On presente ici une methode d’optimisation biniveau de grandes structures de fuselage composite. Ce schema biniveau est inspire de la formulation Quasi Separable Decomposition (QSD)recemment developpee par Haftka et Watson. Le comportement membrane et hors-plan des stratifies est represente au moyen des parametres de stratification. La boucle d’optimisation superieure fait intervenir la redistribution des efforts et a pour contraintes des quantites calculees par des problemes d’optimisation locale en stabilite ou les facteurs critiques de flambage sont approches par des modeles reduits.

. This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the Hodgkin-Huxley description, which is somehow the canonical description for the “biological neuron”. We discuss some models reducing the Hodgkin-Huxley model to a two dimensional dynamical system, keeping one of the main feature of the neuron: its excitability. We present then examples of phase diagram and bifurcation analysis for the Hodgin-Huxley equations. Finally, we end this section by a dynamical system analysis for the nervous flux propagation along the axon. We then consider neuron couplings, with a brief description of synapses, synaptic plasticity and learning, in a second section. We also briefly discuss the delicate issue of causal action from one neuron to another when complex feedback effects and non linear dynamics are involved. The third section presents the limit of weak coupling and the use of normal forms technics to handle this situation. We consider then several examples of recurrent models with different type of synaptic interactions (symmetric, cooperative, random). We introduce various techniques coming from statistical physics and dynamical systems theory. A last section is devoted to a detailed example of recurrent model where we go in deep in the analysis of the dynamics and discuss the effect of learning on the neuron dynamics. We also present recent methods allowing the analysis of the non linear effects of the neural dynamics on signal propagation and causal action. An appendix, presenting the main notions of dynamical systems theory useful for the comprehension of the chapter, has been added for the convenience of the reader.

This paper presents a new technique for autonomous mobile robot topological localization in a structural environment. This localization is based on visual landmarks, which are combinations of visual cha- racteristic selected thanks to a mathematical formalism called Galois lattice or concept lattice. For large contexts, a decentralized approch is introduced in order to reduce the number of concepts and the lat- tice building time process. All algorithms have been validated through experimentation and are exposed in this paper.

Recent works have shown that biologically motivated net works of spiking neurons can potentially process information very quickly by encoding information in the latency at which different neurons fire, rather than by using frequency of firing as the code. In this paper, the relevant information is the rank vector of latency order of competing neurons. We propose here a Hebbian reinforcement, learning scheme to adjust the weights of a terminal layer of decision neurons in order to process this information. Then this learning rule is shown to be efficient in a simple pattern recognition task. We discuss in conclusion further extensions of that learning strategy for artificial vision.

This article presents a new method for supervised image classification. Given a finite number of image sets, each set corresponding to a place of an environment, we propose a localization strategy, which relies upon supervised classification. For each place, the corresponding landmark is actually a combination of features that have to be detected in the image set. Moreover, these features are extracted using a symbolic knowledge extraction theory, "formal concept analysis." This paper details the full landmark extraction process and its hierarchical organization. A real localization problem in a structured environment is processed as an illustration. This approach is compared with an optimized neural network-based classification, and validated with experimental results. Further research to build up hybrid classifier is outlined in the discussion.

We present a discrimation method for seismic events. One event is described by high level features. Since these variables are both quantitative and qualitative, we develop a processing line, on the cross-road of statistics ("Mixtures of Experts") and Artificial Intelligence ("Fuzzy Inference System"). It can be viewed as an original extension of Radial Basis Function Networks. The method provides an efficient trade-off between high performance and intelligibility. We propose also a graphical presentation of the model satisfying the experts' requirements for intelligibility.

