Adaptation Noise And Self Organizing Systems

We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a systematic way using Van Kanpen's expansion method for Markov processes. We present some results for both stationary and time-dependent states. Our approach allows the effect of fluctuations to be explored, particularly in finite systems where such processes assume increasing importance.

Within the framework of the frozen temperature approximation we develop a strongly-nonlinear theory of one-dimensional pattern formation during directional solidification of binary mixture under nonequilibrium segregation. In the case of small partition coefficient the full problem is reduced to the system of two ordinary differential equations describing the interface motion in terms of its velocity and position coordinate. The type of the oscillatory instability bifurcation is studied in detail in different limits. For the subcrytical bifurcaton relaxation interface oscillations are analyzed analytically and numerically. We show that these oscillation exibit a number of anomalous properies. In particular, such oscillations can be weakly- or strongly-dissipative depending on the physical parameters and the amplitude of the strongly-dissipative oscillations is determined not only by the form of the corresponding nullcline but also by the behavior of the system for small values of the interface velocity. Characteristic parameters of the superlattice occuring in the growing crystal are estimated.

A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their flow diagrams are determined. Various examples are presented and applications to car traffic are indicated. Two nontrivial three-state three-input self-conjugate rules have been found. They can be used to model the dynamics of random walkers.

Surface level instability when tube is injected into vibrating bed of powder, which was originally found in experiments, is investigated numerically. We find that thicker (thiner) tube makes surface level inside tube higher (lower) than surface level outside tube. With fixed acceleration amplitude of vibration, surface level inside tube becomes higher as amplitude of vibration increases, which can be explained by considering the dependence upon strength of convective flow.

This paper is a compact overview of the heuristic approach to the recently elaborated octonionic binocular mobilevision.

We present a theoretical as well as experimental investigation of a population of self-replicating segments of code subject to random mutation and survival of the fittest. Under the assumption that such a system constitutes a minimal system with characteristics of life, we obtain a number of statements on the evolution of complexity and the trade-off between entropy and information.

We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also computationally feasible since it involves no greater than O( N 3 ) arithmetic computations where N is the total number of sites of the system. Key words: Abelian sandpile model; avalanche-finiteness; self-organized criticality

We investigate a problem of the necessary and sufficient conditions for appearance of the 1/f fluctuations in the simple systems affected by the external random perturbations, i.e. the power spectral density of the flux of particles moving in some contours and perturbed by the external forces. In some cases we observe the 1/f behavior but only in some range of frequencies and parameters of the systems.

A random boolean cellular automaton is a network of boolean gates where the inputs, the boolean function, and the initial state of each gate are chosen randomly. In this article, each gate has two inputs. Let a (respectively c ) be the probability the the gate is assigned a constant function (respectively a non-canalyzing function, i.e., {\sc equivalence} or {\sc exclusive or}). Previous work has shown that when a>c , with probability asymptotic to 1, the random automaton exhibits very stable behavior: almost all of the gates stabilize, almost all of them are weak, i.e., they can be perturbed without affecting the state cycle that is entered, and the state cycle is bounded in size. This article gives evidence that the condition a=c is a threshold of chaotic behavior: with probability asymptotic to 1, almost all of the gates are still stable and weak, but the state cycle size is unbounded. In fact, the average state cycle size is superpolynomial in the number of gates.

Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states 0,1,...,n−1 , can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the above density classification task cannot be resolved by a single cellular automaton, this task can be performed efficiently by applying two cellular automaton rules in succession.