Diffusion and pattern formation in spatial games.

Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to promote pattern formation in certain classes of systems. Formation of stable structures often serves as a key factor in promoting the emergence and persistence of cooperative behavior in otherwise competitive environments, however, an in-depth analysis on the impact of diffusion on such systems is lacking. We therefore investigate the effects of diffusion on cooperative behavior using a cellular automaton (CA) model of the noisy spatial iterated prisoner's dilemma (IPD), physical extension, and stochasticity being unavoidable characteristics of several natural phenomena. We further derive a mean-field (MF) model that captures the three-species predation dynamics from the CA model and highlight how pattern formation arises in this new model, then characterize how including diffusion by interchange similarly enables the emergence of large scale structures in the CA model as well. We investigate how these emerging patterns favors cooperative behavior for parameter space regions where IPD error rates classically forbid such dynamics. We thus demonstrate how the coupling of diffusion with nonlinear dynamics can, counterintuitively, promote large-scale structure formation and in return establish new grounds for cooperation to take hold in stochastic spatial systems.

A Mutation Threshold for Cooperative Takeover.

One of the leading theories for the origin of life includes the hypothesis according to which life would have evolved as cooperative networks of molecules. Explaining cooperation-and particularly, its emergence in favoring the evolution of life-bearing molecules-is thus a key element in describing the transition from nonlife to life. Using agent-based modeling of the iterated prisoner's dilemma, we investigate the emergence of cooperative behavior in a stochastic and spatially extended setting and characterize the effects of inheritance and variability. We demonstrate that there is a mutation threshold above which cooperation is-counterintuitively-selected, which drives a dramatic and robust cooperative takeover of the whole system sustained consistently up to the error catastrophe, in a manner reminiscent of typical phase transition phenomena in statistical physics. Moreover, our results also imply that one of the simplest conditional cooperative strategies, "Tit-for-Tat", plays a key role in the emergence of cooperative behavior required for the origin of life.

External approach to rhinoplasty.

The technique of external rhinoplasty is outlined. Having reviewed 74 cases, its advantages and disadvantages are discussed. Reluctance to use this external approach seems to be based on emotional rather than radical grounds, for its seems to be the procedure of choice for many problems.

Continuum analysis of an avalanche model for solar flares.

We investigate the continuum limit of a class of self-organized critical lattice models for solar flares. Such models differ from the classical numerical sandpile model in their formulation of stability criteria in terms of the curvature of the nodal field, and are known to belong to a different universality class. A fourth-order nonlinear hyperdiffusion equation is reverse engineered from the discrete model's redistribution rule. A dynamical renormalization-group analysis of the equation yields scaling exponents that compare favorably with those measured in the discrete lattice model within the relevant spectral range dictated by the sizes of the domain and the lattice grid. We argue that the fourth-order nonlinear diffusion equation that models the behavior of the discrete model in the continuum limit is, in fact, compatible with magnetohydrodynamics (MHD) of the flaring phenomenon in the regime of strong magnetic field and the effective magnetic diffusivity characteristic of strong MHD turbulence.

Geometrical properties of avalanches in self-organized critical models of solar flares.

We investigate the geometrical properties of avalanches in self-organized critical models of solar flares. Traditionally, such models differ from the classical sandpile model in their formulation of stability criteria in terms of the curvature of the nodal field, and belong to a distinct universality class. With a view toward comparing these properties to those inferred from spatially and temporally resolved flare observations, we consider the properties of avalanche peak snapshots, time-integrated avalanches in two and three dimensions, and the two-dimensional projections of the latter. The nature of the relationship between the avalanching volume and its projected area is an issue of particular interest in the solar flare context. Using our simulation results we investigate this relationship, and demonstrate that proper accounting of the fractal nature of avalanches can bring into agreement hitherto discrepant results of observational analyses based on simple, nonfractal geometries for the flaring volume.

Crossover and evolutionary stability in the prisoner's dilemma.

We examine the role played by crossover in a series of genetic algorithm-based evolutionary simulations of the iterated prisoner's dilemma. The simulations are characterized by extended periods of stability, during which evolutionarily meta-stable strategies remain more or less fixed in the population, interrupted by transient, unstable episodes triggered by the appearance of adaptively targeted predators. This leads to a global evolutionary pattern whereby the population shifts from one of a few evolutionarily metastable strategies to another to evade emerging predator strategies. While crossover is not particularly helpful in producing better average scores, it markedly enhances overall evolutionary stability. We show that crossover achieves this by (1) impeding the appearance and spread of targeted predator strategies during stable phases, and (2) greatly reducing the duration of unstable epochs, presumably by efficient recombination of building blocks to rediscover prior metastable strategies. We also speculate that during stable phases, crossover's operation on the persistently heterogeneous gene pool enhances the survival of useful building blocks, thus sustaining long-range temporal correlations in the evolving population. Empirical support for this conjecture is found in the extended tails of probability distribution functions for stable phase lifetimes.