Sur le Web, ces 365 derniers jours

vendredi 26 avril 2013

• Asymptotic behavior of compositions of under-relaxed nonexpansive operators
In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.

jeudi 25 avril 2013

• Weak error in negative Sobolev spaces for the stochastic heat equation
In this paper, we make another step in the study of weak error of the stochastic heat equation by considering norms as functional.

• Weak error expansion of the implicit Euler scheme
In this paper, we extend the Talay Tubaro theorem to the implicit Euler scheme.

• Multiple kernel self-organizing maps
In a number of real-life applications, the user is interested in analyzing several sources of information together: a graph combined with the additional information known on its nodes, numerical variables measured on individuals and factors describing these individuals... The combination of all sources of information can help him to understand the dataset in its whole better. The present article focuses on such an issue, by using self-organizing maps. The use a kernel version of the algorithm allows us to combine various types of information and automatically tune the data combination. This approach is illustrated on a simulated example.

mercredi 13 mars 2013

• Model selection and clustering in stochastic block models with the exact integrated complete data likelihood
The stochastic block model (SBM) is a mixture model used for the clustering of nodes in networks. It has now been employed for more than a decade to analyze very different types of networks in many scientific fields such as Biology and social sciences. Because of conditional dependency, there is no analytical expression for the posterior distribution over the latent variables, given the data and model parameters. Therefore, approximation strategies, based on variational techniques or sampling, have been proposed for clustering. Moreover, two SBM model selection criteria exist for the estimation of the number K of clusters in networks but, again, both of them rely on some approximations. In this paper, we show how an analytical expression can be derived for the integrated complete data log likelihood. We then propose an inference algorithm to maximize this exact quantity. This strategy enables the clustering of nodes as well as the estimation of the number clusters to be performed at the same time and no model selection criterion has to be computed for various values of K. The algorithm we propose has a better computational cost than existing inference techniques for SBM and can be employed to analyze large networks with ten thousand nodes. Using toy and true data sets, we compare our work with other approaches.

samedi 2 mars 2013

• Cartographie de la Chronique d'Henri de Livonie
The Livonian Chronicle of Henry is the oldest written document about the History of the eastern baltic shores. We try to apply statistical and algorithmical methods on toponimic and chronological data from this chronicle, in order to build static and dynamic maps. With this study we hope to gain some historical insight into both the redaction of the chronicle itself and the events it describes.

mardi 26 février 2013

• Semi-periodic solutions of difference and differential equations
The spaces of semi-periodic sequences and functions are examined in the relationship to the closely related notions of almost-periodicity, quasi-periodicity and periodicity. Besides the main theorems, several illustrative examples of this type are supplied. As an application, the existence and uniqueness results are formulated for semi-periodic solutions of quasi-linear difference and differential equations.

• S-asymptotically ω-periodic functions and applications to evolution equations.
• Problèmes économétriques d'analyse des séries temporelles à mémoire longue
Les modalités d'investigation de notre thèse sont menées, sous trois angles : épistémologique, statistique et économique. En première partie de la thèse, dans une approche épistémologique, nous spécifions en quoi le concept de mémoire longue peut apparaître, comme un nouveau paradigme kühnien pour la macroéconomie et la finance. En deuxième partie de la thèse, dans une approche statistique, semi-paramétrique, nous proposons trois extensions de la statistique IR (Increment Ratio) de Surgailis et al, (2008). Premièrement, un théorème central limite multidimensionnelle est établi pour un vecteur composé de plusieurs statistiques IR. Deuxièmement, un test d'adéquation de qualité d'ajustement de type chi2 est déduit de ce théorème. Troisièmement, ce théorème nous a permis de construire des versions adaptatives de l'estimateur et du test d'adéquation étudiés dans un cadre semi-paramétrique général. Nous prouvons que l'estimateur adaptatif du paramètre de la mémoire longue suit une propriété d'Oracle. Les simulations que nous avons menées attestent de la précision et de la robustesse de l'estimateur et du test d'adéquation, même dans le cas non gaussien. En troisième partie de la thèse, nous en déduisons deux tests respectivement de stationnarité et de non stationnarité pour les processus I(d) stationnaires et non stationnaires, pour tout réel d tel que (-0.5< d<1.25). Dans une approche économique, au sein de cette troisième partie de la thèse, nous mettons en oeuvre les résultats théoriques précédents comparés à ceux issus d'autres méthodes statistiques: paramétriques, semi-paramétriques ou non paramétriques (ou heuristiques) appliquées à des séries économiques et financières.

samedi 23 février 2013

• Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process
The purpose of this paper is to estimate the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.

