Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

Voir le monde à travers les lunettes du métacontraste : un modèle mathématique inspiré de la psychologie sociale

Résumé La théorie de l'autocatégorisation est une théorie de psychologie sociale qui porte sur la relation entre l'individu et le groupe. Elle explique le comportement de groupe par la conception de soi et des autres en tant que membres de catégories sociales, et par l'attribution aux individus des caractéristiques prototypiques de ces catégories. Il s'agit donc d'une théorie de l'individu qui est censée expliquer des phénomènes collectifs. Les situations dans lesquelles un grand nombre d'individus interagissent de manière non triviale génèrent typiquement des comportements collectifs complexes qui sont difficiles à prévoir sur la base des comportements individuels. La simulation informatique de tels systèmes est un moyen fiable d'explorer de manière systématique la dynamique du comportement collectif en fonction des spécifications individuelles. Dans cette thèse, nous présentons un modèle formel d'une partie de la théorie de l'autocatégorisation appelée principe du métacontraste. À partir de la distribution d'un ensemble d'individus sur une ou plusieurs dimensions comparatives, le modèle génère les catégories et les prototypes associés. Nous montrons que le modèle se comporte de manière cohérente par rapport à la théorie et est capable de répliquer des données expérimentales concernant divers phénomènes de groupe, dont par exemple la polarisation. De plus, il permet de décrire systématiquement les prédictions de la théorie dont il dérive, notamment dans des situations nouvelles. Au niveau collectif, plusieurs dynamiques peuvent être observées, dont la convergence vers le consensus, vers une fragmentation ou vers l'émergence d'attitudes extrêmes. Nous étudions également l'effet du réseau social sur la dynamique et montrons qu'à l'exception de la vitesse de convergence, qui augmente lorsque les distances moyennes du réseau diminuent, les types de convergences dépendent peu du réseau choisi. Nous constatons d'autre part que les individus qui se situent à la frontière des groupes (dans le réseau social ou spatialement) ont une influence déterminante sur l'issue de la dynamique. Le modèle peut par ailleurs être utilisé comme un algorithme de classification automatique. Il identifie des prototypes autour desquels sont construits des groupes. Les prototypes sont positionnés de sorte à accentuer les caractéristiques typiques des groupes, et ne sont pas forcément centraux. Enfin, si l'on considère l'ensemble des pixels d'une image comme des individus dans un espace de couleur tridimensionnel, le modèle fournit un filtre qui permet d'atténuer du bruit, d'aider à la détection d'objets et de simuler des biais de perception comme l'induction chromatique. Abstract Self-categorization theory is a social psychology theory dealing with the relation between the individual and the group. It explains group behaviour through self- and others' conception as members of social categories, and through the attribution of the proto-typical categories' characteristics to the individuals. Hence, it is a theory of the individual that intends to explain collective phenomena. Situations involving a large number of non-trivially interacting individuals typically generate complex collective behaviours, which are difficult to anticipate on the basis of individual behaviour. Computer simulation of such systems is a reliable way of systematically exploring the dynamics of the collective behaviour depending on individual specifications. In this thesis, we present a formal model of a part of self-categorization theory named metacontrast principle. Given the distribution of a set of individuals on one or several comparison dimensions, the model generates categories and their associated prototypes. We show that the model behaves coherently with respect to the theory and is able to replicate experimental data concerning various group phenomena, for example polarization. Moreover, it allows to systematically describe the predictions of the theory from which it is derived, specially in unencountered situations. At the collective level, several dynamics can be observed, among which convergence towards consensus, towards frag-mentation or towards the emergence of extreme attitudes. We also study the effect of the social network on the dynamics and show that, except for the convergence speed which raises as the mean distances on the network decrease, the observed convergence types do not depend much on the chosen network. We further note that individuals located at the border of the groups (whether in the social network or spatially) have a decisive influence on the dynamics' issue. In addition, the model can be used as an automatic classification algorithm. It identifies prototypes around which groups are built. Prototypes are positioned such as to accentuate groups' typical characteristics and are not necessarily central. Finally, if we consider the set of pixels of an image as individuals in a three-dimensional color space, the model provides a filter that allows to lessen noise, to help detecting objects and to simulate perception biases such as chromatic induction.

Quantification of the local heartwall motion by magnetic resonance myocardial tagging.

Sophisticated magnetic resonance tagging techniques provide powerful tools for the non-invasive assessment of the local heartwall motion towards a deeper fundamental understanding of local heart function. For the extraction of motion data from the time series of magnetic resonance tagged images and for the visualization of the local heartwall motion a new image analysis procedure has been developed. New parameters have been derived which allows quantification of the motion patterns and are highly sensitive to any changes in these patterns. The new procedure has been applied for heart motion analysis in healthy volunteers and in patient collectives with different heart diseases. The achieved results are summarized and discussed.

