## Archives des Séminaires de l'équipe Interfaces

 14/01/2011 11h Salle de conférences

 Jeremie Unterberger (Universite de Nancy) L'algebre de Schrodinger-Virasoro L'invariance d'echelle locale (invariance conforme) en dimension 2 a contribue a la resolution explicite de nombreux modeles de physique statistique a l'equilibre et au point critique, comme le modele d'Ising et  la percolation, via une approche algebrico-physique (theorie conforme des champs) ou analytico-probabiliste (travaux de Smirnov). La cle de l'integrabilite reside dans l'existence d'une algebre de Lie de symetries conformes de dimension infinie appelee algebre de Virasoro. L'algebre de Schrodinger-Virasoro  -- introduite a l'origine par M. Henkel, du laboratoire de physique des materiaux de Nancy -- se veut une generalisation de l'algebre de Virasoro au cas de la physique statistique hors-equilibre.  Cette algebre a ete etudiee de maniere systematique. Elle permet d'obtenir notamment une classification des formes normales d'une famille d'operateurs de Schrodinger dependant periodiquement du temps. Les structures de Poisson sous-jacentes augurent de l'existence de systemes integrables caches. Les applications potentielles a la physique statistique hors-equilibre (cinetique de formation de domaines ordonnes sous la temperature critique, dynamiques d'interfaces...) sont encore a construire. Ces travaux ont ete reunis recemment dans une monographie en collaboration avec Claude Roger de l'universite de Lyon.

 21/01/2011 11h Salle de conférences

 Bastien Fernandez (CPT, Marseille) Agrégats macroscopiques vs. microscopiques pour des populations d'oscillateurs génétiques couplés Dans ce séminaire, je présenterai un modèle simplifié de dynamique de populations inspiré d'une expérience récente de synchronisation de colonies d'oscillateurs génétiques. Le modèle est suffisamment simple pour que la dynamique globale puisse être exactement décrite pour toutes les valeurs des paramètres. En particulier, je montrerai l'existence d'une transition nette avec l'intensité des interactions, entre un régime où les populations peuvent rester arbitrairement dispersées dans l'espace et un régime d'agrégation sur des amas de taille extensive.
 31/01/2011 11h Salle de conférences

 Yuri Stepanyants (University of Southern Queensland, Toowoomba, Australia) Scalar description of three-dimensional flows of incompressible fluid As it is well-known, the essential progress in the investigation of flows of incompressible fluid may be achieved when the basic hydrodynamic equations can be reduced to one equation for any scalar function, e.g., for the potential function or stream-function. It is much easier to deal with only one scalar function rather than with the three-dimensional vector field and scalar pressure field. Many interesting and physically important problems were solved in this way. However, usage of the traditional scalar functions, either the potential or stream-function, is restricted by the consideration of either potential flows only or assumption of certain symmetry of the flow. The stream-function approach is applicable only to two-component flows, i.e. when the corresponding velocity field is effectively two-dimensional (e.g., the plane flow or flow possessing cylindrical or spherical symmetry). In this work another approach is proposed, when only one scalar function, the quasi-potential, can be used for the description of a wide class of non-stationary three-dimensional vortical flows of incompressible fluid. This class of flows includes both the potential and vortex flows. In the latter case, the corresponding vorticity field may be two-component, in general. Governing equations for the quasi-potential are derived. The generalised Bernoulli integral is deduced from these equations for the viscous non-stationary motion, in general. Particular examples of this class of flows are presented.
 04/02/2011 11h Salle de conférences

 Jean-Marc Di Méglio (Paris 7) Locomotion de C. elegans et environnement mécanique C. elegans  est un des organismes modèles des biologistes. Premier être multicellulaire dont le génome a été séquencé, ce ver cylindrique d'environ un millimètre de long rampe sur des substrats humides et nage dans les liquides. Nous montrerons comment l'environnement mécanique du ver (friction, confinement) modifie son allure et aborderons le difficile problème de la régulation de la locomotion du ver par sa perception ou sa proprioception.

 11/02/2011 11h Salle de conférences

 Nils Berglund (MAPMO, Orléans) Chasse aux canards en environnement bruité Les oscillations multimodales sont fréquentes dans les systèmes biologiques et chimiques à plusieurs échelles de temps. Ces solutions se distinguent par l'alternance d'oscillations de petite et de grande amplitude. L'un des mécanismes pouvant produire ce genre de comportement est la singularité dite "folded node" dans les sytèmes à une variable rapide et deux variables lentes, qui induit l'existence de solutionscanard. Nous quantifions l'effet d'un bruit blanc additif sur ces systèmes, (1) en calculant des niveaux de bruit seuil au-dela desquels les oscillations de petite amplitude deviennent indiscernables des fluctuations, et (2) en montrant qu'un bruit suffisamment fort conduit à une déstabilisation précoce des canards qui peut modifier les motifs des oscillations.                                 Travail en commun avec Barbara Gentz (Université de Bielefeld) et Christian Kuehn (MPI Dresden).

 18/02/2011 11h Salle de conférences

 Francesco Ginelli (CEA Saclay) Collective motion in active matter systems Active particles are able to self propel themselves in a systematic way by extracting and dissipating energy from their surroundings. Systems of interacting active particles describe the collective motion observed in systems as diverse as  animal groups (bird flocks, fish school, etc.), bacteria, molecular motors, as well as driven granular matter. In this talk I will describe the different classes of active matter which emerge from minimal models for collective motion, which capture the essential features of this fascinating kind of matter, and discuss some results concerning their out-of-equilibrium properties.

 25/02/2011 11h Salle 2

 Grégory Faye (INRIA) Bifurcation of hyperbolic planforms in relation with a model for visual texture perception Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for integro-differential equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We can restrict the problem to a bifurcation problem in the hyperbolic plane D (Poincaré disc) and apply the machinery of equivariant bifurcation theory in order to classify all possible H-planforms satisfying the hypotheses of the Equivariant Branching Lemma. For the one, two and three dimensional irreductible representations, we give generic bifurcation diagrams. We study separately the four dimensional cases as no simple reduction can be made.                                 Joint work with: Pascal Chossat and Olivier Faugeras.

 25/02/2011 14h Salle 2
 Sylvain Condamin Temps de premier passage en milieu confiné: du mouvement brownien à la sous-diffusion Les temps de premier passage sont un outil essentiel pour l'étude des réactions limitées par la diffusion en milieu confiné. Dans ce séminaire, j'exposerai mes résultats sur les propriétés de premier passage, pour la diffusion normale et anormale. Je montrerai en particulier que, selon le modèle utilisé pour générer une diffusion anormale, les propriétés de premier passage peuvent être très différentes, ce qui fait des propriétés de premier passage un excellent outil pour étudier l'origine microscopique de la diffusion anormale.
 04/03/2011 11h Salle de conférences
 Laura Messio (EFPL) Symmetries and topological defects in 2D frustrated classical spin models Some materials can be modelised by interacting spins on a lattice. Their phase transitions (e.g. the well-known Ising transition) will be discussed in the classical limit where spins are unitary 1D, 2D or 3D vectors. At low temperature (T), phases with broken symmetries can exist, reminiscent of the ground state broken symmetries. Even if the Mermin-Wagner theorem forbids the breaking of a continuous symmetry on 2D lattices for T>0, discrete symmetries can be broken (as lattice or time-reversal symmetries). Some examples will be given and states called ''regular magnetic orders'' will be defined. They are states where the lattice symmetries are respected. Some of them possess topological defects called vortices, including chiral states. After a brief review of the vortex properties, we will explain why vortex density and chirality are interacting.

 07/03/2011 14h Salle de conférences

 Raphael Chetrite (LJAD) Irréversibilité, création d’entropie et fluctuation pour un processus Markovien Le but de la physique hors d’équilibre est de comprendre les propriétés de systèmes dont l’évolution est irréversible. En terme heuristique, c’est une évolution qui filmée puis projetée à l’envers nousapparait irréaliste. En dépit de longs siècles d’efforts, il n’existe pas pour l’instant de théorie ultimeet complète de ce type de systèmes. Il n’en existera probablement jamais tant le champ d’étude est vaste ; en paraphrasant Stanislas Ulam :                         ”The study on non-equilibrium physics is like the study of non-elephant biology”. Néanmoins, ces deux dernières décennies ont vu l’émergence de résultats robustes et universels, appelés relations de fluctuations et valables pour des systèmes même loin de la réversibilité. Ce sont ces relations qui nous serviront de fil directeur pour notre excursion dans le monde de l’irréversibilité. Je vous présenterai une unification, une rationalisation, et des extensions de ces relations qui résultent de l’introduction de fonctionnelles qui représentent la création d’entropie d’un processus Markovien inhomogène. Une grande partie de l’exposé sera historique et peu technique. Bibliographie Chetrite, R., Gaw ̧dzki, K. : Fluctuation relations for diffusion process. Comm. Math. Phys. 282, (2008)

 09/03/2011 11h Salle de conférences

 Franck Raynaud (Paris Dauphine) Dynamique  et comportements collectifs dans les systèmes complexes: des marchés financiers aux vols d'étourneaux Les systèmes composés d'un grand nombre d'agents en interaction exhibent souvent des propriétés macroscopiques qui ne peuvent être déduites du comportement individuel des individus. Récemment, de nombreuses études se sont intéressées aux comportements collectifs dans les systèmes biologiques (où des comportements collectifs apparaissent à différentes échelles), économiques et sociaux. Dans la                          plupart des cas, les interactions locales entre agents sont à l'origine d'un consensus qui s'étend à l'intégralité du système.          Au cours de ce séminaire je présenterai deux aspects des comportements collectifs.  Dans la première partie je présenterai une étude empirique du risque systémique dans les marchés financiers. La seconde partie sera dédiée aux comportements des groupes d'animaux et en particulier à la modélisation des nuées d' étourneaux.

 11/03/2011 11h Salle de conférences
 Francesca di Patti System-size expansion of stochastic models in population biology: usefulness and limitation of the van Kampen method Using the formalism of the master equation, we will discuss the nature of the stochastic time evolution of systems consisting of a large number of  discrete entities. The behaviour of these models may be analyzed using the well known van Kampen system size expansion.  With reference to the autocatalytic reaction models, we will show how this technique allows one to account for the finite-size effects due to the discrete nature of the problem, and provides a very useful tool to approximate the temporal evolution of the probability distribution. However, we will see how such an approach is able to characterize the ﬂuctuations properly when the system has no absorbing boundaries or when it evolves far from them.  In other words, if a system is driven toward ultimate extinction, the van Kampen approximation is appropriate only at short times, when fluctuations are Gaussian.  As a paradigmatic example of a system with an absorbing state, we will consider the voter model with speciation, a simple model that can be handled analytically. In this case, we will present an improvement of the classical van Kampen technique by introducing a new prescription leading to non-Gaussian ﬂuctuations around the absorbing state.

