Resources

 

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Contents

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Statistical Mechanics

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Online Books

  • James P. Sethna. Statistical Mechanics: Entropy, Order Parameters, and Complexity. Oxford Master Series in Statistical, Computational, and Theoretical Physics. Oxford University Press, 2006.
    • Abstract
    In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics — a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.
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Complex Networks

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Academic Papers

  • S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes.Critical Phenomena in Complex Networks. arXiv. 2007.
    • Abstract
    The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.
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Comlex Dynamical Systems

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Lists of Frequently Asked Questions

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Courses

  • Computational Methods for Nonlinear Systems taught as Computing & Information Sciences 629 and Physics 682 by Chris Myers at Cornell University.
    • Abstract
    Computational science involves the synthesis of data structures, algorithms, numerical analysis, programming methodologies, simulation, visualization, data analysis, and performance optimization, all applied to the study of complex problems in science and engineering. CIS 629 / Physics 682 is a graduate computational science laboratory course, emphasizing hands-on programming to address a number of interesting problems arising in physics, biology, engineering, applied mathematics, and computer science. The course is largely self-paced, allowing students to choose from among a variety of topics, and explore new problems of particular interest.
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Evolutionary Game Theory and Social Interaction

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Surveys

  • Robert E. Marks. Playing Games with the Genetic Algorithm. February, 2000.
    • Abstract
    Over the past 25 years, non-coöperative game theory has moved from the periphery of mainstream economics to the centre of micro-economics and macro-economics. Issues of information, signalling, reputation, and strategic interaction can best be analysed in a game-theoretic framework. But solution of the behaviour and equilibrium of a dynamic or repeated game is not as simple as that for a static or one-shot game. The multiplicity of Nash equilibria of repeated games has led to attempts to eliminate many of these through refinements of the equilibrium concept. At the same time, the use of the rational expectations assumption to cut the Gordian Knot of the intractability of dynamic problems has led to a reaction against the super-rational Homo calculans model towards boundedly rational models of human behaviour. In the late 'eighties the Genetic Algorithm (GA) was first used to solve a dynamic game, the repeated Prisoner's Dilemma (RPD). Mimicking Darwinian natural selection, as a simulation it could only elucidate sufficient conditions for its Markov Perfect Equilibria (MPE), rather than the necessary conditions of closed-formed solution, but over the past twenty-odd years, its use in economics has grown to facilitate much greater understanding of evolution, learning, and adaptation of economic agents. This brief survey attempts to highlight emergence of the marriage of GAs and game theory.
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Academic Papers

  • David Chavalarias. Cooperation: Popularity or Cliquishness? European Conference on Complex Systems. Oxford, September 2006.
    • Abstract
    We propose an analytical and computational insight about the role of endogenous networks in emergence and sustainability of cooperation and exhibits an alternative to the choice and refusal mechanism that is often proposed to explain cooperation.
  • Rui Dilão and João Graciano. Evaluating Deterministic Policies in Two-Player Iterated Games. arXiv, 2006.
    • Abstract
    We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the deterministic policies with finite memory. In particular, we show that if one of the players has a generalized tit-for-tat policy, the mean payoff per move of both players is the same, forcing the equalization of the mean payoffs per move of both players. In the case of symmetric, non-cooperative and dilemmatic games, we show that generalized tit-for-tat policies together with the condition of not being the first to defect, leads to the highest mean payoffs per move for the players.
  • Thomas Fent, Patrick Groeber, Frank Schweitzer. Coexistence of Social Norms based on In- and Out-group Interactions. ACS — Advances in Complex Systems, vol. 10, no. 2 (2007), pp. 271-286.
    • Abstract
    The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper we propose an agent-based model to show that randomly distributed social behavior by way of local interaction converges to a state with a multimodal distribution of behavior. This can be interpreted as a coexistence of different social norms, a result that goes beyond previous investigations. The model is discrete in time and space, behavior is characterized in a continuous state space. The adaptation of social behavior by each agent is based on attractive and repulsive forces caused by friendly and adversary relations among agents. The model is analyzed both analytically and by means of spatio-temporal computer simulations. It provides conditions under which we find convergence towards a single norm, coexistence of two opposing norms, and coexistence of a multitude of norms. For the latter case, we also show the evolution of the spatio-temporal distribution of behavior.
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Video Lectures

  • Evaluating Deterministic Policies in Two-Player Iterated Games. A video lecture Rui Dilão, NonLinear Dynamics Group, IST - Instituto Superior Técnico.
    • Abstract
    We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the deterministic policies with finite memory. In particular,we show that if one of the players has a generalized tit-for-tat policy,the mean payoff per move of both players is the same, forcing the equalization of the mean payoffs per move of both players. In the case of symmetric, non-cooperative and dilemmatic games, we show that generalized tit-for-tat or imitation policies together with the condition of not being the first to defect, leads to the highest mean payoffs per move for the players. Within this approach, it can be decided which policies perform better than others.The Prisoner’s Dilemma and the Hawk-Dove games have been analyzed,and the equilibrium states of the infinitely iterated games have been determined. The infinitely iterated Prisoner's Dilemma game can have Nash solutions only if players have deterministic policies.
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Multi-Agent Systems

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Academic Papers

  • Liviu Panait, Sean Luke. Cooperative Multi-Agent Learning: The State of the Art. Autonomous Agents and Multi-Agent Systems. Springer Netherlands. Volume 11, Number 3 / November, 2005.
    • Abstract
    Cooperative multi-agent systems are ones in which several agents attempt, through their interaction, to jointly solve tasks or to maximize utility. Due to the interactions among the agents, multi-agent problem complexity can rise rapidly with the number of agents or their behavioral sophistication. The challenge this presents to the task of programming solutions to multi-agent problems has spawned increasing interest in machine learning techniques to automate the search and optimization process.
    We provide a broad survey of the cooperative multi-agent learning literature. Previous surveys of this area have largely focused on issues common to specific subareas (for example, reinforcement learning or robotics). In this survey we attempt to draw from multi-agent learning work in a spectrum of areas, including reinforcement learning, evolutionary computation, game theory, complex systems, agent modeling, and robotics.
    We find that this broad view leads to a division of the work into two categories, each with its own special issues: applying a single learner to discover joint solutions to multi-agent problems (team learning), or using multiple simultaneous learners, often one per agent (concurrent learning). Additionally, we discuss direct and indirect communication in connection with learning, plus open issues in task decomposition, scalability, and adaptive dynamics. We conclude with a presentation of multi-agent learning problem domains, and a list of multi-agent learning resources.
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Miscellaneous

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Document Preparation

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LaTeX

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Tutorials

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LaTeX Packages

These are some of my favourite LaTex: \LaTeX packages:

  • listings. The listings package is a source code printer for LaTex: \LaTeX . You can typeset standalone files as well as listings with an environment similar to verbatim as well as you can print code snippets using a command similar to \verb. Many parameters control the output and if your preferred programming language isn't already supported, you can make your own definition.
  • PSTricks. A collection of PostScript based LaTex: \TeX macros that is compatible with most LaTex: \TeX macro packages, including LaTex: \LaTeX that implements colour, graphics, rotation, trees and overlays. It's extremely useful for diagrams, such as phase portraits, etc.
  • epigraph. A package for typesetting epigraphs.
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