Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A set-valued upper semi-continuous map is called an Rδ -map if each of its values is an Rδ -set (we recall that an Rδ -set is a space that can be represented as the intersection of a decreasing sequence of compact AR-spaces). We prove that a compact set-valued map of an AR-space into itself has a fixed point provided it can be factorized by an arbitrary finite number of Rδ -maps through ANR-spaces. This fact is a consequence of a more general result which is the main goal of this note. The proof relies on a refinement of the approximation technique and does not make use of homological tools.
ISSN: 0166-8641

hal-00699222
https://hal.archives-ouvertes.fr/hal-00699222

Éditeur(s) : HAL CCSD Public Library of Science
Résumé : International audience
Little is known of how linkage patterns between species change along environmental gradients. The small, spatially discrete food webs inhabiting tank-bromeliads provide an excellent opportunity to analyse patterns of community diversity and food-web topology (connectance, linkage density, nestedness) in relation to key environmental variables (habitat size, detrital resource, incident radiation) and predators: prey ratios. We sampled 365 bromeliads in a wide range of understorey environments in French Guiana and used gut contents of invertebrates to draw the corresponding 365 connectance webs. At the bromeliad scale, habitat size (water volume) determined the number of species that constitute food-web nodes, the proportion of predators, and food-web topology. The number of species as well as the proportion of predators within bromeliads declined from open to forested habitats, where the volume of water collected by bromeliads was generally lower because of rainfall interception by the canopy. A core group of microorganisms and generalist detritivores remained relatively constant across environments. This suggests that (i) a highly-connected core ensures food-web stability and key ecosystem functions across environments, and (ii) larger deviations in food-web structures can be expected following disturbance if detritivores share traits that determine responses to environmental changes. While linkage density and nestedness were lower in bromeliads in the forest than in open areas, experiments are needed to confirm a trend for lower food-web stability in the understorey of primary forests.
PLoS ONE

hal-00913931
https://hal.archives-ouvertes.fr/hal-00913931
https://hal.archives-ouvertes.fr/hal-00913931/document
DOI : 10.1371/journal.pone.0071735
OATAO : 10204

Éditeur(s) : HAL CCSD
Résumé : International audience
Given a topological R-module or algebra E and an asymptotic scale MR Λ, we define a natural M-extended topology on the sequence space E Λ, and the M-extension of E as the Hausdorff space associated with the subspace of sequences for which multiplication is continuous with respect to this topology. Colombeau's generalized functions and similar constructions are obtained as special cases, but this new approach also allows the iteration of the construction, which was not possible with previously existing theories. We use only the topology, i.e. neigbourhoods of zero, but not its explicit definition in terms of seminorms, inductive or projective limits etc., which is particularly useful in non-metrizable spaces. Many ideas commonly used in generalized function spaces (functoriality, association, sheaf structure, algebraic analysis, ...) can be applied to a large extent; but reasoning on a category-theoretic level allows the establishment of several results so far only known for particular cases, to the whole class of such spaces.
Integral Transforms and Special Functions
Bedlewo, Poland

hal-00761666
https://hal.univ-antilles.fr/hal-00761666
DOI : 10.1080/10652460802565040

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Since the first molecular study of the suborder Notothenioidei in 1994, many phylogenetic studies have been published. Among these, those with a sufficient number of taxa have all suggested that the Nototheniidae, as currently defined, is monophyletic only with the inclusion of the Channichthyidae, Artedidraconidae, Bathydraconidae and Harpagiferidae. This is corroborated by more recent studies including more taxa, but in these studies either the number of nuclear markers or the number of taxa included remained low. We obtained sequences for a large sampling covering most nototheniid genera for five markers described previously for other samplings (COI, Rhodopsin retrogene, Pkd1, HECW2, and SSRP1) and one nuclear marker never used before in phylogenetic inference (PPM1d). The topology for the combined analysis of the nuclear coding genes, as well as the topology for SSRP1 (non-coding) and the combined analysis for all markers all support the paraphyly of Nototheniidae, the genus Notothenia (including Paranotothenia) is the sister group of the clade Channichthyidae, Artedidraconidae, Bathydraconidae and Harpagiferidae, and genus Gobionotothen is a sister group to both. As in previous studies, Trematomus, Lepidonotothen and Patagonotothen form a clade that also includes Indonotothenia cyanobrancha. The position of Pleuragramma antarctica, Dissostichus species and Aethotaxis mitopteryx remains unstable and dependant on markers and analyses. We therefore propose the inclusion of the four families of the High Antarctic clade in the Nototheniidae, and their transformation into subfamilies. We transfer Paranotothenia magellanica to the genus Notothenia, as Notothenia magellanica.
ISSN: 1874-7787