 18/03/2011 11h Salle 2
 Laurent Jutier (Marne-La-Vallee) Effet Renner-Teller dans les molécules tetra-atomiques L'effet Renner-Teller est un effet de couplage entre mouvements électroniques et nucléaires, qui apparaît dans les molécules présentant une dégénérescence électronique à la linéarité. Dans ce cas, l'approximation de Born-Oppenheimer n'est plus valide, y compris en première approximation. Les spectres expérimentaux des systèmes concernés sont particulièrement complexes, en raison de structures de niveaux peu communs et d'une plus grande densité d'états. Il s'est donc avéré nécessaire de développer une méthodologie purement ab initio en tenant compte des couplages entre l'ensemble des degrés de liberté.

 21/03/2011 11h Salles de conferences
 Stefano Berti Réaction-diffusion et dynamique de populations dans un environnement hétérogène Dans cet exposé je présente une étude sur l'évolution d'une population dans un environnement hétérogène en présence d'advection. L'habitat est constitué d'une alternance périodique de zones favorables, où la population croît avec une dynamique logistique, et de zones désavantageuses, où elle diminue avec un taux de décroissance fixé. Je montre que la population ne peut survivre et envahir l'habitat que pour des zones favorables plus grandes qu'une taille critique et pour des vitesses du milieu inférieures à une vitesse critique. Je caractérise la transition survie/extinction en fonction de l'intensité de l'advection, et je présente des résultats analytiques et numériques sur la vitesse de propagation. Finalement, je discuterai certaines limitations du modèle pour des densités de population petites, en présentant des résultats obtenus avec un terme de croissance différent, qui prend en compte une capacité reproductive réduite pour des densités petites. Ce modèle possède une phénoménologie plus riche en fonction de l'intensité de l'advection.

 25/03/2011 11h Salles de conferences

 Pas de seminaire (conference GDR renormalisation)
 29/03/2011 11h Salles de conferences
 Guillaume Chevereau (Lyon)

 01/04/2011 11h Salle de conférences

 08/04/2011 11h Salle de conférences
 Des systèmes dynamiques à la biomédecine La théorie des systèmes dynamiques s’est développée, en partie, sur l’analyse des attracteurs chaotiques, solutions d’équations différentielles non linéaires. En effet, là où règne le nonlinéaire, l’analyse spectrale (en série de Fourier)  ne parvient pas, dans la plupart des cas, à distinguer les modifications subtiles qui peuvent survenir dans les dynamiques sensibles aux conditions initiales. Aussi, des techniques spécifiques ont été nécessaires pour une analyse fine des comportements chaotiques dont les principales propriétés sont la récurrence, le caractère borné, l’apériodicité,  la sensibilité aux conditions initiales, et, une nature déterministe. Cette dernière propriété est très certainement la plus délicate à démontrer lorsque des données expérimentales (ou observationnelles) sont considérées.       La biomédecine, avec les rythmes de la vie, offre certainement un domaine d’application de prédilection à ces techniques d’analyse. Le propos n’est pas de démontrer la nature chaotique de telle ou telle processus physiologique, mais plutôt d’aider le médecin à distinguer les dynamiques pathologiques des autres, ceci afin de disposer de techniques objectives de diagnostic. Dans cette perspective, des applications de la théorie du chaos en biomédecine seront discutées autour de l’activité cardiaque, l’assistance ventilatoire non invasive, et l’activité cérébrale (codage du sommeil).
 12/04/2011 11h Salle de conférences
 Annulé

 15/04/2011 11h Salle de conférences
 Fulvio Baldovin (Padova) Nonequilibrium statistics of long-range systems in contact with a heat bath On the basis of analytical results and numerical simulations of a toy model representing a system of globally coupled XY spins in contact with a reservoir, we discuss statistical mechanics techniques which can be generalized to describe the properties of quasi-stationary dynamical states. These states typically emerge after a violent relaxation process and their lifetime is influenced by the system size and by the coupling strength associated to fast collisions or to the interactions with the heat bath. It is possible for instance to identify the submanifold of the system's phase space in which the dynamics takes place, and by restricting the Gibbs approach to this submanifold to obtain the statistical mechanics of the quasi-stationary states. It is also possible to identify dynamical phase transitions which mark the end of the quasi-stationary dynamics and that corresponds to a restoring of full ergodic properties for the system. Our results apply to those situations in which the effects of Boltzmann collisions and/or interactions with the heat bath are sufficiently small.  Under these assumptions, the dynamical stability of the quasi-stationary states is ruled by the Vlasov equation.
 19/04/2011 11h Salle de conférences
 Benjamin Pfeuty Phase Response Curves and Robust Synchronization of Biological Oscillators Oscillatory behavior is ubiquitous in physiology ranging from the electrical activities of neural and cardiac cells to the daily intracellular variations of circadian molecular regulators. The main function of some of these endogenous rhythms is to synchronize to other rhythms within other cells or within the environment. An important mathematical tool to deal with synchronization of coupled biological oscillators is the Phase Response Curve (PRC):(i) it measures how much a given perturbation affects the phase of the oscillator; (ii) It allows to predict synchronization properties of oscillators. ; (iii) It is an experimentally assessable characteristic.       In this seminar, I will illustrate the key position of the PRC in biological synchronization studies through two examples that show how the shape of the PRC, that depends on some specific biophysical properties, determines whether oscillator can achieve synchronization and how much robust synchronization is. These two examples concern the synchronization of neuronal oscillators and of circadian clocks, respectively.

 22/04/2011 11h Salle de conférences
 Pablo Jensen (Lyon)

 06/05/2011 11h Salle de conférences
 Vincent Hakim (ENS Paris)

 13/05/2011 11h Salle de conférences
 Alvaro Dominguez (Sevilla) Capillary collapse of colloids. Cosmology in a Petri dish? Colloidal particles form a monolayer when they get trapped by a fluid interface. Under generic conditions the dominant interparticle force  is the capillary attraction due to the deformation of the  interface. This force is formally analogous to two-dimensional  screened gravity, whereby the screening length is typically one  hundred times the mean interparticle separation. We investigate how  the dynamics driven by this screened gravity analogue resembles the  one induced by true gravity. Since the monolayers provide an easily  realizable and tunable experimental system, it is very interesting to  sort out to what extent the features of gravity-induced structure   formation can be studied with monolayers.                In the first part of the presentation I will review briefly the basic  aspects of colloidal monolayers and the theoretical description of  capillary forces. In the second part I will introduce a theoretical  model for the dynamical evolution of the particle density field and present the results from numerical simulations

 20/05/2011 11h Salle de conférences
 Kurusch Ebrahimi-Fard (Dep Physique, Univ Saragosse) Two interacting Hopf algebras of trees. A Hopf-algebraic approach to composition and substitution of B-series Hopf algebra structures on rooted trees are by now a well-studied object, especially in the context of combinatorics. In this work we consider a Hopf algebra H by introducing a coproduct on a (commutative) algebra of rooted forests, considering each tree of the forest (which must contain at least one edge) as a Feynman-like graph without loops. The primitive part of the graded dual is endowed with a pre-Lie product defined in terms of insertion of a tree inside another. We establish a surprising link between the Hopf algebra H obtained this way and the well-known Connes-Kreimer Hopf algebra of rooted trees by means of a natural H-bicomodule structure on the latter. This enables us to recover recent results in the field of numerical methods for differential equations due to Chartier, Hairer and Vilmart as well as Murua.

 27/05/2011 11h Salle de conférences
 Jean-René Chazottes (École Polytechnique) Quelques resultats recents sur les fluctuations d'observables dans les systemes dynamiques Nous presentons un mini-panorama des resultats relatifs aux fluctuations d'observables dans une classe de systemes non-uniformement hyperboliques (theoreme central limite, grandes deviations). Nous presentons ensuite les inegalites de concentration et quelques unes de leurs applications.
 03/06/2011 11h Salle de conférences
 Christophe Letellier (Rouen) Des systèmes dynamiques à la biomédecine La théorie des systèmes dynamiques s'est développée, en partie, sur l'analyse des attracteurs chaotiques, solutions d'équations différentielles non linéaires. En effet, là où règne le nonlinéaire, l'analyse spectrale (en série de Fourier)  ne parvient pas, dans la plupart des cas, à distinguer les modifications subtiles qui peuvent survenir dans les dynamiques sensibles aux conditions initiales. Aussi, des techniques spécifiques ont été nécessaires pour une analyse fine des comportements chaotiques dont les principales propriétés sont la récurrence, le caractère borné, l'apériodicité,  la sensibilité aux conditions initiales, et, une nature déterministe. Cette dernière propriété est très certainement la plus délicate à démontrer lorsque des données expérimentales (ou observationnelles) sont considérées.   La biomédecine, avec les rythmes de la vie, offre certainement un domaine d'application de prédilection à ces techniques d'analyse. Le propos n'est pas de démontrer la nature chaotique de telle ou telle processus physiologique, mais plutôt d'aider le médecin à distinguer les dynamiques pathologiques des autres, ceci afin de disposer de techniques objectives de diagnostic. Dans cette perspective, des applications de la théorie du chaos en biomédecine seront discutées autour de l'activité cardiaque, l'assistance ventilatoire non invasive, et l'activité cérébrale (codage du sommeil).