• Étude des corrélations spatio-temporelles des appels mobiles en France
Nous proposons dans cet article de présenter une application d'analyse d'une base de données de grande taille issue du secteur des télécommunications. Le problème consiste à segmenter un territoire et caractériser les zones ainsi définies grâce au comportement des habitants en terme de téléphonie mobile. Nous disposons pour cela d'un réseau d'appels inter-antennes construit pendant une période de cinq mois sur l'ensemble de la France. Nous proposons une analyse en deux phases. La première couple les antennes émettrices dont les appels sont similairement distribués sur les antennes réceptrices et vice versa. Une projection de ces groupes d'antennes sur une carte de France permet une visualisation des corrélations entre la géographie du territoire et le comportement de ses habitants en terme de téléphonie. La seconde phase découpe l'année en périodes entre lesquelles on observe un changement de distributions d'appels sortant des groupes d'antennes. On peut ainsi caractériser l'évolution temporelle du comportement des usagers de mobiles dans chacune des zones du pays.

• Classifications croisées de données de trajectoires contraintes
Le clustering (ou classification non supervisée) de trajectoires a fait l'objet d'un nombre considérable de travaux de recherche. La majorité de ces travaux s'est intéressée au cas où les objets mobiles engendrant ces trajectoires se déplacent librement dans un espace euclidien et ne prennent pas en compte les contraintes liées à la structure sous-jacente du réseau qu'ils parcourent (ex. réseau routier). Dans le présent article, nous proposons au contraire la prise en compte explicite de ces contraintes. Nous représenterons les relations entre trajectoires et segments routiers par un graphe biparti et nous étudierons la classification de ses sommets. Nous illustrerons, sur un jeu de données synthétiques, l'utilité d'une telle étude pour comprendre la dynamique du mouvement dans le réseau routier et analyser le comportement des véhicules qui l'empruntent.

jeudi 21 février 2013

• A test for parameter change in general causal time series using quasi-likelihood estimator
In this paper, we propose a new procedure to test a change in the parameter of a process $X= (X_t)_{t\in \Z}$ belonging to a class of causal models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models. Two statistics $\widehat{Q}^{(1)}_n$ and $\widehat{Q}^{(2)}_n$ are constructed using the quasi-likelihood estimator (QMLE) of the parameter. Under the null hypothesis that there is no change, each of these statistics converges weakly to a well-known distribution and the maximum diverges to infinity under the alternative of one change. Some simulation results are reported.

vendredi 15 février 2013

• Illustration par quelques exemples des lois strictement stables dans un cône convexe
The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach spaces. Some examples of strictly stable distributions and max-stable distributions are presented in this paper in order to exhibit the relationship between the Poisson process and the stable distributions on convex cones.

vendredi 1er février 2013

• Carte auto-organisatrice pour graphes étiquetés.
Dans de nombreux cas d'études concrets, l'analyse de données sur les graphes n'est pas limitée à la seule connaissance du graphe. Il est courant que des informations supplémentaires soient disponibles sur les sommets et que l'utilisateur souhaite combiner ces informations à la structure du graphe lui-même pour comprendre l'intégralité des données en sa possession. C'est ce problème que nous souhaitons aborder dans cet article, en nous focalisant sur une méthode de fouille de données qui combine classification (non supervisée) et visualisation : les cartes auto-organisatrices. Nous expliquons comment l'utilisation de méthodes à noyaux permet de combiner de manière efficace des informations de natures diverses (graphe, variables numériques, facteurs, variables textuelles...) pour décortiquer la structure des données et en offrir une représentation simplifiée. Notre approche est illustrée sur divers exemples : un premier exemple, sur des données simulées, permet de comprendre comment se comporte l'algorithme. Un second exemple illustre la méthode sur un graphe réel de plusieurs centaines de sommets, qui modélise un corpus de documents médiévaux.

