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International audience; The French nuclear community is highly active in the field of earthquake engineering and more precisely, regarding seismic risk assessment. Among the existing safety-oriented frameworks, there is one which involves not only nuclear operators such as Electricité de France (EDF), the French Sustainable Energies and Atomic Energy Commission (CEA) and FRAMATOME, but also the French technical support organization which is the Institute for Radiological Protection and Nuclear Safety (IRSN). Within this framework, research activities are conducted, aiming to enhance knowledge in order to improve nuclear safety of either existing or new facilities. These activities deal with topics and challenging issues that appear to be significant in the seismic risk assessment process. More precisely, they aim to better assess the seismic margins when available, to better understand the beyond-design behavior of nuclear buildings or related equipment and to improve the necessary knowledge to produce robust seismic hazard assessment studies. The main objective of this paper is to give an overview of the past, ongoing, and future joint activities carried out by CEA-EDF-FRAMATOME-IRSN and will especially highlight main findings and future challenges and opportunities in the field of seismic safety of nuclear facilities. To reach the objective, technical focus will be made during the presentation.

International audience; The quantification of historical earthquakes is a key element in seismic hazard assessment.Historical buildings recorded in their walls disorders induced by ancient earthquakes as "stone seismometers".We developped an innovative methodology to infer key ground motion characteristics of historical earthquakes by connecting building archaeology, seismology and earthquake engineering through the case study of the medieval church of Sant'Agata del Mugello (Central Apennines, Italy) for which many historical sources described the damage induced by past earthquakes, and their post seismic repair. The largest known events occurred in 1542 (Mw 6) and 1919 (Mw 6.3).The church's history is described by combining stratigraphic analysis of walls with an in-depth study of archives. Ambient vibration measurements provide a structural identification of the church in its present state. A preliminary model of the church is updated through a Vibration-Based model updating process. Strategies to compute the seismic response of the church are discussed. Preliminary results using a continuum damage model to identify the limit of the updated model is discussed.

International audience

In this memoir , I examine different aspects of a simple but ubiquitous computer object: the string or sequence of symbols. The string of characters concept is at the crossroads of areas as information theory and language theory. Although simple, this notion is fundamental: data will always be represented, encoded and stored in computers as sequences of symbols at one time or another The increasing amount of information and data to which we have access, such as genomes of individuals or scanned documents, justifies that the algorithms and data structures handling them need to be optimized. Consequently, rigourous analysis is needed in order to guide the end-user and the designer of programs that manipulate these data. The average analysis is particularly appropriate here because the data reach such variety and large volumes that the typical case is best reflected than with the more usual worst case complexity. This obviously raises the very difficult problem of data modeling. Indeed in our setting we want two contradictory things: a model closer to the data, which really translates their specificities, but also a model yielding results, that is to say, able to predict the performance. Methods are most often those of analytic combinatorics and use a mathematical object , generating functions, to carry out the analyzes., Dans ce mémoire, j'examine différents aspects d'un objet simple mais omniprésent en informatique: la séquence de symboles (appelée selon le contexte mot ou chaîne de caractères). La notion de mot est au carrefour de domaines comme la théorie de l'information et la théorie des langages. S'il est simple, il reste fondamental: nous n'avons, au plus bas niveau, que cela à disposition puisqu'il arrive toujours un moment où une donnée doit être encodée en symboles stockables en mémoire. La quantité d'information croissante de données mise à disposition et qu'on peut stocker, par exemple des génomes d'individus ou des documents numérisés, justifie que les algorithmes et les structures de données qui les manipulent soient optimisés. En conséquence, les besoins d'analyse se font sentir pour guider le choix et la conception des programmes qui manipulent ces données. L'analyse en moyenne est ici particulièrement adaptée puisque les données atteignent une variété et des volumes tellement importants que c'est le cas typique qui traduit le mieux la complexité et non pas le cas le pire. Cela évidemment pose le problème de la modélisation de données qui reste encore très épineux. En effet on souhaite deux choses contradictoires: un modèle au plus près des données, qui traduise vraiment leurs spécificités, mais aussi un modèle permettant de donner des résultats, c'est-à-dire de prédire les performances (et on comprend vite que le modèle doit donc rester relativement simple pour qu'il subsiste un espoir de le traiter!). Les méthodes sont le plus souvent celles de la combinatoire analytique et font appel à un objet mathématique, les séries génératrices, pour mener les analyses à bien.

International audience; Laïcité, conflits de civilisation, croyances irrationnelles : ces notions ne font pas partie de leur vocabulaire. En cette fin de mois de janvier où les religions ont été au cœur des débats, des anthropologues se sont retrouvés au musée du quai Branly pour discuter des matérialités religieuses. Au départ cette idée simple : la croyance religieuse s’inscrit dans un ensemble de matières, de substances, de corps. Faire croire, ce n’est pas manipuler les croyants, c’est faire faire avec des choses.

