Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

La filière bois-énergie en Auvergne : une typologie des chaînes d'approvisionnement

National audienceWith increasing environmental and energy concerns, the use of wood as an energy source has been encouraged by public policies in France. The development of a wood-energy market also represents an economic opportunity for rural areas. Who are the stakeholders contributing to the wood-energy supply and how they interact is still not well-known. The paper offers a typology of wood-energy supply chains as they have developed in Auvergne. Private residential use mainly relies on wood pellets supplied by distributors. The supply of local governments, mostly based on sawmill residues, is characterized by the participation of one or several suppliers able to produce large fuel quantities. Most businesses using wood-energy are part of the timber industry and thus consume the residues of their activity. Identifying the types of supply chains and their relative importance also shows that the wood-energy supply has developed mainly at the local level and that producers are increasingly adapting to the specific features of the wood fuel demand.Le développement du bois-énergie constitue, au-delà des enjeux environnementaux et énergétiques, une opportunité économique pour les territoires ruraux. La question se pose des opérateurs impliqués dans l’approvisionnement en bois-énergie et de leur coordination. L’article présente une typologie des chaînes d’approvisionnement en bois-énergie ayant émergé sur le territoire auvergnat. L’achat de granulés auprès d’un distributeur domine l’approvisionnement des particuliers. L’approvisionnement des chaudières de collectivités en bois déchiqueté est marqué par l’intervention d’un ou plusieurs fournisseurs à même de fournir d’importants volumes. La majorité des entreprises utilisant le bois-énergie sont des entreprises de la filière bois qui auto-consomment les sous-produits de leur activité. L’identification des types de chaînes et de leur importance relative met en évidence le caractère local de l’approvisionnement en bois-énergie dans la région et une professionnalisation de la production de combustible, réponse à la demande des consommateurs

Lipases et lipolyse des laits de vache et de chevre

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Substrates and routes of migration of early generated neurons in the developing rat thalamus

We investigated the substrates supporting neuronal migration, and its routes, during early thalamic development in the rat. Neurons and axonal and glial fibres were identified in embryos with single and double immunohistochemistry; dynamic data were obtained with cell tracers in short-term organotypic cultured slices. The earliest thalamic neurons, originating from the ventricular neuroepithelium between embryonic days 13 and 15, include those of the reticular thalamic nucleus. At this developmental stage, calretinin, calbindin or γ-aminobutyric acid immunostaining revealed both radially and nonradially orientated neurons in the region of reticular thalamic migration, between the dorsal and ventral thalamic primordia. In cultured slices, injections of fluorescent dyes in the neuroepithelium labelled neurons in a migratory stream along radial glia in the same zone. Some labelled fusiform cells departed from this radial trajectory along orthogonal routes within the dorsal thalamus. Confocal microscopy revealed nonradially orientated neurons in close apposition with a fibre system parallel to the lateral thalamic surface. These fibres expressed axonal markers, including the intermediate filament protein α-internexin and a polysialylated form of neuronal cell adhesion molecule. Active migration of nonradially orientated neurons along neuronal substrates was confirmed in living cultured slices. In addition, in vitro and ex vivo experiments revealed neurons migrating tangentially in association with glial fibres. These results provide novel evidence that: (i) early generated thalamic neurons follow nonradial routes in addition to glia-linked radial migration; and (ii), nonradially migrating thalamic neurons move along both glial and axonal substrates, which could represent a distinctive feature of thalamic development.This work was supported by grants of the Italian Ministry of Health to C.F. and by grants PB97-0582-CO2-01 and PGC2000-2756-E of the Spanish Ministry of Science and Technology to A.F.Peer reviewe

Lipolytic enzymes and hydrolytic rancidity

Lipolysis, the enzymic hydrolysis of milk lipids to free fatty acids and partial glycerides, is a constant concern to the dairy industry because of the detrimental effcts it can have on the flvor and other properties of milk and milk products. However, free fatty acids also contribute to the desirable flavor of milk and milk products when present at low concentrations and, in some cheeses, when present at high concentrations. The enzymes responsible for the detrimental effects of lipolysis are of two main types: those indigenous to milk, and those of microbial origin. The major indigenous milk enzyme is lipoprotein lipase. It is active on the fat in natural milk fat globules only after their disruption by physical treatments or if certain blood serum lipoproteins are present. The major microbial lipases are produced by psychrotrophic bacteria. Many of these enzymes are heat stable and are particularly significant in stored products. Human milk differs from cows' milk in that it contains two lipases, a lipoprotein lipase and a bile salt-stimulated lipase. The ability of the latter to cause considerable hydrolysis of ingested milk lipids has important nutritional implications