 17/06/2011 11h Salle de conférences
 Raphael Clement (LJAD) Mécanismes du développement pulmonaire chez les mammifères La forme émerge dans tous les systèmes physiques, vivants ou non, comme le résultat de l'interaction suivant certaines règles des éléments constituant le système. En biologie du développement, le contexte bio-moléculaire et l'importance du gène masquent souvent que, comme dans tout système, la forme naît suite a des interactions inscrites dans l'espace et dans le temps, interactions dont les gènes et les protéines pour lesquelles ils codent sont certainement acteurs. Le développement du poumon est représentatif de cette différence de point de vue puisque les mécanismes de morphogenèse semblent rester obscurs à la pure génétique, ne serait-ce qu'à cause de la quantité énorme d'information que nécessiterait un organe si ramifié et dont les branches s'évitent systématiquement, comme c'est le cas du poumon. L'action élémentaire de branchement reste elle aussi énigmatique. Dans mon exposé, je présenterai un modèle simple basé sur la géométrie du primordium trachéo-bronchique et le patterning des gènes et protéines clefs impliqués dans le développement. Ce modèle montre que l'émergence des traits frappants de la morphologie du poumon s'expliquent très simplement à travers des considérations de géométrie et de diffusion des protéines dans le mésenchyme, tissu dans lequel pousse l'organe.
 24/06/2011 11h Salle 1
 Jim McKenzie (Durham) Negative Energy Waves The idea of negative energy waves first arose in travelling wave tube theory and plasma physics,in which the interaction between positive and negative energy waves can lead to instability and over-reflection.Here we examine these ideas and their application to problems in fluid mechanics and space plasmas.
 08/09/2011 11 heures Salle de Conférences
 Clément Sire (CNRS, Toulouse) The physics of poker, baseball, and football tournaments. I will present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: a) the minimal bet grows exponentially with time; b) players have a finite probability to bet all their money. The distribution of the fortunes of players not yet eliminated is found to be independent of time during most of the tournament, and reproduces accurately data obtained from Internet tournaments and world championship events. This model also makes the connection between poker and the persistence problem widely studied in physics, as well as some recent physical models of biological evolution, and extreme value statistics. Other applications of physical methods to the understanding of baseball/football tournaments (winning probability vs final ranking, streaks...) and to games having a tree structure will be briefly presented.
 30/09/2011 11 heures Salle 2
 Kirone Mallick (IPhT Saclay) Solutions exactes en Physique Statistique loin de l'équilibre Les lois classiques de la thermodynamique et de la physique statistique s'appliquent uniquement à des systèmes au voisinage de l'équilibre thermique. Il n'existe aujourd'hui aucune théorie physique générale des processus loin de l'équilibre : on ne dispose ni d'une description macroscopique à partir de fonctions d'états (qui jouerait un rôle analogue à celui de l'entropie ou de l'énergie libre), ni d'un principe combinatoire à l'échelle microscopique (qui, tel la loi de Boltzmann, nous permettrait d'énumérer les états fondamentaux). Une stratégie possible pour construire une physique statistique hors d'équilibre est de chercher des solutions exactes de modèles épurés mais pertinents. Dans cette optique, le processus d'exclusion asymétrique (ASEP) est considéré comme un paradigme. Ce modèle stochastique de particules en interaction peut être résolu par des techniques inspirées de la théorie des systèmes intégrables. Nous décrirons ces méthodes en mettant l'accent sur les fonction de grandes déviations. Nous montrerons aussi que certaines généralisations de ce modèle font apparaître des problèmes intéressants de représentations d'algèbre quadratiques.
 07/10/2011 11 heures Salle de conferences
 Sylvain Prolhac (Munich) Height fluctuations in the one-dimensional Kardar-Parisi-Zhang universality class. The Kardar-Parisi-Zhang (KPZ) equation describes the stochastic evolution of a growing surface. In one dimension, exact scaling functions for  the fluctuations of the height of the interface around its mean value have been           obtained. These scaling functions have been derived first from microscopic realizations of the KPZ equation. More recently, it has been possible to obtain some of these scaling functions directly from the Cole-Hopf solution of the KPZ equation using the replica method. The calculations involve a summation over all the Bethe eigenfunctions of the attractive quantum delta-Bose gas in one dimension.
 20/10/2011 11 heures Salle de conferences
 Harunori Nakagawa-Yoshikawa (LJAD) Spiral pattern formation in a simple two-phase flow system Spiral patterns are found in different physical, chemical and biological systems. In this seminar, I talk about the spiral arrangement of bubbles moving on a liquid free surface. These bubbles emerge periodically from the surface at the centre of a cylindrical tank. Interacting with the preceding and succeeding bubbles, they are ejected from the emerging point with a constant angular shift between two consecutive bubbles. Spiral bubble arms are then seen on the surface. This spiral pattern resembles the leaf arrangement of plants called phyllotaxis, where the frequently observed angular shift by the Fibonacci angle (137.5°) between two consecutive leaves has attracted researchers in botany. Experimental investigation of the bubble behaviour shows similarities of the formation process of the bubble spirals with that of the phyllotaxis: both consist in the radial advection and repulsive interaction of elements born periodically. The constant angular shift is a consequence of the compaction of these elements at their births. A simple mathematical model is developed for the bubble spiral formation by a consideration of the forces acting on each bubble. It is shown by numerical simulations that the model can reproduce experimentally observed patterns. The model also shows that the angular shift becomes the Fibonacci angle in the limit of small advection with a certain choice of potential for the repulsive interaction between bubbles.
 20/01/2012 11 heures Salle de conférences
 Christian Bracco (Labo Fizeau et IUFM) Poincaré et la relativité en 1905 : un pionnier de la physique théorique du XXe siècle À la suite du travail d’Arthur Miller, historien de la physique, sur le Mémoire de Palerme de Poincaré concernant la dynamique de l’électron, il a été souvent considéré que l’approche de la relativité par Poincaré était prisonnière d’une vision électromagnétique du monde et dépendait de modèles obsolètes de l’électron. « Son mode de pensée essentiellement mathématique » aurait même été « l’un des facteurs qui l’a empêché de tirer des conclusions physiquement pertinentes de ses recherches dans la théorie électromagnétique » (invariance de la vitesse c de la lumière, remise en cause explicite du temps). Comme on le verra, la logique du Mémoire est au contraire extrêmement moderne car elle s’appuie sur les concepts de groupe de symétrie et d’action invariante qui seront au cœur de toute la physique théorique du XXe siècle, à commencer par l’approche d’Hilbert de la relativité générale en 1915. Quatre clés permettent de comprendre cette logique du Mémoire. La première concerne, comme nous l’avons montré, l’utilisation de transformations actives par Poincaré. Elles lui servent à corriger le travail antérieur de Lorentz sur l’invariance de l’électromagnétisme et le dispensent de changer de référentiel. La seconde est la nécessité pour la mécanique d’exclure de ce groupe de transformations les dilatations (par la condition qui lui est venue à l’esprit suite à sa correspondance avec Lorentz). La troisième concerne la place dans le Mémoire de l’action et de son invariance, propriété que Poincaré étend au-delà de l’électromagnétisme et qui lui permet d’obtenir trivialement (avant Max Planck) le lagrangien relativiste. Finalement, les modèles discutés par Poincaré font plutôt figure d’exemple et contre-exemples, même si la « pression de Poincaré » que l’histoire a retenue et qui assure de façon covariante la stabilité nécessaire de l’électron, est proche de modèles actuels de confinement des quarks. Je terminerai cette présentation par une confrontation du Mémoire, seul article scientifique rédigé par Poincaré sur la relativité, à ses textes secondaires, qui présentent un historique lorentzien de la relativité, sans rapport avec le contenu du Mémoire, et sur lesquels de nombreux historiens ou physiciens se sont basés pour faire porter à Poincaré des jugements erronés sur la relativité.
 27/01/2012 11 heures Salle de conférences
 Guillaume Attuel Assessing atrial fibrillation as a chaotic dynamical state of coupled oscillators. Clinical Background:                                 Fibrillation is an electrical pathology of the heart responsible for sudden death, when striking the ventricles. The more common atrial fibrillation (AF), which though in itself not lethal highly increases the risk of stroke. It has been shown that a pathology called conduction block, between atria and ventricle exhibits typical patterns of chaotic map (Glass 1981). However, it is generally believed that fibrillation is a consequence of the substrate abnormalities alone, such as fibrosis, and therefore is due to fractionated propagation, thereby inflicting a kind of wave turbulence, the so called functional reentry (Allessie 1973). This vision has been challenged more recently with the discovery of foci, especially near the pulmonary veins, triggering AF in certain occasions, after the electrical isolation of which normal sinus rhythm is spontaneously recovered in patients suffering paroxysmal AF, i.e. episodes of AF lesser than 24h (Haissaguerre 1998). Since then, an intense debate holds on the identification of the zones to target in the case of sustained AF, i.e. episodes lasting weeks. No consensus has emerged in identifying more regular behaviors, as rotors, or apparently random fractionation, and the means to quantify these hypothesized areas. The possibility that AF stems from a quasi periodic route to chaos has been first pointed out by Garfinkel (1999). Motivations: We are addressing the clinical and physiological concern of trigger and perpetuation of fibrillation as being a manifestation of one single phenomenon. Methods: Our aim is to assess a fibrillatory state as a state past a dynamical phase transition of a system of many coupled oscillators. Collective motion in these systems is known to show synchronized or desynchronized phases (Kuramoto 1981), as well as intermediate more complex phases. We would like to present a non exhaustive overview of this class of systems, in particular to insist on the importance of the mean field interaction among the oscillators, and its influence on the collective behavior, such as the possibility to ignite a trapping instability. We describe then a transition due to this instability, the critical neighborhood of which is abnormally wide, the parameter window where fluctuations are found to be relatively large. The intrinsic mean field plays a key role in perpetuating the fluctuations far from the transition point. In this respect, we will also cast a bridge with the aspects of spatio-temporal intermittency, seen in Rayleigh-Bénard turbulence. We will point out an open question, of great relevance in our opinion, which deals with the classification of the possible dynamical states arising in such systems, according for instance to how much non local the mean field is. We will put forward during the presentation as many key experimental facts of AF as known to us which support this approach.
 3/02/2012 11 heures Salle de conférences
 Bernard Raffaelli TOWARDS A “REGGEIZATION” OF BLACK HOLE PHYSICS? Beyond the purely mathematical definition of a black hole as a solution of Einstein equations in vacuum, there are some observational clues, as pointed out by Kip Thorne, from the first observation of the binary system Cygnus X1 to recent assumptions related to the presence of hypothetical supermassive black holes in the center of various galaxies, concerning their existence in our Universe and, consequently, encouraging their study. But, what is a black hole? In physics, it is well-known that in order to obtain information on interactions between fundamental particles, atoms, molecules, etc…, and on the structure of composite objects, we have to make collision experiments or, more precisely, scattering experiments. This is exactly the aim of this talk. Indeed, after defining “roughly” what a black hole is (and is not!), studying how it can interact with its environment should allow us to obtain fundamental information about those “invisible weird objects”. It should be noted that this study is also useful to understand the kind of signals one could detect by the future gravitational waves astronomy devices and, so to speak, to finally have a way to observe directly the presence of a black hole in a given region of our Universe. We will mainly focus on resonance and absorption phenomena of a scalar field by (the “quite simple” example of) the Schwarzschild black hole. The originality of this study is about the use of an old semiclassical method known as the “complex angular momentum theory”, which brings concepts like S-matrix, Regge poles techniques, into high energy black holes physics, as suggested implicitly by Chandrasekhar in the middle of the seventies, in order to understand related properties as the so-called quasinormal modes and the behavior of the absorption cross section. This approach allows us to have simple and quite intuitive physical interpretations of resonance and absorption phenomena, supported by very accurately novel analytical expressions within the framework of a field theory. References : - Y. Decanini, A. Folacci, B. R, « Resonance and absorption spectra of the Schwarzschild black hole for massive scalar perturbations: a complex angular momentum analysis », PhysRevD.84:084035, 2011 - Y. Decanini, A. Folacci, B. R., « Fine structure of high energy absorption cross sections for black holes », Class. Quantum Grav. 28:175021, 2011 - Y. Decanini, A. Folacci, B. R., « Unstable circular null geodesics of static spherically symmetric black holes, Regge poles and quasinormal frequencies », Phys.Rev.D81:104039, 2010
 15/02/2012 14 heures Salle de conférences
 Olivier Faugeras INRIA Représentations sobres de grands ensembles de neurones Le cerveau humain contient plus de 100 milliards de neurones, chacun d'entre eux étant connecté par des synapses à quelques dizaines voire quelques centaines de milliers de voisins. L'étude mathématique de ces populations s'appuie sur les systèmes d'équations différentielles stochastiques qui permettent d\'exprimer leur dynamique temporelle et son caractère stochastique. Pour rendre compte des phénomènes multi-échelles qui apparaissent au sein de ces populations les chercheurs en neuroscience mathématique tentent de développer des méthodes de champ moyen qui permettent d'aboutir à des représentations de l'activité neuronale plus compactes à des échelles méso- et macroscopiques. Je présenterai deux exemples de telles méthodes, une première inspirée des travaux de Sompolinsky, Ben Arous et Guionnet dans laquelle l'aléa des connections synaptiques est représenté par des variables aléatoires et une seconde, inspirée des travaux de McKean, Tanaka et Sznitman dans laquelle il est représenté par des processus stochastiques. J'indiquerai pour finir quelques directions de recherche futures.