In order to account for the rapidity of visual processing, we explore visual coding strategies using a one-pass feed-forward spiking neural network. We based our model on the work of Van Rullen and Thorpe Neural Comput. 13 (6) (2001) 1255, which constructs a retinal representation using an orthogonal wavelet transform. This strategy provides a spike code, thanks to a rank order coding scheme which offers an alternative to the classical spike frequency coding scheme. We extended this model to efficient representations in arbitrary linear generative models by implementing lateral interactions on top of this feed-forward model. This method uses a matching pursuit scheme—recursively detecting in the image the best match with the elements of a dictionary and then subtracting it—and which may similarly define a visual spike code. In particular, this transform could be used with large and arbitrary dictionaries, so that we may define an over-complete representation which may define an efficient sparse spike coding scheme in arbitrary multi-layered architectures. We show here extensions of this method of computing with spike events, introducing an adaptive scheme leading to the emergence of V1-like receptive fields and then a model of bottom-up saliency pursuit.

We present here a new methodology to perform active visual localization in the context of autonomous mobile robotics. The robot is endowed with a topological map of its environment. During the learning phase, the robot takes a lot of pictures from the environment; each picture is labelled by its origin place in the topological map. After the learning phase, the robot is supposed to locate itself in the learnt environment using the visual sensor. Since the discriminating information is sparse, the usual supervised classification techniques as neural networks are not sufficient to perform efficiently this task. Therefore, we propose to use a symbolic learning approach, the "formal concept analysis". The relevant information is gathered into one concept lattice. A formal classification rule is proposed to achieve localization on the topological map. In order to improve the response rate of the decision process, the original formal landmark set is extended to plausible landmarks for a given confidence level. Experimental results in a structured environment support this approach. Perspectives for implementing active strategy to look for visual information and to improve on-line learning and localization process are presented in the final discussion

Ce papier presente une nouvelle methode pour la classification supervisee d'ensembles d'images. A chacun de ces ensembles est attache, pour le caracteriser et le distinguer des autres, une entite appelee amer. Differentes caracteristiques, deduites de primitives visuelles, sont extraites de chaque image, et la relation qui lie certaines images a certaines caracteristiques sont structurees et hierarchisees grâce a un formalisme mathematique appele treillis de Galois (ou treillis de concepts). De tels treillis permettent de selectionner des combinaisons de caracteristiques qui serviront d'amers visuels pour chaque ensemble d'images. Cette approche s'inscrit dans le cadre de la robotique mobile autonome et de la localisation topologique dans un environnement structure, pour laquelle chaque ensemble d'images est issu de d'une meme piece qu'il est necessaire de caracteriser. Ce papier expose cette demarche originale et les resultats obtenus apres experimentation.

This paper presents an original application of the Galois lattice theory, the visual landmark selection for topological localization of an autonomous mobile robot, equipped with a color camera. First, visual landmarks have to be selected in order to characterize a structural environment. Second, such landmarks have to be detected and updated for localization. These landmarks are combinations of attributes, and the selection process is done through a Galois lattice. This paper exposes the landmark selection process and focuses on probabilistic landmarks, which give the robot thorough information on how to locate itself. As a result, landmarks are no longer binary, but probabilistic. The full process of using such landmarks is described in this paper and validated through a robotics experiment.

This paper presents a new decentralized method for selecting visual landmarks in a structured environment. Different images, issued from the different places, are analyzed, and primitives are extracted to determine whether or not features are present in the images. Subsequently, landmarks are selected as a combination of these features with a mathematical formalism called Galois -or concept- lattices. The main drawback of the general approach is the exponential complexity of lattice building algorithms. A decentralized approach is therefore defined and detailed here: it leads to smaller lattices, and thus to better performance as well as an improved legibility.

