | montanari2003instability |
arxiv-669247 | cond-mat/0308288 | Compact Routing on Internet-Like Graphs | <|reference_start|>Compact Routing on Internet-Like Graphs: The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal local memory upper bound. Using both direct analysis and simulation, we calculate the stretch distribution of this routing scheme on random graphs with power-law node degree distributions, $P_k \sim k^{-\gamma}$. We find that the average stretch is very low and virtually independent of $\gamma$. In particular, for the Internet interdomain graph, $\gamma \sim 2.1$, the average stretch is around 1.1, with up to 70% of paths being shortest. As the network grows, the average stretch slowly decreases. The routing table is very small, too. It is well below its upper bounds, and its size is around 50 records for $10^4$-node networks. Furthermore, we find that both the average shortest path length (i.e. distance) $\bar{d}$ and width of the distance distribution $\sigma$ observed in the real Internet inter-AS graph have values that are very close to the minimums of the average stretch in the $\bar{d}$- and $\sigma$-directions. This leads us to the discovery of a unique critical quasi-stationary point of the average TZ stretch as a function of $\bar{d}$ and $\sigma$. The Internet distance distribution is located in a close neighborhood of this point. This observation suggests the analytical structure of the average stretch function may be an indirect indicator of some hidden optimization criteria influencing the Internet's interdomain topology evolution.<|reference_end|> | arxiv | @article{krioukov2003compact,
title={Compact Routing on Internet-Like Graphs},
author={Dmitri Krioukov, Kevin Fall, and Xiaowei Yang},
journal={INFOCOM 2004},
year={2003},
doi={10.1109/INFCOM.2004.1354495},
number={IRB-TR-03-10},
archivePrefix={arXiv},
eprint={cond-mat/0308288},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.NI}
} | krioukov2003compact |
arxiv-669248 | cond-mat/0310227 | Random k-SAT: Two Moments Suffice to Cross a Sharp Threshold | <|reference_start|>Random k-SAT: Two Moments Suffice to Cross a Sharp Threshold: Many NP-complete constraint satisfaction problems appear to undergo a "phase transition'' from solubility to insolubility when the constraint density passes through a critical threshold. In all such cases it is easy to derive upper bounds on the location of the threshold by showing that above a certain density the first moment (expectation) of the number of solutions tends to zero. We show that in the case of certain symmetric constraints, considering the second moment of the number of solutions yields nearly matching lower bounds for the location of the threshold. Specifically, we prove that the threshold for both random hypergraph 2-colorability (Property B) and random Not-All-Equal k-SAT is 2^{k-1} ln 2 -O(1). As a corollary, we establish that the threshold for random k-SAT is of order Theta(2^k), resolving a long-standing open problem.<|reference_end|> | arxiv | @article{achlioptas2003random,
title={Random k-SAT: Two Moments Suffice to Cross a Sharp Threshold},
author={Dimitris Achlioptas and Cristopher Moore},
journal={arXiv preprint arXiv:cond-mat/0310227},
year={2003},
archivePrefix={arXiv},
eprint={cond-mat/0310227},
primaryClass={cond-mat.stat-mech cs.CC math.CO math.PR}
} | achlioptas2003random |
arxiv-669249 | cond-mat/0310600 | Finding Communities in Linear Time: A Physics Approach | <|reference_start|>Finding Communities in Linear Time: A Physics Approach: We present a method that allows for the discovery of communities within graphs of arbitrary size in times that scale linearly with their size. This method avoids edge cutting and is based on notions of voltage drops across networks that are both intuitive and easy to solve regardless of the complexity of the graph involved. We additionally show how this algorithm allows for the swift discovery of the community surrounding a given node without having to extract all the communities out of a graph.<|reference_end|> | arxiv | @article{wu2003finding,
title={Finding Communities in Linear Time: A Physics Approach},
author={Fang Wu and Bernardo A. Huberman},
journal={arXiv preprint arXiv:cond-mat/0310600},
year={2003},
doi={10.1140/epjb/e2004-00125-x},
archivePrefix={arXiv},
eprint={cond-mat/0310600},
primaryClass={cond-mat.stat-mech cs.DS}
} | wu2003finding |
arxiv-669250 | cond-mat/0311552 | Extremal Properties of Random Structures | <|reference_start|>Extremal Properties of Random Structures: The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety of unusual time dependences and system-size dependences for basic extremal properties are obtained.<|reference_end|> | arxiv | @article{ben-naim2003extremal,
title={Extremal Properties of Random Structures},
author={E. Ben-Naim, P. L. Krapivsky, S. Redner},
journal={Lecture Notes in Physics 650, 211 (2004)},
year={2003},
doi={10.1007/b98716},
archivePrefix={arXiv},
eprint={cond-mat/0311552},
primaryClass={cond-mat.stat-mech cs.DS math.PR}
} | ben-naim2003extremal |
arxiv-669251 | cond-mat/0312019 | A theoretical investigation of ferromagnetic tunnel junctions with 4-valued conductances | <|reference_start|>A theoretical investigation of ferromagnetic tunnel junctions with 4-valued conductances: In considering a novel function in ferromagnetic tunnel junctions consisting of ferromagnet(FM)/barrier/FM junctions, we theoretically investigate multiple valued (or multi-level) cell property, which is in principle realized by sensing conductances of four states recorded with magnetization configurations of two FMs; that is, (up,up), (up,down), (down,up), (down,down). To obtain such 4-valued conductances, we propose FM1/spin-polarized barrier/FM2 junctions, where the FM1 and FM2 are different ferromagnets, and the barrier has spin dependence. The proposed idea is applied to the case of the barrier having localized spins. Assuming that all the localized spins are pinned parallel to magnetization axes of the FM1 and FM2, 4-valued conductances are explicitly obtained for the case of many localized spins. Furthermore, objectives for an ideal spin-polarized barrier are discussed.<|reference_end|> | arxiv | @article{kokado2003a,
title={A theoretical investigation of ferromagnetic tunnel junctions with
4-valued conductances},
author={Satoshi Kokado, Kikuo Harigaya},
journal={J. Phys.: Condens. Matter 15 (2003) 8797-8804},
year={2003},
doi={10.1088/0953-8984/15/50/012},
archivePrefix={arXiv},
eprint={cond-mat/0312019},
primaryClass={cond-mat.mes-hall cond-mat.mtrl-sci cs.CE physics.ins-det quant-ph}
} | kokado2003a |
arxiv-669252 | cond-mat/0312483 | Survey Propagation as local equilibrium equations | <|reference_start|>Survey Propagation as local equilibrium equations: It has been shown experimentally that a decimation algorithm based on Survey Propagation (SP) equations allows to solve efficiently some combinatorial problems over random graphs. We show that these equations can be derived as sum-product equations for the computation of marginals in an extended space where the variables are allowed to take an additional value -- $*$ -- when they are not forced by the combinatorial constraints. An appropriate ``local equilibrium condition'' cost/energy function is introduced and its entropy is shown to coincide with the expected logarithm of the number of clusters of solutions as computed by SP. These results may help to clarify the geometrical notion of clusters assumed by SP for the random K-SAT or random graph coloring (where it is conjectured to be exact) and helps to explain which kind of clustering operation or approximation is enforced in general/small sized models in which it is known to be inexact.<|reference_end|> | arxiv | @article{braunstein2003survey,
title={Survey Propagation as local equilibrium equations},
author={A. Braunstein, R. Zecchina},
journal={J. Stat. Mech., P06007 (2004)},
year={2003},
doi={10.1088/1742-5468/2004/06/P06007},
archivePrefix={arXiv},
eprint={cond-mat/0312483},
primaryClass={cond-mat.dis-nn cs.CC}
} | braunstein2003survey |
