Éditeur(s) : HAL CCSD Hindawi Publishing Corporation
Résumé : International audience
This paper is concerned with the study of a penalization-gradient algorithmfor solving variational inequalities, namely, find x ∈ C such that Ax, y − x ≥ 0 for all y ∈ C, where A : H → H is a single-valued operator, C is a closed convex set of a real Hilbert space H. Given Ψ : H → ∪ { ∞} which acts as a penalization function with respect to the constraint x ∈ C, and a penalization parameter βk, we consider an algorithm which alternates a proximal step with respect to ∂Ψ and a gradient step with respect to A and reads as xk I λkβk∂Ψ −1 xk−1 − λkAxk−1 . Under mild hypotheses, we obtain weak convergence for an inverse strongly monotone operator and strong convergence for a Lipschitz continuous and strongly monotone operator. Applications to hierarchical minimization and fixed-point problems are also given and the multivalued case is reached by replacing themultivalued operator by its Yosida approximatewhich is always Lipschitz continuous.
ISSN: 0161-1712

hal-00776654
https://hal.univ-antilles.fr/hal-00776654
https://hal.univ-antilles.fr/hal-00776654/document
https://hal.univ-antilles.fr/hal-00776654/file/305856.pdf
DOI : 10.1155/2011/305856

Résumé : Les processus ponctuels sont souvent utilisés comme modèles de répartitions spatiales ou spatio-temporelles d'occurrences Dans cette thèse, nous nous intéressons à des processus de Cox dirigés par un processus caché associé à un processus de Dirichlet. Ce modèle correspond à des occurrences cachées influençant l'intensité stochastique des occurrences observées. Nous généralisons la notion de Shot noise Cox process et développons le traitement bayésien. Nous focalisons l'inférence statistique sur l'estimation de la valeur espérée de chaque contribution cachée, leur nombre espéré, degré d'influence spatiale et degré de corrélation L'utilité en épidémiologie et en écologie est démontrée à partir de données de Rubus fruticosa, lbicella lutea et de mortalité dans les cantons de Georgie, USA. En termes de données observées, deux situations sont considérées: d'abord, les positions spatiales des occurrences sont observées entre plusieurs paires de dates consécutives; puis, des comptages sont effectués dans des unités d'échantillonnage spatiales. D'autre part, nous nous intéressons aux processus ponctuels à mémoire introduits par Kagan, Ogata et Vere-Jones. En effet, les processus ponctuels ont une place importante dans l'étude des catalogues sismiques. Nous avons étudié un modèle Epidemie Type Aftershock Sequence avec une intensité d'arrière-plan indépendante du temps et plusieurs fonctions déclenchantes permettant d'intégrer les événements antérieurs récents. Cette approche est utilisée pour étudier la sismicité des Petites Antilles. Une étude comparative des modèles Gamma, Weibull, Log-Normal et loi d'Omori modifiée pour les fonctions déclenchantes est menée.
Point processes are often used as spatial or spatio-temporal distribution models of occurrences. In this Phd dissertation, we focus first on Cox processes driven by a hidden process associated with a Dirichlet process. This model corresponds to hidden occurrences influencing the stochastic intensity of observed occurrences. We generalize the notion of Shot noise Cox process and develop its bayesian analysis. We focus the statistical inference on the estimation of the hidden contribution expected value, the hidden contribution expected number, the spatial influence and correlation parameters. Applications in epidemiology and ecology are shown from Rubus fruticosa data, Ibicella lutea data and death number data in counties of Georgia, USA. Two situations are considered with respect to available data: firstly, the spatial positions of occurrences are observed between several pairs of consecutive dates; secondly, counts are carried out over a fixed time interval in several spatial sampling units. Secondly, we focus on point processes with memory intr oduced by Kagan, Ogata and Vere-Jones. Spatio-temporal point processes play an important role in the studies of earthquake catalogs since they consist of seismic events with their dates and spatial locations. We studied an Epidemic Type Aftershock Sequence model with time independent background intensity and several triggering functions taking into account previous events. We illustrate our approach with a seismicity study of the Lesser Antilles arc. A comparaison study of Gamma, Weibull, Log-Normal and modified Omori law triggering function models is also carried out