vendredi 11 janvier 2013

• A Triclustering Approach for Time Evolving Graphs
This paper introduces a novel technique to track structures in time evolving graphs. The method is based on a parameter free approach for three-dimensional co-clustering of the source vertices, the target vertices and the time. All these features are simultaneously segmented in order to build time segments and clusters of vertices whose edge distributions are similar and evolve in the same way over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make an a priori discretization. Experiments conducted on a synthetic dataset illustrate the good behaviour of the technique, and a study of a real-life dataset shows the potential of the proposed approach for exploratory data analysis.

jeudi 3 janvier 2013

• A Schelling-class system with spatially-fixed switching agents
We study the behaviour of a Schelling-class system where spatially-fixed switching agents are introduced. Agent types are to be interpreted as social groups, and switching as social mobility. Dynamical simulations allow us to provide cross-sections of the 3-dimensional phase diagram $F(\rho, \tau, f)$, where $\rho$ is the occupation density, $f$ the fraction of agents able to switch from one group to the other, and $\tau$ is generally interpreted as the tolerance of agents toward neighbours of the opposite type. We investigate different transitions between segregated and mixed phases both at $f=0$ and along lines of increasing $f$, where the nature of the transition changes. We also find that the presence of switching agents in a segregative Schelling-type dynamics can induce de-segregation even with values of $f$ lower than 1/2.

mercredi 26 décembre 2012

• On-line relational SOM for dissimilarity data
In some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self Organizing Map algorithm were introduced to generalize the original algorithm to this framework. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual combination of all elements in the data set. However, this latter approach suffers from two main drawbacks. First, its complexity can be large. Second, only a batch version of this algorithm has been studied so far and it often provides results having a bad topographic organization. In this article, an on-line version of relational SOM is described and justified. The algorithm is tested on several datasets, including categorical data and graphs, and compared with the batch version and with other SOM algorithms for non vector data.

vendredi 21 décembre 2012

• The Random Subgraph Model for the Analysis of an Ecclesiastical Network in Merovingian Gaul
In the last two decades, many random graph models have been proposed to extract knowledge from networks. Most of them look for communities or more generally clusters of vertices with homogeneous connection profiles. While the first models focused on networks with binary edges only, extensions now allow to deal with valued networks. Recently, new models were also introduced in order to characterize connection patterns in networks through mixed memberships. This work was motivated by the need of analyzing a historical network where a partition of the vertices is given and where edges are typed. A known partition is seen as a decomposition of a network into subgraphs that we propose to model using a stochastic model with unknown latent clusters. Each subgraph has its own mixing vector and sees its vertices associated to the clusters. The vertices then connect with a probability depending on the subgraphs only, while the types of the edges are assumed to be sampled from the latent clusters. A variational Bayes expectation-maximization algorithm is proposed for inference as well as a model selection criterion for the estimation of the cluster number. Experiments are carried out on simulated data to assess the approach. The proposed methodology is then applied to an ecclesiastical network in merovingian Gaul. An R code implementing the inference algorithm is available from the authors upon request.

vendredi 7 décembre 2012

• Spatial Statistics and Modeling
Les modèles et les méthodes statistiques pour les principaux modèles spatiaux, second ordre, géostatistiques, champs markoviens et processus spatiaux. En s'appuyant sur R, de nombreux exemples illustrent ces méthodes.

mercredi 5 décembre 2012

• Contributions à l'apprentissage statistique en grande dimension, adaptatif et sur données atypiques
Ce mémoire rend compte de mes activités de recherche depuis ma thèse de doctorat. Mes travaux s'inscrivent dans le cadre de l'apprentissage statistique et s'articulent plus précisément autour des quatre thématiques suivantes: * apprentissage statistique en grande dimension, * apprentissage statistique adaptatif, * apprentissage statistique sur données atypiques, * applications de l'apprentissage statistique. Mes contributions à ces quatre thématiques sont décrites en autant de chapitres, numérotés de 2 à 5, pouvant être lus indépendamment. Ce mémoire se veut également être, en quelque sorte, un plaidoyer pour l'usage des méthodes génératives (reposant sur un modèle probabiliste) en apprentissage statistique moderne. Il sera en effet démontré dans ce document, je l'espère de façon convaincante, que les méthodes génératives peuvent résoudre efficacement les problèmes actuels de l'apprentissage statistique tout en présentant l'avantage de l'interprétabilité des résultats et de la connaissance du risque de prédiction.