 21/02/2012 11 heures Salle de conférences
 Mario Gattobigio (UNSA - INLN) Few-body physics: an Hyperspherical Harmonics approach The few-body physics is the study of quantum systems made up of only few particles, typically from three up to six particles. Historically, this field started in nuclear physics; the basic problem were, and is, the ab-initio description of light nuclei starting from the knowledge of the "true" nucleon-nucleon interaction. Nowadays, the few-body physics has extended its domain also to (cold)-atomic physics, especially after the experimental realization of the Efimov state, an universal three-body state(s) predicted long time ago by the russian physicist Vitaly Efimov [1].                                 In the few-body nuclear-research program there are two major problems; first, we need to know the fundamental nucleon-nucleon interaction [2]. Second, we must be able to solve the few-body Schroedinger equation; without an effective method of solution, we can not discriminate between the different proposed models of nucleon-nucleon interaction. In our group we have developed a method based on Hyperspherical Harmonics (HH) functions that allows us to solve few-body problems up to six particles [3]. The HH basis set has been extensively used to describe bound and low energy scattering states in three- and four-body systems in nuclear as well as in atomic physics. The extension of the method to describe heavier systems has encountered difficulties mainly due to two causes: the large degeneracy of the basis, and the complexity required in the construction of states with well defined symmetry. In our approach we circumvent the two difficulties: the large degeneracy of the HH basis has been tackled noticing that the Hamiltonian can be expressed as a sum of products of sparse matrices; the use of a dedicated algebra for sparse matrices produces a fast matrix vector product that allows for an efficient eigenvalue search algorithm. In addition, the HH basis has been implemented without a preliminary construction of specific symmetries. However, the eigenvectors reflect the symmetries of the Hamiltonian and, in the case of identical particles, the eigenvectors have well defined symmetry and can be readily identified.
 23/02/2012
 Fabio Tonineli
 2/03/2012 11 heures Salle de conférences
 Pas de séminaire (vacances)
 05/03/2012 16 heures Salle de conférences
 Robert McCann University of Toronto New perspectives and regularity results for optimal transportation The Monge-Kantorovich optimal transportation problem is to pair producers with consumers                          so as to minimize a given transportation cost.  When the producers and consumers are modeled by probability densities on two given manifolds or subdomains,  it is interesting to try to understand  the structure of the optimal pairing as a subset of the product manifold. We first explain how topological features of the cost function yield rectifiability of this subset (meaning it is contained a Lipschitz  submanifold of appropriate dimension).   We also recall how, following work of  Caffarelli, Delanoe and Urbas on the quadratic cost, Ma, Trudinger and Wang found geometrical conditions on a general cost which guarantee the subset is the graph a diffeomorphism,  assuming both mass distributions are smooth.  We finish by explaining a conclusion which persists under a weaker hypotheses:  namely that the optimal map remains a $$C^\alpha_{loc}$$ homeomorphism if the mass  distributions are merely bounded above and below on domains with suitable geometry. The Hoelder exponent $$\alpha$$ turns out to be  uniform among (A3w) costs, depending only on the bounds for the  distributions. This last result is joint work with Alessio Figalli and Young-Heon Kim.
 15/03/2012 11 heures Salle de conférences
 Andre Barato
 23/03/2012 11 heures Salle de conférences
 Kurusch Ebrahimi-Fard The Magnus expansion, trees and Knuth's rotation correspondence In numerical analysis the successful use of combinatorics on trees can be traced back to the pioneering work of John Butcher on an algebraic theory of integration methods. Since then, exploring and unfolding algebraic structures in the context of the theory of numerical integration methods became a useful tool. In this talk we report on recent work on the fine structure of the so-called Magnus expansion. The latter is a peculiar Lie series involving Bernoulli numbers, iterated Lie brackets and integrals. It results from the recursive solution of a particular differential equation, which was  introduced by Wilhelm Magnus in 1954, and which characterizes the logarithm of the solution of linear initial value problems for linear operators. Arieh Iserles and collaborators were the first to use planar tree structures in an intriguing way to study the Magnus expansion. Our work is based on using simple combinatorics on planar rooted trees, which allows us to prove a closed formula for the Magnus expansion in the context of free dendriform algebra. From this, by using a well-known dendriform algebra structure on the vector space generated by the disjoint union of the symmetric groups, we derive the Mielnik-Plebanski-Strichartz formula for the continuous Baker-Campbell-Hausdorff series.
 06/04/2012 10h30 heures Salle de conférences
 16/04/2012 16h30 heures Salle de conférences
 Clint McCrory University of Georgia, Athens Topology of smooth algebraic varieties -- real and complex By Hironaka's resolution of singularities every smooth real or complex algebraic                   variety X has a nice smooth compactification Y. The topology of the inclusion of X in Y can be used to define natural subgroups of the homology of X that do not depend on the choice of compactification. For a complex variety these subgroups comprise Deligne's weight filtration (1970), and for a real variety we obtain a new filtration analogous to Deligne's. I will give elementary descriptions of these constructions and some simple examples.
 20/04/2012 14 heures Salle 2
 Chiu Fan Lee  (Max Planck Institute for the Physics of Complex Systems, Dresden, Germany) Spatial organisation of the cell cytoplasm: P granule localisation by phase separation in the C. elegans embryo Pattern formation in the cell cytoplasm plays an important role in a number of biological processes. During cell division, the cell cytoplasm undergoes dramatic spatial reorganization. In the case of asymmetric cell division, cytoplasmic components are segregated spatially. An intriguing example is the spatial organization of the cytoplasm during asymmetric cell division in the C. elegans embryo, which involves the generation of a concentration gradient of the protein Mex-5 that in turn drives localization of P granules to the posterior side. P granules                    are liquid drops consisting of RNA and proteins that are important for germline specification. In this talk, I will describe how the Mex-5 concentration gradient controls the spatial profile of P granule formation and as a result the localization of P-granules to the posterior of the cell. Furthermore, we demonstrate that with the help of phase separation, the P granule concentration gradient can be drastically amplified in comparison to the Mex-5 concentration gradient.
 03/05/2012 11 heures Salle de conférences
 Krzysztof Gawedzki
 11/05/2012 11 heures Salle 2
 Martin Krupa (Donders Institute for Brain, Cognition and Behaviour) Systèmes dynamiques lents-rapides et canards: aspects théoriques, numériques, applications et problèmes ouverts. Dans cet exposé, je commencerai par donner quelques éléments historiques sur la découverte des canards au sein de l'école non-standard de Strasbourg, et de leur présence dans de nombreuses applications (aérodynamique, réactions chimiques, oscillateurs neuronaux). Ensuite, je présenterai rapidement les principales techniques d'analyse mathématique de ces objets (analyse non-standard, recollement de développements  asymptotiques, asymptotique des séries Gevrey, éclatements à paramètres et réduction à des variétés centrales) puis j'insisterai plus longuement sur mon travail utilisant  des éclatements à paramètres. Dans une seconde partie, je passerai aux applications de la théorie des canards en neuroscience, dans le cadre des systèmes à trois dimensions avec deux variables lentes, explicitant en particulier le lien avec les oscillations complexes (mixed-mode oscillations ou MMOs). Je mentionnerai également brièvement les techniques numériquesqui permettent d'étudier au mieux ces systèmes. Je terminerai mon exposé en donnant une liste de problèmes ouverts.
 29/05/2012 16 heures Salle 1
 Richard Hain Duke University Morse theory and mapping class groups in low genus This talk will be a gentle introduction to Morse theory and its applications to understanding                       mapping class groups in low genus. Morse theory is a tool for understanding topological spaces. Mapping class groups are groups of topological symmetries of a compact orientable surface. They occur as fundamental groups of moduli spaces of curves. After reviewing classical Morse theory, I will introduce the main ideas of stratified Morse theory, a generalization of classical Morse theory developed by Goresky and MacPherson in the 1980s to study singular spaces. The talk will conclude with several examples how stratified Morse theory can be used to prove results about mapping class groups in low genus.
 08/06/2012 11 heures Salle de conférences
 Serge Antonczak (Nice) Theoretical Study of a Metabolon in the natural biosynthesis of Flavonoids In each living system, the concentration of functional biological entities (e.g. proteins, enzymes, peptides…) is incredibly high. Though most of them are located in separate compartments in the cell, depending on their structure or function, each individual entity is led to show with others spatial proximity, or even close contacts, due to diffusion movements for instance. Thus, some transient complex-structures may appear and, depending on the affinity they exhibit for each other, may subsist during sufficiently long timescales that may lead to new functional systems. Recent investigations put forward the existence of a supramolecular complex in the course of flavonoid production in which the successive enzymes remain in interaction. Indeed, it is now recognized that the mechanisms underlying the biosynthesis of natural products involve the creation of such transient structures, built around several proteins or enzymes. The product of an enzymatic reaction becoming the substrate for the neighbour enzyme, it just has to “jump” from an active site to the next one, diminishing the time lost during diffusion processes and the energy lost during solvation and desolvation processes, leading then to enhance the catalytic efficiency.             Accessing to a precise description of the overall structures of such macromolecular assemblies has then become a key-point to understand the underlying biological mechanisms but also for developing new therapeutic strategies. Our goal in this project is to simulate the various phenomena in this complex, including the chemical transformations but also the way products and substrates are transferred from the active site of an enzyme to the following. To this end, a broad spectrum of theoretical methods is used to unravel the mechanisms and interactions at different levels of complexity: QM and QM/MM methodologies are applied to decipher at the most the reaction mechanisms, Molecular Dynamics procedures help in describing, both structurally and energetically, the interactions between substrate-cofactors and enzymes and up-to-date Protein-Protein docking protocols aim at building protein-protein complex structures. In this talk, will be presented our first results concerning an enzyme of the supramolecular system and the strategies that will be applied to gain insights in the biochemical cascade responsible for the production of these natural compounds of the polyphenol family.
 22/06/2012 Vladimir Kulinskii Odessa 11 heures Self-propelling particles as a new challenge for the non-equilibrium statistical mechanics Salle 2 The dynamics of the systems of self-propelling particles have attracted much attention in last two decades. The minimal model which is widely used for modeling such systems is the Vicsek model. In essential, this model is represented as the mechanical systems with the nonholonomical constraints for the velocities. The introduction of noise leads to the transitions between different dynamical regimes. The microscopic dynamical equations for such systems are nonhamiltonian. This hinders the application of the machinery of the standard nonequilibrium theory based on the Liouville equation etc. In such situation the only way is the kinetic approach much like the Boltzmann original derivation of the kinetic equation. We present some results on the kinetic regime of the Vicsek model considered in the continuum time limit and its relation with the Kuramoto model of the spontaneous synchronization. The corresponding hydrodynamic equations based on the microscopic conservation laws (conservation of number of particles and the kinetic energy) is also discussed.

