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- Driss Moumida, Eric Goles
- 2006

Abst ract. We stu dy t he dyn ami cs of an automaton wit h me mory whose equation is t he following: '-1 Xntl = lC L: a j Xn _ l-0] i =O wher e a = (ai)i=o...k_ l deno tes the cou pling coefficients vector. We show that if a is symmetric, then wecan introduce an energy operator; thereby we slate that the periods of the automaton always divide (k + 1) and… (More)

One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic… (More)

- Pablo A. Estévez, Claudio A. Perez, Eric Goles, Gerardo Bühler, Rodrigo Caballero, Marcelo Fernández +3 others
- 2003

utomatic detection of defects on wood boards and grading of the products into quality categories is one of the key areas of interest in the forest products industry. A defect is considered to be any characteristic that makes wood unsuitable for a given use. With the aim of improving yield and increasing productivity , in the last decades several automated… (More)

In this paper, we study the dynamics of sand grains falling in sand piles. Usually sand piles are characterized by a decreasing integer partition and grain moves are described in terms of transitions between such partitions. We study here four main transition rules. The more classical one, introduced by Brylawski [5] induces a lattice structure L B (n)… (More)

- E. Goles, A. M. Odlyzko
- 1998

The work of Ghiglia, Mastin, and Romero on a ''phase-unwrapping'' algorithm gives rise to the following operation: for any undirected graph with arbitrary integer values attached to the vertices, simultaneous updates are performed on these values, with the value of a vertex being changed by one in the direction of the average of the values of the adjacent… (More)

In this paper we consider the Schelling social segregation model for two different populations. In Schelling's model, segregation appears as a consequence of discrimination, measured by the local difference between two populations. For that, the model defines a tolerance criterion on the neighborhood of an individual, indicating wether the individual is… (More)

- Eric Goles
- 2006

We study the dynamical behavior of automata networks defined by x(t + 1) = x(t) + f(Ax(t) + b); where A is a symmetric n x n matrix, b is a real n-vector and f is the subgradient of a convex function. More precisely we prove, by using Lyapunov operators associated to the network, that the steady state behavior of these au-tomata is simple: fixed points or… (More)

- Eric Goles, Gregorio González, Hans Herrmann, Servet Mart́ınez
- 1998

In this article we make a critical analysis of the model proposed by Weber, present an improvement that gives the logarithmic correction on the shape of sandpiles properly, and study the normal forces on the surface supporting a pile using the improved model. Much attention has been given to the physics of granular media, partly because of the many… (More)

We investigate the spread of an infection or other malfunction of cascading nature when a system component can recover only if it remains reachable from a functioning central component. We consider the susceptible-infected-susceptible model, typical of mathematical epidemiology, on a network. Infection spreads from infected to healthy nodes, with the… (More)

We present an evolutionary model that marks an encounter of two seemingly unrelated disciplines: population dynamics and number theory. Assuming mutations and selection of predators and prey, we show that prey cycles with non-prime lengths are unstable, while cycles with prime lenghts are stable. Allowing arbitrarily long cycles, this model is a… (More)