45 research outputs found

    Complex and Adaptive Dynamical Systems: A Primer

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    An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

    Self-organised criticality in the evolution of a thermodynamic model of rodent thermoregulatory huddling

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    A thermodynamic model of thermoregulatory huddling interactions between endotherms is developed. The model is presented as a Monte Carlo algorithm in which animals are iteratively exchanged between groups, with a probability of exchanging groups defined in terms of the temperature of the environment and the body temperatures of the animals. The temperature-dependent exchange of animals between groups is shown to reproduce a second-order critical phase transition, i.e., a smooth switch to huddling when the environment gets colder, as measured in recent experiments. A peak in the rate at which group sizes change, referred to as pup flow, is predicted at the critical temperature of the phase transition, consistent with a thermodynamic description of huddling, and with a description of the huddle as a self-organising system. The model was subjected to a simple evolutionary procedure, by iteratively substituting the physiologies of individuals that fail to balance the costs of thermoregulation (by huddling in groups) with the costs of thermogenesis (by contributing heat). The resulting tension between cooperative and competitive interactions was found to generate a phenomenon called self-organised criticality, as evidenced by the emergence of avalanches in fitness that propagate across many generations. The emergence of avalanches reveals how huddling can introduce correlations in fitness between individuals and thereby constrain evolutionary dynamics. Finally, a full agent-based model of huddling interactions is also shown to generate criticality when subjected to the same evolutionary pressures. The agent-based model is related to the Monte Carlo model in the way that a Vicsek model is related to an Ising model in statistical physics. Huddling therefore presents an opportunity to use thermodynamic theory to study an emergent adaptive animal behaviour. In more general terms, huddling is proposed as an ideal system for investigating the interaction between self-organisation and natural selection empirically

    Toy models for macroevolutionary patterns and trends

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    A B S T R A C T Many models have been used to simplify and operationalize the subtle but complex mechanisms of biological evolution. Toy models are gross simplifications that nevertheless attempt to retain major essential features of evolution, bridging the gap between empirical reality and formal theoretical understanding. In this paper, we examine thirteen models which describe evolution that also qualify as such toy models, including the tree of life, branching processes, adaptive ratchets, fitness landscapes, and the role of nonlinear avalanches in evolutionary dynamics. Such toy models are intended to capture features such as evolutionary trends, coupled evolutionary dynamics of phenotype and genotype, adaptive change, branching, and evolutionary transience. The models discussed herein are applied to specific evolutionary contexts in various ways that simplify the complexity inherent in evolving populations. While toy models are overly simplistic, they also provide sufficient dynamics for capturing the fundamental mechanism(s) of evolution. Toy models might also be used to aid in high-throughput data analysis and the understanding of cultural evolutionary trends. This paper should serve as an introductory guide to the toy modeling of evolutionary complexity

    Self-organised criticality in the evolution of a thermodynamic model of rodent thermoregulatory huddling

    Get PDF
    A thermodynamic model of thermoregulatory huddling interactions between endotherms is developed. The model is presented as a Monte Carlo algorithm in which animals are iteratively exchanged between groups, with a probability of exchanging groups defined in terms of the temperature of the environment and the body temperatures of the animals. The temperature-dependent exchange of animals between groups is shown to reproduce a second-order critical phase transition, i.e., a smooth switch to huddling when the environment gets colder, as measured in recent experiments. A peak in the rate at which group sizes change, referred to as pup flow, is predicted at the critical temperature of the phase transition, consistent with a thermodynamic description of huddling, and with a description of the huddle as a self-organising system. The model was subjected to a simple evolutionary procedure, by iteratively substituting the physiologies of individuals that fail to balance the costs of thermoregulation (by huddling in groups) with the costs of thermogenesis (by contributing heat). The resulting tension between cooperative and competitive interactions was found to generate a phenomenon called self-organised criticality, as evidenced by the emergence of avalanches in fitness that propagate across many generations. The emergence of avalanches reveals how huddling can introduce correlations in fitness between individuals and thereby constrain evolutionary dynamics. Finally, a full agent-based model of huddling interactions is also shown to generate criticality when subjected to the same evolutionary pressures. The agent-based model is related to the Monte Carlo model in the way that a Vicsek model is related to an Ising model in statistical physics. Huddling therefore presents an opportunity to use thermodynamic theory to study an emergent adaptive animal behaviour. In more general terms, huddling is proposed as an ideal system for investigating the interaction between self-organisation and natural selection empirically