arxiv-669253 | cond-mat/0312603 | Complex Grid Computing | <|reference_start|>Complex Grid Computing: This article investigates the performance of grid computing systems whose interconnections are given by random and scale-free complex network models. Regular networks, which are common in parallel computing architectures, are also used as a standard for comparison. The processing load is assigned to the processing nodes on demand, and the efficiency of the overall computing is quantified in terms of the respective speed-ups. It is found that random networks allow higher computing efficiency than their scale-free counterparts as a consequence of the smaller number of isolated clusters implied by the former model. At the same time, for fixed cluster sizes, the scale free model tend to provide slightly better efficiency. Two modifications of the random and scale free paradigms, where new connections tend to favor more recently added nodes, are proposed and shown to be more effective for grid computing than the standard models. A well-defined correlation is observed between the topological properties of the network and their respective computing efficiency.<|reference_end|> | arxiv | @article{costa2003complex,
title={Complex Grid Computing},
author={Luciano da Fontoura Costa, Gonzalo Travieso and Carlos Antonio
Ruggiero},
journal={Eur. Phys. J. B, 44 (2005) p.119},
year={2003},
doi={10.1140/epjb/e2005-00107-6},
archivePrefix={arXiv},
eprint={cond-mat/0312603},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.DC}
} | costa2003complex |
arxiv-669254 | cond-mat/0401065 | Exploration of scale-free networks | <|reference_start|>Exploration of scale-free networks: The increased availability of data on real networks has favoured an explosion of activity in the elaboration of models able to reproduce both qualitatively and quantitatively the measured properties. What has been less explored is the reliability of the data, and whether the measurement technique biases them. Here we show that tree-like explorations (similar in principle to traceroute) can indeed change the measured exponents of a scale-free network.<|reference_end|> | arxiv | @article{petermann2004exploration,
title={Exploration of scale-free networks},
author={Thomas Petermann and Paolo De Los Rios},
journal={Eur. Phys. J. B 38, 201 (2004)},
year={2004},
doi={10.1140/epjb/e2004-00021-5},
archivePrefix={arXiv},
eprint={cond-mat/0401065},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.NI}
} | petermann2004exploration |
arxiv-669255 | cond-mat/0401191 | Chaos and Annealing in Social networks | <|reference_start|>Chaos and Annealing in Social networks: In this work we compare social clusters with spin clusters and compare different properties. We also try to compare phase changes in market and labor stratification with phase changes of spin clusters. Then we compare the requisites for redrawing the boundaries of social clusters with respect to energy minimization and efficiency. We finally do a simulation experiment and show that by choosing suitable link matrices for agents and attributes of the same and of different agents it is possible to have at the same time behavior similar to chaos or punctuated equilibrium in some attributes or fairly regular oscillations of preferences for other attributes, using greatest utility or efficiency as a criterion for change in conflicting social networks with different agents having different preferences with respect to the attributes in the agent himself or with similar attributes in other agents.<|reference_end|> | arxiv | @article{shafee2004chaos,
title={Chaos and Annealing in Social networks},
author={Fariel Shafee},
journal={arXiv preprint arXiv:cond-mat/0401191},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0401191},
primaryClass={cond-mat.dis-nn cs.GT nlin.AO}
} | shafee2004chaos |
arxiv-669256 | cond-mat/0401229 | On the Evolution of Time Horizons in Parallel and Grid Simulations | <|reference_start|>On the Evolution of Time Horizons in Parallel and Grid Simulations: We analyze the evolution of the local simulation times (LST) in Parallel Discrete Event Simulations. The new ingredients introduced are i) we associate the LST with the nodes and not with the processing elements, and 2) we propose to minimize the exchange of information between different processing elements by freezing the LST on the boundaries between processing elements for some time of processing and then releasing them by a wide-stream memory exchange between processing elements. Highlights of our approach are i) it keeps the highest level of processor time utilization during the algorithm evolution, ii) it takes a reasonable time for the memory exchange excluding the time-consuming and complicated process of message exchange between processors, and iii) the communication between processors is decoupled from the calculations performed on a processor. The effectiveness of our algorithm grows with the number of nodes (or threads). This algorithm should be applicable for any parallel simulation with short-range interactions, including parallel or grid simulations of partial differential equations.<|reference_end|> | arxiv | @article{shchur2004on,
title={On the Evolution of Time Horizons in Parallel and Grid Simulations},
author={L.N. Shchur, M.A. Novotny},
journal={Phys. Rev. E 70 (2004) 026703},
year={2004},
doi={10.1103/PhysRevE.70.026703},
archivePrefix={arXiv},
eprint={cond-mat/0401229},
primaryClass={cond-mat.stat-mech cs.DC}
} | shchur2004on |
arxiv-669257 | cond-mat/0402143 | Personal Email Networks: An Effective Anti-Spam Tool | <|reference_start|>Personal Email Networks: An Effective Anti-Spam Tool: We provide an automated graph theoretic method for identifying individual users' trusted networks of friends in cyberspace. We routinely use our social networks to judge the trustworthiness of outsiders, i.e., to decide where to buy our next car, or to find a good mechanic for it. In this work, we show that an email user may similarly use his email network, constructed solely from sender and recipient information available in the email headers, to distinguish between unsolicited commercial emails, commonly called "spam", and emails associated with his circles of friends. We exploit the properties of social networks to construct an automated anti-spam tool which processes an individual user's personal email network to simultaneously identify the user's core trusted networks of friends, as well as subnetworks generated by spams. In our empirical studies of individual mail boxes, our algorithm classified approximately 53% of all emails as spam or non-spam, with 100% accuracy. Some of the emails are left unclassified by this network analysis tool. However, one can exploit two of the following useful features. First, it requires no user intervention or supervised training; second, it results in no false negatives i.e., spam being misclassified as non-spam, or vice versa. We demonstrate that these two features suggest that our algorithm may be used as a platform for a comprehensive solution to the spam problem when used in concert with more sophisticated, but more cumbersome, content-based filters.<|reference_end|> | arxiv | @article{boykin2004personal,
title={Personal Email Networks: An Effective Anti-Spam Tool},
author={P. Oscar Boykin and Vwani Roychowdhury},
journal={IEEE Computer, Vol. 38, No. 4, pages 61-68, April 2005},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0402143},
primaryClass={cond-mat.dis-nn cs.NI}
} | boykin2004personal |
arxiv-669258 | cond-mat/0402268 | Competition-Induced Preferential Attachment | <|reference_start|>Competition-Induced Preferential Attachment: Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an explanation of how it can arise from a more basic underlying mechanism of competition between opposing forces. We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics. This family admits an equivalent description as a graph process with no reference to the underlying geometry. Moreover, the resulting graph process is shown to be preferential attachment with an upper cutoff. We rigorously determine the degree distribution for the family of random graph models, showing that it obeys a power law up to a finite threshold and decays exponentially above this threshold. We also introduce and rigorously analyze a generalized version of our graph process, with two natural parameters, one corresponding to the cutoff and the other a ``fertility'' parameter. Limiting cases of this process include the standard Barabasi-Albert preferential attachment model and the uniform attachment model. In the general case, we prove that the process has a power law degree distribution up to a cutoff, and establish monotonicity of the power as a function of the two parameters.<|reference_end|> | arxiv | @article{berger2004competition-induced,