mardi 4 décembre 2012

• Éditorial du numéro spécial RNTI - MASHS 2011/2012 : Modèles et Apprentissage en Sciences Humaines et Sociales
• Spatial correlation in bipartite networks
In this article, the influence between a spatial information and interactions between individuals is addressed. This issue is illustrated through the analysis of a corpus of notarial acts established during the Middle Ages. In this corpus, the persons interact in common transactions that are geolocalized. The present work tries to quantify the impact of this spatial information on the relations between people. As the spatial information as well as the relations between individuals are derived from the same source (the transactions in which the individuals have been involved), a standard Mantel test (Mantel, 1967) is not suited to address this issue. A similar methodology, based on the adaptation of the original permutation test, is thus proposed and illustrated in that context.

lundi 3 décembre 2012

• Model-based Clustering of High-dimensional Data Streams with Online Mixture of Probabilistic PCA
Model-based clustering is a popular tool which is renowned for its probabilistic foundations and its flexibility. However, model-based clustering techniques usually perform poorly when dealing with high-dimensional data streams, which are nowadays a frequent data type. To overcome this limitation of model-based clustering, we propose an online inference algorithm for the mixture of probabilistic PCA model. The proposed algorithm relies on an EM-based procedure and on a probabilistic and incremental version of PCA. Model selection is also considered in the online setting through parallel computing. Numerical experiments on simulated and real data demonstrate the effectiveness of our approach and compare it to sate-of-the-art online EM-based algorithms.

• Lexical Recount between Factor Analysis and Kohonen Map: Mathematical Vocabulary of Arithmetic in the Vernacular Language of the Late Middle Ages
In this paper we present a combination of factorial projections and of SOM algorithm applied to a text mining problem. The corpus consists of 8 medieval texts which were used to teach arithmetic techniques to merchants. Classical Factorial Component Analysis (FCA) gives nice representations of the selected words in association with the texts, but the quality of the representation is poor in the center of the graphs and it is not easy to look for the successive projections to conclude. So using the nice properties of Kohonen maps, we can highlight the words which seems to play a special role in the vocabulary since they are associated with very different words from a map to another. Finally we show that combination of both representations is a powerful help to text analysis.

• Théorèmes limite pour des tableaux triangulaires de fonctionnelles de vecteurs gaussiens et applications statistiques à des processus non stationnaires
En premier lieu, on montre une borne générale pour les moments de produits de fonctionnelles de vecteurs gaussiens, étendant le résultat de Taqqu (1977, Lemme 4,5). Un théorème de la limite centrale pour les tableaux triangulaires de fonctionnelles non linéaires de suites de vecteurs gaussiens non stationnaires est ensuite établi. Ce théorème étend notamment les résultats précédents de Breuer et Major (1981), Arcones (1994). Une inégalité de type Berry-Esseen type lié au théorème de la limite centrale est également obtenues en suivant la démarche Nourdin, Peccati et Podolskij (2011). Deux applications statistiques de ces résultats sont alors étudiées. La première se réfère au comportement asymptotique d'une statistique mesurant l'irrégularité de processus gaussiens à temps continu. La seconde est un théorème de la limite centrale satisfait par processus à longue mémoire localement stationnaires.

mardi 27 novembre 2012

• Determinants of human adipose tissue gene expression: impact of diet, sex, metabolic status, and cis genetic regulation.
Weight control diets favorably affect parameters of the metabolic syndrome and delay the onset of diabetic complications. The adaptations occurring in adipose tissue (AT) are likely to have a profound impact on the whole body response as AT is a key target of dietary intervention. Identification of environmental and individual factors controlling AT adaptation is therefore essential. Here, expression of 271 transcripts, selected for regulation according to obesity and weight changes, was determined in 515 individuals before, after 8-week low-calorie diet-induced weight loss, and after 26-week ad libitum weight maintenance diets. For 175 genes, opposite regulation was observed during calorie restriction and weight maintenance phases, independently of variations in body weight. Metabolism and immunity genes showed inverse profiles. During the dietary intervention, network-based analyses revealed strong interconnection between expression of genes involved in de novo lipogenesis and components of the metabolic syndrome. Sex had a marked influence on AT expression of 88 transcripts, which persisted during the entire dietary intervention and after control for fat mass. In women, the influence of body mass index on expression of a subset of genes persisted during the dietary intervention. Twenty-two genes revealed a metabolic syndrome signature common to men and women. Genetic control of AT gene expression by cis signals was observed for 46 genes. Dietary intervention, sex, and cis genetic variants independently controlled AT gene expression. These analyses help understanding the relative importance of environmental and individual factors that control the expression of human AT genes and therefore may foster strategies aimed at improving AT function in metabolic diseases.

