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Book abstract: Setting out core theory and reviewing a range of new methods, theoretical problems and applications, this handbook shows how hybrid dynamical systems can be modelled and understood. 60 expert authors involved in the recent research activities and industrial application studies provide practical insights on topics ranging from the theoretical investigations over computer-aided design to applications in energy management and the process industry. Structured into three parts, the book opens with a thorough introduction to hybrid systems theory, illustrating new dynamical phenomena through numerous examples. Part II then provides a survey of key tools and tool integration activities. Finally, Part III is dedicated to applications, implementation issues and system integration, considering different domains such as industrial control, automotive systems and digital networks. Three running examples are referred to throughout the book, together with numerous illustrations, helping both researchers and industry professionals to understand complex theory, recognise problems and find appropriate solutions.

We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks. ., 6 pages, 5 figures, 1 table; new version with new figures in order to clarify our method, where we look more carefully at the role played by the ordering of the nodes and where we compare our method with that of Wakita and Tsurumi

We consider local leaders in random uncorrelated networks, i.e. nodes whose degree is higher or equal than the degree of all of their neighbors. An analytical expression is found for the probability of a node of degree $k$ to be a local leader. This quantity is shown to exhibit a transition from a situation where high degree nodes are local leaders to a situation where they are not when the tail of the degree distribution behaves like the power-law $\sim k^{-\gamma_c}$ with $\gamma_c=3$. Theoretical results are verified by computer simulations and the importance of finite-size effects is discussed., Comment: 4 pages, 2 figures

We deal with the issue of automatic discovery of similar words (synonyms and near-synonyms) from different kinds of sources: from large corpora of documents, from the Web, and from monolingual dictionaries. We present in detail three algorithms that extract similar words from a large corpus of documents and consider the specific case of the World Wide Web. We then describe a recent method of automatic synonym extraction in a monolingual dictionary. The method is based on an algorithm that computes similarity measures between vertices in graphs. We use the 1913 Webster’s Dictionary and apply the method on four synonym queries. The results obtained are analyzed and compared with those obtained by two other methods.

In this paper we study problems such as: given a discrete time dynamical system of the form x(t + 1)= f(x(t)) where f: R-n --> R-n is a piecewise affine function, decide whether all trajectories converge to 0. We show in our main theorem that this Attractivity Problem is undecidable as soon as n greater than or equal to2. The same is true of two related problems: Stability (is the dynamical system globally asymptotically stable?) and Mortality (do all trajectories go through 0?). We then show that AM-activity and Stability become decidable in dimension 1 for continuous functions. (C) 2001 Elsevier Science B.V. All rights reserved.

Colloque avec actes et comité de lecture. internationale.; International audience; We prove that several global properties (global convergence, global asymptotic stability, mortality, and nilpotence) of particular classes of discrete time dynamical systems are undecidable. Such results had been known only for point-to-point properties. We prove these properties undecidable for saturated linear dynamical systems, and for continuous piecewise affine dynamical systems in dimension three. We also describe some consequences of our results on the possible dynamics of such systems.

We consider the iterates of bilinear functions over the semiring (max, +). Equivalently, our object of study can be viewed as recognizable tree series over the semiring (max, +). In this semiring, a fundamental result associates the asymptotic behaviour of the iterates of a linear function with the maximal average weight of the circuits in a graph naturally associated with the function. Here we provide an analog for the 'iterates' of bilinear functions. We also give a triple recognizing the formal power series of the worst case behaviour. Remark. Due to space limitations, the proofs have been omitted. A full version can be obtained from the authors on request.