Biomedical subjects
Publications and source records attributed to Jesus Urias.
It is proved that the multifractal characterizations of diametrically regular measures that are provided by the wavelet and by the Hentschel-Procaccia formalisms are identical. (c) 2001 American Institute of Physics.
A polynomial representation of elementary cellular automata (ECA) is used to give a complete characterization of the local internal symmetries of all ECA. It is also shown that the polynomial representation is a natural choice for the study of local internal transformations of all cellular automata with two symbols. This is achieved by proving that local internal transformations are simply expressed in this representation as sums of polynomials. (c) 1998 American Institute of Physics.
The phenomenon of synchronization in pairs of cellular automata coupled in a driver-replica mode is studied. Necessary and sufficient conditions for synchronization in linear cellular automaton pairs are given. The couplings that make a pair synchronize are determined for all linear elementary cellular automata. (c) 1998 American Institute of Physics.
Cryptosystems for binary information are based on two primitives: an indexed family of permutations of binary words and a generator of pseudorandom sequences of indices. A very efficient implementation of the primitives is constructed using the phenomenon of synchronization in cellular automata. (c) 1998 American Institute of Physics.
(Internal) transformations on the space Sigma of automaton configurations are defined as bi-infinite sequences of permutations of the cell symbols. A pair of transformations (gamma,theta) is said to be an internal symmetry of a cellular automaton f:Sigma-->Sigma if f=theta(-1)fgamma. It is shown that the full group of internal symmetries of an automaton f can be encoded as a group homomorphism F such that theta=F(gamma). The domain and image of the homomorphism F have, in general, infinite order and F is presented by a local automaton-like rule. Algorithms to compute the symmetry homomorphism F and to classify automata by their symmetries are presented. Examples on the types of dynamical implications of internal symmetries are discussed in detail. (c) 1997 American Institute of Physics.
The property of sensitive dependence on intial conditions is the basis of a rigorous mathematical construction of local maximum Lyapunov exponents for cellular automata. The maximum Lyapunov exponent is given by the fastest average velocity of either the left or right propagating damage fronts. Deviations from the long term behavior of the finite time Lyapunov exponents due to generation of information are quantified and could be used for the characterization of the space time complexity of cellular automata. (c) 1997 American Institute of Physics.
A method to identify the invariant subsets of bi-infinite configurations of cellular automata that propagate rigidly with a constant velocity nu is described. Causal traveling configurations, propagating at speeds not greater than the automaton range, mid R:numid R:</=r, are considered. The sets of traveling configurations are presented by finite automata and its topological entropy is calculated. When the invariant subset of traveling configurations has nonzero topological entropy, the dynamics is dominated by the interaction of domains, composed of traveling patterns of finite size. The sets of traveling patterns and domains are presented by finite automata. End-resolving CA are shown to always have sets of traveling configurations that are spatially periodic with zero entropy, except possibly for traveling configurations at top speed. The elementary CA are examined exhaustively along these lines. (c) 1996 American Institute of Physics.