title={Competition-Induced Preferential Attachment},
author={N. Berger (1), C. Borgs (1), J. T. Chayes (1), R. M. D'Souza (1) and
R. D. Kleinberg (2) ((1) Microsoft Research, Redmond WA, USA, (2) M.I.T.
CSAIL, Cambridge MA, USA.)},
journal={Proceedings of the 31st International Colloquium on Automata,
Languages and Programming, 208-221 (2004).},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0402268},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.NI}
} | berger2004competition-induced |
arxiv-669259 | cond-mat/0402508 | Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics | <|reference_start|>Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics: A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principled formulation of bounded rationality and a set of new types of mean field theory in statistical physics. It also shows that those topics are fundamentally one and the same.<|reference_end|> | arxiv | @article{wolpert2004information,
title={Information Theory - The Bridge Connecting Bounded Rational Game Theory
and Statistical Physics},
author={David H. Wolpert},
journal={arXiv preprint arXiv:cond-mat/0402508},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0402508},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.GT cs.MA nlin.AO}
} | wolpert2004information |
arxiv-669260 | cond-mat/0402581 | Dictionary based methods for information extraction | <|reference_start|>Dictionary based methods for information extraction: In this paper we present a general method for information extraction that exploits the features of data compression techniques. We first define and focus our attention on the so-called "dictionary" of a sequence. Dictionaries are intrinsically interesting and a study of their features can be of great usefulness to investigate the properties of the sequences they have been extracted from (e.g. DNA strings). We then describe a procedure of string comparison between dictionary-created sequences (or "artificial texts") that gives very good results in several contexts. We finally present some results on self-consistent classification problems.<|reference_end|> | arxiv | @article{baronchelli2004dictionary,
title={Dictionary based methods for information extraction},
author={A. Baronchelli, E. Caglioti, V. Loreto, E. Pizzi},
journal={Physica A - Vol 342/1-2 pp 294-300 (2004)},
year={2004},
doi={10.1016/j.physa.2004.01.072},
archivePrefix={arXiv},
eprint={cond-mat/0402581},
primaryClass={cond-mat.stat-mech cond-mat.other cs.IR q-bio.GN q-bio.OT}
} | baronchelli2004dictionary |
arxiv-669261 | cond-mat/0403233 | Artificial Sequences and Complexity Measures | <|reference_start|>Artificial Sequences and Complexity Measures: In this paper we exploit concepts of information theory to address the fundamental problem of identifying and defining the most suitable tools to extract, in a automatic and agnostic way, information from a generic string of characters. We introduce in particular a class of methods which use in a crucial way data compression techniques in order to define a measure of remoteness and distance between pairs of sequences of characters (e.g. texts) based on their relative information content. We also discuss in detail how specific features of data compression techniques could be used to introduce the notion of dictionary of a given sequence and of Artificial Text and we show how these new tools can be used for information extraction purposes. We point out the versatility and generality of our method that applies to any kind of corpora of character strings independently of the type of coding behind them. We consider as a case study linguistic motivated problems and we present results for automatic language recognition, authorship attribution and self consistent-classification.<|reference_end|> | arxiv | @article{baronchelli2004artificial,
title={Artificial Sequences and Complexity Measures},
author={Andrea Baronchelli, Emanuele Caglioti, Vittorio Loreto},
journal={J. Stat. Mech., P04002 (2005)},
year={2004},
doi={10.1088/1742-5468/2005/04/P04002},
archivePrefix={arXiv},
eprint={cond-mat/0403233},
primaryClass={cond-mat.stat-mech cs.CL cs.IR cs.IT math.IT}
} | baronchelli2004artificial |
arxiv-669262 | cond-mat/0403341 | Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition | <|reference_start|>Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition: We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early non-scaling phase in the interface evolution. The length of this initial phase is a non-universal parameter, but its presence is universal. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.<|reference_end|> | arxiv | @article{kolakowska2004roughening,
title={Roughening of the (1+1) interfaces in two-component surface growth with
an admixture of random deposition},
author={A. Kolakowska, M. A. Novotny, P. S. Verma},
journal={Phys. Rev. E, Vol.70, 051602 (2004)},
year={2004},
doi={10.1103/PhysRevE.70.051602},
archivePrefix={arXiv},
eprint={cond-mat/0403341},
primaryClass={cond-mat.mtrl-sci cs.DC cs.OH physics.comp-ph}
} | kolakowska2004roughening |
arxiv-669263 | cond-mat/0403453 | Unicyclic Components in Random Graphs | <|reference_start|>Unicyclic Components in Random Graphs: The distribution of unicyclic components in a random graph is obtained analytically. The number of unicyclic components of a given size approaches a self-similar form in the vicinity of the gelation transition. At the gelation point, this distribution decays algebraically, U_k ~ 1/(4k) for k>>1. As a result, the total number of unicyclic components grows logarithmically with the system size.<|reference_end|> | arxiv | @article{ben-naim2004unicyclic,
title={Unicyclic Components in Random Graphs},
author={E. Ben-Naim, P.L. Krapivsky},
journal={J. Phys. A 37, L189 (2004)},
year={2004},
doi={10.1088/0305-4470/37/18/L01},
archivePrefix={arXiv},
eprint={cond-mat/0403453},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.DS math.PR}
} | ben-naim2004unicyclic |
arxiv-669264 | cond-mat/0403725 | Threshold values, stability analysis and high-q asymptotics for the coloring problem on random graphs | <|reference_start|>Threshold values, stability analysis and high-q asymptotics for the coloring problem on random graphs: We consider the problem of coloring Erdos-Renyi and regular random graphs of finite connectivity using q colors. It has been studied so far using the cavity approach within the so-called one-step replica symmetry breaking (1RSB) ansatz. We derive a general criterion for the validity of this ansatz and, applying it to the ground state, we provide evidence that the 1RSB solution gives exact threshold values c_q for the q-COL/UNCOL phase transition. We also study the asymptotic thresholds for q >> 1 finding c_q = 2qlog(q)-log(q)-1+o(1) in perfect agreement with rigorous mathematical bounds, as well as the nature of excited states, and give a global phase diagram of the problem.<|reference_end|> | arxiv | @article{krzakala2004threshold,
title={Threshold values, stability analysis and high-q asymptotics for the
coloring problem on random graphs},
author={Florent Krzakala, Andrea Pagnani and Martin Weigt},
journal={Phys. Rev. E 70, 046705 (2004)},
year={2004},
doi={10.1103/PhysRevE.70.046705},
archivePrefix={arXiv},
eprint={cond-mat/0403725},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC}
} | krzakala2004threshold |
arxiv-669265 | cond-mat/0404424 | Travelling Salesman Problem with a Center | <|reference_start|>Travelling Salesman Problem with a Center: We study a travelling salesman problem where the path is optimized with a cost function that includes its length $L$ as well as a certain measure $C$ of its distance from the geometrical center of the graph. Using simulated annealing (SA) we show that such a problem has a transition point that separates two phases differing in the scaling behaviour of $L$ and $C$, in efficiency of SA, and in the shape of minimal paths.<|reference_end|> | arxiv | @article{lipowski2004travelling,
title={Travelling Salesman Problem with a Center},
author={Adam Lipowski and Dorota Lipowska},
journal={Phys. Rev. E 71, 067701 (2005)},
year={2004},
doi={10.1103/PhysRevE.71.067701},
archivePrefix={arXiv},
eprint={cond-mat/0404424},
primaryClass={cond-mat.stat-mech cs.CC}
} | lipowski2004travelling |
arxiv-669266 | cond-mat/0404593 | The shortest path to complex networks | <|reference_start|>The shortest path to complex networks: 1. The birth of network science. 2. What are random networks? 3. Adjacency matrix. 4. Degree distribution. 5. What are simple networks? Classical random graphs. 6. Birth of the giant component. 7. Topology of the Web. 8.Uncorrelated networks. 9. What are small worlds? 10. Real networks are mesoscopic objects. 11. What are complex networks? 12. The configuration model. 13. The absence of degree--degree correlations. 14.Networks with correlated degrees.15.Clustering. 16. What are small-world networks? 17. `Small worlds' is not the same as `small-world networks'. 18. Fat-tailed degree distributions. 19.Reasons for the fat-tailed degree distributions. 20. Preferential linking. 21. Condensation of edges. 22. Cut-offs of degree distributions. 23. Reasons for correlations in networks. 24. Classical random graphs cannot be used for comparison with real networks. 25. How to measure degree--degree correlations. 26. Assortative and disassortative mixing. 27. Disassortative mixing does not mean that vertices of high degrees rarely connect to each other. 28. Reciprocal links in directed nets. 29. Ultra-small-world effect. 30. Tree ansatz. 31.Ultraresilience against random failures. 32. When correlated nets are ultraresilient. 33. Vulnerability of complex networks. 34. The absence of an epidemic threshold. 35. Search based on local information. 36.Ultraresilience disappears in finite nets. 37.Critical behavior of cooperative models on networks. 38. Berezinskii-Kosterlitz-Thouless phase transitions in networks. 39.Cascading failures. 40.Cliques & communities. 41. Betweenness. 42.Extracting communities. 43. Optimal paths. 44.Distributions of the shortest-path length & of the loop's length are narrow. 45. Diffusion on networks. 46. What is modularity? 47.Hierarchical organization of networks. 48. Convincing modelling of real-world networks:Is it possible? 49. The small Web..<|reference_end|> | arxiv | @article{dorogovtsev2004the,
