Adaptation Noise And Self Organizing Systems

We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value' distribution when the parameter is explicitly a function of time and the dynamics are controlled by additive Gaussian noise. We derive a new expression for the small correction introduced if the noise is coloured (exponentially correlated). There is good agreement with results obtained from simulation of sample paths of the appropriate stochastic differential equations. Multiplicative noise does not produce noise-controlled dynamics in this fashion.

A class of models with applications to swarm behavior as well as many other types of spatially extended complex biological and physical systems is studied. Internal fluctuations can play an active role in the organization of the phase structure of such systems. Consequently, it is not possible to fully understand the behavior of these systems without explicitly incorporating the fluctuations. In particular, for the class of models studied here the effect of internal fluctuations due to finite size is a renormalized decrease in the temperature near the point of spontaneous symmetry breaking. We briefly outline how these models can be applied to the behavior of an ant swarm.

A set of hard spheres with tangential inelastic collision is found to reproduce observations of real and numerical granular matter. After time is scaled so as to cancel energy dissipation due to inelastic collisions out, inelastically colliding hard spheres in two dimensional space come to have 1/ f α fluctuation of total energy, non-Gaussian distribution of displacement vectors, and convective motion of spheres, which hard spheres with elastic collision, a conventional model of granular matter, cannot reproduce.

A simple model for the formation of a complex organism is introduced. Individuals can communicate and specialize, leading to an increase in productivity. If there are limits to the capacity of individuals to communicate with other individuals, the individuals form groups that interact with each other, leading to a complex organism that has interacting units on all scales.

We report some numerical simulations to investigate the existence of a self-organized critical (SOC) state in a random-neighbor version of the OFC model for a range of parameters corresponding to a non-conservative case. In contrast to a recent work, we do not find any evidence of SOC. We use a more realistic distribution of energy among sites to perform some analytical calculations that agree with our numerical conclusions.

Using an artificial system of self-replicating strings, we show a correlation between the age of a genotype and its abundance that reflects a punctuated rather than gradual picture of evolution, as suggested long ago by Willis. In support of this correlation, we measure genotype abundance distributions and find universal coefficients. Finally, we propose a simple stochastic model which describes the dynamics of equilibrium periods and which correctly predicts most of the observed distributions.

Extending the classic works of Berg and Purcell on the biophysics of bacterial chemotaxis, we find the optimal chemotactic strategy for the peritrichous bacterium E. Coli in the high and low signal to noise ratio limits. The optimal strategy depends on properties of the environment and properties of the individual bacterium and is therefore highly adaptive. We review experiments relevant to testing both the form of the proposed strategy and its adaptability and propose extensions of them which could test the limits of the adaptability in this simplest sensory processing system.

We analyze a simple model of adaptive competition which captures essential features of a variety of adaptive competitive systems in the social and biological sciences. Each of N agents, at each time step of a game, joins one of two groups. The agents in the minority group are awarded a point, while the agents in the majority group get nothing. Each agent has a fixed set of strategies drawn at the beginning of the game from a common pool, and chooses his current best-performing strategy to determine which group to join. For a fixed N, the system exhibits a phase change as a function of the size of the common strategy pool from which the agents initially draw their strategies. For small pool sizes, the system is in an efficient market phase. All information that can be used by the agents' strategies is traded away, no agent can accumulate more points than would an agent making random guesses, and thus the commons suffer,since relatively few points are awarded to the agents in total. For large initial strategy pool sizes, the system is in an inefficient market phase, in which there is predictive information available to the agents' strategies, and some agents can do better than random at accumulating points. In this phase, the total number of points awarded to the agents is greater than in a game in which all agents guess randomly, and so the commons do relatively well. At a critical size of the strategy pool marking the cross-over from the efficient market to the inefficient market phases, the commons do best. This critical size of the pool grows monotonically with N. The behavior of this system has some features reminiscent of a spin-glass.

In this paper, we investigate the associative memory in recurrent neural networks, based on the model of evolving neural networks proposed by Nolfi, Miglino and Parisi. Experimentally developed network has highly asymmetric synaptic weights and dilute connections, quite different from those of the Hopfield model. Some results on the effect of learning efficiency on the evolution are also presented.

We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as ``self-organized critical,'' including forest-fire, sandpile, and slider-block models.