• Phenotypic prediction based on metabolomic data on the growing pig from three main European breeds.
Predicting phenotypes is a statistical and biotechnical challenge, both in medicine (predicting an illness) and animal breeding (predicting the carcass economical value on a young living animal). High-throughput fine phenotyping is possible using metabolomics, which describes the global metabolic status of an individual, and is the closest to the terminal phenotype. The purpose of this work was to quantify the prediction power of metabolomic profiles for commonly used production phenotypes from a single blood sample from the growing pig. Several statistical approaches were investigated and compared on the basis of cross validation: raw data vs. signal preprocessing (wavelet transformation), with a single-feature selection method. The best results in terms of prediction accuracy were obtained when data were preprocessed using wavelet transformations on the Daubechies basis. The phenotypes related to meat quality were not well predicted because the blood sample was taken some time prior to slaughter, and slaughter is known to have a strong influence on these traits. In contrast, phenotypes of potential economic interest (e.g., lean meat percentage and ADFI) were well predicted (R(2) = 0.7; P < 0.0001) using metabolomic data.

lundi 26 novembre 2012

• Professional Trajectories of Workers Using Disconnected Self-Organizing Maps
Using the Panel Study of Income Dynamics (PSID) collected on the period 1984-2003, we study the situations of American workers with respect to employment. The data include all heads of household (men or women) as well as the partners who are on the labor market, working or not. They are extracted from the complete survey by computing a few relevant features which characterize the worker's situations. To perform this analysis, we suggest to use a Self-Organizing Map (Kohonen algorithm) with specific topology. In this paper we present a new topology for SOM based on a planar graph with disconnected components (called D-SOM) which is especially interesting for clustering. Each component takes the form of a string and corresponds to an organized cluster. From this clustering, we study the dynamics at the individual level, that is the trajectories of the individuals among the classes during the observed period. Then we estimate the transition probability matrices for each studied year and the corresponding stationary distributions. Finally, we try to give an answer to the question: is there a significant change in 1992 (new economic policies after the Reaganomics).

dimanche 18 novembre 2012

• Dissemination of Health Information within Social Networks
In this paper, we investigate, how information about a common food born health hazard, known as Campylobacter, spreads once it was delivered to a random sample of individuals in France. The central question addressed here is how individual characteristics and the various aspects of social network influence the spread of information. A key claim of our paper is that information diffusion processes occur in a patterned network of social ties of heterogeneous actors. Our percolation models show that the characteristics of the recipients of the information matter as much if not more than the characteristics of the sender of the information in deciding whether the information will be transmitted through a particular tie. We also found that at least for this particular advisory, it is not the perceived need of the recipients for the information that matters but their general interest in the topic.

vendredi 16 novembre 2012

• Modeling First Line Of An Order Book With Multivariate Marked Point Processes
We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the corresponding volume of orders. The model is motivated by the fact that the "excitation" of the market is different in periods of time with low exchanged volume and high volume exchanged. We illustrate our result by numerical simulations on foreign exchange data sampling in millisecond. By checking the main stylized facts, we show that the model is consistent with the empirical data. We also find an interesting relation between the distribution of the volume of limited order and the volume of market orders. To conclude, we propose an application to risk management and we introduce a forecast procedure.

lundi 12 novembre 2012

• Model-Based Clustering of High-Dimensional Data: A review
Model-based clustering is a popular tool which is renowned for its probabilistic foundations and its flexibility. However, high-dimensional data are nowadays more and more frequent and, unfortunately, classical model-based clustering techniques show a disappointing behavior in high-dimensional spaces. This is mainly due to the fact that model-based clustering methods are dramatically over-parametrized in this case. However, high-dimensional spaces have specific characteristics which are useful for clustering and recent techniques exploit those characteristics. After having recalled the bases of model-based clustering, this article will review dimension reduction approaches, regularization-based techniques, parsimonious modeling, subspace clustering methods and clustering methods based on variable selection. Existing softwares for model-based clustering of high-dimensional data will be also reviewed and their practical use will be illustrated on real-world data sets.