 25/06/2012 Alexandru Buium Albuquerque, New Mexico  et Max-Planck Institut 16 heures Differential equations satisfied by numbers Salle 1 The analogies between functions and numbers proved to be one of the most fruitful source of ideas in number theory. One can therefore ask: is there an analog of differential calculus in which functions are replaced by numbers? In particular is there a derivative of 23 with respect to 7? And does 23 (or its square or cube root, etc.)   satisfy remarkable differential equations with respect to the "variable" 7? Also, provided one has definitions for these concepts, can one apply such ideas to prove anything new in number theory/diophantine geometry?  The answer to all these questions is YES and the talk is devoted to explaining how this comes about.

 29/06/2012  René Lozi  (LJAD - UNSA) 11 heures  Emergence du pseudo-hasard à partir du chaos dans des systèmes dynamiques couplés Salle de conférences  Le terme chaos, pour désigner le comportement de certains systèmes dynamiques non linéaires, a semble-t-il, été introduit par James Yorke et son étudiant Tien-Yen Li dans leur fameux article « Period three implies chaos » publié en 1974. Depuis, 40 années se sont écoulées et les milliers d’études effectuées dans de nombreuses disciplines (physique, informatique, mathématiques, biologie, chimie, théorie du contrôle…) sur les systèmes dynamiques chaotiques ont permis d’explorer de façon très approfondie ce champ de recherche. La génération de nombres chaotiques (c’est-à-dire dont on ne perçoit pas directement le rapport entre eux) est très simple à obtenir avec un ordinateur, cependant elle ne satisfait pas les besoins de plus en plus nombreux de générer des nombres au hasard (plus exactement des nombres pseudo-aléatoires) pour les simulations numériques, les loteries en ligne, les méthodes d’intégration numériques pour des intégrales multiples (méthode de Monte-Carlo ou quasi-Monte Carlo) des problèmes économiques… Nous présenterons dans cet exposé tout d’abord rapidement quelques exemples d’utilisation actuelle des nombres chaotiques (comme pour le réglage des dispositifs PID dans l’industrie via l’optimisation chaotique), puis nous montrerons comment on peut en couplant de façon particulière des générateurs de nombres chaotiques, obtenir des générateurs de nombres pseudo-aléatoires dont les propriétés sont comparables à celles des meilleurs générateurs actuels basés sur d’autres branches des mathématiques, tout en étant ultra-rapides (plusieurs dizaines de millions de nombres à la seconde). En outre ces générateurs sont multi-dimensionnels, c’est-à-dire qu’ils produisent des séries simultanées de nombres pseudo-aléatoires non corrélés, ce qui permet de construire des algorithmes de cryptage symétriques.

 21/09/2012 11 heures Salle de séminaires physique (Fizeau)
 Eric Bertin (ENS Lyon) On the statistical physics of macroscopic interacting entities Numerous systems of interest can be considered as composed of a large number of macroscopic interacting "entities", these entities being either real objects or more abstract mathematical modes. Examples range from physical systems like granular matter, foams, or turbulent flows, to complex systems outside physics like bird flocks or social systems. The dynamics of the involved macroscopic entities differs from that of standard microscopic particles, due for instance to energy dissipation in collisions between grains, or to selfishness in the decision process of social agents, thus questioning the possibility to apply standard statistical physics approaches to such systems. This issue is illustrated on several simple solvable models.
 01/10/2012 16 heures Salle de conférences
 Dimitar  Dimitrov Universidade Estadual Paulista, Brésil Zeros of entire Fourier transforms, the Riemann hypothesis and Lee--Yang measures The following fundamental problem arose independently in two seemingly completely distinct areas as number theory and statistical mechanics. The principal question was formulated first by George P\\'olya in 1926 who was motivated by his efforts to settle the Riemann hypothesis. It states: under what additional conditions on the sufficiently smooth and rapidly decreasing kernel $$K(t)$$ its Fourier transform $$\psi(z)=\int_{-\infty}^{\infty} K(t) e^{itz} dt$$ is an entire function which possesses only real zeros? Essentially the same question arose in statistical mechanics where a measure is said to have the Lee-Yang property if all zeros of its Fourier transform are real. It has been motivated by the celebrated Lee--Yang theorem, established in 1952. For their work Lee and Yang were awarded the 1957 Nobel Prize in physics. The theorem states that if the partition functions of models with ferromagnetic interactions are considered as functions of an external field, then all zeros are purely imaginary. The original version of the result concerns the so-called Ising model. Further extensions and generalizations are due to R. Griffiths and B. Simon (1973), C. Newman (1974) and Lieb and Sokal (1981).  We report a result which provides  a characterization of the Lee--Yang measures, so that a solution of P\\'olya\'s problem too, in terms of the polynomials, orthogonal with respect to the measure.
 05/10/2012 11 heures Salle de conférences
 Valentin Bonzom (Perimeter Institute Waterloo) Random tensor models The study of random tensors generalizes random matrices to objects with d>2 indices. Remarkably, Feynman expansions in tensor models generate sums over triangulations of pseudo-manifolds in dimension d. Such models have been actively developed and solved in the past two years. I will introduce a suitable ensemble of random tensors and present the main results I have obtained: universality at large N (large size of the tensor), a notion of continuum limit and existence of critical behaviors, and a new algebra which generalizes the Virasoro algebra found in matrix models and provides gluing rules for triangulations in dimension d.

 19/10/2012 11 heures Salle de conférences
 Julien Tailleur Statistical physics of run-and-tumble bacteria and other self-propelled particles Suspensions of self-propelled particles have attracted lots of interest from the physics community over the last decade. Bacteria and algae are prototypical self-propelled particles but self-propulsion can also be met outside biology, for instance due to self-diffusiophoresis. In this talk, I will briefly review several types of self-propelled particles and describe how one can build a statistical physics treatment of their collective behavior. I will describe various interesting features of these suspensions, such as ratchet effects, effective temperature and pattern formation.
 23/11/2012
 Francois Sicard (Université de Bourgogne) Reconstructing the free-energy landscape of protein with biased MD simulations: Metadynamics and dihedral Principal Component Analysis Since the late 1980s emerges the idea that a global overview of the protein's energy surface is of paramount importance for a quantitative understanding of the relationships between structure, dynamics, stability, and functional behavior of proteins. Thanks to continuous increase of the computing power and of the reliability of empirical force fields, all-atom molecular dynamics (MD) simulations become a widely employed computational technique to simulate the dynamics of complex systems such as proteins through discrete integration of the Newtons's equations of motions of each atom. However in several cases all-atom MD simulations are still not competitive to describe the protein conformational dynamics, due to the fact that using an atomistic model is computationally expensive, as sufficiently realistic potential energy functions are intrinsically complex. Moreover, most phenomena of interest take place on times scales that are orders of magnitude larger than the accessible time that can be currently simulated with classical all-atom MD. This issue can be addressed by accelerating the exploration of the conformational space in (all-atom) MD simulations. In this case, a large variety of methods referred to as enhanced sampling techniques have been proposed. They exploit a methodology aimed at accelerating rare events and based on constrained MD. Metadynamics (metaD) belongs to this class of methods: it enhances the sampling of the conformational space of a system along a few selected degrees of freedom, named collective variables (CVs) and reconstructs the probability distribution as a function of these CVs. However, the succes of metaD depends on the critical choice of a reasonable number of relevant CVs. All the relevant slow varying degrees of freedom must be catched by the CVs. In addition, the number of CVs must be small enough to avoid exceedingly long computational time, while being able to distinguish among the different conformational states of the system. Consequently, identifying a set of CVs appropriate for describing complex processes involves a right understanding of the physics and chemistry of the process under study. Choosing a correct set of CVs thus remains a challenge, as a whole, independently of the enhanced sampling technique one could consider.   I will present that coupling Well-Tempered Metadynamics, i.e. the most recent variant of the method, with a set of CVs generated from a dihedral Principal Component Analysis on the Ramachandran dihedral angles (describing the backbone structure of the protein) provides an efficient reconstruction of the free-energy landscape of the small and very diffusive Met-enkephalin pentapeptide.
 30/11/2012
 Pierre Degond Modèles macroscopiques d'auto-organisation Les phénomènes d'auto-organisation et d’émergence apparaissent au sein de systèmes constitués d’agents autonomes interagissant localement sans leader. Ils s’observent dans tous les domaines (physique, biologique, sociaux) et à toutes les échelles au point qu’ils doivent être considérés comme la norme plutôt que l’exception. Pourtant, leur étude théorique en est encore à ses balbutiements car ils posent des questions fondamentalement nouvelles que les méthodes classiques de la théorie cinétique et de la physique statistique peinent à résoudre. Une des questions fondamentales est l’obtention (quasi)-rigoureuse de modèles macroscopiques à partir des modèles agents-centrés (ou particulaires). L’une des difficultés rencontrées est la perte des lois de conservation (comme celles de l’impulsion), qui sont la pierre angulaire des modèles continus en physique. Nous discuterons de cette difficulté et des moyens d’y remédier en prenant l’exemple de dynamiques d’alignement qui ont suscité beaucoup de travaux dans les quinze dernières années.