    Self-Organization and Complex Networks

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    In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.Comment: Book chapter in "Adaptive Networks: Theory, Models and Applications", Editors: Thilo Gross and Hiroki Sayama (Springer/NECSI Studies on Complexity Series

    Computability and Evolutionary Complexity: Markets As Complex Adaptive Systems (CAS)

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    The purpose of this Feature is to critically examine and to contribute to the burgeoning multi disciplinary literature on markets as complex adaptive systems (CAS). Three economists, Robert Axtell, Steven Durlauf and Arthur Robson who have distinguished themselves as pioneers in different aspects of how the thesis of evolutionary complexity pertains to market environments have contributed to this special issue. Axtell is concerned about the procedural aspects of attaining market equilibria in a decentralized setting and argues that principles on the complexity of feasible computation should rule in or out widely held models such as the Walrasian one. Robson puts forward the hypothesis called the Red Queen principle, well known from evolutionary biology, as a possible explanation for the evolution of complexity itself. Durlauf examines some of the claims that have been made in the name of complex systems theory to see whether these present testable hypothesis for economic models. My overview aims to use the wider literature on complex systems to provide a conceptual framework within which to discuss the issues raised for Economics in the above contributions and elsewhere. In particular, some assessment will be made on the extent to which modern complex systems theory and its application to markets as CAS constitutes a paradigm shift from more mainstream economic analysis

    The Tightness of the Kesten-Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations

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    It is well known that reconstruction problems, as the interdisciplinary subject, have been studied in numerous contexts including statistical physics, information theory and computational biology, to name a few. We consider a 2q2q-state symmetric model, with two categories of qq states in each category, and 3 transition probabilities: the probability to remain in the same state, the probability to change states but remain in the same category, and the probability to change categories. We construct a nonlinear second order dynamical system based on this model and show that the Kesten-Stigum reconstruction bound is not tight when q4q \geq 4.Comment: Accepted, to appear Journal of Statistical Physic

    Steady state particle swarm

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    The following grant information was disclosed by the authors: Fundação para a Ciência e Tecnologia (FCT), Research Fellowship: SFRH/BPD/66876/2009. FCT PROJECT: UID/EEA/50009/2013. EPHEMECH: TIN2014-56494-C4-3-P, Spanish Ministry of Economy and Competitivity. PROY-PP2015-06: Plan Propio 2015 UGR. CEI2015-MP-V17 of the Microprojects program 2015 from CEI BioTIC Granada.This paper investigates the performance and scalability of a new update strategy for the particle swarm optimization (PSO) algorithm. The strategy is inspired by the Bak–Sneppen model of co-evolution between interacting species, which is basically a network of fitness values (representing species) that change over time according to a simple rule: the least fit species and its neighbors are iteratively replaced with random values. Following these guidelines, a steady state and dynamic update strategy for PSO algorithms is proposed: only the least fit particle and its neighbors are updated and evaluated in each time-step; the remaining particles maintain the same position and fitness, unless they meet the update criterion. The steady state PSO was tested on a set of unimodal, multimodal, noisy and rotated benchmark functions, significantly improving the quality of results and convergence speed of the standard PSOs and more sophisticated PSOs with dynamic parameters and neighborhood. A sensitivity analysis of the parameters confirms the performance enhancement with different parameter settings and scalability tests show that the algorithm behavior is consistent throughout a substantial range of solution vector dimensions.This work was supported by Fundação para a Ciência e Tecnologia (FCT) Research Fellowship SFRH/BPD/66876/2009 and FCT Project (UID/EEA/50009/2013), EPHEMECH (TIN2014-56494-C4-3-P, Spanish Ministry of Economy and Competitivity), PROY-PP2015-06 (Plan Propio 2015 UGR), project CEI2015-MP-V17 of the Microprojects program 2015 from CEI BioTIC Granada
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