Alexandru Agapie

Probabilistic Cellular Automata

Cellular automata are binary lattices used for modeling complex dynamical systems. The automaton evolves iteratively from one configuration to another, using some local transition rule based on the number of ones in the neighborhood of each cell. With respect to the number of cells allowed to change per iteration, we speak of either synchronous or asynchronous automata. If randomness is involved to some degree in the transition rule, we speak of probabilistic automata, otherwise they are called deterministic. With either type of cellular automaton we are dealing with, the main theoretical challenge stays the same: starting from an arbitrary initial configuration, predict (with highest accuracy) the end configuration. If the automaton is deterministic, the outcome simplifies to one of two configurations, all zeros or all ones. If the automaton is probabilistic, the whole process is modeled by a finite homogeneous Markov chain, and the outcome is the corresponding stationary distribution. Based on our previous results for the asynchronous case-connecting the probability of a configuration in the stationary distribution to its number of zero-one borders-the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata.

Economic Forecasting Using Genetic Algorithms

When one deals with short-length, non-stationary time series with seasonal components, the statistical procedures of forecasting or even the neural networks prove to be unsatisfactory. We propose in this paper a Genetic Algorithm method for finding the optimal parameters involved in the classical Holt-Winters model of time series forecasting.

Genetic Algorithms for Solving Systems of Fuzzy Relational Equations

We propose in this paper a unified method for approximating the solution of a System of Fuzzy Relational Equations (SFRE). The method is essentially based on the use of Genetic Algorithms (GA) and on a probabilistic algorithm for solving a SFRE — presented elsewhere. This approach is useful both in classical SFRE problems and in dynamic system identification. Some numerical results regarding both aspects show that our method can be successfully applied.

Predictability in Cellular Automata

Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automatons binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case.

Function Approximation Using Tensor Product Bernstein Polynomials-Neuro & Evolutionary Approaches

This paper introduces an approximation technique based on Tensor Product Bernstein Polynomials (TPBPs) and Genetic Algorithms (GAs), res. Neural Networks (NN). First we present the basic model of TPBP, for which suitable control points need to be found, and some of the GA & NN theoretical features. Then we illustrate the efficiency of GAs on multi-parameter optimization in problem of finding optimal control points for TPBPs and the efficiency of NN in our approximation problem. We find these approaches very robust and having good generalization abilities.