Invariant measures for Burgers equation with stochastic forcing

In this paper we study the following Burgers equation du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t) where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise in t. We prove the existence and uniqueness of an invariant measure by establishing a ``one force, one solution'' principle, namely that for almost every realization of the force, there is a unique distinguished solution that exists for the time interval (-infty, +infty) and this solution attracts all other solutions with the same forcing. This is done by studying the so-called one-sided minimizers. We also give a detailed description of the structure and regularity properties for the stationary solutions. In particular, we prove, under some non-degeneracy conditions on the forcing, that almost surely there is a unique main shock and a unique global minimizer for the stationary solutions. Furthermore the global minimizer is a hyperbolic trajectory of the underlying system of characteristics.Comment: 84 pages, published version, abstract added in migratio

Big Cwatsets and Hamming Code

In contrast to Lagrange\u27s Theorem in Finite Group Theory, we show that the ratio of the largest proper cwatset of degree d to the size of binary d-space approaches 1 as d approaches infinity. We show how to explicitly construct large cwatsets as cosets of Hamming Codes, and discuss many open questions that arise

Les ancêtres préhistoriques des Animaux domestiques peints et gravés dans la grotte de Lascaux

Mazel M. Les ancêtres préhistoriques des Animaux domestiques peints et gravés dans la grotte de Lascaux. In: Bulletin de l'Académie Vétérinaire de France tome 104 n°1, 1951. pp. 73-80

Structural Features of Single-Stranded Integron Cassette attC Sites and Their Role in Strand Selection

We recently showed that cassette integration and deletion in integron platforms were occurring through unconventional site-specific recombination reactions involving only the bottom strand of attC sites. The lack of sequence conservation among attC sites led us to hypothesize that sequence-independent structural recognition determinants must exist within attC sites. The structural data obtained from a synaptic complex of the Vibrio cholerae integrase with the bottom strand of an attC site has shown the importance of extra helical bases (EHB) inside the stem-loop structure formed from the bottom strand. Here, we systematically determined the contribution of three structural elements common to all known single-stranded attC site recombination substrates (the EHBs, the unpaired central spacer (UCS), and the variable terminal structure (VTS)) to strand choice and recombination. Their roles have been evaluated in vivo in the attl x attC reaction context using the suicide conjugation assay we previously developed, but also in an attC x attC reaction using a deletion assay. Conjugation was used to deliver the attC sites in single-stranded form. Our results show that strand choice is primarily directed by the first EHB, but the presence of the two other EHBs also serves to increase this strand selection. We found that the structure of the central spacer is essential to achieve high level recombination of the bottom strand, suggesting a dual role for this structure in active site exclusion and for hindering the reverse reaction after the first strand exchange. Moreover, we have shown that the VTS has apparently no role in strand selectivity

Nucleolar localization of influenza A NS1: striking differences between mammalian and avian cells

In mammalian cells, nucleolar localization of influenza A NS1 requires the presence of a C-terminal nucleolar localization signal. This nucleolar localization signal is present only in certain strains of influenza A viruses. Therefore, only certain NS1 accumulate in the nucleolus of mammalian cells. In contrast, we show that all NS1 tested in this study accumulated in the nucleolus of avian cells even in the absence of the above described C-terminal nucleolar localization signal. Thus, nucleolar localization of NS1 in avian cells appears to rely on a different nucleolar localization signal that is more conserved among influenza virus strains

Pseudo-Random Streams for Distributed and Parallel Stochastic Simulations on GP-GPU

International audienceRandom number generation is a key element of stochastic simulations. It has been widely studied for sequential applications purposes, enabling us to reliably use pseudo-random numbers in this case. Unfortunately, we cannot be so enthusiastic when dealing with parallel stochastic simulations. Many applications still neglect random stream parallelization, leading to potentially biased results. In particular parallel execution platforms, such as Graphics Processing Units (GPUs), add their constraints to those of Pseudo-Random Number Generators (PRNGs) used in parallel. This results in a situation where potential biases can be combined with performance drops when parallelization of random streams has not been carried out rigorously. Here, we propose criteria guiding the design of good GPU-enabled PRNGs. We enhance our comments with a study of the techniques aiming to parallelize random streams correctly, in the context of GPU-enabled stochastic simulations

A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page

Class I Integrons and SXT Elements in El Tor Strains Isolated before and after 1992 Vibrio cholerae O139 Outbreak, Calcutta, India

We examined the distribution of class I integrons and SXT elements in Vibrio cholerae O1 El Tor strains, isolated in Calcutta, India, before and after the V. cholerae O139 outbreak in 1992. Class I integrons, with aadA1 gene cassette, were detected primarily in the pre-O139 strains; the SXT element was found mainly in the post-O139 strains

Rigorous Proof of a Liquid-Vapor Phase Transition in a Continuum Particle System

We consider particles in ${\Bbb R}^d, d \geq 2$, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquid-gas phase transition when the interaction range is finite but long compared to the interparticle spacing.Comment: 11 pages, in ReVTeX, e-mail addresses: [email protected], [email protected], [email protected]

Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models

We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not particle symmetry is broken. The transition at z_d(M) appears to be first order for M \geq 5 putting it in the Potts model universality class. For large M the transition between the crystalline and demixed phase at z_d(M) can be proven to be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one component hard square lattice gas has a transition, and to be always of the Ising type. Explicit calculations for the Bethe lattice with the coordination number q=4 give results similar to those for the square lattice except that the transition at z_d(M) becomes first order at M>2. This happens for all q, consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure