Random Topologies and the emergence of cooperation: the role of short-cuts

We study in detail the role of short-cuts in promoting the emergence of cooperation in a network of agents playing the Prisoner's Dilemma Game (PDG). We introduce a model whose topology interpolates between the one-dimensional euclidean lattice (a ring) and the complete graph by changing the value of one parameter (the probability p to add a link between two nodes not already connected in the euclidean configuration). We show that there is a region of values of p in which cooperation is largely enhanced, whilst for smaller values of p only a few cooperators are present in the final state, and for p \rightarrow 1- cooperation is totally suppressed. We present analytical arguments that provide a very plausible interpretation of the simulation results, thus unveiling the mechanism by which short-cuts contribute to promote (or suppress) cooperation

Composite Fermion Wavefunctions Derived by Conformal Field Theory

The Jain theory of hierarchical Hall states is reconsidered in the light of recent analyses that have found exact relations between projected Jain wavefunctions and conformal field theory correlators. We show that the underlying conformal theory is precisely given by the W-infinity minimal models introduced earlier. This theory involves a reduction of the multicomponent Abelian theory that is similar to the projection to the lowest Landau level in the Jain approach. The projection yields quasihole excitations obeying non-Abelian fractional statistics. The analysis closely parallels the bosonic conformal theory description of the Pfaffian and Read-Rezayi states.Comment: 4 pages, 1 figur

Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas II: The many point particles system

We study the stationary nonequilibrium states of N point particles moving under the influence of an electric field E among fixed obstacles (discs) in a two dimensional torus. The total kinetic energy of the system is kept constant through a Gaussian thermostat which produces a velocity dependent mean field interaction between the particles. The current and the particle distribution functions are obtained numerically and compared for small E with analytic solutions of a Boltzmann type equation obtained by treating the collisions with the obstacles as random independent scatterings. The agreement is surprisingly good for both small and large N. The latter system in turn agrees with a self consistent one particle evolution expected to hold in the limit of N going to infinity.Comment: 14 pages, 9 figure

Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood

A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least squares approach is fundamentally flawed in that it assumes independent, normally distributed (IND) forecast errors: nonlinear models will not yield IND errors even if the noise is IND. A new cost function is obtained via the maximum likelihood principle; superior results are illustrated both for small data sets and infinitely long data streams.Comment: RevTex, 11 pages, 4 figure

Photography as an act of collaboration

The camera is usually considered to be a passive tool under the control of the operator. This definition implicitly constrains how we use the medium, as well as how we look at – and what we see in – its interpretations of scenes, objects, events and ‘moments’. This text will suggest another way of thinking about – and using – the photographic medium. Based on the evidence of photographic practice (mine and others’), I will suggest that, as a result of the ways in which the medium interprets, juxtaposes and renders the elements in front of the lens, the camera is capable of depicting scenes, events and moments that did not exist and could not have existed until brought into being by the act of photographing them. Accordingly, I will propose that the affective power of many photographs is inseparable from their ‘photographicness’ – and that the photographic medium should therefore be considered as an active collaborator in the creation of uniquely photographic images

Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical "device" that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.Comment: 34 pages, 4 figure

Lyapunov Exponents from Kinetic Theory for a Dilute, Field-driven Lorentz Gas

Positive and negative Lyapunov exponents for a dilute, random, two-dimensional Lorentz gas in an applied field, $\vec{E}$, in a steady state at constant energy are computed to order $E^{2}$. The results are: $\lambda_{\pm}=\lambda_{\pm}^{0}-a_{\pm}(qE/mv)^{2}t_{0}$ where $\lambda_{\pm}^{0}$ are the exponents for the field-free Lorentz gas, $a_{+}=11/48, a_{-}=7/48$, $t_{0}$ is the mean free time between collisions, $q$ is the charge, $m$ the mass and $v$ is the speed of the particle. The calculation is based on an extended Boltzmann equation in which a radius of curvature, characterizing the separation of two nearby trajectories, is one of the variables in the distribution function. The analytical results are in excellent agreement with computer simulations. These simulations provide additional evidence for logarithmic terms in the density expansion of the diffusion coefficient.Comment: 7 pages, revtex, 3 postscript figure

Stability ordering of cycle expansions

We propose that cycle expansions be ordered with respect to stability rather than orbit length for many chaotic systems, particularly those exhibiting crises. This is illustrated with the strong field Lorentz gas, where we obtain significant improvements over traditional approaches.Comment: Revtex, 5 incorporated figures, total size 200