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2079 results in Statistical Physics

Page 11 of 104

Complexity Science
  • The Study of Emergence
  • Henrik Jeldtoft Jensen
  • Published online:
    13 December 2022
    Print publication:
    17 November 2022
  • Ecosystems, the human brain, ant colonies, and economic networks are all complex systems displaying collective behaviour, or emergence, beyond the sum of their parts. Complexity science is the systematic investigation of these emergent phenomena, and stretches across disciplines, from physics and mathematics, to biological and social sciences. This introductory textbook provides detailed coverage of this rapidly growing field, accommodating readers from a variety of backgrounds, and with varying levels of mathematical skill. Part I presents the underlying principles of complexity science, to ensure students have a solid understanding of the conceptual framework. The second part introduces the key mathematical tools central to complexity science, gradually developing the mathematical formalism, with more advanced material provided in boxes. A broad range of end of chapter problems and extended projects offer opportunities for homework assignments and student research projects, with solutions available to instructors online. Key terms are highlighted in bold and listed in a glossary for easy reference, while annotated reading lists offer the option for extended reading and research.
Gillespie Algorithms for Stochastic Multiagent Dynamics in Populations and Networks

Gillespie Algorithms for Stochastic Multiagent Dynamics in Populations and Networks
  • Naoki Masuda, Christian L. Vestergaard
  • Published online:
    12 December 2022
    Print publication:
    05 January 2023
    • Element
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  • Many multiagent dynamics can be modeled as a stochastic process in which the agents in the system change their state over time in interaction with each other. The Gillespie algorithms are popular algorithms that exactly simulate such stochastic multiagent dynamics when each state change is driven by a discrete event, the dynamics is defined in continuous time, and the stochastic law of event occurrence is governed by independent Poisson processes. The first main part of this volume provides a tutorial on the Gillespie algorithms focusing on simulation of social multiagent dynamics occurring in populations and networks. The authors clarify why one should use the continuous-time models and the Gillespie algorithms in many cases, instead of easier-to-understand discrete-time models. The remainder of the Element reviews recent extensions of the Gillespie algorithms aiming to add more reality to the model (i.e., non-Poissonian cases) or to speed up the simulations. This title is also available as open access on Cambridge Core.

  • 6 - Statistical Mechanics

  • from II - Mathematical Tools of Complexity Science
  • Henrik Jeldtoft Jensen, Imperial College London
  • Book:
    Complexity Science
    Published online:
    13 December 2022
    Print publication:
    17 November 2022, pp 110-162

  • Summary

    Properties and behaviours at the systemic aggregate level are derived as statistical averages from probability distributions describing the likelihoods of the various states available to the components.

  • 9 - Information Theory and Entropy

  • from II - Mathematical Tools of Complexity Science
  • Henrik Jeldtoft Jensen, Imperial College London
  • Book:
    Complexity Science
    Published online:
    13 December 2022
    Print publication:
    17 November 2022, pp 230-278

  • Summary

    Assume we are able to obtain the joint probability for a set of time series representing a complex system. Based on the joint probabilities, information theory can help to analyse the nature of the interdependence in the system. It is particularly important to be able to distinguish between different types of emergent behaviour, such as synergy or redundancy.

  • 14 - Concluding Comments and a Look to the Future

  • from II - Mathematical Tools of Complexity Science
  • Henrik Jeldtoft Jensen, Imperial College London
  • Book:
    Complexity Science
    Published online:
    13 December 2022
    Print publication:
    17 November 2022, pp 397-400

  • Summary

    We point out that complexity science is developing fast and that present and future scientific and societal challenges will need fundamental improvements in our ability to analyse and deal with complex emergent behaviour. It is therefore desirable to spread widely the awareness of approaches and insights from complexity science.

  • 4 - The Value of Prototypical Models of Emergence

  • from I - Conceptual Foundation of Complexity Science
  • Henrik Jeldtoft Jensen, Imperial College London
  • Book:
    Complexity Science
    Published online:
    13 December 2022
    Print publication:
    17 November 2022, pp 75-86

  • Summary

    Conceptual and mathematical models can serve many purposes. We will discuss why simple stylistic models are particularly useful in complexity science since they can help to identify the most essential mechanisms amongst the profusion of interdependencies at play.

  • 7 - Synchronisation

  • from II - Mathematical Tools of Complexity Science
  • Henrik Jeldtoft Jensen, Imperial College London
  • Book:
    Complexity Science
    Published online:
    13 December 2022
    Print publication:
    17 November 2022, pp 163-176

  • Summary

    When interactions between individual dynamical components are sufficiently strong, coordinated dynamics at the systemic level can emerge. This is called synchronisation.

  • 3 - Specific Types of Emergent Behaviour

  • from I - Conceptual Foundation of Complexity Science
  • Henrik Jeldtoft Jensen, Imperial College London
  • Book:
    Complexity Science
    Published online:
    13 December 2022
    Print publication:
    17 November 2022, pp 46-74

  • Summary

    We present a few paradigmatic modelling strategies selected due to their generality in addressing the emergence of spatio-temporal structure, including criticality, synchronisation, intermittency, adaptation and forecasting.

  • I - Conceptual Foundation of Complexity Science

  • Henrik Jeldtoft Jensen, Imperial College London
  • Book:
    Complexity Science
    Published online:
    13 December 2022
    Print publication:
    17 November 2022, pp 1-86

  • Summary

    The chapters of Part I will discuss why complexity science is important, how this science relates to other sciences and also a little bit about its philosophical status. The aim is to make clear what makes complexity science special and in which way it contributes to our understanding of the surrounding world.

Page 11 of 104