Drift without flux: Brownian walker with a space dependent diffusion coefficient

Space dependent diffusion of micrometer sized particles has been directly observed using digital video microscopy. The particles were trapped between two nearly parallel walls making their confinement position dependent. Consequently, not only did we measure a diffusion coefficient which depended on the particles' position, but also report and explain a new effect: a drift of the particles' individual positions in the direction of the diffusion coefficient gradient, in the absence of any external force or concentration gradient.Comment: 4 pages, 4 ps figures, include

The peaking Phenomenon and Singular Perturbations : An Extension of Tikhonov's Theorem

We study the asymptotic behaviour, when the parameter $\gamma$ tends to infinity, of a class of singularly perturbed triangular systems $\dot x=f(x,y)$, $\dot y=G(y,\gamma)$. The first equation may be considered as a control system recieving the inputs from the states of the second equation. With zero input, the origin of the first equation is globally asymptotically stable. We assume that all solutions of the second equation tend to zero arbitrarily fast when $\gamma$ tends to infinity. Some states of the second equation may peak to very large values, before they rapidly decay to zero. Such peaking states can destabilize the first equation. The paper introduces the concept of \em instantaneous stability, to measure the fast decay to zero of the solutions of the second equation, and the concept of uniform infinitesimal boundedness to measure the effects of peaking on the first equation. Whe show that all the solutions of the triangular system tend to zero when $\gamma$ and $t$ tend to infinity. Our results are a generalization of the classical Tikhonov's theorem of singular perturbation theory, concerning the asymptotic behaviour of the solutions in the particular case where the second equation is of the form $\dot y=\gamma G(y)$. Our results are formulated in both classical mathematics and nonstandard analysis

Asymmetric directional mutation pressures in bacteria

BACKGROUND: When there are no strand-specific biases in mutation and selection rates (that is, in the substitution rates) between the two strands of DNA, the average nucleotide composition is theoretically expected to be A = T and G = C within each strand. Deviations from these equalities are therefore evidence for an asymmetry in selection and/or mutation between the two strands. By focusing on weakly selected regions that could be oriented with respect to replication in 43 out of 51 completely sequenced bacterial chromosomes, we have been able to detect asymmetric directional mutation pressures. RESULTS: Most of the 43 chromosomes were found to be relatively enriched in G over C and T over A, and slightly depleted in G+C, in their weakly selected positions (intergenic regions and third codon positions) in the leading strand compared with the lagging strand. Deviations from A = T and G = C were highly correlated between third codon positions and intergenic regions, with a lower degree of deviation in intergenic regions, and were not correlated with overall genomic G+C content. CONCLUSIONS: During the course of bacterial chromosome evolution, the effects of asymmetric directional mutation pressures are commonly observed in weakly selected positions. The degree of deviation from equality is highly variable among species, and within species is higher in third codon positions than in intergenic regions. The orientation of these effects is almost universal and is compatible in most cases with the hypothesis of an excess of cytosine deamination in the single-stranded state during DNA replication. However, the variation in G+C content between species is influenced by factors other than asymmetric mutation pressure

La méthode des élucidations successives

International audienceIn the process of elaboration of a model one emphasize on the necessity of confronting the model with the reality which it is supposed to represent. There is another aspect of the modelling process, to my opinion also essential, about which one usually do not speak. It consists in a logico-linguistic work where formal models are used to produce prediction which are not confronted with the reality but serve for falsifying assertions which nevertheless seemed to be derived from the not formalized model. More exactly a first informal model is described in the natural language and, considered in the natural language, seems to say some thing but in a more or less clear way. Then we translate the informal model into a formal model (mathematical model or computer model) where what was argumentation becomes demonstration.The formal model so serves for raising ambiguities of the natural language. But conversely a too much formalized text quickly loses any sense for a human brain what makes necessary the return for a less formal language. It is these successive "translations" between more or less formal languages that I try to analyze on two examples, the first one in population dynamics, the second in mathematics.Dans le processus d’élaboration d’un modèle on insiste beaucoup sur la nécessité de confronter le modèle à la réalité qu’il est sensé représenter. Il est un autre aspect de la modélisation, à mon avis tout aussi essentiel, dont on ne parle pas. Il s’agit d’un travail logico-linguistique où des modèles formels sont utilisés pour produire des prédiction qui ne sont pas confrontées à la réalité mais servent à falsifier des affirmations qui semblaient pourtant se déduire du modèle. Plus précisément un premier modèle informel est décrit dans la langue naturelle et, toujours dans la langue naturelle, semble dire quelques chose mais de façon plus ou moins claire. Alors on traduit le modèle informel en un modèle formel (mathématique ou informatique) où ce qui était argumentation devient démonstration. Le modèle formel sert ainsi à lever des ambiguïtés de la langue naturelle. Mais inversement un texte trop formalisé perd rapidement tout sens pour un cerveau humain ce qui rend nécessaire le retour à une langue moins formelle. Ce sont ces “traductions" successives entre langues plus ou moins formelles que je cherche à analyser sur deux exemples, le premier en dynamique des populations, le second en mathématiques