Shift operators and complex systems

International audienceIn this paper, we deal with some multiagent systems modelling, based on population of automata.We focus our attention with automatic computation of emerging systems. A multiscale representation is proposed here and consists in representing the internal states of an agent behaviour by a automaton with multiplicities, on the one hand and an adaptive global system behaviour by a genetic algorithm over a population of automata, on the other hand. This genetic process can lead to generate many new automata which behaviour can be eventually similar. The role played by shift operators is to identify these similar behaviours. Two applications are presented. The first one concerns adaptive strategies in game theory. The second one concerns an automatic emerging computation of self-organised multiagent systems based on the efficience of operation expressivity of automata with multiplicities

Control on System Diffusion Using Genetic Automata

International audienceComplex systems \citep{Moigne1999} are models which describe dynamic organizations or systems where the internal interaction network between their components does not allow the control of individual components with efficience. In a lot of cases, the individual control leads to break the whole structure itself. In other cases, some complex systems exhibit resilience properties which lead them to recover their initial state after small perturbations or individual controls. Controlling complex systems need to not trying to manage the individual controls but to manage the global control, guiding the whole system without directly act on individuals themselves. The study presented in this paper explains how to control a high level system property, the diffusive behavior, by spectral analysis over genetic automata. First experiments are presented using MuPad implementation

Moderate Growth Time Series for Dynamic Combinatorics Modelisation

Here, we present a family of time series with a simple growth constraint. This family can be the basis of a model to apply to emerging computation in business and micro-economy where global functions can be expressed from local rules. We explicit a double statistics on these series which allows to establish a one-to-one correspondence between three other ballot-like strunctures

Structures de Données dynamiques pour les Systèmes Complèxes

My work concerns the dynamics of some data structures and complex systems. We presented a combinatorial approach of tableaux and permutations based on dynamics. This approach, which we call(Dynamic Data Structures) opens us the door towardsapplications in economy via complex systems.The data structures which we studied are the permutations of n letters that have no increasing subsequences of length more than two, the rectangular standard Young tableaux with two lines,the Dyck words and the codes which link these data structures.We have proposed an economic model which models the benefit of a bank account whose possible enumeration of the configurations is done using an adapted code. The second application deals with the evolution of genetic automata populations. These populations are studied by spectral analysis. Experiments are given on probabilistic automata whose evolution results in controlling dissipation by auto-regulation. The aim of this work is to give somecomputation tools related to the dynamics of data structures to analyze the complexity of systems.Mon travail porte sur la dynamique de certaines structures de données et sur les systèmes complexes. Nous avons présenté une approche de la combinatoire des tableaux et des permutations basée sur la dynamique. Cette approche, que nous appelons (Structures de Données Dynamiques) nous ouvrela porte vers des applications en économie via les systèmes complexes.Les structures de données que nous avons étudiées sont les permutations qui ne contiennent pas de sous-suite croissante de longueur plus que deux, les tableaux de Young standards rectangles à deux lignes, les mots de Dyck et les codes qui lient ces structures de données.Nous avons proposé un modèle économique qui modélise le bénéfice d'un compte bancaire dont l'énumération des configurations possible se fait à l'aide d'un code adapté. Une seconde applicationconcerne l'évolution de populations d'automate génétique . Ces populations sont étudiées par analyse spectrale et des expérimentations sont données sur des automates probabilistes dont l'évolution conduit à contrôler la dissipation par auto-régulation.L'ensemble de ce travail a pour ambition de donner quelques outils calculatoires liés à la dynamique de structures de données pour analyser la complexité des systèmes