title={The shortest path to complex networks},
author={S.N. Dorogovtsev, J.F.F. Mendes},
journal={arXiv preprint arXiv:cond-mat/0404593},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0404593},
primaryClass={cond-mat.stat-mech cs.NI nlin.AO q-bio.MN}
} | dorogovtsev2004the |
arxiv-669267 | cond-mat/0405319 | Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class | <|reference_start|>Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class: The probability P(alpha, N) that search algorithms for random Satisfiability problems successfully find a solution is studied as a function of the ratio alpha of constraints per variable and the number N of variables. P is shown to be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and exponentially small in N above. The critical behaviour is universal for all algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon) alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to the critical behaviour of random graphs, and the scaling function Phi is exactly calculated through a mapping onto a diffusion-and-death problem.<|reference_end|> | arxiv | @article{deroulers2004critical,
title={Critical behaviour of combinatorial search algorithms, and the
unitary-propagation universality class},
author={Christophe Deroulers (LPTENS), R'emi Monasson (LPTENS)},
journal={Europhysics Letters 68 (2004) 153-159},
year={2004},
doi={10.1209/epl/i2004-10177-6},
number={preprint LPTENS 04/25},
archivePrefix={arXiv},
eprint={cond-mat/0405319},
primaryClass={cond-mat.stat-mech cs.CC}
} | deroulers2004critical |
arxiv-669268 | cond-mat/0406152 | Scalable Percolation Search in Power Law Networks | <|reference_start|>Scalable Percolation Search in Power Law Networks: We introduce a scalable searching algorithm for finding nodes and contents in random networks with Power-Law (PL) and heavy-tailed degree distributions. The network is searched using a probabilistic broadcast algorithm, where a query message is relayed on each edge with probability just above the bond percolation threshold of the network. We show that if each node caches its directory via a short random walk, then the total number of {\em accessible contents exhibits a first-order phase transition}, ensuring very high hit rates just above the percolation threshold. In any random PL network of size, $N$, and exponent, $2 \leq \tau < 3$, the total traffic per query scales sub-linearly, while the search time scales as $O(\log N)$. In a PL network with exponent, $\tau \approx 2$, {\em any content or node} can be located in the network with {\em probability approaching one} in time $O(\log N)$, while generating traffic that scales as $O(\log^2 N)$, if the maximum degree, $k_{max}$, is unconstrained, and as $O(N^{{1/2}+\epsilon})$ (for any $\epsilon>0$) if $ k_{max}=O(\sqrt{N})$. Extensive large-scale simulations show these scaling laws to be precise. We discuss how this percolation search algorithm can be directly adapted to solve the well-known scaling problem in unstructured Peer-to-Peer (P2P) networks. Simulations of the protocol on sample large-scale subnetworks of existing P2P services show that overall traffic can be reduced by almost two-orders of magnitude, without any significant loss in search performance.<|reference_end|> | arxiv | @article{sarshar2004scalable,
title={Scalable Percolation Search in Power Law Networks},
author={Nima Sarshar and P.Oscar Boykin and Vwani P. Roychowdhury},
journal={Best paper award Fourth International Conference on Peer-to-Peer
Computing, pp. 2-9, 2004},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0406152},
primaryClass={cond-mat.dis-nn cs.NI}
} | sarshar2004scalable |
arxiv-669269 | cond-mat/0406404 | A statistical approach to the traceroute-like exploration of networks: theory and simulations | <|reference_start|>A statistical approach to the traceroute-like exploration of networks: theory and simulations: Mapping the Internet generally consists in sampling the network from a limited set of sources by using "traceroute"-like probes. This methodology, akin to the merging of different spanning trees to a set of destinations, has been argued to introduce uncontrolled sampling biases that might produce statistical properties of the sampled graph which sharply differ from the original ones. Here we explore these biases and provide a statistical analysis of their origin. We derive a mean-field analytical approximation for the probability of edge and vertex detection that exploits the role of the number of sources and targets and allows us to relate the global topological properties of the underlying network with the statistical accuracy of the sampled graph. In particular we find that the edge and vertex detection probability is depending on the betweenness centrality of each element. This allows us to show that shortest path routed sampling provides a better characterization of underlying graphs with scale-free topology. We complement the analytical discussion with a throughout numerical investigation of simulated mapping strategies in different network models. We show that sampled graphs provide a fair qualitative characterization of the statistical properties of the original networks in a fair range of different strategies and exploration parameters. The numerical study also allows the identification of intervals of the exploration parameters that optimize the fraction of nodes and edges discovered in the sampled graph. This finding might hint the steps toward more efficient mapping strategies.<|reference_end|> | arxiv | @article{dall'asta2004a,
title={A statistical approach to the traceroute-like exploration of networks:
theory and simulations},
author={Luca Dall'Asta, Ignacio Alvarez-Hamelin, Alain Barrat, Alexei Vazquez,
Alessandro Vespignani},
journal={CAAN 2004, LNCS 3405, p. 140 (2005) .},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0406404},
primaryClass={cond-mat.stat-mech cs.NI}
} | dall'asta2004a |
arxiv-669270 | cond-mat/0406765 | Competition and adaptation in an Internet evolution model | <|reference_start|>Competition and adaptation in an Internet evolution model: We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of the number of autonomous systems and the total number of connections in the Internet, both empirically measurable quantities. This fact place our model apart from others in which this exponent depends on parameters that need to be adjusted in a model dependent way. Our approach also accounts for a high level of clustering as well as degree-degree correlations, both with the same hierarchical structure present in the real Internet. Further, it also highlights the interplay between bandwidth, connectivity and traffic of the network.<|reference_end|> | arxiv | @article{serrano2004competition,
title={Competition and adaptation in an Internet evolution model},
author={M. Angeles Serrano, Marian Boguna and Albert Diaz-Guilera},
journal={Physical Review Letters 94, 038701 (2005)},
year={2004},
doi={10.1103/PhysRevLett.94.038701},
archivePrefix={arXiv},
eprint={cond-mat/0406765},
primaryClass={cond-mat.dis-nn cs.NI}
} | serrano2004competition |
arxiv-669271 | cond-mat/0407439 | A Theoretical Study on Spin-Dependent Transport of "Ferromagnet/Carbon Nanotube Encapsulating Magnetic Atoms/Ferromagnet" Junctions with 4-Valued Conductances | <|reference_start|>A Theoretical Study on Spin-Dependent Transport of "Ferromagnet/Carbon Nanotube Encapsulating Magnetic Atoms/Ferromagnet" Junctions with 4-Valued Conductances: As a novel function of ferromagnet (FM)/spacer/FM junctions, we theoretically investigate multiple-valued (or multi-level) cell property, which is in principle realized by sensing conductances of four states recorded with magnetization configurations of two FMs; (up,up), (up,down), (down,up), (down,down). In order to sense all the states, 4-valued conductances corresponding to the respective states are necessary. We previously proposed that 4-valued conductances are obtained in FM1/spin-polarized spacer (SPS)/FM2 junctions, where FM1 and FM2 have different spin polarizations, and the spacer depends on spin [J. Phys.: Condens. Matter 15, 8797 (2003)]. In this paper, an ideal SPS is considered as a single-wall armchair carbon nanotube encapsulating magnetic atoms, where the nanotube shows on-resonance or off-resonance at the Fermi level according to its length. The magnitude of the obtained 4-valued conductances has an opposite order between the on-resonant nanotube and the off-resonant one, and this property can be understood by considering electronic states of the nanotube. Also, the magnetoresistance ratio between (up,up) and (down,down) can be larger than the conventional one between parallel and anti-parallel configurations.<|reference_end|> | arxiv | @article{kokado2004a,