To understand possible strategies of temporal spike coding in the central nervous system, we study functional neuromimetic models of visual processing for static images. We will first present the retinal model which was introduced by Van Rullen and Thorpe and which represents the multiscale contrast values of the image using an orthonormal wavelet transform. These analog values activate a set of spiking neurons which each fire once to produce an asynchronous wave of spikes. According to this model, the image may be progressively reconstructed from this spike wave thanks to regularities in the statistics of the coefficients determined with natural images. Here, we study mathematically how the quality of information transmission carried by this temporal representation varies over time. In particular, we study how these regularities can be used to optimize information transmission by using a form of temporal cooperation of neurons to code analog values. The original model used wavelet transforms that are close to orthogonal. However, the selectivity of realistic neurons overlap, and we propose an extension of the previous model by adding a spatial cooperation between filters. This model extends the previous scheme for arbitrary--and possibly nonorthogonal--representations of features in the images. In particular, we compared the performance of increasingly over-complete representations in the retina. Results show that this algorithm provides an efficient spike coding strategy for low-level visual processing which may adapt to the complexity of the visual input.

Nous presentons un nouvel algorithme qui contribue a etendre le formalisme de l'Apprentissage par Renforcement (RL) aux Processus Decisionnels Markoviens Partiellement Observes (POMDP). L'idee principale de notre methode est de construire une extension d'etat, appelee observable exhaustif, qui permet de definir un nouveau processus qui est alors markovien. Nous demontrons que resoudre ce nouveau processus, auquel on peut appliquer les techniques classiques de RL, apporte une solution optimale au POMDP original. Nous appliquons l'algorithme deduit de ce resultat sur plusieurs exemples pour en tester la validite et la robustesse.

This paper presents a new method for supervised image classification. One or several landmarks are attached to each class, with the intention of characterizing it and discriminating it from the other classes. The different features, deduced from image primitives, and their relationships with the sets of images are structured and organized into a hierarchy thanks to an original method relying on a mathematical formalism called Galois (or Concept) Lattices. Such lattices allow us to select features as landmarks of specific classes. This paper details the feature selection process and illustrates this through a robotic example in a structured environment. The class of any image is the room from which the image is shot by the robot camera. In the discussion, we compare this approach with decision trees and we give some issues for future research.

We explore visual spike coding strategies in a neural layer in order to build a dynamical model of primary vision. A strictly feed-forward architecture is compared to a strategy accounting for lateral interactions that shows sparse spike coding of the image as is observed in the primary visual areas [1]. This transform is defined over a neural layer according to a greedy matching pursuit scheme and we show that for natural images its coefficients may be simply carried by the rank of spike arrival. This model is easily expandable to multiple layers and despite its simplicity has applications to image compression comparable to industrial standards but also novel strategies for pattern detection.

In order to explore visual coding strategies, we use a wavelet-like transform which output is sparse, as is observed in the primary visual areas [ 6]. This transform is defined in the context of a feed-forward spiking neural network, and the output is the list of its neurons’ spikes: it is recursively constructed using a greedy matching pursuit scheme which first selects best matches and then laterally interacts with its correlated neighbors. We study the quality of this algorithm and its enhancement by the prior knowledge of the statistics of its input, namely natural images. An application to image compression is shown which is comparable to other techniques such as JPEG at low bit compression.

In this article, we study the asymptotic dynamics of a noisy discrete time neural network, with random asymmetric couplings and thresholds. More precisely, we focus our interest on the limit behaviour of the network when its size grows to infinity with bounded time. In the case of gaussian connection weights, we use the same techniques as Ben Arous and Guionnet (see [3]) to prove that the image law of the distribution of the neurons' activation states by the empirical measure satisfies a temperature free large deviation principle. Moreover, we prove that if the connection weights satisfy a general condition of domination by gaussian tails, then the distribution of the activation potential of each neuron converges weakly towards an explicit gaussian law, the characteristics of which are contained in the mean-field equations stated by Cessac-Doyon-Quoy-Samuelides (see [4–6]). Furthermore, under this hypothesis, we obtain a law of large numbers and a propagation of chaos result. Finally, we show that many classical distributions on the couplings fulfill our general condition. Thus, this paper provides rigorous mean-field results for a large class of neural networks which is currently investigated in neural network literature.