29-03-2013 - Léa Cot (INSA Toulouse),

Structural airframe maintenance strategy comparison

Résumé :

In recent years, airline maintenance cost has steadily increased and significant investigations are made to improve it. Currently, preventive maintenance approach based on predetermined inspections over all the life of the aircraft, including airframe and engine maintenance, is used. Our purpose focuses on structural airframe maintenance. Regarding the structural airframe maintenance, damages that could in a near future threaten the integrity of the structure are detected at these scheduled maintenances. In-service, an aircraft is subject to a sequence of cycles with each cycle consisting of a flight phase, followed by a ground phase (which then precedes the next flight). Consequently, the fuselage undergoes frequent pressurization/depressurization cycles leading repeated loading and unloading. During any phase, fatigue damage may occur and a crack can initiate and propagate in fuselage panels. Scheduled inspection intervals are calculated to ensure the safety of the structure, that means such that no crack can grow to critical size before the next inspection. Accordingly, a threshold corresponding to panel replacement has been defined and each panel with a crack reaching this threshold is repaired or replaced. The maintenance intervals and the threshold affect both the safety and lifecycle cost of an aircraft undergoing scheduled maintenance. Alternative condition-based maintenance (CBM) doesnt required scheduled inspections. In this approach, structural damage is continuously tracked by an on-board system assessing the status of the health of a structure. SHM systems allow to monitor the condition of a structure using embedded sensors and actuators which detect structural damages. The SHM-based conditional maintenance (SHM-CBM) provides a real-time status of a structure. Maintenance is requested (and not scheduled) when a detected crack size exceeds a predetermined threshold different of the scheduled maintenance one. This threshold is chosen according to safety requirements. Our paper proposes a general mathematical framework to compare SHM-CBM maintenance to scheduled maintenance in terms of the average number of fuselage panels replaced over the in-service aircraft operational life. New analytical formulas are demonstrated to express the probability to change a fuselage panel at any cycle. The recursive analytical expressions obtained only depend on both panel crack size with no replacement from the entry into service of the aircraft and thresholds defined before according to strategy maintenances. The average number of panels to be changed after any number of cycles can be straightforwardly deduced, especially at times of scheduled maintenances as well as SHM-CBM maintenances. Based on the average number of panels replaced, the efficiency of the SHM-CBM solution can be quantified compared to results obtained with traditional scheduled maintenances. The fatigue crack growth propagation in the panel is modelled using Paris law. Uncertainties on amplitude fatigue loading, initial crack size and material properties are modelled as random variables. The usefulness of the proposed approach is shown by simulating real-world cases of short range aircraft fuselages provided by Airbus company.

03/04/2013 - Antonio Celani (Institut Pasteur)

The entropic anomaly

Résumé :

Particle motion at the micro-scale is an incessant tug-of-war between thermal  fluctuations and applied forces on one side, and the strong resistance exerted by fluid viscosity on the other. Friction is so strong that completely neglecting inertia  the overdamped approximation  gives an excellent effective description of the actual particle mechanics. In sharp contrast with this result, here we show  that the overdamped approximation dramatically fails when thermodynamic quantities such as the entropy production in the environment is considered, in presence of  temperature gradients. In the limit of vanishingly small, yet finite inertia, we  find that the entropy production features a contribution that is anomalous, i.e.  has no counterpart in the overdamped approximation. This phenomenon, that we call entropic anomaly, is due to a symmetry-breaking that occurs when moving to the  small, finite inertia limit.

As a consequence of this phenomenon, quasi-static engines, whose efficiency is  maximal in a fluid at uniform temperature, have in fact vanishing efficiency in presence of temperature gradients. For slow cycles the efficiency falls off as the  inverse of the period. The maximum efficiency is reached at a finite value of the cycle period that is inversely proportional to the square root of the gradient intensity. The relative loss in maximal efficiency with respect to the thermally homogeneous case grows as the square root of the gradient. As an illustration of these general results, we construct an explicit, analytically solvable example of a Carnot stochastic engine. In this thought experiment, a Brownian particle is confined by a harmonic trap and immersed in a fluid with a linear temperature profile. This example may serve as a template for the design of real experiments in which the effect of the entropic anomaly can be measured.

12/04/2013 - K. Boehmer (Philipps University Marburg)

Dew drops on spider webs: a symmetry breaking bifurcation for a parabolic differential-algebraic equation

Lines of dew drops on spider webs are frequently observed on cold mornings. In this lecture we present a model explaining their generation. Although dew is supposed to condense somehow evenly along the thread, only lines of drops are observed along the spider thread. What are the reasons for this difference? We try to give an explanation by concentrating on some essential aspects only. This every-day observation is an example of one of the fascinating scenarios of nonlinear problems, symmetry breaking bifurcation. Despite many simplifications the model still provides very interesting mathematical challenges. In fact the necessary mathematical model and the corresponding  numerical methods for this problem are so complicated that in its full complexity it never has been studied before. We analyse and numerically study symmetry breaking  bifurcations for a free boundary value problem of a degenerate parabolic differential-algebraic equation employing a combination of analytical and numerical tools.

This lecture is an appetizer for my two books in OUP:

Numerical Methods for  Nonlinear  Elliptic Differential Equations, A Synopsis, 2010  Numerical Methods for Bifurcation  and Center Manifolds  in  Nonlinear  Elliptic and Parabolic Differential Equations, 2011.

30/04/2013 - Ivan Zelinka (université d'Ostrava, République Tchèque),
On Relations Between Evolutionary Dynamics and Complex Networks

Résumé :

This topic introduces the notion of complex structures synthesis by
means of evolutionary algorithms and develops a new method for complex
systems synthesis.
This method is similar to genetic programming and grammatical evolution
and is applied alongside evolutionary algorithms: differential
evolution, self-organizing migrating, genetic algorithm, simulated
annealing and evolutionary strategies. The aim of this investigation is
to synthesize electronic circuits, complex structures and systems like
a new and “simple” chaotic systems based on some elements contained in
a pre-chosen existing chaotic system and a properly defined cost
function. The investigation consists of two case studies based on the
aforementioned evolutionary algorithms in various versions. For all
algorithms, 100 simulations of chaos synthesis were repeated and then
averaged to guarantee the reliability and robustness of the proposed
method. The most significant results are carefully selected, visualized
and commented in this speech.
The second part will contain three mutually joined parts, namely
introducing a novel approach joining evolutionary dynamics, complex
networks and CML systems exhibiting chaotic behavior. The first part
will discuss a novel method on how dynamics of evolutionary algorithms
can be visualized in the form of complex networks. An analogy between
individuals in the populations in an arbitrary evolutionary algorithm
and the vertices in a complex network will be discussed as well as the
relationship between the communications of individuals in a population
and the edges in a complex network. The second part will discuss the
possibility of how to visualize the dynamics of a complex network by
means of coupled map lattices and to control by means of chaos control
techniques.
The last part will discuss some possibilities on CML systems control,
especially by means of evolutionary algorithms. The spirit of this
keynote speech is to create a closed loop in the following schematic:
evolutionary dynamics --> complex network --> CML system -->
control CML --> control evolutionary dynamics. Real-time simulations
as well as animations and pictures demonstrating the presented ideas
will be presented through this keynote speech.

14/06/2013 - Olivier Dauchot (UMR Gulliver, CNRS and ESPCI-ParisTech)

"Interplay between hard core repulsion and self propulsion in active matter"

Résumé :   Collective motion in driven or self-propelled particle systems is a topic of
recent interdisciplinary interest. Within physics, following the works
of Vicsek et al. and Toner and Tu, most progress was achieved by
studying microscopic point-like particles models and their continuous
descriptions. For the simplest situation in which the surrounding fluid
can be neglected (dry flocking) and the sole interaction is some local
effective alignment, a picture of basic universality classes has
emerged. When dealing with real systems, hard core repulsion comes into
play. In a recent experiment of vibrated polar disks, i.e.
millimeter-size objects with a built-in oriented axis, we have shown
that hard core repulsion and self-propulsion produce some effective
alignment leading at large scale to collective streams and anomalous,
giant number fluctuations [1,2]. More recently, it was shown that a
slowing down of the self propulsion velocity with the local density
could lead to a sharp clustering transition. Hard core repulsive systems
will a priori experience such an effect because of self-trapping,
glassy like phenomenology. As a result hard core repulsion and self
propulsion build up both effective alignment and effective slowing down.
Each of these effect produce very different transitions. In the present
talk I will the interplay between these two transitions in the light of
both experimental and numerical results for self propelled hard discs
as well as of numerical simulations of a point-like particles model
encompassing both effects.

17/09/2013 - Guillaume Dhont (Univ. du Littoral Côte d'Opale)

Interprétation symbolique de la fonction génératrice en théorie des invariants

Résumé :

De nombreuses molécules admettent un groupe ponctuel de symétrie G non tri-
vial dans leur configuration d’équilibre. L’étude de tels systèmes amène à construire
des objets appartenant à une représentation irréductible Γ 2 de G à partir de va-
riables élémentaires appartenant à une représentation Γ 1 , réductible en général.
Les objets ainsi générés sont souvent exprimés sous une forme polynomiale. Le
problème posé ici est alors de trouver et caractériser l’ensemble des polynômes
susceptibles d’apparaître dans ce développement polynomial.
La fonction génératrice de Molien est un outil pertinent pour ce travail. Elle se
calcule directement à partir de la représentation matricielle de l’action du groupe
sur les objets élémentaires et des caractères de la représentation irréductible Γ 2 .
Le coefficient de degré n dans le développement en série de cette fonction donne le
nombre de polynômes linéairement indépendants de degré n qui se transforment
selon Γ 2 .
Cette fonction de Molien peut se mettre sous la forme d’une ou plusieurs fonc-
tions rationnelles. Nous discuterons dans cet exposé de l’interprétation symbolique
de cette fonction génératrice à l’aide d’exemples concrets. Nous commencerons par
des rappels sur le cas classique des invariants de groupes finis pour terminer avec
le cas des covariants de groupes continus compacts illustré par le groupe SO(2).

