Cette derniere Newsletter avant les Grandes Vacances est, pur concours de circonstances, entierement consacree a l’Education. Mais l’Education sous l’angle de son importance pour la consecration dans l’excellence. La consecration, c’est ce qu’a obtenu Gisele Mophou-Massengo, quand son jury de soutenance l’a declaree Habilitee a Diriger des Recherches. C’est egalement la reconnaissance qui est accordee a Elina Marie Devoue par le jury du prix « Religions et Developpement » pour son article consacre aux Religions et a leurs impacts sur la societe dans la Caraibe.La reconnaissance du savoir et du savoir-faire ne passe pas forcement par sa consecration. Elle passe egalement par sa diffusion la plus large. C’est ce que tente de faire le Ceregmia en organisant depuis 2009 ses « seminaires intra Ceregmia » qui permettent l’expression de la transversalite du laboratoire sur des chantiers en cours ou deja finalises autour de thematiques que nous vous invitons a decouvrir en page 2. De meme, le Ceregmia a lance une nouvelle publication en 2010, ses « Documents de Travail ». Ces Documents d’audience plus confidentielle sont reellement reserves a un public de scientifiques. Diffuser le savoir en l’adaptant aux evolutions de l’environnement et aux exigences du marche. C’est ce qu’a fait le Ceregmia grâce a sa nouvelle offre de formation en Masters qui a ete habilitee par le Ministere et qui ouvrira des la rentree 2010 (p. 4). Par ailleurs, nous avions eu l’occasion de vous entretenir des changements intervenus a l’IFGCar suite au seisme du 12 janvier 2010 en Haiti. Nous sommes heureux aujourd’hui, de vous annoncer que l’IFGCar qui est desormais l’IAC retourne s’installer en Haiti. Les formations en Master reprendront des le 1 er . Octobre. Enfin, Nous vous signalons la parution de deux ouvrages aux Editions Ibis Rouge ils vous invitent a decouvrir la Guyane sous un angle moins connu, celui de l’anthropologie. Charley Granvorka

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Habilitation a diriger des recherches

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as follows. For each component, the probability of having a spike at the next time unit depends on the entire time evolution of the system after the last spike time of the component. This class of systems extends in a non trivial way both the interacting particle systems, which are Markovian (Spitzer in Adv. Math. 5:246–290, 1970) and the stochastic chains with memory of variable length which have finite state space (Rissanen in IEEE Trans. Inf. Theory 29(5):656–664, 1983). These features make it suitable to describe the time evolution of biological neural systems. We construct a stationary version of the process by using a probabilistic tool which is a Kalikow-type decomposition either in random environment or in space-time. This construction implies uniqueness of the stationary process. Finally we consider the case where the interactions between components are given by a critical directed Erdos-Renyi-type random graph with a large but finite number of components. In this framework we obtain an explicit upper-bound for the correlation between successive inter-spike intervals which is compatible with previous empirical findings.

/pdf/infinite-systems-of-interacting-chains-with-memory-of-4jvc001s0s.pdf

Infinite Systems of Interacting Chains with Memory of Variable Length—A Stochastic Model for Biological Neural Nets

We introduce a statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail σ-algebra, short-range correlations, realization via infinite-volume limits and ergodicity. (ii) Two new sufficient conditions for the uniqueness of the consistent chain. The first one is a transcription of a criterion due to Georgii for one-dimensional Gibbs measures, and the second one corresponds to the Dobrushin’s criterion in statistical mechanics. (iii) Results on loss of memory and mixing properties for chains in the Dobrushin regime. These results are complementary to those existing in the literature, and generalize the Markovian results based on the Dobrushin ergodic coefficient.

/pdf/chains-with-complete-connections-general-theory-uniqueness-381i922t6p.pdf

Chains with complete connections: General theory, uniqueness, loss of memory and mixing properties

We discuss the relationship between one-dimensional Gibbs measures and discrete-time processes (chains). We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic process to define a Gibbs measure and vice versa. Our conditions generalize well known equivalence results between ergodic Markov chains and fields, as well as the known Gibbsian character of processes with exponential continuity rate. Our arguments are purely probabilistic; they are based on the study of regular systems of conditional probabilities (specifications). Furthermore, we discuss the equivalence of uniqueness criteria for chains and fields and we establish bounds for the continuity rates of the respective systems of finite-volume conditional probabilities. As an auxiliary result we prove a (re)construction theorem for specifications starting from single-site conditioning, which applies in a more general setting (general spin space, specifications not necessarily Gibbsian).

/pdf/chains-with-complete-connections-and-one-dimensional-gibbs-1jllmk526w.pdf

Chains with Complete Connections and One-Dimensional Gibbs Measures

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.

A discrete time neural network model with spiking neurons: II: Dynamics with noise

We prove uniqueness of $g$-measures for $g$-functions satisfying quadratic summability of variations. Our result is in contrast to the situation of, \eg, the one-dimensional Ising model with long-range interactions, since $\ell_1$-summability of variations is required for general potentials. We illustrate this difference with some examples. To prove our main result we use a product martingale argument. We also give conditions for uniqueness of general $G$-measures, \ie, the case for general potentials, based on our investigation of the probabilistic case involving $g$-functions.

http://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/2003/0010/0005/MRL-2003-0010-0005-a003.pdf

Square summability of variations of g-functions and uniqueness of g-measures

We prove a multifractal formalismfor Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.

Multifractal analysis of non-uniformly hyperbolic systems

In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend an earlier result that square summability of variations of g ensures uniqueness of g-measures. The first extension is to the case of countably many symbols. The second extension is to some cases where g >= 0, relaxing the earlier requirement that inf g > 0.

/pdf/countable-state-shifts-and-uniqueness-of-g-measures-1mxie580o4.pdf

Countable state shifts and uniqueness of g -measures

We weaken the assumption of summable variations in a paper by Verbitskiy [On factors of -function. But we also prove by means of a counterexample that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is a critical inverse temperature in a one-sided long-range Ising model which is at most eight times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.

Phase transitions in long-range Ising models and an optimal condition for factors of g-measures

We improve and subsume the conditions of Johansson and Oberg and Berbee for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique g-measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the g-measure.

https://ems.press/content/serial-article-files/4145

Anders Johansson

Papers

Square summability of variations of g-functions and uniqueness of g-measures

Multifractal analysis of non-uniformly hyperbolic systems

Countable state shifts and uniqueness of g -measures

Phase transitions in long-range Ising models and an optimal condition for factors of g-measures

Unique Bernoulli g-measures