hal-01544914
https://hal.archives-ouvertes.fr/hal-01544914
DOI : 10.1016/j.margen.2012.02.003

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We show that a new definition of the asymptotic structure of the (C,E,P)-algebras (which are a refinement of the Colombeau Generalized Algebras) allows to define a natural topology on them. Furthermore, this topology can be mixed with functorial aspects of the construction in order to give extension principles, which give powerful tools to solve singular differential problems in this framework.
ISSN: 0022-247X

hal-01529551
https://hal.univ-antilles.fr/hal-01529551
DOI : 10.1016/j.jmaa.2009.05.046

Éditeur(s) : HAL CCSD
Résumé : International audience
Based on a previously established framework of asymptotic extensions of topological modules and algebras, we use results concerning sheaf theoretic properties and functoriality of the construction, to develop some tools for microlocal algebraic analysis in this setting. In particular, we introduce the notion of singular spectrum of sections, and give results concerning its linear and non-linear properties.
Progress in Analysis and its Applications
London, United Kingdom

hal-00761660
https://hal.univ-antilles.fr/hal-00761660
DOI : 10.1142/9789814313179_0079

Éditeur(s) : HAL CCSD
Résumé : International audience
Topology and its Appl.

hal-00756774
https://hal.archives-ouvertes.fr/hal-00756774

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Starting from a locally convex metrisable topological space and from any asymptotic scale, we construct a generalized extension of this space. To those extensions, we associate Hausdorff topologies. We introduce the notion of a temperate map, with respect to a given asymptotic scale, between two locally convex metrisable semi-normed spaces. We show that such mappings extend in a canonical way to mappings between the respective generalized extensions. We give an application to nonlinear Dirichlet boundary value problems with singular data in the framework of generalized extensions
ISSN: 0026-9255

hal-01529549
https://hal.univ-antilles.fr/hal-01529549

Éditeur(s) : HAL CCSD Oxford University Press (OUP)
Résumé : International audience
Motivation: Gene fusion is an important evolutionary process. It can yield valuable information to infer the interactions and functions of proteins. Fused genes have been identified as non-transitive patterns of similarity in triplets of genes. To be computationally tractable, this approach usually imposes an a priori distinction between a dataset in which fused genes are searched for, and a dataset that may have provided genetic material for fusion. This reduces the `genetic space' in which fusion can be discovered, as only a subset of triplets of genes is investigated. Moreover, this approach may have a high-false-positive rate, and it does not identify gene families descending from a common fusion event. Results: We represent similarities between sequences as a network. This leads to an efficient formulation of previous methods of fused gene identification, which we implemented in the Python program FusedTriplets. Furthermore, we propose a new characterization of families of fused genes, as clique minimal separators of the sequence similarity network. This well-studied graph topology provides a robust and fast method of detection, well suited for automatic analyses of big datasets. We implemented this method in the C++ program MosaicFinder, which additionally uses local alignments to discard false-positive candidates and indicates potential fusion points. The grouping into families will help distinguish sequencing or prediction errors from real biological fusions, and it will yield additional insight into the function and history of fused genes.
ISSN: 1367-4803

hal-01544795
https://hal.archives-ouvertes.fr/hal-01544795
DOI : 10.1093/bioinformatics/btt049

Éditeur(s) : HAL CCSD Chapman & Hall/CRC
Résumé : International audience
Nonlinear Theory of Generalized Functions