International audience

International audience; We describe a general framework for realistic analysis of sorting and searching algorithms, and we apply it to the average-case analysis of five basic algorithms: three sorting algorithms (QuickSort, InsertionSort, BubbleSort) and two selection algorithms (QuickMin and SelectionMin). Usually, the analysis deals with the mean number of key comparisons, but, here, we view keys as words produced by the same source, which are compared via their symbols in the lexicographic order. The "realistic" cost of the algorithm is now the total number of symbol comparisons performed by the algorithm, and, in this context, the average-case analysis aims to providee stimates for the mean number of symbol comparisons used by the algorithm. For sorting algorithms, and with respect to key comparisons, the average-case complexity of QuickSort is asymptotic to 2n log n, InsertionSort to n^2/4 and BubbleSort to n^2/2. With respect to symbol comparisons, we prove that their average-case complexity becomes Theta(n log^2n), Theta(n^2), Theta (n^2 log n). For selection algorithms, and with respect to key comparisons, the average-case complexity of QuickMin is asymptotic to 2n, of SelectionMin is n - 1. With respect to symbol comparisons, we prove that their average-case complexity remains Theta(n). In these five cases, we describe the dominant constants which exhibit the probabilistic behaviour of the source (namely, entropy, and various notions of coincidence) with respect to the algo

In this memoir , I examine different aspects of a simple but ubiquitous computer object: the string or sequence of symbols. The string of characters concept is at the crossroads of areas as information theory and language theory. Although simple, this notion is fundamental: data will always be represented, encoded and stored in computers as sequences of symbols at one time or another The increasing amount of information and data to which we have access, such as genomes of individuals or scanned documents, justifies that the algorithms and data structures handling them need to be optimized. Consequently, rigourous analysis is needed in order to guide the end-user and the designer of programs that manipulate these data. The average analysis is particularly appropriate here because the data reach such variety and large volumes that the typical case is best reflected than with the more usual worst case complexity. This obviously raises the very difficult problem of data modeling. Indeed in our setting we want two contradictory things: a model closer to the data, which really translates their specificities, but also a model yielding results, that is to say, able to predict the performance. Methods are most often those of analytic combinatorics and use a mathematical object , generating functions, to carry out the analyzes.; Dans ce mémoire, j'examine différents aspects d'un objet simple mais omniprésent en informatique: la séquence de symboles (appelée selon le contexte mot ou chaîne de caractères). La notion de mot est au carrefour de domaines comme la théorie de l'information et la théorie des langages. S'il est simple, il reste fondamental: nous n'avons, au plus bas niveau, que cela à disposition puisqu'il arrive toujours un moment où une donnée doit être encodée en symboles stockables en mémoire. La quantité d'information croissante de données mise à disposition et qu'on peut stocker, par exemple des génomes d'individus ou des documents numérisés, justifie que les algorithmes et les structures de données qui les manipulent soient optimisés. En conséquence, les besoins d'analyse se font sentir pour guider le choix et la conception des programmes qui manipulent ces données. L'analyse en moyenne est ici particulièrement adaptée puisque les données atteignent une variété et des volumes tellement importants que c'est le cas typique qui traduit le mieux la complexité et non pas le cas le pire. Cela évidemment pose le problème de la modélisation de données qui reste encore très épineux. En effet on souhaite deux choses contradictoires: un modèle au plus près des données, qui traduise vraiment leurs spécificités, mais aussi un modèle permettant de donner des résultats, c'est-à-dire de prédire les performances (et on comprend vite que le modèle doit donc rester relativement simple pour qu'il subsiste un espoir de le traiter!). Les méthodes sont le plus souvent celles de la combinatoire analytique et font appel à un objet mathématique, les séries génératrices, pour mener les analyses à bien.

International audience; Cet article est consacré à la vérification basée sur le modèle model-checking du modèle des protocoles de population introduit par Angluin et al.~\cite{AngluinADFP2006}. Ces deux dernières années, la vérification des protocoles de population par model-checking a fait l'objet denombreuses études et de nouveaux outils ont été proposés. Nous montrons dans cet article que, dans une certaine mesure, les outils classiques de model-checking tels que Spin et Prism peuvent être utilisés pour effectuer les vérifications. Pour cela, nous appliquons la technique d'abstraction par comptage pour obtenir des modèles abstraits de protocoles de population qui peuvent être vérifiés efficacement par les outils de model-checking existants. Le problème essentiel pour la complexité de la vérification des protocoles de population concerne la condition d'équité forte. Cette dernière ne peut être utilisée directement avec Spin même pour des exemples de relativement petite taille. Nous montrons qu'on peut cependant remplacer dans de nombreux cas cette équité par une équité faible efficacement vérifiable en Spin. Plus notable encore, nous montrons que la vérification avec la condition d'équité forte est équivalente à un problème de vérification d'un modèle probabiliste. Ainsi, le model-checker probabiliste Prism s'avère être un outil de vérification adapté aux protocoles de population.

