Conjecture de Bloch et nombres de Milnor

In this paper, we prove that the conductor formula of Bloch implies the conjecture of Deligne on Milnor numbers of isolated singularities. In particular, thanks to the work of Bloch on his conjecture, our result implies that this so-called Deligne-Milnor's conjecture is equally true in the unequal characteristic case

Isomotifs de dimension inférieure ou égale à un

International audienceAprès avoir rappelé quelques résultats de V. Voevodsky sur sa catégorie de motifs (cf. [Voe00]), on démontre l'équivalence de catégories, annoncée dans loc. cit. § 3.4 (p. 218), entre la catégorie dérivée des 1-isomotifs de P. Deligne sur un corps parfait d'une part et la catégorie triangulée des motifs géométriques effectifs de dimension inférieure ou égale à un

Replaying the tape of life in the twenty-first century

International audienceShould the tape of life be replayed, would it produce similar living beings? A classical answer has long been ‘no’, but accumulating data are now challenging this view. Repeatability in experimental evolution, in phenotypic evolution of diverse species and in the genes underlying phenotypic evolution indicates that despite unpredictability at the level of basic evolutionary processes (such as apparition of mutations), a certain kind of predictability can emerge at higher levels over long time periods. For instance, a survey of the alleles described in the literature that cause non-deleterious phenotypic differences among animals, plants and yeasts indicates that similar phenotypes have often evolved in distinct taxa through independent mutations in the same genes. Does this mean that the range of possibilities for evolution is limited? Does this mean that we can predict the outcomes of a replayed tape of life? Imagining other possible paths for evolution runs into four important issues: (i) resolving the influence of contingency, (ii) imagining living organisms that are different from the ones we know, (iii) finding the relevant concepts for predicting evolution, and (iv) estimating the probability of occurrence for complex evolutionary events that occurred only once during the evolution of life on earth

Modifications et cycles proches sur une base générale

International audienceSi l'on étudie les cycles évanescents, c'est-à-dire la cohomologie (étale) des fibres de Milnor d'un morphisme de but de dimension >1, on perd les propriétés, démontrées par P. Deligne dans SGA 4 1/2, de commutation au changement de base et constructibliité. Dans cet article, on montre, après avoir rappelé la définition du complexe des cycles proches dans ce contexte, qu'on retrouve ces propriétés après modification de la base. L'ingrédient essentiel est un théorème de A.J. de Jong sur les fibrations plurinodales. Une application du formalisme aux pinceaux de Lefschetz est donnée

The differential view of genotype–phenotype relationships

International audienceAn integrative view of diversity and singularity in the living world requires a better understanding of the intricate link between genotypes and phenotypes. Here we re-emphasize the old standpoint that the genotype–phenotype (GP) relationship is best viewed as a connection between two differences, one at the genetic level and one at the phenotypic level. As of today, predominant thinking in biology research is that multiple genes interact with multiple environmental variables (such as abiotic factors, culture, or symbionts) to produce the phenotype. Often, the problem of linking genotypes and phenotypes is framed in terms of genotype and phenotype maps, and such graphical representations implicitly bring us away from the differential view of GP relationships. Here we show that the differential view of GP relationships is a useful explanatory framework in the context of pervasive pleiotropy, epistasis, and environmental effects. In such cases, it is relevant to view GP relationships as differences embedded into differences. Thinking in terms of differences clarifies the comparison between environmental and genetic effects on phenotypes and helps to further understand the connection between genotypes and phenotypes

The " Mendelian Gene " and the " Molecular Gene " : Two Relevant Concepts of Genetic Units

International audienceWe focus here on two prevalent meanings of the word gene in research articles. On one hand, the gene, named here “molecular gene”, is a stretch of DNA that is transcribed and codes for an RNA or a polypeptide with a known or presumed function (as in “gene network'), whose exact spatial delimitation on the chromosome remains a matter of debate, especially in cases with alternative splicing, antisense transcripts, etc. On the other hand, the gene, called here “Mendelian gene”, is a segregating genetic unit which is detected through phenotypic differences associated with different alleles at the same locus (as in “gene flow”). We show that the “Mendelian gene” concept is still extensively used today in biology research and is sometimes confused with the “molecular gene”. We try here to clarify the distinction between both concepts. Efforts to delineate the beginning and the end of the DNA sequence corresponding to the “Mendelian gene” and the “molecular gene” reveal that both entities do not always match. We argue that both concepts are part of two relevant frameworks for explaining the biological world

Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions

In this work, we upscale a pore-scale description of mass transport in a porous medium containing biofilm to develop the relevant Darcy-scale equations. We begin with the pore-scale descriptions of mass transport, interphase mass transfer, and biologically-mediated reactions; these processes are then upscaled using the method of volume averaging to obtain the macroscale mass balance equations. We focus on the case of local mass equilibrium conditions where the averaged concentrations in the fluid and biological phases can be assumed to be proportional and for which a one-equation macroscopic model may be developed. We predict the effective dispersion tensor by a closure scheme that is solved for the cases of both simple and complex unit cells. The domain of validity of the approach is clearly identified, both theoretically and numerically, and unitless groupings indicating the domain of validity are reported

Nori 1-motives

Let EHM be Nori's category of effective homological mixed motives. In this paper, we consider the thick abelian subcategory EHM_1 generated by the i-th relative homology of pairs of varieties for i = 0,1. We show that EHM_1 is naturally equivalent to the abelian category M_1 of Deligne 1-motives with torsion; this is our main theorem. Along the way, we obtain several interesting results. Firstly, we realize M_1 as the universal abelian category obtained, using Nori's formalism, from the Betti representation of an explicit diagram of curves. Secondly, we obtain a conceptual proof of a theorem of Vologodsky on realizations of 1-motives. Thirdly, we verify a conjecture of Deligne on extensions of 1-motives in the category of mixed realizations for those extensions that are effective in Nori's sense