ISBN : 9780849306495
hal-01529543
https://hal.univ-antilles.fr/hal-01529543

Éditeur(s) : HAL CCSD American Mathematical Society
Résumé : International audience
A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra( pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac's delta distribution induces discrete topology on the basic space. This result is in analogy to Schwartz' impossibility result concerning multiplication of distributions.
ISSN: 0002-9939

hal-00758571
https://hal.univ-antilles.fr/hal-00758571
https://hal.univ-antilles.fr/hal-00758571/document
https://hal.univ-antilles.fr/hal-00758571/file/0206039v1.pdf

Éditeur(s) : HAL CCSD
Résumé : 6 pages
In a Spiking Neural Networks (SNN), spike emissions are sparsely and irregularly distributed both in time and in the network architecture. Since a current feature of SNNs is a low average activity, efficient implementations of SNNs are usually based on an Event-Driven Simulation (EDS). On the other hand, simulations of large scale neural networks can take advantage of distributing the neurons on a set of processors (either workstation cluster or parallel computer). This article presents DAMNED, a large scale SNN simulation framework able to gather the benefits of EDS and parallel computing. Two levels of parallelism are combined: Distributed mapping of the neural topology, at the network level, and local multithreaded allocation of resources for simultaneous processing of events, at the neuron level. Based on the causality of events, a distributed solution is proposed for solving the complex problem of scheduling without synchronization barrier.
https://hal.archives-ouvertes.fr/hal-00015137

hal-00015137
https://hal.archives-ouvertes.fr/hal-00015137
https://hal.archives-ouvertes.fr/hal-00015137v2/document
https://hal.archives-ouvertes.fr/hal-00015137/file/hal_damned.pdf
ARXIV : cs.NE/0512018

Éditeur(s) : HAL CCSD American Mathematical Society
Résumé : International audience
We show that if n sets in a topological space are given so that all the sets are closed or all are open, and for each k ≤ n every k of the sets have a (k − 2)-connected union, then the n sets have a point in common. As a consequence, we obtain the following starshaped version of Helly's theorem: If every n + 1 or fewer members of a finite family of closed sets in Rn have a starshaped union, then all the members of the family have a point in common. The proof relies on a topological KKM-type intersection theorem.
ISSN: 0002-9939

hal-00699217
https://hal.archives-ouvertes.fr/hal-00699217

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
The brittle to ductile transition (BDT) in rocks may strongly influence their transport properties (i.e., permeability, porosity topology ...) and the maximum depth and temperature where hydrothermal fluids may circulate. To examine this transition in the context of Icelandic crust, we conducted deformation experiments on a glassy basalt (GB) and a glass-free basalt (GFB) under oceanic crust conditions. Mechanical and micro-structural observations at a constant strain rate of 10(-5) s(-1) and at confining pressure of 100-300 MPa indicate that the rocks are brittle and dilatant up to 700-800 degrees C. At higher temperatures and effective pressures the deformation mode becomes macroscopically ductile, i.e., deformation is distributed throughout the sample and no localized shear rupture plane develops. The presence of glass is a key component reducing the sample strength and lowering the pressure of the BDT. In the brittle field, strength is consistent with a Mohr-Coulomb failure criterion with an internal coefficient of friction of 0.42 for both samples. In the ductile field, strength is strain rate-and temperature-dependent and both samples were characterized by the same stress exponent in the range 3 < n < 4.2 but by very different activation energy Q(GB) = 59 +/- 15 KJ/mol and Q(GFB) = 456 +/- 4 KJ/mol. Extrapolation of these results to the Iceland oceanic crust conditions predicts a BDT at similar to 100 degrees C for a glassy basalt, whereas the BDT might occur in non-glassy basalts at deeper conditions, i.e., temperatures higher than 550 +/- 100 degrees C, in agreement with the Icelandic seismogenic zone.
ISSN: 0148-0227

hal-00760905
https://hal.archives-ouvertes.fr/hal-00760905
DOI : 10.1029/2011JB008884