http://www.theses.fr/2012AGUY0555/document

Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : Dehydration reactions result in minerals’ replacement and a transient fluid-filled porosity. These reactions involve interface-coupled dissolution–precipitation and might therefore lead to fixed crystallographic orientation relations between reactant (protolith) and product phases (i.e. topotaxy). We investigate these two phenomena in the dehydration of a foliated antigorite (atg) serpentinite by comparing the crystallographic preferred orientation (CPO) developed by olivine (ol), orthopyroxene (opx) and chlorite (chl) during high-pressure antigorite and chlorite dehydration in piston-cylinder experiments and in natural samples recording the dehydration of antigorite (Cerro del Almirez, Betic Cordillera, Spain). Experiments were performed under undrained conditions resulting in fluid-filled porosity and in strong CPO of the prograde minerals, controlled by the pre-existing antigorite CPO in the reactant foliated serpentinite. The orientation of a ol,opx and c∗chl is parallel to c∗atg from the protolith. The Cerro del Almirez samples show similar, locally well-developed topotactic relations between orthopyroxene, chlorite and antigorite, but the product CPOs are weaker and more complex at the thin section scale. In contrast to the experiments, olivine from natural samples shows a weak correlation between b ol and the former c∗atg. We relate the strengthening of local topotactic relations and the weakening of the inherited CPO at a larger scale in natural samples to compaction and associated fluid migration. Microstructural features that might be related to compaction in the natural samples include: (1) smooth bending of the former foliation, (2) gradual crystallographic misorientation (up to 16°) of prismatic orthopyroxene due to buckling by dislocation creep, (3) inversion of enstatite to low clinoenstatite (P21/c) along lamellae and (4) brittle fracturing of prismatic orthopyroxene enclosed by plastically deformed chlorite. The coexistence of orthopyroxene buckling and clinoenstatite lamellae enables estimating the local strain rates and shear stresses generated during compaction. An lower bound for the strain rates in the order of 10−12 to 10−13 s−1 and shear stresses of 60–70 MPa are estimated based on creep data. Lower shear stresses (20–40 MPa) are retrieved using a theoretical approach. These data point to slow compaction (and fluid extraction) in nature if the system is not perturbed by external forces, with rates only marginally higher than the viscoplastic deformation of the solid matrix.
ISSN: 0010-7999

hal-01174158
https://hal.archives-ouvertes.fr/hal-01174158
DOI : 10.1007/s00410-015-1129-4

Éditeur(s) : HAL CCSD University of Szeged, Bolyai Institute
Résumé : International audience
We consider the semilinear heat equation in a boundeddomain of R^m. We prove the null controllability of the systemwith a finite number of constraints on the normal derivative, whenthe control acts on a bounded subset of the domain. First, weshow that the problem can be transformed into a null controllabilityproblem with constraint on the control, for a linear system.Then, we use an appropriate observability inequality to solve thelinearized problem. Finally, we prove the main result by means ofa fixed-point method.
ISSN: 1417-3875

hal-01679144
https://hal.archives-ouvertes.fr/hal-01679144
DOI : 10.14232/ejqtde.2012.1.95

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Relying on the Yosida approximate, we investigate the problem of finding zeroes for a difference of two maximal monotone operators in Hilbert spaces. These zeroes are compared to those of the corresponding regularized and dual problems. The behavior of the regularized operator is also studied and a splitting algorithm involving the resolvents of both operators is suggested via a fixed-point formulation of the regularized problem. A particular attention is given to the DC programming case.
ISSN: 0096-3003

hal-00779986
https://hal.univ-antilles.fr/hal-00779986
DOI : 10.1016/j.amc.2008.01.024

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
This article is concerned with a generalization of the hybrid steepest descent method from variational inequalities to the multivalued case. This will be reached by replacing the multivalued operator by its Yosida approximate, which is always Lipschitz continuous. It is worth mentioning that the hybrid steepest descent method is an algorithmic solution to variational inequality problems over the fixed point set of certain nonexpansive mappings and has remarkable applicability to the constrained nonlinear inverse problems like image recovery and MIMO communication systems
ISSN: 0163-0563

hal-00776641
https://hal.univ-antilles.fr/hal-00776641
DOI : 10.1080/01630563.2011.619676

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Nous montrons d'abord que les versions ''fermée'' et ''ouverte'' du Principe KKM se déduisent l'une de l'autre. Nous montrons ensuite que, comme la version ''fermée'' (dont les applications sont bien connues), la version ''ouverte'' possède quelques conséquences remarquables : par exemple, elle conduit directement au théorème de ''matching'' de Fan et permet une démonstration particulièrement simple du théorème de point fixe de Kakutani-Fan-Glicksberg.
ISSN: 0764-4442

hal-00699227
https://hal.archives-ouvertes.fr/hal-00699227