07/01/2014 - Emilie Lebarbier (AgroParisTech)

31/01/2014 - Christophe Pouzat (MAP5, Paris 5)

Analyse de séquences de potentiels d'actions émises par plusieurs
neurones : l'exemple du premier relais olfactif de la blatte, Periplaneta
americana
.

Résumé :

La communication entre régions distantes du cerveaux s'effectue
par la propagation de brèves « déviations » du potentiel membranaire
des neurones : les potentiels d'action. Ces potentiels d'action ne
transmettent de l'information que par leur temps d'arrivée et non
par leur forme ou leur amplitude qui sont « toujours » les mêmes.
Une analyse dont le but est de « décoder » l'information portée les
séquences de potentiels d'action peut donc, à priori, se baser sur
une modélisation des temps d'apparition des potentiels d'action,
indépendamment des mécanismes biophysiques qui les génèrent
effectivement ; c'est-à-dire que le formalisme probabiliste des
processus ponctuels / processus de comptage devrait s'appliquer à ce
cas. Poursuivant une désormais longue tradition d'analyse des
séquence de potentiels d'action par ce formalisme, nous présenterons
dans le cadre concret de l'étude du premier relais olfactif d'un
insecte — la blatte, Periplaneta america — une approche non
paramétrique de l'estimation de l'élément fondamental d'un processus
ponctuel : son intensité conditionnelle.

17/04/2014 - Eric Simonnet (INLN, Unice) - [joint seminar with EDP and ProbaStat teams à 14h]

A splitting method for computing rare events with applications

18/04/2014 - Paul Johnson (University Mc Master, Canada)

Bethe Ansatz and related wavefunction forms for strong correlation in quantum chemistry

Résumé:

In quantum chemistry, we are tasked with solving the Schrödinger
equation for atoms and molecules: the energies and allowed states are
respectively the eigenvalues and eigenvectors of the physical
Hamiltonian. The main difficulty is in employing a method which is
both sufficiently accurate and computationally tractable.
Conventional approaches are reliable when a single configuration of
the electrons is dominant (weak correlation), but tend to fail when
many confi gurations contribute to the physical state (strong
correlation). To this end, we have employed the Bethe Ansatz for the
reduced Bardeen-Cooper-Schrie ffer Hamiltonian as a trial vector. The
structure is such that a large number of con figurations are
represented with a reasonable cost.

I will discuss the usage of the Bethe Ansatz along with generalizations
and present various problems encountered in several approaches.

13/06/2014 - Sylvain Maire (Université du Sud Toulon-Var)

Intégration numérique adaptative en dimension modérée: application au pricing d'options européennes.

Résumé: Le calcul numérique d'intégrales reposent sur deux types de
méthodes:
les méthodes de quadrature de type Gauss-produit utilisables plutot en
petite dimension et les méthodes Monte-Carlo ou quasi-Monte Carlo pour les grandes
dimensions. Nous développons dans un premier temps des quadratures efficaces pour des dimensions
intermédiaires (inférieures à 10) construites à partir d'un ajustement par
moindres carrés d'un modèle polynomial creux sur des données
aléatoires bien choisies. Ces quadratures sont très efficaces pour les
fonctions régulières mais pour des fonctions moins régulières, on doit
procéder à un découpage du domaine afin de localiser les zones de fortes
variations. Nous proposerons deux techniques adaptatives pour effectuer ce
découpage utilisant les quadratures précédentes comme éléments de base.
Enfin nous donnerons des exemples numériques pour le pricing d'options ou la
fonction à intégrer est seulement continue au voisinage d'une surface à
localiser numériquement car elle s'écrit comme une partie positive.

04/07/2014 - Guanrong (Ron) Chen (Center for Chaos and Complex Networks, City University of Hong Kong)

Looking for best networks for consensus

Résumé & bio : Within a social community of connected people, what is the
best networking relationship that can facilitate their
interactions towards consensus? For an array of chaotic
oscillators, what is the best network topology that promotes the
synchrony of their coupled dynamics? This talk will discuss such
common issues altogether from a unified graph-theoretic
perspective, presenting them as a synchronizability or
consensusability problem of a connected undirected network. The
corresponding mathematical problem is determined by the spectrum
of the Laplacian matrix of the network, which reflects most
topological characteristics of the network such as degree
distribution, path-length, clustering centrality, and so on.
Recently, we found that networks with best possible
synchronizability are in some sense “homogenous” and “symmetric”,
having some common features such as an identical degree sequence,
a longest girth and a shortest path-sum. This talk will present
the motivation and background of the topical issue, explain the
basic idea and methodology in tackling the problem, and verify the
result by using degree-3 regular networks of small sizes, with a
conjecture that the conclusion is true in general.

Professor Chen received the M.Sc. degree in Computer Science from
the Sun Yat-sen University, China and the Ph.D. degree in Applied
Mathematics from Texas A&M University, USA. Currently he is a
Chair Professor and the Director of the Centre for Chaos and
Complex Networks
at the City University of Hong Kong. He is
a Fellow of the IEEE since 1997, serving as Editor-in-Chief for
the International Journal of Bifurcation and Chaos. He was
conferred Honorary Doctorate by the Saint Petersburg State
University, Russia in 2011, and is an Honorary Professor at
different ranks in some thirty universities worldwide.

05/09/2014 - Patrick Brest (Institute of Research on Cancer and Ageing of Nice (IRCAN))

Analyses multi-niveaux (genomique, transcriptomique, proteique):
Outil d'aide à la Décision thérapeutique en médicine personnalisé pour
une meilleure prise en charge du cancer du poumon.

Résumé:

Le cancer du poumon est la première cause de mortalité par cancer en France et dans le monde.
Aujourd'hui, en France, la survie à cinq ans après un diagnostic de cancer du poumon est de 14 %
(13 % chez les hommes, 18 % chez les femmes). La médecine personnalisée est désormais
l’approche privilégiée pour les cancers du poumon à un stade avancé et métastatique, avec
notamment l’apparition de nouvelles stratégies telle que l’immunothérapie qui fait appelle à notre
système immunitaire pour lutter contre le cancer.
Au sein de notre équipe qui regroupe tous les acteurs de la santé (des chercheurs fondamentaux aux
chercheurs cliniciens), nous étudions principalement les signatures prédictives de l’évolution de ces
cancers. Pour cela, nous avons à notre disposition d’énorme quantité de données OMICS
(génomique, transcriptomique, protéomique), mais leur exploitation reste difficile. L'objectif de
cette réunion est de fédérer nos compétences pour fournir au biologiste et au clinicien des
algorithmes lui permettant
*Au niveau fondamental : Modélisation prédictive de la réponse aux drogues. Certains processus
(Apoptose, Autophagie,...) semblent fondamentaux dans les réponses cellulaires aux
chimiothérapies. A l’aide de rapporteurs protéiques, nous sommes capables d’observer certaines
réponses cellulaires en temps réel au niveau de la cellule unique afin d’extraire un grand nombre de
données dynamiques. A partir de ces données, nous utilisons des modèles mathématiques de voies
de signalisation cellulaires pour prédire le devenir des cellules cancéreuse et chercher des cibles
moléculaires.
* Au niveau clinique : a) En analyse en composantes multiples, chaque patient sera, outre le tableau
clinique, associé à un nombre important de données (génomique, transcriptomique et protéomique)
dans un futur proche. Le but de notre étude serait de déterminer si une analyse multiple multi-
niveaux pourrait être envisagée permettant la liaison de l'ensemble de la variabilité individuelle au
transcriptome, au protéome, et idéalement qui pourraient être associées à une mauvaise survie.
b) En transcriptomique, une signature correspond finalement à une somme de sous-composantes
cellulaires. Le but de notre étude serait de déterminer s’il est possible à partir de cette signature de «
déconvoluer » le signal en ces sous composantes cellulaires afin de définir si leur proportion
respectives pourraient être un signe prédictif de l’évolution cancer du poumon et d’autres cancers.
En conclusion, l'enjeu est de hiérarchiser les signatures moléculaires clés du développement tumoral
pour prédire les résistances et les rechutes pour une prise en charge plus précoce et plus efficace des
patients.

05/09/2014 - Yaouen Fily (Brandeis University, USA) [12h00]

Active particles under strong boundary confinement.

It's been long known that active particles have a tendency to accumulate near walls and get trapped
at corners. More recently, these features have been used to control active suspensions, e.g. direct
bacteria or get them to power micro-devices. However, a general understanding of how boundary
shape affects the properties of active suspensions is still missing. Using a simple model of active
suspension, I will show how one can derive a general relationship between the particle density and
the shape of the box. Despite its limitations (the suspension must be strongly confined and dilute),
the fact that the result holds for arbitrary box shapes makes it a promising tool to better understand
and design confining boxes for active suspensions.

11/09/2014 - Tucker Carrington (Queens University, Canada)

"Pruned basis methods for solving the vibrational Schrödinger equation without approximating the potential"

Spectra are computed by solving the time-independent Schrödinger
equation. If the number of atoms in a molecule is greater than
about 4 the dimensionality of the Schrödinger equation makes solution very
difficult. Standard discretization strategies for large
dimensional systems (D ≥ 9) yield matrices and
vectors that are too large for modern computers. This is the
so-called "curse of dimensionality". Both the basis size
and quadrature grid size are problems. Several ingenious
schemes have been developed in the last decades to reduce the basis
size. We have focused on reducing the size of the quadrature grid. The
Smolyak algorithm allows one to create non-product quadrature grids
with structure. Because of the structure they can be used with
pruned product basis sets and the Lanczos algorithm to compute
spectra. In this talk we shall explain the nature of these grids and why
they are useful for computing spectra.

