Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

On the number of limit cycles bifurcating from a non-global degenerated center

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Creating and using a non-dedicated HPC cluster with ParallelKnoppix

This note describes ParallelKnoppix, a bootable CD that allows econometricians with average knowledge of computers to create and begin using a high performance computing cluster for parallel computing in very little time. The computers used may be heterogeneous machines, and clusters of up to 200 nodes are supported. When the cluster is shut down, all machines are in their original state, so their temporary use in the cluster does not interfere with their normal uses. An example shows how a Monte Carlo study of a bootstrap test procedure may be done in parallel. Using a cluster of 20 nodes, the example runs approximately 20 times faster than it does on a single computer.

ParallelKnoppix - Rapid deployment of a linux cluster for MPI parallel processing using non-dedicated computers

This note describes ParallelKnoppix, a bootable CD that allows creation of a Linux cluster in very little time. An experienced user can create a cluster ready to execute MPI programs in less than 10 minutes. The computers used may be heterogeneous machines, of the IA-32 architecture. When the cluster is shut down, all machines except one are in their original state, and the last can be returned to its original state by deleting a directory. The system thus provides a means of using non-dedicated computers to create a cluster. An example session is documented.

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

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Non compact euclidean cone 3-manifolds with cone angles less than 2∏

We study of noncompact Euclidean cone manifolds with cone angles less than c&2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corol lary we classify those with cone angles & 2π/3 and those with cone angles = 2π/3.

Large deviation for BSDE with subdifferential operator

In this paper we prove that the solution of a backward stochastic differential equation, which involves a subdifferential operator and associated to a family of reflecting diffusion processes, converges to the solution of a deterministic backward equation and satisfes a large deviation principle.

Tropical varieties for non-archimedean analytic spaces

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Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Cooperative vs. non-cooperative mechanisms in the EU decision making process

According to the account of the European Union (EU) decision making proposed in this paper, this is a bargaining process during which actors shift their policy positions with a view to reaching agreements on controversial issues.