Biomedical subjects

Alexandre S Martinez

Publications and source records attributed to Alexandre S Martinez.

3 recordsLinked to original sources

PubMed2006

Deterministic walks as an algorithm of pattern recognition.

New tools for automatically finding data clusters that share statistical properties in a heterogeneous data set are imperative in pattern recognition research. Here we introduce a deterministic procedure as a tool for pattern recognition in a hierarchical way. The algorithm finds attractors of mutually close points based on the neighborhood ranking. A memory parameter mu acts as a hierarchy parameter, in which the clusters are identified. The final result of the method is a general tree that represents the nesting structure of the data in an invariant way by scale transformation.

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PubMed2004

Exploratory behavior, trap models, and glass transitions.

A random walk is performed on a disordered landscape composed of N sites randomly and uniformly distributed inside a d-dimensional hypercube. The walker hops from one site to another with probability proportional to exp[-betaE(D)], where beta=1/T is the inverse of a formal temperature and E(D) is an arbitrary cost function which depends on the hop distance D. Analytic results indicate that, if E(D)=D(d) and N--> infinity, there exists a glass transition at beta(d)=pi(d/2)/[(d/2)Gamma(d/2)]. Below T(d), the average trapping time diverges and the system falls into an out-of-equilibrium regime with aging phenomena. A Lévy flight scenario and applications of exploratory behavior are considered.

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PubMed2003

Escaping from cycles through a glass transition.

A random walk is performed over a disordered media composed of N sites random and uniformly distributed inside a d-dimensional hypercube. The walker cannot remain in the same site and hops to one of its n neighboring sites with a transition probability that depends on the distance D between sites according to a cost function E(D). The stochasticity level is parametrized by a formal temperature T. In the case T=0, the walk is deterministic and ergodicity is broken: the phase space is divided in a O(N) number of attractor basins of two-cycles that trap the walker. For d=1, analytic results indicate the existence of a glass transition at T(1)=1/2 as N--> infinity. Below T1, the average trapping time in two-cycles diverges and an out-of-equilibrium behavior appears. Similar glass transitions occur in higher dimensions when the right cost function is chosen. We also present some results for the statistics of distances for Poisson spatial point processes.

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