title={A Theoretical Study on Spin-Dependent Transport of "Ferromagnet/Carbon
Nanotube Encapsulating Magnetic Atoms/Ferromagnet" Junctions with 4-Valued
Conductances},
author={Satoshi Kokado and Kikuo Harigaya},
journal={J. Phys.: Condens. Matter 16, 5605 (2004)},
year={2004},
doi={10.1088/0953-8984/16/30/020},
archivePrefix={arXiv},
eprint={cond-mat/0407439},
primaryClass={cond-mat.mes-hall cond-mat.mtrl-sci cs.CE physics.chem-ph}
} | kokado2004a |
arxiv-669272 | cond-mat/0408190 | From spin glasses to hard satisfiable formulas | <|reference_start|>From spin glasses to hard satisfiable formulas: We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably "glassy" behavior; that is, it has many local optima with large energy barriers between them, so that local search algorithms get stuck and have difficulty finding the true ground state, i.e., the unique satisfying assignment. We test the hardness of our formulas with two Davis-Putnam solvers, Satz and zChaff, the recently introduced Survey Propagation (SP), and two local search algorithms, Walksat and Record-to-Record Travel (RRT). We compare our formulas to random 3-XOR-SAT formulas and to two other generators of hard satisfiable instances, the minimum disagreement parity formulas of Crawford et al., and Hirsch's hgen. For the complete solvers the running time of our formulas grows exponentially in sqrt(n), and exceeds that of random 3-XOR-SAT formulas for small problem sizes. SP is unable to solve our formulas with as few as 25 variables. For Walksat, our formulas appear to be harder than any other known generator of satisfiable instances. Finally, our formulas can be solved efficiently by RRT but only if the parameter d is tuned to the height of the barriers between local minima, and we use this parameter to measure the barrier heights in random 3-XOR-SAT formulas as well.<|reference_end|> | arxiv | @article{jia2004from,
title={From spin glasses to hard satisfiable formulas},
author={Haixia Jia, Cristopher Moore, and Bart Selman},
journal={arXiv preprint arXiv:cond-mat/0408190},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0408190},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.AI}
} | jia2004from |
arxiv-669273 | cond-mat/0408370 | Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations | <|reference_start|>Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations: Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show, that such a solution is almost certainly unattainable by proving that the sign problem is NP-hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP (nondeterministic polynomial) in polynomial time.<|reference_end|> | arxiv | @article{troyer2004computational,
title={Computational complexity and fundamental limitations to fermionic
quantum Monte Carlo simulations},
author={Matthias Troyer, Uwe-Jens Wiese},
journal={Phys.Rev.Lett. 94 (2005) 170201},
year={2004},
doi={10.1103/PhysRevLett.94.170201},
archivePrefix={arXiv},
eprint={cond-mat/0408370},
primaryClass={cond-mat.stat-mech cond-mat.str-el cs.CC hep-lat physics.comp-ph}
} | troyer2004computational |
arxiv-669274 | cond-mat/0409532 | Poisson convergence in the restricted $k$-partioning problem | <|reference_start|>Poisson convergence in the restricted $k$-partioning problem: The randomized $k$-number partitioning problem is the task to distribute $N$ i.i.d. random variables into $k$ groups in such a way that the sums of the variables in each group are as similar as possible. The restricted $k$-partitioning problem refers to the case where the number of elements in each group is fixed to $N/k$. In the case $k=2$ it has been shown that the properly rescaled differences of the two sums in the close to optimal partitions converge to a Poisson point process, as if they were independent random variables. We generalize this result to the case $k>2$ in the restricted problem and show that the vector of differences between the $k$ sums converges to a $k-1$-dimensional Poisson point process.<|reference_end|> | arxiv | @article{bovier2004poisson,
title={Poisson convergence in the restricted $k$-partioning problem},
author={Anton Bovier (WIAS-Berlin, TU-Berlin), Irina Kurkova (U Paris 6)},
journal={arXiv preprint arXiv:cond-mat/0409532},
year={2004},
number={WIAS-preprint 964},
archivePrefix={arXiv},
eprint={cond-mat/0409532},
primaryClass={cond-mat.dis-nn cs.CC math.PR}
} | bovier2004poisson |
arxiv-669275 | cond-mat/0410059 | Accuracy and Scaling Phenomena in Internet Mapping | <|reference_start|>Accuracy and Scaling Phenomena in Internet Mapping: A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a fundamental bias in the observed degree distribution. We examine this bias analytically and experimentally. For Erdos-Renyi random graphs with mean degree c, we show analytically that traceroute sampling gives an observed degree distribution P(k) ~ 1/k for k < c, even though the underlying degree distribution is Poisson. For graphs whose degree distributions have power-law tails P(k) ~ k^-alpha, traceroute sampling from a small number of sources can significantly underestimate the value of \alpha when the graph has a large excess (i.e., many more edges than vertices). We find that in order to obtain a good estimate of alpha it is necessary to use a number of sources which grows linearly in the average degree of the underlying graph. Based on these observations we comment on the accuracy of the published values of alpha for the Internet.<|reference_end|> | arxiv | @article{clauset2004accuracy,
title={Accuracy and Scaling Phenomena in Internet Mapping},
author={Aaron Clauset, Cristopher Moore},
journal={Phys. Rev. Lett. 94, 018701 (2005)},
year={2004},
doi={10.1103/PhysRevLett.94.018701},
archivePrefix={arXiv},
eprint={cond-mat/0410059},
primaryClass={cond-mat.dis-nn cs.NI physics.soc-ph}
} | clauset2004accuracy |
arxiv-669276 | cond-mat/0410270 | On uniqueness theorems for Tsallis entropy and Tsallis relative entropy | <|reference_start|>On uniqueness theorems for Tsallis entropy and Tsallis relative entropy: The uniqueness theorem for Tsallis entropy was presented in {\it H.Suyari, IEEE Trans. Inform. Theory, Vol.50, pp.1783-1787 (2004)} by introducing the generalized Shannon-Khinchin's axiom. In the present paper, this result is generalized and simplified as follows: {\it Generalization}: The uniqueness theorem for Tsallis relative entropy is shown by means of the generalized Hobson's axiom. {\it Simplification}: The uniqueness theorem for Tsallis entropy is shown by means of the generalized Faddeev's axiom.<|reference_end|> | arxiv | @article{furuichi2004on,
title={On uniqueness theorems for Tsallis entropy and Tsallis relative entropy},
author={Shigeru Furuichi},
journal={IEEE Trans. on Information Theory, Vol.51(2005),pp.3638-3645},
year={2004},
doi={10.1109/TIT.2005.855606},
archivePrefix={arXiv},
eprint={cond-mat/0410270},
primaryClass={cond-mat.stat-mech cs.IT math.IT}
} | furuichi2004on |
arxiv-669277 | cond-mat/0410271 | A generalized Faddeev's axiom and the uniqueness theorem for Tsallis entropy | <|reference_start|>A generalized Faddeev's axiom and the uniqueness theorem for Tsallis entropy: The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev's axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin's axiom in \cite{Suy}, in the sence that our axiom is simpler than his one, as similar that Faddeev's axiom is simpler than Shannon-Khinchin's one.<|reference_end|> | arxiv | @article{furuichi2004a,
title={A generalized Faddeev's axiom and the uniqueness theorem for Tsallis
entropy},
author={Shigeru Furuichi},
journal={arXiv preprint arXiv:cond-mat/0410271},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0410271},
primaryClass={cond-mat.stat-mech cs.IT math.IT}
} | furuichi2004a |
arxiv-669278 | cond-mat/0410460 | A Computational Study of Rotating Spiral Waves and Spatio-Temporal Transient Chaos in a Deterministic Three-Level Active System | <|reference_start|>A Computational Study of Rotating Spiral Waves and Spatio-Temporal Transient Chaos in a Deterministic Three-Level Active System: Spatio-temporal dynamics of a deterministic three-level cellular automaton (TLCA) of Zykov-Mikhailov type (Sov. Phys. - Dokl., 1986, Vol.31, No.1, P.51) is studied numerically. Evolution of spatial structures is investigated both for the original Zykov-Mikhailov model (which is applicable to, for example, Belousov-Zhabotinskii chemical reactions) and for proposed by us TLCA, which is a generalization of Zykov-Mikhailov model for the case of two-channel diffusion. Such the TLCA is a minimal model for an excitable medium of microwave phonon laser, called phaser (D. N. Makovetskii, Tech. Phys., 2004, Vol.49, No.2, P.224; cond-mat/0402640). The most interesting observed forms of TLCA dynamics are as follows: (a) spatio-temporal transient chaos in form of highly bottlenecked collective evolution of excitations by rotating spiral waves (RSW) with variable topological charges; (b) competition of left-handed and right-handed RSW with unexpected features, including self-induced alteration of integral effective topological charge; (c) transient chimera states, i.e. coexistence of regular and chaotic domains in TLCA patterns; (d) branching of TLCA states with different symmetry which may lead to full restoring of symmetry of imperfect starting pattern. Phenomena (a) and (c) are directly related to phaser dynamics features observed earlier in real experiments at liquid helium temperatures on corundum crystals doped by iron-group ions. ACM: F.1.1, I.6, J.2; PACS:05.65.+b, 07.05.Tp, 82.20.Wt<|reference_end|> | arxiv | @article{makovetskiy2004a,