Berguer, Rochedieu: Flournoy's legacy in the Genevan school of the psychology of religion

In 1891 Théodore Flournoy (1854-1920) became the first Professor of Psychology to be appointed at the University of Geneva, and his teaching regularly included references to religion. His successor, Georges Berguer, who taught psychology of religion, began as privat-docent in 1910 and received a full professorship in Religious Psychology and the History of Religion in 1928. French-speaking Switzerland is one of the rare places in the world where psychology of religion has been taught continuously since the very beginning of the 20th century. The aim of this article is to shed light on this tradition and especially on Georges Berguer (retired in 1944) and Edmond Rochedieu (retired in 1965) who succeeded Flournoy. This historical enterprise concludes with some reflections on the role of the psychology of religion at the intersection of psychology and the study of religions.

Brownian motion of spiral waves driven by spatiotemporal structured noise

Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.

Brownian motion in short range random potentials

A numerical study of Brownian motion of noninteracting particles in random potentials is presented. The dynamics are modeled by Langevin equations in the high friction limit. The random potentials are Gaussian distributed and short ranged. The simulations are performed in one and two dimensions. Different dynamical regimes are found and explained. Effective subdiffusive exponents are obtained and commented on.

[Illustrations de Génie du Christianisme ou beautés de la religion chrétienne] / A.Villerey, grav. ; Dambrun, grav. [et al...]; Chateaubriand, aut. du texte

Comprend : [Tome I. Frontispice : la Foi chrétienne commandant aux Arts et aux travaux des hommes.] [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635] ; [Tome I. Pl. en reg. p.110 : Chapitre XI. L'extrême-onction.] [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635] ; [Tome I. Pl. en reg. p.319 : Livre V. Partie I. On se console par la douleur.] L'une apportoit son enfant mort, l'autre son enfant vivant (...) Elle mettoient ensuite leurs enfants sur une branche de catalpa, et les balançoient ensemble, en chantant des airs de leurs pays. Hélas! ces jeux maternels, qui souvent endormoient l'innocence, ne pouvoient réveiller la mort! [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635] ; [Tome II. Pl. en reg. p.239 : Partie II. Livre IV. Les passions. Amélie décidée à rentrer au couvent.] [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635] ; [Tome II. Pl. en reg. p.250 : Partie II. Livre IV. Les passions. Chateaubriand guettant la fenêtre d'Amélie au couvent.] [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635] ; [Tome III. Pl. en reg. p.368 : Partie III. Livre VI. La mort d'Atala. Le Père Aubry et Chactas enterrent Atala.] [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635] ; [Tome III. Pl. en reg. p.372 : Partie III. Livre VI. Chactas pleure sur la tombe d'Atala.] [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635] ; [Tome IV. Pl. en reg. p.167 : Partie IV. Livre III. Chapitre VI. Vue générale du Clergé. Un moine Trappiste.] [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635] ; [Tome IV. Pl. en reg. p.217 : Partie IV. Livre III. Chapitre VI. Vue générale du Clergé. Un missionnaire remonte le Rio de la Plata pour évangéliser les Indiens.] [Cote : Res D 5716/Microfilm R 122368 à 122370 et R 132635]

Retrospective feasibility study of simultaneous integrated boost in cervical cancer using Tomotherapy: the impact of organ motion and tumor regression.

BACKGROUND: Whole pelvis intensity modulated radiotherapy (IMRT) is increasingly being used to treat cervical cancer aiming to reduce side effects. Encouraged by this, some groups have proposed the use of simultaneous integrated boost (SIB) to target the tumor, either to get a higher tumoricidal effect or to replace brachytherapy. Nevertheless, physiological organ movement and rapid tumor regression throughout treatment might substantially reduce any benefit of this approach. PURPOSE: To evaluate the clinical target volume - simultaneous integrated boost (CTV-SIB) regression and motion during chemo-radiotherapy (CRT) for cervical cancer, and to monitor treatment progress dosimetrically and volumetrically to ensure treatment goals are met. METHODS AND MATERIALS: Ten patients treated with standard doses of CRT and brachytherapy were retrospectively re-planned using a helical Tomotherapy - SIB technique for the hypothetical scenario of this feasibility study. Target and organs at risk (OAR) were contoured on deformable fused planning-computed tomography and megavoltage computed tomography images. The CTV-SIB volume regression was determined. The center of mass (CM) was used to evaluate the degree of motion. The Dice's similarity coefficient (DSC) was used to assess the spatial overlap of CTV-SIBs between scans. A cumulative dose-volume histogram modeled estimated delivered doses. RESULTS: The CTV-SIB relative reduction was between 31 and 70%. The mean maximum CM change was 12.5, 9, and 3 mm in the superior-inferior, antero-posterior, and right-left dimensions, respectively. The CTV-SIB-DSC approached 1 in the first week of treatment, indicating almost perfect overlap. CTV-SIB-DSC regressed linearly during therapy, and by the end of treatment was 0.5, indicating 50% discordance. Two patients received less than 95% of the prescribed dose. Much higher doses to the OAR were observed. A multiple regression analysis showed a significant interaction between CTV-SIB reduction and OAR dose increase. CONCLUSIONS: The CTV-SIB had important regression and motion during CRT, receiving lower therapeutic doses than expected. The OAR had unpredictable shifts and received higher doses. The use of SIB without frequent adaptation of the treatment plan exposes cervical cancer patients to an unpredictable risk of under-dosing the target and/or overdosing adjacent critical structures. In that scenario, brachytherapy continues to be the gold standard approach.