Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

La regulación de la Administración electrónica y sus principios rectores

[spa] Actualmente, nos encontramos inmersos en un proceso de globalización y tecnificación al que las Administraciones públicas, como parte integrante de l a sociedad, no pueden permanecer ajenas. Todas las Administraciones, en sus distintos niveles y ámbitos de actuación, han introducido en su actividad las nuevas tecnologías de la información y la comunicación, y han puesto en marcha un proceso transformación de carácter cultural, organizativo y jurídico que ha fructificado en un nuevo modelo de gestión de la actividad pública conocido bajo el nombre de Administración electrónica. El uso de las nuevas tecnologías y la transición de una Administración «en pa pel» a una Administración electrónica han conllevado una serie de reformas de nuestro ordenamiento jurídico: nuevas normas y reforma de otras ya existentes que regulan los aspectos técnicos derivados de la utilización de las nuevas tecnologías por parte de la Administración, así como los derechos y garantías de los que están revestidos los ciudadanos cuando se relacionan con la Administración por medios telemáticos. Con este telón de fondo, podemos definir un elenco de principios que regirán la actuación de la Administración electrónica y en los que se erigen como protagonistas aquellos que persiguen garantizar la igualdad y la no discriminación de los ciudadanos, combatiendo la denominada brecha digital.

Is the influence of quality of life on urban growth non-stationary in space? A case study of Barcelona

There are several determinants that influence household location decisions. More concretely, recent economic literature assigns an increasingly important role to the variables governing quality of life. Nevertheless, the spatial stationarity of the parameters is implicitly assumed in most studies. Here we analyse the role of quality of life in urban economics and test for the spatial stationarity of the relationship between city growth and quality of life.

Optimización del framework de paralelización de tareas COMPSs

El propósito de este trabajo es optimizar el sistema de gestión de workflows COMPSs caracterizando el comportamiento de diferentes dispositivos de memoria a nivel de consumo energético y tiempo de ejecución. Para llevar a cabo este propósito, se ha implementado un servicio de caché para COMPSs para conseguir que sea consciente de la jerarquía de memoria y se han realizado múltiples experimentos para caracterizar los dispositivos de memoria y las mejoras en el rendimiento.