Adaptation Noise And Self Organizing Systems

For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level and the rate of change of the parameter. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density and last crossing time of zero are compared with results from numerical generation of paths.

We study numerically and analytically a stochastic group selection model in which a population of asexually reproducing individuals, each of which can be either altruist or non-altruist, is subdivided into M reproductively isolated groups (demes) of size N . The cost associated with being altruistic is modelled by assigning the fitness 1−τ , with τ∈[0,1] , to the altruists and the fitness 1 to the non-altruists. In the case that the altruistic disadvantage τ is not too large, we show that the finite M fluctuations are small and practically do not alter the deterministic results obtained for M→∞ . However, for large τ these fluctuations greatly increase the instability of the altruistic demes to mutations. These results may be relevant to the dynamics of parasite-host systems and, in particular, to explain the importance of mutation in the evolution of parasite virulence.

We investigate the dynamics of the choice of an active strategy in the minority game. A history distribution is introduced as an analytical tool to study the asymmetry between the two choices offered to the agents. Its properties are studied numerically. It allows us to show that the departure from uniformity in the initial attribution of strategies to the agents is important even in the efficient market. Also, an approximate expression for the variance of the number of agents at one side in the efficient phase is proposed. All the analytical propositions are supported by numerical simulations of the system.

The coupled map lattice by Olami {\it et al.} [Phys. Rev. Lett. {\bf 68}, 1244 (1992)] is ``doped'' by letting just {\it one} site have a threshold, T ∗ max , bigger than the others. On an L×L lattice with periodic boundary conditions this leads to a transition from avalanche sizes of about one to exactly L 2 , and after each avalanche stresses distributes among only five distinct values, τ k , related to the parameters α and T ∗ max by τ k =kα T ∗ max where k=0,1,2,3,4 . This result is independent of lattice size. The transient times are inversely proportional to the amount of doping and increase linearly with L .

We study a modular neuron alternative to the McCulloch-Pitts neuron that arises naturally in analog devices in which the neuron inputs are represented as coherent oscillatory wave signals. Although the modular neuron can compute XOR at the one neuron level, it is still characterized by the same Vapnik-Chervonenkis dimension as the standard neuron. We give the formulas needed for constructing networks using the new neuron and training them using back-propagation. A numerical study of the modular neuron on two data sets is presented, which demonstrates that the new neuron performs at least as well as the standard neuron.

A spacially extended model of the collective behavior of a large number of locally acting organisms is proposed in which organisms move probabilistically between local cells in space, but with weights dependent on local morphogenetic substances, or morphogens. The morphogens are in turn are effected by the passage of an organism. The evolution of the morphogens, and the corresponding flow of the organisms constitutes the collective behavior of the group. Such models have various types of phase transitions and self-organizing properties controlled both by the level of the noise, and other parameters. The model is then applied to the specific case of ants moving on a lattice. The local behavior of the ants is inspired by the actual behavior observed in the laboratory, and analytic results for the collective behavior are compared to the corresponding laboratory results. It is hoped that the present model might serve as a paradigmatic example of a complex cooperative system in nature. In particular swarm models can be used to explore the relation of nonequilibrium phase transitions to at least three important issues encountered in artificial life. Firstly, that of emergence as complex adaptive behavior. Secondly, as an exploration of continuous phase transitions in biological systems. Lastly, to derive behavioral criteria for the evolution of collective behavior in social organisms.

We argue that the phenomenon of symmetry breaking in genetics can enhance the adaptability of a species to changes in the environment. In the case of a virus, the claim is that the codon bias in the neutralization epitope improves the virus' ability to generate mutants that evade the induced immune response. We support our claim with a simple ``toy model'' of a viral epitope evolving in competition with the immune system. The effective selective advantage of a higher mutability leads to a dominance of codons that favour non-synonymous mutations. The results in this paper suggest the possibility of emergence of an algorithmic language in more complicated systems.

Although several synonymous codons can encode the same aminoacid, this symmetry is generally broken in natural genetic systems. In this article, we show that the symmetry breaking can result from selective pressures due to the violation of the synonym symmetry by mutation and recombination. We conjecture that this enhances the probability to produce mutants that are well-adapted to the current environment. Evidence is found in the codon frequencies of the HIV {\it env} protein: the codons most likely to mutate and lead to new viruses resistant to the current immunological attack, are found with a greater frequency than their less mutable synonyms.

We show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the KPZ equation. Numerical simulations in 1d confirm this prediction, and yield other exponents of the multiplicative noise problem. The numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values, and show that the exponent governing the divergence in this range varies continuously with control parameter.

Knowledge of fundamental traffic flow characteristics of traffic simulation models is an essential requirement when using these models for the planning, design, and operation of transportation systems. In this paper we discuss the following: a description of how features relevant to traffic flow are currently under implementation in the TRANSIMS microsimulation, a proposition for standardized traffic flow tests for traffic simulation models, and the results of these tests for two different versions of the TRANSIMS microsimulation.