Guidelines for a Dynamic Ontology - Integrating Tools of Evolution and Versioning in Ontology

Ontologies are built on systems that conceptually evolve over time. In addition, techniques and languages for building ontologies evolve too. This has led to numerous studies in the field of ontology versioning and ontology evolution. This paper presents a new way to manage the lifecycle of an ontology incorporating both versioning tools and evolution process. This solution, called VersionGraph, is integrated in the source ontology since its creation in order to make it possible to evolve and to be versioned. Change management is strongly related to the model in which the ontology is represented. Therefore, we focus on the OWL language in order to take into account the impact of the changes on the logical consistency of the ontology like specified in OWL DL

Spectral properties of a class of random walks on locally finite groups

We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e.g. the infinite symmetric group. On locally finite groups, the random walks under consideration are driven by infinite divisible distributions. This allows us to embed our random walks into continuous time L\'evy processes whose heat kernels have shapes similar to the ones of alpha-stable processes. We obtain examples of fast/slow decays of return probabilities, a recurrence criterion, exact values and estimates of isospectral profiles and spectral distributions, formulae and estimates for the escape rates and for heat kernels.Comment: 62 pages, 1 figure, 2 table

Bounded characteristic classes and flat bundles

Let G be a connected Lie group, G^d the underlying discrete group, and BG, BG^d their classifying spaces. Let R denote the radical of G. We show that all classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R) are bounded if and only if the derived group [R,R] is simply connected. We also give equivalent conditions in terms of stable commutator length and distortion.Comment: 12 pages, no figur

Perspectives dans l'accueil collectif extrafamilial des enfants: prestation de garde ou service public ? : étude de la capacité des directions de développer des stratégies d'innovation en réponse aux enjeux sociaux actuels : exemple de la lutte contre la pauvreté et l'exclusion sociale : module Travail de Master

Depuis 2014, le Conseil fédéral a mis en place un programme national de lutte contre la pauvreté. Ce programme met en évidence différents axes d'investigation et d'action. Parmi ceux-ci, le secteur de l'accueil collectif extrafamilial des enfant figure en bonne place des mesures à développer, car les services dispensés dans ces structures sont reconnus pour une double fonction permettant d'éviter la précarisation des individus. D'une part, le placement des enfants permet aux parents de concilier leur vie familiale et leur vie professionnelle et, d'autre part, les services dispensés dans les structures d'accueil proposent des espaces de stimulation dits d'encouragement précoce, et participent ainsi à doter les enfant des compétences nécessaires à une réussite scolaire

Coulhon Saloff-Coste isoperimetric inequalities for finitely generated groups

We prove an inequality, valid on any finitely generated group with a fixed finite symmetric generating set, involving the growth of successive balls, and the average length of an element in a ball. It generalizes recent improvements of the Coulhon Saloff-Coste inequality. We reformulate the inequality in terms of the F{\o}lner function; in the case the finitely generated group is amenable with exponential growth, this allows us to express the best possible (outer) constant in the Coulhon Saloff-Coste isoperimetric inequality with the help of a formula involving the growth rate and the asymptotic behavior of the F{\o}lner function.Comment: 13 page

Laplace and Schr\"odinger operators without eigenvalues on homogeneous amenable graphs

A one-by-one exhaustion is a combinatorial/geometric condition which excludes eigenvalues from the spectra of Laplace and Schr\"odinger operators on graphs. Isoperimetric inequalities in graphs with a cocompact automorphism group provide an upper bound on the von Neumann dimension of the space of eigenfunctions. Any finitely generated indicable amenable group has a Cayley graph without eigenvalues. There exists a finitely generated group G with finite generating sets S and S' such that the adjacency operator of the Cayley graph of (G,S) has no eigenvalue while the adjacency operator of the Cayley graph of (G,S') has pure point spectrum.Comment: 46 pages, 3 figure

Universal lower bounds for the discrepancies of actions of a locally compact group

We prove universal lower bounds for discrepancies (i.e. sizes of spectral gaps of averaging operators) of measure-preserving actions of a locally compact group on probability spaces. For example, a locally compact Hausdorff unimodular group $G$, acting continuously, by measure-preserving transformations, on a compact atomless probability space $(X,\nu)$, with an orbit $Gx_0$ of measure zero, contained in the support of $\nu$, and with compact stabilizer (i.e. $G_{x_0}$ is compact) has the following property: any finite positive regular Borel measure $\mu$ on $G$ satisfies $$\|\pi_0(\mu)\|_{2\to 2}\geq \|\lambda_G(\mu)\|_{2\to 2},$$ where $\pi_0$ denotes the Koopman representation of $G$, defined by the given action, and $\lambda_G$ denotes the left-regular representation of $G$. The lower bounds we prove generalize the universal lower bounds for the discrepancies of measure-preserving actions of a discrete group. Many examples show that the generalization from discrete groups to locally compact groups requires some additional hypothesis on the action (we detail some examples of actions of amenable groups with a spectral gap, due to Margulis). Well-known examples and results of Kazhdan and Zimmer show that the discrepancies of some actions of Lie groups on homogeneous spaces match exactly the universal lower bounds we prove.Comment: 18 pages, 1 figure, added references and keyword

Radial rapid decay does not imply rapid decay

We provide a new, dynamical criterion for the radial rapid decay property. We work out in detail the special case of the group $\Gamma := \mathbf{SL}_2(A)$, where $A := \mathbb{F}_q[X,X^{-1}]$ is the ring of Laurent polynomials with coefficients in $\mathbb{F}_q$, endowed with the length function coming from a natural action of $\Gamma$ on a product of two trees, to show that is has the radial rapid decay (RRD) property and doesn't have the rapid decay (RD) property. The criterion also applies to irreducible lattices in semisimple Lie groups with finite center endowed with a length function defined with the help of a Finsler metric. These examples answer a question asked by Chatterji and moreover show that, unlike the RD property, the RRD property isn't inherited by open subgroups