title={A Computational Study of Rotating Spiral Waves and Spatio-Temporal
Transient Chaos in a Deterministic Three-Level Active System},
author={S. D. Makovetskiy (1), D. N. Makovetskii (2) ((1) Kharkiv National
University of Radio Electronics, Ukraine, (2) Institute of Radio-Physics and
Electronics of Natl. Acad. Sci., Ukraine)},
journal={arXiv preprint arXiv:cond-mat/0410460},
year={2004},
archivePrefix={arXiv},
eprint={cond-mat/0410460},
primaryClass={cond-mat.other cs.NE nlin.CG}
} | makovetskiy2004a |
arxiv-669279 | cond-mat/0410498 | Understanding Search Trees via Statistical Physics | <|reference_start|>Understanding Search Trees via Statistical Physics: We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain exact asymptotic results. In particular, we show that the probability distributions of extreme observables associated with a random search tree such as the height and the balanced height of a tree have a traveling front structure. In addition, the variance of the number of nodes needed to store a data string of a given size N is shown to undergo a striking phase transition at a critical value of the branching ratio m_c=26. We identify the mechanism of this phase transition, show that it is generic and occurs in various other problems as well. New results are obtained when each element of the data string is a D-dimensional vector. We show that this problem also has a phase transition at a critical dimension, D_c= \pi/\sin^{-1}(1/\sqrt{8})=8.69363...<|reference_end|> | arxiv | @article{majumdar2004understanding,
title={Understanding Search Trees via Statistical Physics},
author={Satya N. Majumdar, David S. Dean and P.L. Krapivsky},
journal={arXiv preprint arXiv:cond-mat/0410498},
year={2004},
doi={10.1007/BF02704178},
archivePrefix={arXiv},
eprint={cond-mat/0410498},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.DS}
} | majumdar2004understanding |
arxiv-669280 | cond-mat/0410594 | A model of student's dilemma | <|reference_start|>A model of student's dilemma: Each year perhaps millions of young people face the following dilemma: should I continue my education or rather start working with already acquired skills. Right decision must take into account somebody's own abilities, accessibility to education institutions, competition, and potential benefits. A multi-agent, evolutionary model of this dilemma predicts a transition between stratified and homogeneous phases, evolution that diminishes fitness, fewer applicants per seat for decreased capacity of the university, and presence of poor students at \'elite universities.<|reference_end|> | arxiv | @article{lipowski2004a,
title={A model of student's dilemma},
author={Adam Lipowski, Antonio L. Ferreira},
journal={Physica A 354-C, pp.539-546 (2005)},
year={2004},
doi={10.1016/j.physa.2005.03.009},
archivePrefix={arXiv},
eprint={cond-mat/0410594},
primaryClass={cond-mat.other cond-mat.stat-mech cs.MA physics.soc-ph}
} | lipowski2004a |
arxiv-669281 | cond-mat/0411077 | Long Range Frustrations in a Spin Glass Model of the Vertex Cover Problem | <|reference_start|>Long Range Frustrations in a Spin Glass Model of the Vertex Cover Problem: In a spin glass system on a random graph, some vertices have their spins changing among different configurations of a ground--state domain. Long range frustrations may exist among these unfrozen vertices in the sense that certain combinations of spin values for these vertices may never appear in any configuration of this domain. We present a mean field theory to tackle such long range frustrations and apply it to the NP-hard minimum vertex cover (hard-core gas condensation) problem. Our analytical results on the ground-state energy density and on the fraction of frozen vertices are in good agreement with known numerical and mathematical results.<|reference_end|> | arxiv | @article{zhou2004long,
title={Long Range Frustrations in a Spin Glass Model of the Vertex Cover
Problem},
author={Haijun Zhou},
journal={Physical Review Letters 94, 217203 (2005)},
year={2004},
doi={10.1103/PhysRevLett.94.217203},
archivePrefix={arXiv},
eprint={cond-mat/0411077},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC}
} | zhou2004long |
arxiv-669282 | cond-mat/0411079 | Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random $K$-satisfiability problem | <|reference_start|>Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random $K$-satisfiability problem: Shortened abstract: A mean field theory of long range frustration is constructed for spin glass systems with quenched randomness of vertex--vertex connections and of spin--spin coupling strengths. This theory is applied to a spin glass model of the random $K$-satisfiability problem (K=2 or K=3). The zero--temperature phase diagram of the $\pm J$ Viana--Bray model is also determined, which is identical to that of the random 2-SAT problem. The predicted phase transition between a non-frustrated and a long--rangely frustrated spin glass phase might also be observable in real materials at a finite temperature.<|reference_end|> | arxiv | @article{zhou2004long,
title={Long range frustration in finite connectivity spin glasses: A mean field
theory and its application to the random $K$-satisfiability problem},
author={Haijun Zhou},
journal={New Journal of Physics 7: 123 (2005)},
year={2004},
doi={10.1088/1367-2630/7/1/123},
archivePrefix={arXiv},
eprint={cond-mat/0411079},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC}
} | zhou2004long |
arxiv-669283 | cond-mat/0412460 | Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics | <|reference_start|>Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics: The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a "binary decision", exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems.<|reference_end|> | arxiv | @article{niven2004exact,
title={Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics},
author={Robert K. Niven},
journal={arXiv preprint arXiv:cond-mat/0412460},
year={2004},
doi={10.1016/j.physleta.2005.05.063},
archivePrefix={arXiv},
eprint={cond-mat/0412460},
primaryClass={cond-mat.stat-mech cs.IT math.IT quant-ph}
} | niven2004exact |
arxiv-669284 | cond-mat/0412587 | Spin dependent transport of ``nonmagnetic metal/zigzag nanotube encapsulating magnetic atoms/nonmagnetic metal'' junctions | <|reference_start|>Spin dependent transport of ``nonmagnetic metal/zigzag nanotube encapsulating magnetic atoms/nonmagnetic metal'' junctions: Towards a novel magnetoresistance (MR) device with a carbon nanotube, we propose ``nonmagnetic metal/zigzag nanotube encapsulating magnetic atoms/nonmagnetic metal'' junctions. We theoretically investigate how spin-polarized edges of the nanotube and the encapsulated magnetic atoms influence on transport. When the on-site Coulomb energy divided by the magnitude of transfer integral, $U/|t|$, is larger than 0.8, large MR effect due to the direction of spins of magnetic atoms, which has the magnitude of the MR ratio of about 100%, appears reflecting such spin-polarized edges.<|reference_end|> | arxiv | @article{kokado2004spin,
title={Spin dependent transport of ``nonmagnetic metal/zigzag nanotube
encapsulating magnetic atoms/nonmagnetic metal'' junctions},
author={Satoshi Kokado and Kikuo Harigaya},
journal={Synthetic Metals, Volume 152, Issues 1-3, 20 September 2005, Pages
465-468},
year={2004},
doi={10.1016/j.synthmet.2005.07.187},
archivePrefix={arXiv},
eprint={cond-mat/0412587},
primaryClass={cond-mat.mes-hall cond-mat.mtrl-sci cs.CE physics.chem-ph quant-ph}
} | kokado2004spin |
arxiv-669285 | cond-mat/0412723 | Modelling financial markets by the multiplicative sequence of trades | <|reference_start|>Modelling financial markets by the multiplicative sequence of trades: We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autocorrelations and the origin of the power-law probability distribution of the trading activity. The model reproduces the spectral properties of trading activity and explains the mechanism of power-law distribution in real markets.<|reference_end|> | arxiv | @article{gontis2004modelling,
title={Modelling financial markets by the multiplicative sequence of trades},
author={Vygintas Gontis, Bronislovas Kaulakys},
journal={Gontis V., Kaulakys B., Physica A 344 (2004) 128-133},
year={2004},
doi={10.1016/j.physa.2004.06.153},
archivePrefix={arXiv},
eprint={cond-mat/0412723},
primaryClass={cond-mat.stat-mech cs.CE math.SP physics.data-an q-fin.ST}
} | gontis2004modelling |
arxiv-669286 | cond-mat/0501169 | Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version) | <|reference_start|>Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version): Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.<|reference_end|> | arxiv | @article{li2005towards,
title={Towards a Theory of Scale-Free Graphs: Definition, Properties, and
Implications (Extended Version)},
author={Lun Li, David Alderson, Reiko Tanaka, John C. Doyle, Walter Willinger},
journal={arXiv preprint arXiv:cond-mat/0501169},
year={2005},
number={CIT-CDS-04-006},
archivePrefix={arXiv},
eprint={cond-mat/0501169},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.NI math.CO q-bio.MN}
} | li2005towards |
