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  • Fractional Fields and Applications

    Collections series Mathematics and Statistics (R0)
    This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A ... En savoir plus

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  • Conflict and Complexity

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    Collections series Physics and Astronomy (R0)
    This book follows the methodologies of complex adaptive systems research in their application to addressing the problems of terrorism, specifically terrorist networks, their structure and various methods of mapping and interdicting them as well as exploring the complex landscape of network-centric and irregular warfare. A variety of new models and approaches are presented here, including Dynamic ... En savoir plus

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  • An Introduction to Statistical Mechanics and Thermodynamics

    Collections series Oxford Graduate Texts
    This text presents the two complementary aspects of thermal physics as an integrated theory of the properties of matter. Conceptual understanding is promoted by thorough development of basic concepts. In contrast to many texts, statistical mechanics, including discussion of the required probability theory, is presented first. This provides a statistical foundation for the concept of entropy, which ... En savoir plus

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  • Stochastic Tools in Mathematics and Science

    Collections series Mathematics and Statistics (R0)
    "Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, ... En savoir plus

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  • Breakdown in Traffic Networks

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    This book offers a detailed investigation of breakdowns in traffic and transportation networks. It shows empirically that transitions from free flow to so-called synchronized flow, initiated by local disturbances at network bottlenecks, display a nucleation-type behavior: while small disturbances in free flow decay, larger ones grow further and lead to breakdowns at the bottlenecks. Further, it ... En savoir plus

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  • Limit Theorems for Multi-Indexed Sums of Random Variables

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    Collections series Mathematics and Statistics (R0)
    Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek ... En savoir plus

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  • Automatic trend estimation

    Collections series Physics and Astronomy (R0)
    Our book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series ... En savoir plus

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  • Discrete–Time Stochastic Control and Dynamic Potential Games

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    Collections series Mathematics and Statistics (R0)
    There are several techniques to study noncooperative dynamic games, such as dynamic programming and the maximum principle (also called the Lagrange method). It turns out, however, that one way to characterize dynamic potential games requires to analyze inverse optimal control problems, and it is here where the Euler equation approach comes in because it is particularly well–suited to solve inverse ... En savoir plus

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  • Temporal Networks

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    The concept of temporal networks is an extension of complex networks as a modeling framework to include information on when interactions between nodes happen.Many studies of the last decade examine how the static network structure affect dynamic systems on the network. In this traditional approach the temporal aspects are pre-encoded in the dynamic system model.Temporal-network methods, on the ... En savoir plus

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  • Deterministic Abelian Sandpile Models and Patterns

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    The model investigated in this work, a particular cellular automaton with stochastic evolution, was introduced as the simplest case of self-organized-criticality, that is, a dynamical system which shows algebraic long-range correlations without any tuning of parameters. The author derives exact results which are potentially also interesting outside the area of critical phenomena. Exact means also ... En savoir plus

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  • Probabilistic Cellular Automata

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    This book explores Probabilistic Cellular Automata (PCA) from the perspectives of statistical mechanics, probability theory, computational biology and computer science. PCA are extensions of the well-known Cellular Automata models of complex systems, characterized by random updating rules. Thanks to their probabilistic component, PCA offer flexible computing tools for complex numerical ... En savoir plus

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