Adaptation Noise And Self Organizing Systems

We applied multiresolution wavelet analysis to the sequence of times between human heartbeats (R-R intervals) and have found a scale window, between 16 and 32 heartbeats, over which the widths of the R-R wavelet coefficients fall into disjoint sets for normal and heart-failure patients. This has enabled us to correctly classify every patient in a standard data set as either belonging to the heart-failure or normal group with 100% accuracy, thereby providing a clinically significant measure of the presence of heart-failure from the R-R intervals alone. Comparison is made with previous approaches, which have provided only statistically significant measures.

The bit-string model of biological aging is used to simulate the catastrophic senescence of Pacific Salmon. We have shown that reproduction occuring only once and at a fixed age is the only ingredient needed to explain the catastrophic senescence according the mutation accumulation theory. Several results are presented, some of them with up to 10 8 fishes, showing how the survival rates in catastrophic senescence are affected by changes in the parameters of the model.

This paper shows that a new type of artificial neural network (ANN) -- the Simultaneous Recurrent Network (SRN) -- can, if properly trained, solve a difficult function approximation problem which conventional ANNs -- either feedforward or Hebbian -- cannot. This problem, the problem of generalized maze navigation, is typical of problems which arise in building true intelligent control systems using neural networks. (Such systems are discussed in the chapter by Werbos in K.Pribram, Brain and Values, Erlbaum 1998.) The paper provides a general review of other types of recurrent networks and alternative training techniques, including a flowchart of the Error Critic training design, arguable the only plausible approach to explain how the brain adapts time-lagged recurrent systems in real-time. The C code of the test is appended. As in the first tests of backprop, the training here was slow, but there are ways to do better after more experience using this type of network.

We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and given by the principal eigenvector of the network's adjacency matrix. Moreover, the average number of neutral mutant neighbors per individual is given by the matrix spectral radius. This quantifies the extent to which populations evolve mutational robustness: the insensitivity of the phenotype to mutations. Since the average neutrality is independent of evolutionary parameters---such as, mutation rate, population size, and selective advantage---one can infer global statistics of neutral network topology using simple population data available from {\it in vitro} or {\it in vivo} evolution. Populations evolving on neutral networks of RNA secondary structures show excellent agreement with our theoretical predictions.

A parabolic stochastic PDE is studied analytically and numerically, when a bifurcation parameter is slowly increased through its critical value. The aim is to understand the effect of noise on delayed bifurcations in systems with spatial degrees of freedom. Realisations of the nonautonomous stochastic PDE remain near the unstable configuration for a long time after the bifurcation parameter passes through its critical value, then jump to a new configuration. The effect of the nonlinearity is to freeze in the spatial structure formed from the noise near the critical value.

Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems can be described in terms of a one-dimensional map, and previous work has shown how the effect of noise can be modelled by a simple adjustment to the map. Here we undertake an in depth investigation of a particular set of equations, using the methods of stochastic integration. We confirm the prediction of the earlier studies that the noise becomes important when mu|log(epsilon)| = O(1), where mu is the small timescale ratio and \epsilon is the noise level. In addition, we present detailed information about the statistics of the solution when the noise is a dominant effect; the analytical results show excellent agreement with numerical simulations.

We consider swarms formed by populations of self-propelled particles with attractive long-range interactions. These swarms represent multistable dynamical systems and can be found either in coherent traveling states or in an incoherent oscillatory state where translational motion of the entire swarm is absent. Under increasing the noise intensity, the coherent traveling state of the swarms is destroyed and an abrupt transition to the oscillatory state takes place.

We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations thus retaining long-term memory of previous states. The exponents are robust and model-independent. We discuss novel implications of these results for the functioning of cortical neurons as well as for networks of neurons.

We provide rigorous proofs which show that the main features of the Parisi solution of the Sherrington-Kirkpatrick spin glass are not valid for more realistic spin glass models in any dimension and at any temperature.

This paper presents a complete description of noise-induced decay of a metastable state in a wide range of noise intensity. Recurrent formulas of exact moments of decay time valid for arbitrary noise intensity have been obtained. The nondecay probability of a metastable state was found to be really close to the exponent even for the case when the potential barrier height is comparable or smaller than the noise intensity.