Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems

In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron-Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

From Hardware Processes to asynchronous circuits via petri nets: An Application to Arbiter Design

International audience

A software tool that generates symbolic model verifier (SMV) input language from a predicate transition net

The purpose of this research was to apply model checking by using a symbolic model checker on Predicate Transition Nets (PrT Nets). A PrT Net is a formal model of information flow which allows system properties to be modeled and analyzed. The aim of this thesis was to use the modeling and analysis power of PrT nets to provide a mechanism for the system model to be verified. Symbolic Model Verifier (SMV) was the model checker chosen in this thesis, and in order to verify the PrT net model of a system, it was translated to SMV input language. A software tool was implemented which translates the PrT Net into SMV language, hence enabling the process of model checking. The system includes two parts: the PrT net editor where the representation of a system can be edited, and the translator which converts the PrT net into an SMV program.

Histoire de l'interprétation de la transition néolithique : évolution des théories, modèles et hypothèses

Ce mémoire reconstitue l’histoire des théories, modèles et hypothèses qui ont été formulés, principalement en archéologie, afin d’expliquer la naissance de l’agriculture qui correspond, du point de vue chronologique, à la transition (ou révolution) néolithique. Ces schèmes explicatifs sont décrits chronologiquement depuis la naissance de l’archéologie préhistorique, dans la première moitié du XIXe siècle, jusqu’à maintenant. Ils sont classifiés en fonction des principales écoles qui ont joué un rôle prédominant en archéologie préhistorique depuis son origine, soit : l’évolutionnisme multilinéaire, l’école culturelle-historique, le processualisme, le néodarwinisme et le postprocessualisme. Les théories spécifiques (dites de « niveau mitoyen » ou « régionales ») qui ont été avancées par ces écoles sont présentées dans leur ordre chronologique, soit (principalement) : les théories de la dessiccation ou de l’oasis, des flancs de colline, de la périphérie, du stress démographique, du festin compétitif, de la révolution des symboles, etc. Ce mémoire pose enfin les jalons d’une théorie multifactorielle qui intègre ou synthétise les principaux facteurs qui ont pu influer sur la naissance de l’agriculture et sur la transition néolithique.

La transition postcommuniste en Roumanie (entre 1989 et 2004) : une étude à partir de la structuration de la famille

Cette thèse propose une analyse des transformations postcommunistes en Roumanie à partir d’une étude de la structuration de trajectoires familiales. La réflexion sur les itinéraires très variés de ces trajectoires familiales met en valeur les pratiques développées par les familles dans la construction de leur mode de vie quotidienne après la chute du communisme. L’approche utilisée privilégie deux axes d’analyse. Le premier vise les aspects socio-structurels concernant les cadres de la vie incluant les aspects matériels, alors que le deuxième, l’axe socio-symbolique, concerne les aspects subjectifs liés au vécu des acteurs en corrélation avec le contexte social en mutation. L’analyse est fondée sur des éléments issus de la théorie de la structuration qui ont contribué à la construction du cadre conceptuel. Elle s’appuie aussi sur la méthodologie qualitative qui comprend des récits de vie obtenus à partir des entretiens semi-dirigés réalisés avec les membres de 11 familles. Les thématiques retenues après l’analyse du corpus de données nous ont permis d’identifier des stratégies que les familles ont mises en place et les projets familiaux qui ont orienté leur parcours de vie durant la période de transition postcommuniste. Ces deux concepts révèlent des éléments liés à l’ordre général permettant ainsi la mise en évidence des tendances structurelles de la société postcommuniste.

Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Signal-flow graphs: Direct method of reduction and MATLAB implementation

Block diagrams and signal-flow graphs are used to represent and to obtain the transfer function of interconnected systems. The reduction of signal-flow graphs is considered simpler than the reduction of block diagrams for systems with complex interrelationships. Signal-flow graphs reduction can be made without graphic manipulations of diagrams, and it is attractive for a computational implementation. In this paper the authors propose a computational method for direct reduction of signal-flow graphs. This method uses results presented in this paper about the calculation of literal determinants without symbolic mathematics tools. The Cramer's rule is applied for the solution of a set of linear equations, A program in MATLAB language for reduction of signal-flow graphs with the proposed method is presented.

Complex Transition to Cooperative Behavior in a Structured Population Model

Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner's dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the cooperative behavior.

The Hungarian Economic Elite After the Political Transition

Erzsebet Szalai (Hungary). The Hungarian Economic Elite after the Political Transition. Ms. Szalai is a research fellow in the Institute of Political Sciences in Budapest and worked on this project from July 1996 to June 1998. In the period following the political changes of 1989, the leading forces of the economic elite have gained increasing superiority over the political and cultural elites, with the clear ambition of putting the latter to their service. The power relations within the economic elite were characterised by "a war of all against all". The desire to gain precedence over others became an openly declared value. The formation of estates and the intensification of competition became embodied in a multitude of lobbies which cropped up to assert short-term interests. After the state socialist period, possession of at least two of the social, economic and cultural forms of capital is necessary to join one of the three segments of the elite: political, cultural or economic. What defines the ability of the members of the three elite groups to assert their interests is their ability to convert any of the three types of capital into another. That is to say, the basis on which they can retain and extend their position is "symbolic capital" as interpreted by Bourdieu. The concept of symbolic capital is useful for describing the power relations following the collapse of state socialist systems and societies. In the state-socialist system, the political, economic and cultural spheres are tightly interwoven, and this interpenetration slackens only slowly after the system's disintegration. A close institutional relationship between the three spheres continues to make it easier for power actors to convert social, economic and cultural capital from one type to another. Symbolic capital, or the easy transfer between the three spheres, in turn reproduces the institutional relationship, or more precisely, complicates the separation of the three spheres after the fall of state socialism.

Quasiperiodic graphs at the onset of chaos

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers

Formal verification of ASM designs using the MDG tool

In this paper, we present a formal hardware verification framework linking ASM with MDG. ASM (Abstract State Machine) is a state based language for describing transition systems. MDG (Multiway Decision Graphs) provides symbolic representation of transition systems with support of abstract sorts and functions. We implemented a transformation tool that automatically generates MDG models from ASM specifications, then formal verification techniques provided by the MDG tool, such as model checking or equivalence checking, can be applied on the generated models. We support this work with a case study of an Island Tunnel Controller, which behavior and structure were specified in ASM then using our ASM-MDG tool successfully verified within the MDG tool.