arxiv-669287 | cond-mat/0501707 | Focused Local Search for Random 3-Satisfiability | <|reference_start|>Focused Local Search for Random 3-Satisfiability: A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of focusing the local moves on the presently unsatisfiedclauses is known to be very effective: the time to solution has been observed to grow only linearly in the number of variables, for a given clauses-to-variables ratio $\alpha$ sufficiently far below the critical satisfiability threshold $\alpha_c \approx 4.27$. We present numerical results on the behaviour of three focused local search algorithms for this problem, considering in particular the characteristics of a focused variant of the simple Metropolis dynamics. We estimate the optimal value for the ``temperature'' parameter $\eta$ for this algorithm, such that its linear-time regime extends as close to $\alpha_c$ as possible. Similar parameter optimisation is performed also for the well-known WalkSAT algorithm and for the less studied, but very well performing Focused Record-to-Record Travel method. We observe that with an appropriate choice of parameters, the linear time regime for each of these algorithms seems to extend well into ratios $\alpha > 4.2$ -- much further than has so far been generally assumed. We discuss the statistics of solution times for the algorithms, relate their performance to the process of ``whitening'', and present some conjectures on the shape of their computational phase diagrams.<|reference_end|> | arxiv | @article{seitz2005focused,
title={Focused Local Search for Random 3-Satisfiability},
author={Sakari Seitz, Mikko Alava, and Pekka Orponen},
journal={arXiv preprint arXiv:cond-mat/0501707},
year={2005},
doi={10.1088/1742-5468/2005/06/P06006},
archivePrefix={arXiv},
eprint={cond-mat/0501707},
primaryClass={cond-mat.stat-mech cs.CC}
} | seitz2005focused |
arxiv-669288 | cond-mat/0502205 | Degree Distribution of Competition-Induced Preferential Attachment Graphs | <|reference_start|>Degree Distribution of Competition-Induced Preferential Attachment Graphs: We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment random graph models with upper cutoffs. This is the first explanation of how preferential attachment can arise from a more basic underlying mechanism of local competition. We rigorously determine the degree distribution for the family of random graph models, showing that it obeys a power law up to a finite threshold and decays exponentially above this threshold. We also rigorously analyze a generalized version of our graph process, with two natural parameters, one corresponding to the cutoff and the other a ``fertility'' parameter. We prove that the general model has a power-law degree distribution up to a cutoff, and establish monotonicity of the power as a function of the two parameters. Limiting cases of the general model include the standard preferential attachment model without cutoff and the uniform attachment model.<|reference_end|> | arxiv | @article{berger2005degree,
title={Degree Distribution of Competition-Induced Preferential Attachment
Graphs},
author={N. Berger, C. Borgs, J. T. Chayes, R. M. D'Souza, R. D. Kleinberg},
journal={arXiv preprint arXiv:cond-mat/0502205},
year={2005},
archivePrefix={arXiv},
eprint={cond-mat/0502205},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.NI math.PR}
} | berger2005degree |
arxiv-669289 | cond-mat/0503087 | On the Bias of Traceroute Sampling; or, Power-law Degree Distributions in Regular Graphs | <|reference_start|>On the Bias of Traceroute Sampling; or, Power-law Degree Distributions in Regular Graphs: Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph structure is a surprisingly difficult task, as edges cannot be explicitly queried. Instead, empirical studies rely on traceroutes to build what are essentially single-source, all-destinations, shortest-path trees. These trees only sample a fraction of the network's edges, and a recent paper by Lakhina et al. found empirically that the resuting sample is intrinsically biased. For instance, the observed degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is Poisson. In this paper, we study the bias of traceroute sampling systematically, and, for a very general class of underlying degree distributions, calculate the likely observed distributions explicitly. To do this, we use a continuous-time realization of the process of exposing the BFS tree of a random graph with a given degree distribution, calculate the expected degree distribution of the tree, and show that it is sharply concentrated. As example applications of our machinery, we show how traceroute sampling finds power-law degree distributions in both delta-regular and Poisson-distributed random graphs. Thus, our work puts the observations of Lakhina et al. on a rigorous footing, and extends them to nearly arbitrary degree distributions.<|reference_end|> | arxiv | @article{achlioptas2005on,
title={On the Bias of Traceroute Sampling; or, Power-law Degree Distributions
in Regular Graphs},
author={Dimitris Achlioptas, Aaron Clauset, David Kempe, and Cristopher Moore},
journal={Proc. 37th ACM Symposium on Theory of Computing (STOC) 2005},
year={2005},
archivePrefix={arXiv},
eprint={cond-mat/0503087},
primaryClass={cond-mat.dis-nn cs.NI math.CO math.PR}
} | achlioptas2005on |
arxiv-669290 | cond-mat/0503627 | How to Simulate Billiards and Similar Systems | <|reference_start|>How to Simulate Billiards and Similar Systems: An N-component continuous-time dynamic system is considered whose components evolve autonomously all the time except for in discrete asynchronous instances of pairwise interactions. Examples include chaotically colliding billiard balls and combat models. A new efficient serial event-driven algorithm is described for simulating such systems. Rather than maintaining and updating the global state of the system, the algorithm tries to examine only essential events, i.e., component interactions. The events are processed in a non-decreasing order of time; new interactions are scheduled on the basis of the examined interactions using preintegrated equations of the evolutions of the components. If the components are distributed uniformly enough in the evolution space, so that this space can be subdivided into small sectors such that only O(1) sectors and O(1)$components are in the neighborhood of a sector, then the algorithm spends time O (log N) for processing an event which is the asymptotical minimum. The algorithm uses a simple strategy for handling data: only two states are maintained for each simulated component. Fast data access in this strategy assures the practical efficiency of the algorithm. It works noticeably faster than other algorithms proposed for this model. Key phrases: collision detection, dense packing, molecular dynamics, hard spheres, granular flow<|reference_end|> | arxiv | @article{lubachevsky2005how,
title={How to Simulate Billiards and Similar Systems},
author={Boris D. Lubachevsky},
journal={Journal of Computational Physics, v.94 n.2, p.255-283, June 1991},
year={2005},
doi={10.1016/0021-9991(91)90222-7},
archivePrefix={arXiv},
eprint={cond-mat/0503627},
primaryClass={cond-mat.mtrl-sci cs.DS math.DS}
} | lubachevsky2005how |
arxiv-669291 | cond-mat/0504025 | Point process model of 1/f noise versus a sum of Lorentzians | <|reference_start|>Point process model of 1/f noise versus a sum of Lorentzians: We present a simple point process model of $1/f^{\beta}$ noise, covering different values of the exponent $\beta$. The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interval resulting in the power-law distribution. Our model is free from the requirement of a wide distribution of relaxation times and from the power-law forms of the pulses. It contains only one relaxation rate and yields $1/f^ {\beta}$ spectra in a wide range of frequency. We obtain explicit expressions for the power spectra and present numerical illustrations of the model. Further we analyze the relation of the point process model of $1/f$ noise with the Bernamont-Surdin-McWhorter model, representing the signals as a sum of the uncorrelated components. We show that the point process model is complementary to the model based on the sum of signals with a wide-range distribution of the relaxation times. In contrast to the Gaussian distribution of the signal intensity of the sum of the uncorrelated components, the point process exhibits asymptotically a power-law distribution of the signal intensity. The developed multiplicative point process model of $1/f^{\beta}$ noise may be used for modeling and analysis of stochastic processes in different systems with the power-law distribution of the intensity of pulsing signals.<|reference_end|> | arxiv | @article{kaulakys2005point,
title={Point process model of 1/f noise versus a sum of Lorentzians},
author={B. Kaulakys, V. Gontis, and M. Alaburda},
journal={Phys.Rev. E71 (2005) 051105},
year={2005},
doi={10.1103/PhysRevE.71.051105},
archivePrefix={arXiv},
eprint={cond-mat/0504025},
primaryClass={cond-mat.stat-mech astro-ph cond-mat.dis-nn cs.CE math.ST nlin.AO physics.data-an q-bio.NC stat.TH}
} | kaulakys2005point |
arxiv-669292 | cond-mat/0504070 | Clustering of solutions in the random satisfiability problem | <|reference_start|>Clustering of solutions in the random satisfiability problem: Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in agreement with previous predictions of the cavity method and give a rigorous confirmation to one of its main building blocks. It can be generalized to other systems of both physical and computational interest.<|reference_end|> | arxiv | @article{mezard2005clustering,
title={Clustering of solutions in the random satisfiability problem},
author={M. Mezard, T. Mora, R. Zecchina},
journal={Phys. Rev. Lett. 94, 197205 (2005)},
year={2005},
doi={10.1103/PhysRevLett.94.197205},
archivePrefix={arXiv},
eprint={cond-mat/0504070},
primaryClass={cond-mat.dis-nn cs.CC}
} | mezard2005clustering |