Éditeur(s) : HAL CCSD Juliusz Schauder University Centre for Nonlinear Studies
Résumé : International audience
ISSN: 1230-3429

hal-01545552
https://hal.archives-ouvertes.fr/hal-01545552
DOI : 10.12775/TMNA.1999.016

Éditeur(s) : HAL CCSD
Résumé : To appear in TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS (16 pages).
In the last two decades, many algebras of generalized functions have been constructed, particularly the so-called generalized Sobolev algebras. Our goal is to study the latter and some of their main properties. In this framework, we pose and solve a nonlinear degenerated Dirichlet problem with irregular data such as Dirac generalized functions.
https://hal.archives-ouvertes.fr/hal-00004903

Droits : info:eu-repo/semantics/OpenAccess
hal-00004903
https://hal.archives-ouvertes.fr/hal-00004903
https://hal.archives-ouvertes.fr/hal-00004903/document
https://hal.archives-ouvertes.fr/hal-00004903/file/sb_psn_pjm.pdf
ARXIV : math.GM/0505228

Éditeur(s) : HAL CCSD
Résumé : National audience
We propose a method to solve the problem of clustering individuals described by mixed variables structured in blocks. It is a hierarchical method with two levels similar to Hierarchical Principal Component Analysis presented by Wold, based on the mixed topology maps (MTM). The first step consists in establishing, for each block of mixed variables, a clustering representing a synthesis of local individuals at the block level. The second step is to re-apply MTM on the weighted results of the first level. We obtain a global clustering of individuals, consensus among the partitions from level 1. The proposed method is illustrated on data from the national survey in the French housing stock carried out in 2003-2005 by the Observatory for Indoor Air Quality (OQAI).
Fouille de Données Complexes, complexité liée aux données multiples et massives (FDC)
bordeaux, France

hal-00748841
https://hal.archives-ouvertes.fr/hal-00748841
https://hal.archives-ouvertes.fr/hal-00748841/document

Éditeur(s) : HAL CCSD IGI Global
Résumé : International audience
Standard data mining techniques have been applied and adapted for eliciting knowledge from social networks, by achieving classical tasks such as classification, search for frequent patterns or link prediction. Most works have exploited only the network topological structure, and therefore cannot be used to answer questions involving nodes features. For instance, the frequent pattern discovery task generally refers to the search for sub-networks frequently found in a single network or in a set of networks. In the same area, this paper focuses on the concept of frequent link that stands as a regularity found in a network on links between node groups that share common characteristics. The extraction of such links from a social network is a particularly challenging and computationally intensive problem, since it is much dependent on the number of links and attributes. In this study, we propose a solution for reducing the search space of frequent links, by filtering the nodes features on a criterion of frequency. We make the assumption that frequent links occur between sets of features that are themselves frequent. This property is used to reduce the search space and speed up the extraction process. We empirically show that it is well founded. We discuss the efficiency of the solution in terms of computation time and number of frequent patterns found depending on several frequency thresholds.
ISSN: 1947-8186

hal-00786166
https://hal.archives-ouvertes.fr/hal-00786166

Éditeur(s) : HAL CCSD
Résumé : International audience
Topological Methods in Nonlinear Analysis

hal-00699218
https://hal.archives-ouvertes.fr/hal-00699218

Éditeur(s) : HAL CCSD Cambridge University Press (CUP)
Résumé : International audience
In a recent paper, we gave a topological description of Colombeau type algebras introducing algebras of sequences with exponential weights. Embeddings of Schwartz spaces into the Colombeau algebra G are well known, but for ultradistribution and periodic hyperfunction type spaces we give new constructions. We show that the multiplication of regular enough functions (smooth, ultradifferentiable or quasianalytic), embedded into corresponding algebras, is the ordinary multiplication.
ISSN: 0305-0041

hal-00758568
https://hal.univ-antilles.fr/hal-00758568
https://hal.univ-antilles.fr/hal-00758568/document
https://hal.univ-antilles.fr/hal-00758568/file/DHPV2-9sep03-singlespaced.pdf
DOI : 10.1017/S0305004104007923