mercredi 24 octobre 2012

• Neural Networks for Complex Data
Artificial neural networks are simple and efficient machine learning tools. Defined originally in the traditional setting of simple vector data, neural network models have evolved to address more and more difficulties of complex real world problems, ranging from time evolving data to sophisticated data structures such as graphs and functions. This paper summarizes advances on those themes from the last decade, with a focus on results obtained by members of the SAMM team of Université Paris 1

samedi 20 octobre 2012

• Triclustering pour la détection de structures temporelles dans les graphes
This paper introduces a novel technique to track structures in time evolving graphs. The method is based on a parameter free approach for three-dimensional co-clustering of the source vertices, the target vertices and the time. All these features are simultaneously segmented in order to build time segments and clusters of vertices whose edge distributions are similar and evolve in the same way over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make an a priori discretization. Experiments conducted on a synthetic dataset illustrate the good behaviour of the technique, and a study of a real-life dataset shows the potential of the proposed approach for exploratory data analysis

lundi 1er octobre 2012

• Graph-Based Approaches to Clustering Network-Constrained Trajectory Data
Even though clustering trajectory data attracted considerable attention in the last few years, most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network and its influence on evaluating the similarity between trajectories. In this paper, we present two approaches to clustering network-constrained trajectory data. The first approach discovers clusters of trajectories that traveled along the same parts of the road network. The second approach is segment-oriented and aims to group together road segments based on trajectories that they have in common. Both approaches use a graph model to depict the interactions between observations w.r.t. their similarity and cluster this similarity graph using a community detection algorithm. We also present experimental results obtained on synthetic data to showcase our propositions.

jeudi 20 septembre 2012

• Multifractal random walks with fractional Brownian motion via Malliavin calculus
We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a dependent fractional Brownian motion. Using the techniques of the Malliavin calculus, we study the existence of this object and its properties. We then propose a continuous time model in finance that captures the main properties observed in the empirical data, including the leverage effect. We illustrate our result by numerical simulations.

mercredi 19 septembre 2012

• Convex hull of n planar Brownian paths: an exact formula for the average number of edges
We establish an exact formula for the average number of edges appearing on the boundary of the global convex hull of n independent Brownian paths in the plane. This requires the introduction of a counting criterion which amounts to "cutting off" edges that are, in a specific sense, small. The main argument consists in a mapping between planar Brownian convex hulls and configurations of constrained, independent linear Brownian motions. This new formula is confirmed by retrieving an existing exact result on the average perimeter of the boundary of Brownian convex hulls in the plane.

dimanche 16 septembre 2012

• On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact riemannian manifold
We prove the existence and the uniqueness of a solution to the stochastic NSLE on a two-dimensional compact riemannian manifold. Thus we generalize a recent work by Burq, Gérard and Tzvetkov in the deterministic setting, and a series of papers by de Bouard and Debussche, who have examined similar questions in the case of the flat euclidean space with random perturbation. We prove the existence and the uniqueness of a local maximal solution to stochastic nonlinear Schrödinger equations with multiplicative noise on a compact d-dimensional riemannian manifold. Under more regularity on the noise, we prove that the solution is global when the nonlinearity is of defocusing or of focusing type, d=2 and the initial data belongs to the finite energy space. Our proof is based on improved stochastic Strichartz inequalities.

vendredi 14 septembre 2012

• Clustering patterns of urban built-up areas with curves of fractal scaling behaviour
Fractal dimension is an index which can be used for characterizing urban areas. The use of the curve of scaling behavior is less common. However its shape gives local information about the morphology of the built‐up area. This paper suggests a method based on a k‐medoid for clustering these curves. It is applied to 49 ward of European cities, and shows that the curves add interesting intra‐ward information to our knowledge of the spatial variation of the urban texture. Moreover, morphological similarities are observed between cities: living, architectural and planning trends are not specific to individual cities.

vendredi 7 septembre 2012

• Nonparametric estimation of the local Hurst function of multifractional Gaussian processes
A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator.

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