arxiv-669293 | cond-mat/0504185 | Disaster Management in Scale-Free Networks: Recovery from and Protection Against Intentional Attacks | <|reference_start|>Disaster Management in Scale-Free Networks: Recovery from and Protection Against Intentional Attacks: Susceptibility of scale free Power Law (PL) networks to attacks has been traditionally studied in the context of what may be termed as {\em instantaneous attacks}, where a randomly selected set of nodes and edges are deleted while the network is kept {\em static}. In this paper, we shift the focus to the study of {\em progressive} and instantaneous attacks on {\em reactive} grown and random PL networks, which can respond to attacks and take remedial steps. In the process, we present several techniques that managed networks can adopt to minimize the damages during attacks, and also to efficiently recover from the aftermath of successful attacks. For example, we present (i) compensatory dynamics that minimize the damages inflicted by targeted progressive attacks, such as linear-preferential deletions of nodes in grown PL networks; the resulting dynamic naturally leads to the emergence of networks with PL degree distributions with exponential cutoffs; (ii) distributed healing algorithms that can scale the maximum degree of nodes in a PL network using only local decisions, and (iii) efficient means of creating giant connected components in a PL network that has been fragmented by attacks on a large number of high-degree nodes. Such targeted attacks are considered to be a major vulnerability of PL networks; however, our results show that the introduction of only a small number of random edges, through a {\em reverse percolation} process, can restore connectivity, which in turn allows restoration of other topological properties of the original network. Thus, the scale-free nature of the networks can itself be effectively utilized for protection and recovery purposes.<|reference_end|> | arxiv | @article{rezaei2005disaster,
title={Disaster Management in Scale-Free Networks: Recovery from and Protection
Against Intentional Attacks},
author={Behnam A. Rezaei, Nima Sarshar, P. Oscar Boykin, Vwani P. Roychowdhury},
journal={arXiv preprint arXiv:cond-mat/0504185},
year={2005},
archivePrefix={arXiv},
eprint={cond-mat/0504185},
primaryClass={cond-mat.stat-mech cs.DS cs.NI physics.data-an physics.soc-ph}
} | rezaei2005disaster |
arxiv-669294 | cond-mat/0505193 | Organization of complex networks without multiple connections | <|reference_start|>Organization of complex networks without multiple connections: We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these networks contain a core of highly interconnected vertices. The number of vertices in this core varies in the range between $const N^{1/2}$ and $const N^{2/3}$, where $N$ is the number of vertices in a network. At the birth point of the core, we obtain the size-dependent cut-off of the distribution of the number of connections and find that its position differs from earlier estimates.<|reference_end|> | arxiv | @article{dorogovtsev2005organization,
title={Organization of complex networks without multiple connections},
author={S.N. Dorogovtsev, J.F.F. Mendes, A.M. Povolotsky, A.N. Samukhin},
journal={Phys.Rev.Lett. 95 (2005) 195701},
year={2005},
doi={10.1103/PhysRevLett.95.195701},
archivePrefix={arXiv},
eprint={cond-mat/0505193},
primaryClass={cond-mat.stat-mech cs.NI hep-lat physics.soc-ph}
} | dorogovtsev2005organization |
arxiv-669295 | cond-mat/0506002 | Correlations in interacting systems with a network topology | <|reference_start|>Correlations in interacting systems with a network topology: We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance $\ell$, decay, on average, faster than $1/(\ell z_\ell)$. Here $z_\ell$ is the mean number of the $\ell$-th nearest neighbors of a vertex in a network. This behavior, in particular, leads to a dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions, which have a divergent number $z_2$ in the infinite network limit. In this case, only the pair correlations between the nearest neighbors are observable. We obtain the pair correlation function of the Ising model on a complex network and also derive our results in the framework of a phenomenological approach.<|reference_end|> | arxiv | @article{dorogovtsev2005correlations,
title={Correlations in interacting systems with a network topology},
author={S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes},
journal={Phys. Rev. E 72, 066130 (2005)},
year={2005},
doi={10.1103/PhysRevE.72.066130},
archivePrefix={arXiv},
eprint={cond-mat/0506002},
primaryClass={cond-mat.stat-mech cs.NI math-ph math.MP physics.soc-ph}
} | dorogovtsev2005correlations |
arxiv-669296 | cond-mat/0506037 | Diagnosis of weaknesses in modern error correction codes: a physics approach | <|reference_start|>Diagnosis of weaknesses in modern error correction codes: a physics approach: One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the Bit-Error-Rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.<|reference_end|> | arxiv | @article{stepanov2005diagnosis,
title={Diagnosis of weaknesses in modern error correction codes: a physics
approach},
author={M.G. Stepanov (LANL), V. Chernyak (Wayne State), M. Chertkov (LANL),
B. Vasic (U. of Arizona)},
journal={arXiv preprint arXiv:cond-mat/0506037},
year={2005},
doi={10.1103/PhysRevLett.95.228701},
number={LA-UR-05-2591},
archivePrefix={arXiv},
eprint={cond-mat/0506037},
primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.IT math.IT}
} | stepanov2005diagnosis |
arxiv-669297 | cond-mat/0506053 | Pairs of SAT Assignment in Random Boolean Formulae | <|reference_start|>Pairs of SAT Assignment in Random Boolean Formulae: We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp threshold for this property as a function of the clause density. For large enough K, we prove that there exists a region of clause density, below the satisfiability threshold, where the landscape of Hamming distances between SAT assignments experiences a gap: pairs of SAT-assignments exist at small x, and around x=1/2, but they donot exist at intermediate values of x. This result is consistent with the clustering scenario which is at the heart of the recent heuristic analysis of satisfiability using statistical physics analysis (the cavity method), and its algorithmic counterpart (the survey propagation algorithm). The method uses elementary probabilistic arguments (first and second moment methods), and might be useful in other problems of computational and physical interest where similar phenomena appear.<|reference_end|> | arxiv | @article{daudé2005pairs,
title={Pairs of SAT Assignment in Random Boolean Formulae},
author={Herv'e Daud'e (LATP), Marc Mezard (LPTMS), Thierry Mora (LPTMS),
Riccardo Zecchina (POLITO)},
journal={Theoretical Computer Science 393 (2008) 260-279},
year={2005},
doi={10.1016/j.tcs.2008.01.005},
archivePrefix={arXiv},
eprint={cond-mat/0506053},
primaryClass={cond-mat.dis-nn cs.CC}
} | daudé2005pairs |
arxiv-669298 | cond-mat/0506330 | A program generating homogeneous random graphs with given weights | <|reference_start|>A program generating homogeneous random graphs with given weights: We present a program package which generates homogeneous random graphs with probabilities prescribed by the user. The statistical weight of a labeled graph $\alpha$ is given in the form $W(\alpha)=\prod_{i=1}^N p(q_i)$, where $p(q)$ is an arbitrary user function and $q_i$ are the degrees of the graph nodes. The program can be used to generate two types of graphs (simple graphs and pseudo-graphs) from three types of ensembles (micro-canonical, canonical and grand-canonical).<|reference_end|> | arxiv | @article{bogacz2005a,
title={A program generating homogeneous random graphs with given weights},
author={L. Bogacz, Z. Burda, W. Janke, B. Waclaw},
journal={Comp. Phys. Comm. 173 (2005) 162-174},
year={2005},
doi={10.1016/j.cpc.2005.07.010},
archivePrefix={arXiv},
eprint={cond-mat/0506330},
primaryClass={cond-mat.dis-nn cs.NI physics.comp-ph}
} | bogacz2005a |
arxiv-669299 | cond-mat/0506652 | The theoretical capacity of the Parity Source Coder | <|reference_start|>The theoretical capacity of the Parity Source Coder: The Parity Source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that the theoretical capacity saturate the Shannon limit at large K. We also find that the first corrections to the leading behavior are exponentially small, so that the behavior at finite K is very close to the optimal one.<|reference_end|> | arxiv | @article{ciliberti2005the,
title={The theoretical capacity of the Parity Source Coder},
author={Stefano Ciliberti, Marc Mezard},
journal={J. Stat Mech P10003 (2005)},
year={2005},
doi={10.1088/1742-5468/2005/10/P10003},
archivePrefix={arXiv},
eprint={cond-mat/0506652},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.IT math.IT}
} | ciliberti2005the |
arxiv-669300 | cond-mat/0507451 | Landscape of solutions in constraint satisfaction problems | <|reference_start|>Landscape of solutions in constraint satisfaction problems: We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the distribution of distances between solutions.<|reference_end|> | arxiv | @article{mezard2005landscape,
title={Landscape of solutions in constraint satisfaction problems},
author={Marc Mezard, Matteo Palassini, Olivier Rivoire},
journal={Phys. Rev. Lett. 95, 200202 (2005)},
year={2005},
doi={10.1103/PhysRevLett.95.200202},
archivePrefix={arXiv},
eprint={cond-mat/0507451},
primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC}
} | mezard2005landscape |
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