具有外部输入和偏差的细胞神经网络的完全稳定性

本文证明了对于由两个细胞组成的细胞神经网络，外部输入和偏差不影响网络的稳定平衡点的存在性和完全稳定性．     

Fractal dimension at the phase transition of inhomogeneous cellular automata

For random binary mixtures of cellular automata in the square lattice, calculations are made of the fractal dimensions associated with the damage spreading and the propagation time of damage at the transition to chaos. Two rules are mixed and universalities of these quantities are sought with respect to change of the rules.     

Measurement and correlation of volumetric heat transfer coefficients of cellular ceramics

The volumetric heat transfer coefficients (h_v) between cellular ceramics and a stream of air were measured using the single-blow transient experimental technique in conjunction with an inverse analysis. Test specimen made of mullite, YZA, SiC, cordierite and cordierite with LS-2 coating was studied. The number of pores per centimeter (PPC) ranged from 4 to 26 and the specimen thickness ranged from 6 to 12 mm. Based on the experimental data, the volumetric heat transfer coefficients were generalized by developing Nusselt number vs. Reynolds number correlations of the form Nu_v=C Re^m for the materials studied. The effects of pore length-scale and specimen thickness on the volumetric heat transfer coefficients are presented and discussed.     

On the law of entropy increase of some cellular automata on Zd

We consider some time-reversible cellular automata on thed-dimensional integral latticeZ ^d and study their time evolution properties. We show first that a Boltzmann-type entropy can be defined which is not less than its initial value for initial States which have no spatial correlation. For monotonic increase of the entropies for such initial States we need an additional condition which we call renewality. Under the renewality condition entropy is monotonic nondecreasing. We give some examples of cellular automata which satisfy the renewality condition     

Traffic flow models with ‘slow-to-start’ rules

We investigate two models for traffic flow with modified acceleration (‘slow-to-start’) rules. Even in the simplest case v_max = 1 these rules break the ‘particle-hole’ symmetry of the model. We determine the fundamental diagram (flow-density relationship) using the so-called car-oriented mean-field approach (COMF) which yields the exact solution of the basic model with v_max = 1. Here we find that this is no longer true for the models with modified acceleration rules, but the results are still in good agreement with simulations. We also compare the effects of the two different slow-to-start rules and discuss their relevance for real traffic. In addition, in one of these models we find a new phase transition to a completely jammed state.     

A percolation approach to the Kauffman model

A study is made of the spreading of damage in the random but deterministic Kauffman model on the square lattice with the spreading from one edge of the lattice. The critical value of the parameterp _c above which the system becomes chaotic is found to bep _c0.298. The possibility of suppression of the chaotic phase by noise is also studied. It is found that forpp _c, an extremely large noise levelg>0.99 is required, if possible at all.On leave from Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

Invariant strings and pattern-recognizing properties of one-dimensional cellular automata

A cellular automaton is a discrete dynamical system whose evolution is governed by a deterministic rule involving local interactions. It is shown that given an arbitrary string of values and an arbitrary neighborhood size (representing the range of interaction), a simple procedure can be used to find the rules of that neighborhood size under which the string is invariant. The set of nearestneighbor rules for which invariant strings exist is completely specified, as is the set of strings invariant under each such rule. For any automaton rule, an associated filtering rule is defined for which the only attractors are spatial sequences consisting of concatenations of invariant strings. A result is provided defining the rule of minimum neighborhood size for which an arbitrarily chosen string is the unique invariant string. The applications of filtering rules to pattern recognition problems are discussed.     

Critical behavior of sandpile vortices under variable charge

In the following, we consider a sandpile cellular automaton model (height version), which also takes account of lattice cyclicity for variable charge of grains projected upon the board. The size of the charge or additional grains of sand used to upset the equilibrium and to induce an avalanche is found to affect the distributional forms and in particular the convergence of the estimate for the dynamic exponent. Exponent estimates show slow variation with lattice dimensionL and some evidence of evolution with charge. The scaling region is limited in all cases with noisy decay at all levels of charge. Results presented extend the work of Duarte and Goncalves (1990) on the triangular lattice.     

Cellular automata and statistical mechanical models

We elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata. Transient and stationary properties of probabilistic automata are linked to surface and bulk properties, respectively, of restricted statistical mechanical systems. It is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata. Some exact results are derived, including duality transformations, exact mappings, disorder, and linear solutions. Many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties. This approach is considered to be a first step toward the design of fully parallel,probabilistic systems whose computational abilities rely on the cooperative behavior of their components.On leave from Institute for Theoretical Physics, Roland Eötvös University, Budapest, Hungary.