International audience; Conférence invitée dont la présentation est accessible par ce lien : http://aofa2011.im.pwr.wroc.pl/Tuesday/1%20clement-aofa2011.pdf

International audience; In this paper, we look at the time complexity of two agreement problems in networks of oblivious mobile robots, namely, at the gathering and scattering problems. Given a set of robots with arbitrary initial locations and no initial agreement on a global coordinate system, gathering requires that all robots reach the exact same but not predetermined location. In contrast, scattering requires that no two robots share the same location. These two abstractions are fundamental coordination problems in cooperative mobile robotics. Oblivious solutions are appealing for self-stabilization since they are self-stabilizing at no extra cost. As neither gathering nor scattering can be solved deterministically under arbitrary schedulers, probabilistic solutions have been proposed recently.The contribution of this paper is twofold. First, we propose a detailed time complexity analysis of a modified probabilistic gathering algorithm. Using Markov chains tools and additional assumptions on the environment, we prove that the convergence time of gathering can be reduced from $O(n^2)$ (the best known bound) to $O(1)$ or $O(\log{n} \log(\log{n}))$, depending on the model of multiplicity detection. Second, using the same technique, we prove that scattering can also be achieved in fault-free systems with the same bounds.

We address the problem of verification by model-checking of the basic population protocol (\pp) model of Angluin et al. This problem has received special attention the last two years and new tools have been proposed to deal with it. We show that the problem can be solved using the existing model-checking tools, e.g., Spin and Prism. For this, we apply the counting abstraction to obtain an abstract model of a \pp\ which can be efficiently verified by the existing model-checking tools. Moreover, this abstraction preserves the correct stabilization property of \pp. To deal with the fairness assumed in the \pp\ model, we provide two recipes. The first one gives sufficient conditions under which the \pp\ fairness can be replaced by the weak fairness implemented in Spin. We show that this recipe can be applied to several \pp\ models. In the second recipe, we show how to use the probabilistic model-checking and the tool Prism to deal completely with the fairness of the \pp\ model. The correctness of this recipe is based on existing theorems on finite discrete Markov chains.

International audience; A quite general model of source that comes from dynamical systems theory is introduced. Within this model, basic problems of algorithmic information theory contexts are analysed. The main tool for the analysis is a (generalized) trans-fer operator, which can be viewed as a "generating" operator for "fundamental" probabilities. Its dominant spectral objects are related to important parameters of the source, such as the entropy rate, and play a central rôle in all the results. 1 Dynamical sources. In information theory contexts, data items are (infinite) words that are pro-duced by a common mechanism, called a source. Real-life sources are often complex objects. We introduce here a general framework of sources related to dynamical systems theory which can be viewed as a generalization of numer-ation systems. This model goes beyond the cases of memoryless and Markov chains, it can describe nonmarkovian processes, where the dependency on past history is unbounded, and as such, it attains a high level of generality. A probabilistic dynamical source is defined by five elements: (a) an alphabet Σ, finite or denumerable, (b) a topological partition of I := [0, 1] with disjoint open intervals (I m) m∈Σ , (c) an encoding mapping σ which is constant and equal to m on each I m , (d) a shift mapping T whose restriction to I m is a bijection of class C 2 from I m to J m := T (I m). The local inverse of T | Im is denoted by h m , (e) a real density f on interval I, and its associated distribution function F . The dynamical system S := (I, T), defined by the first four elements, asso-ciates to a real number x ∈ I the word M (x) := (σx, σT x, σT 2 x, .

International audience

Digital trees, also known as tries, are a general purpose flexible data structure that implements dictionaries built on sets of words. An analysis is given of three major representations of tries in the form of array-tries, list tries, and bst-tries (``ternary search tries''). The size and the search costs of the corresponding representations are analysed precisely in the average case, while a complete distributional analysis of height of tries is given. The unifying data model used is that of dynamical sources and it encompasses classical models like those of memoryless sources with independent symbols, of finite Markov chains, and of nonuniform densities. The probabilistic behaviour of the main parameters, namely size, path length, or height, appears to be determined by two intrinsic characteristics of the source: the entropy and the probability of letter coincidence. These characteristics are themselves related in a natural way to spectral properties of specific transfer operators of the Ruelle type.

This paper provides a detailed analysis of various implementations of digital tries, including the «ternary search tries» of Bentley and Sedgewick. The methods employed combine symbolic uses of generating functions, Poisson models, and Mellin transforms. Theoretical results are matched against real-life data and justify the claim that ternary search tries are a highly efficient dynamic dictionary structure for strings and textual data.

Lossless compression is studied for pairs of independent integer-valued symbols emitted by a source with a geometric probability distribution of parameter q /spl isin/ (0,1). Optimal prefix codes are described for q = 1/2/sup k/ (k > 1) and q = 1/k/spl radic/2 (k > 0). The codes described differ from previously characterized cases related to the geometric distribution in that their corresponding trees are of unbounded width, and in that an infinite set of distinct optimal codes is required to cover any interval (0, /spl epsi/), /spl epsi/ > 0, of values of q.

Optimal prefix codes are studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter $q$, $0{1$), covering the range $q, Comment: To appear in IEEE Transactions on Information Theory