Gonzalo Hernández

DYNAMICAL BEHAVIOR OF KAUFFMAN NETWORKS WITH AND-OR GATES

We study the parallel dynamics of a class of Kauffman boolean nets such that each vertex has a binary state machine {AND, OR} as local transition function. We have called this class of nets AON. In a finite, connected and undirected graph, the transient length, attractors and its basins of attraction are completely determined in the case of only OR (AND) functions in the net. For finite, connected and undirected AON, an exact linear bound is given for the transient time using a Lyapunov functional. Also, a necessary and sufficient condition is given for the diffusion problem of spreading a one all over the net, which generalizes the primitivity notion on graphs. This condition also characterizes its architecture. For finite, strongly connected and directed AON a non-polynomial time bound is given for the transient time and for the period on planar graphs, together with an example where this transient time and period are attained. Furthermore, on infinite but finite connected, directed and non planar AON we simulate an universal two-register machine, which allows us to exhibit universal computing capabilities.

Two-dimensional model for binary fragmentation process with random system of forces, random stopping and material resistance

This work presents the numerical results obtained from large-scale parallel distributed simulations of a self-similar model for two-dimensional discrete in time and continuous in space binary fragmentation. Its main characteristics are: (1) continuous material; (2) uniform and independent random distribution of the net forces, denoted by fx and fy, that produce the fracture; (3) these net forces act at random positions of the fragments and generate the fracture following a maximum criterion; (4) the fragmentation process has the property that every fragment fracture stops at each time step with an uniform probability p; (5) the material presents an uniform resistance r to the fracture process. Through a numerical study was obtained an approximate power law behavior for the small fragments size distribution for a wide range of the main parameters of the model: the stopping probability p and the resistance r. The visualizations of the model resemble real systems. The approximate power law distribution is a non-trivial result, which reproduces empirical results of some highly energetic fracture processes.

Parallel and distributed simulations and visualizations of the Olami–Feder–Christiensen earthquake model

In this work we present some numerical results and visualizations obtained from parallel and distributed simulations of the Olami–Feder–Christiensen earthquake model. This model is a two-dimensional cellular automata, continuous in space and discrete in time, constructed in order to simulate earthquake activity and it was introduced as a generalization of the one-dimensional spring block model defined by Burridge–Knopoff. For this model we determine with high accuracy its exponents of the power-law behavior of the histogram of the size of earthquakes; we study the final state for several values of the parameters of the model; and we determine the path to criticality by visualizations of the site frequency histogram

Discrete model for fragmentation with random stopping

In this work, we present the numerical results obtained from large scale parallel and distributed simulations of a model for two- and three-dimensional discrete fragmentation. Its main features are: (1) uniform and independent random distribution of the forces that generate the fracture; (2) deterministic criteria for the fracture process at each step of the fragmentation, based on these forces and a random stopping criteria. By large scale parallel and distributed simulations, implemented over a heterogeneous network of high performance computers, different behaviors were obtained for the fragment size distribution, which includes power law behavior with positive exponents for a wide range of the main parameter of the model: the stopping probability. Also, by a sensitive analysis we prove that the value of the main parameter of the model does not affect these results. The power law distribution is a non-trivial result which reproduces empirical results of some highly energetic fracture processes.

Social connections and access charges in networks

In this paper we present a model where two interconnected network operators compete in linear prices in a market characterized by the existence of social connections among consumers, which are represented by a random regular graph. Assuming horizontal differentiation among operators, the customers select their network provider based on their preferences and the prices offered by the competing firms. In equilibrium the number of calls made to other agents depends on where they are located in the social network.

Extremal Automata For Image Sharpening

We study numerically the parallel iteration of Extremal Rules. For four Extremal Rules, conceived for sharpening algorithms for image processing, we measured, on the square lattice with Von Neumann neighborhood and free boundary conditions, the typical transient length, the loss of information and the damage spreading response considering random and smoothening random damage. The same qualitative behavior was found for all the rules, with no noticeable finite size effect. They have a fast logarithmic convergence towards the fixed points of the parallel update. The linear damage spreading response has no discontinuity at zero damage, for both kinds of damage. Three of these rules produce similar effects. We propose these rules as sharpening algorithms for image processing.

Sequential Iteration For Extremal Automata

We study the sequential iteration of an automata class defined by local rules evolving only to local extreme values. Under the symmetry assumption of the cellular space we determine a Lyapunov operator driving the automaton dynamics. This operator allows us to characterize the steady state as a set of fixed points and to give bounds for the transient phase.

Q2R+Q2R AS A UNIVERSAL BILLIARD

In this work we study the computing capabilities as well as some dynamical properties of an automaton called M4R. This automaton corresponds to the mixing of the energy profiles of two independent copies of the Q2R automaton with frustrations. We associate to each copy of a Q2R an equivalent automaton M2R, which, with the Margoluos neighborhood, exhibits the local changes of the Q2R energy.1 By doing so we generalize the dynamics by upgrading M2R according to four partitions of the lattice. This new dynamics — called M4R — is based on a local rule which corresponds to the local energy change of two independent copies of Q2R. The M4R model is reversible and conservative (magnetization is constant in time) and it has properties of a discrete billiard (as some of the hydrodynamics discrete versions of Navier-Stokes models). Moreover, this automaton has powerful computing capabilities. In fact, by using some special configurations of M4R, we exhibit universal gates and register that allow us to code any algorithm.

Application of Computational Intelligence Techniques for Forecasting Problematic Wine Fermentations Using Data from Classical Chemical Measurements

The early forecasting of normal and problematic wine fermentations is one of the main problems of winemaking processes, due to its significant impacts in wine quality and utility. In Chile this is a critical problem because it is one of the top ten wine-producing countries. In this chapter, we review the computational intelligence methods that have been applied to solve this problem. Both methods studied, support vector machines and artificial neural networks, show excellent results with respect to the overall prediction error for different training/testing/validation percentages, different time cutoffs, and several parameter configurations. These results are of great importance for wine production because they are based only on measurement of classical chemical variables and they confirm that computational intelligence methods are a useful tool to the winemakers in order to correct in time a potential problem in the fermentation process.

Visualizations of a n‐ary Fragmentation Process with Neighborhood Interaction

It is defined a multiple fragmentation model in 2 dimensions. To represent the material defects, a random distribution of point flaws is considered. The number of generated fragments and breaking criterion also are random variables. The n‐ary fragmentation process is produced by a breaking criterion that depends on the distribution of point flaws and neighboring fragments. The total mass is conserved. To stop each fragment iterative fracture a random stop is evaluated. The visualizations of the model present complex patterns of fracture that resemble real systems.