12/09/2014 - Leon Chua (Imperial College, UK, University of California, Berkeley et Distinguished Professor, Techniche Universitat München)

Memristors : Device with intelligence

Although postulated in 1971, the memristor has attracted worldwide attention from
academia and industry only after Hewlett-Packard published a working nano-memristor
device in the 1 May 2008 issue of Nature [1]. An acronym for memory resistor, the memristor
is poised to revolutionalize future generations of computers, ipad, smart phones, etc.
Among many applications from numerous disciplines including biology, botany , physics,
mathematics, etc., the memristor can be used to emulate synapses and the Hodgin-Huxley
Equations, and is therefore the right stuff for building intelligent brain-like machines. This
lecture explains what makes the memristor such a versatile device and answers many
questions that memristor researchers are afraid to ask.
Biographie: Leon Chua is a foreign member of Academia Europeia and the Hungarian
Academy of Sciences. He has been awarded 7 patents and 14 Doctor Honoris Causa from
major universities worldwide. He has won many prizes, including the Guggenheim Fellow
and the EC Marie Curie Fellow.

19/09/2014 - Rodrigo Soto (Universidad de Chile, Chili) [12h00]

Natural and self-assembled swimmers.

Bacteria, like E. coli, constitute a natural example of self-propelled objects. The permanent energy
flux from the fuel, to the swimmers and lately to the fluid, puts these systems in permanent non-
equilibrium conditions. Swimmers constitute paradigmatic examples of active matters and
constitute an interesting playground for non-equilibrium matter. In this talk I will describe the
properties of natural (E. coli) and artificial self-assembled (colloidal) swimmers.
When bacteria are placed in confined environments they are attracted to solid surfaces and swim in
contact with them for long times. In this talk, several aspects related to the motion of bacteria near
surfaces are considered. First, a simple swimmer model will be introduced, which reproduces the
main features of bacteria-surface interaction including the observed circular motion. Second, the
induced diffusion of tracers in presence of a bacterial bath is studied. A kinetic theory combined
with a hydrodynamic approach allow us to compute the resulting diffusivity. It is shown that close
to surfaces, the induced diffusivity is enhanced as a result of the smaller swimming efficiency of
bacteria.
Artificial swimmers are also possible to build. In this talk the case of self-assembled colloidal
particles is described.
Catalytically active colloids maintain non-equilibrium conditions in which they produce and deplete
chemicals. The concentration fields resulting from the chemical activity produce gradients that
attract or repel other colloids depending on their surface chemistry and ambient variables. This
results in a non-equilibrium analogue of ionic systems, but with the remarkable novel feature of
action-reaction symmetry breaking. In dilute conditions they join up to form (colloidal) molecules.
The molecules could be inert or have spontaneous activity in the form of net translational velocity
and spin depending on their symmetry properties and their constituents. Also, oscillatory states are
possible as well as spontaneous transitions from active to passive states, mimicking the run-and-
tumble motion of bacteria.

17/10/2014 - Timothée Masquelier (Institut de la Vision, CNRS, Paris) [14h30 - salle conf.]

Spike-based computing and learning in brains, machines, and visual systems in particular

Résumé

Using simulations, we have first shown that, thanks to the physiological learning mechanism
referred to as spike timing-dependent plasticity (STDP), neurons can detect and learn repeating
spike patterns, in an unsupervised manner, even when those patterns are embedded in noise [1], [2].
Importantly, the spike patterns do not need to repeat exactly: it also works when only a firing
probability pattern repeats, providing this profile has narrow (10-20ms) temporal peaks [3]. Brain
oscillations may help in getting the required temporal precision [4], in particular when dealing with
slowly changing stimuli. All together, these studies show that some envisaged problems associated
to spike timing codes, in particular noise-resistance, the need for a reference time, or the decoding
issue, might not be as severe as once thought. These generic STDP-based mechanisms are probably
at work in particular the visual system, where they can explain how selectivity to visual primitives
emerges [5], [6]. Finally, these mechanisms are also appealing for neuromorphic engineering: they
can be efficiently implemented in hardware, leading to reactive systems with self-learning abilities
[7].
References
[1] T. Masquelier, R. Guyonneau, and S. J. Thorpe, “Spike timing dependent
plasticity finds the start of repeating patterns in continuous spike trains.,”
PLoS ONE, vol. 3, no. 1, p. e1377, Jan. 2008.
[2] T. Masquelier, R. Guyonneau, and S. J. Thorpe, “Competitive STDP-Based Spike
Pattern Learning.,” Neural Comput, vol. 21, no. 5, pp. 1259–1276, May 2009.
[3] M. Gilson, T. Masquelier, and E. Hugues, “STDP allows fast rate-modulated
coding with Poisson-like spike trains.,” PLoS computational biology, vol. 7, no.
10, p. e1002231, Oct. 2011.
[4] T. Masquelier, E. Hugues, G. Deco, and S. J. Thorpe, “Oscillations, phase-
of-firing coding, and spike timing-dependent plasticity: an efficient learning
scheme.,” The Journal of neuroscience, vol. 29, no. 43, pp. 13484–93, Oct. 2009.
[5] T. Masquelier and S. J. Thorpe, “Unsupervised learning of visual features
through spike timing dependent plasticity.,” PLoS Comput Biol, vol. 3, no. 2, p.
e31, Feb. 2007.
[6] T. Masquelier, “Relative spike time coding and STDP-based orientation
selectivity in the early visual system in natural continuous and saccadic
vision: a computational model.,” Journal of computational neuroscience, vol. 32,
no. 3, pp. 425–41, Jun. 2012.
[7] C. Zamarreño-Ramos, L. A. Camuñas-Mesa, J. A. Pérez-Carrasco, T. Masquelier,
T. Serrano-Gotarredona, and B. Linares-Barranco, “On Spike-Timing-Dependent-
Plasticity, Memristive Devices, and Building a Self-Learning Visual Cortex,”
Frontiers in neuroscience, vol. 5, no. March, p. 22, 2011.

16/01/2015 - Ivan Zelinka  (Ostrava University, République Tchèque) "Evolutionary synthesis"

Résumé:

This talk discusses an alternative approach for symbolic
structures and solutions synthesis and demonstrates a comparison with other
methods, for example Genetic Programming (GP) or Grammatical
Evolution (GE). Generally, there are two well known methods, which can be
used for symbolic structures synthesis by means of computers. The
first one is called GP and the other is GE. Another interesting research
was carried out by Artificial Immune Systems (AIS) or/and
systems, which do not use tree structures like linear GP and other similar
algorithm like Multi Expression Programming (MEP), etc. In this talk,
a different method called Analytic Programming (AP), is
presented. AP is a grammar free algorithmic superstructure, which can be
used by any programming language and also by any arbitrary
Evolutionary Algorithm (EA) or another class of numerical optimization
method. It describes not only theoretical principles of AP, but also
its comparative study with selected well known case examples
from GP as well as applications on synthesis of: controller, systems of
deterministic chaos, electronics circuits, etc. For simulation
purposes, AP has been co-joined with EA's like Differential
Evolution (DE), Self-Organising Migrating Algorithm (SOMA), Genetic
Algorithms (GA) and Simulated Annealing (SA). All case studies has been
carefully prepared and repeated in order to get valid statistical
data for proper conclusions.

23/01/2015 - Tarcísio M. Rocha Filho (Université de Brasília)
"Using Graphics Processing Units in Statistical Mechanics Simulations - The Vlasov equation and Molecuar Dynamics of Many particles system with long-range interactions"

Résumé:

We present the algorithms and implementations of Vlasov equation
integrator for one spatial dimension of systems with
long-range interactions, discussing the caveats in memory access
and some examples of how to choose the most adequate algorithms
for better efficiency of the parallel code in the GPU. Multi-GPU
implementations are illustrated with a Molecular Dynamics code for the
same type of systems. We also present some relevant results obtained
using such codes at the Statystical Physics group at the University
of Brasília
.

05/02/2015 - Isabelle Kleiner (Lab. Interuniversitaire des Systèmes Atmosphériques (LISA), CNRS/IPSL et Universités Paris Est-UPEC et Paris Diderot)

"Spectroscopy of internal rotors and applications to astrophysical, prebiotic and biological molecules "

In this talk I will first give a general introduction to the high
resolution spectroscopy techniques in the microwave,
millimetre and infrared spectral range and how they can
contribute to the knowledge of the astrophysical medium or the
planet atmospheres. The topic of our work concerned mainly
molecules containing large amplitude motions and in particular
molecules containing one or two methyl (CH3) internal. One of
the goals of our work is to describe with our theoretical
method and codes the energy levels, and then the line
positions and intensities for this type of molecules.

That way we are able to provide reliable predictions of line positions and
intensities for astrophysical molecules containing one
internal rotor CH3, such as the isotopic species of methyl
formate HCOOCH3, methanol CH3OH, acetic acid CH3COOH,
acetaldehyde CH3CHO or acetamide CH3CONH2. The major new
facilities, the Herschel Space Observatory and the Atacama
Large Millimeter Array (ALMA), in Chili, have now opened the
submillimeter region up to a few THz for astronomical
observations by making investigations with unprecedented high
sensitivity and resolution. Molecules which undergo internal
rotation of a methyl group present thousands of lines in this
spectral range and therefore their spectra are particularly
important to model.

I will show some of the recent results in the microwave or infrared range
for those molecules, and some applications in astrophysics. We
will also present recent results for the study of a two-top
internal rotor, the methyl acetate molecule CH3-O-C(=O)-CH3,
which has been very recently detected in the interstellar
cloud Orion thanks our prediction.

Another goal of our work is to get some knowledge of the structural
properties of small organic molecules or biomimetic molecules.
Fourier transform microwave spectroscopy in the gas phase
coupled with high level quantum chemical calculations or ab
initio calculations has led to the precise and detailed
determination of molecular structures for the lowest energy
conformers of a number of molecules. In this talk, I will show
results from molecules which can be considered as prototypes
of odorant molecules, like isoamyl acetate (so-called “banana
oil”) or linalool, an acyclic mono-terpene present in lavender
and other plants and emitted in the earth atmosphere.

27/03/2015 - Pascal Viot (UPMC)

"Blocking in single-file particulate flows".

Résumé:

Filtration,  flows in micro/nano­channels and traffic flows are examples
of processes subject to blockingwhen the channel conveying the particles
becomes too crowded. We investigate a concurrent flow model where
particles enter a channel randomly. If at any time two particles are
simultaneously present in the channel, failure occurs. We   obtain   the
exact   solution   for   the   survival   probability,   the
distribution   of   the number of particles that pass before failure,
and the instantaneous flux exiting the channel. Generalizations of this
simple model are also considered.

Second, we consider  a counterflow model with two opposing Poisson
streams. There is   no   restriction   on   the   number   of
particles   passing   in   the   same   direction,   but blockage occurs
if, at any time, two opposing particles are simultaneously present in
the passage. All relevant quantities have been obtained exactly

[1] Non­Markovian Models of Blocking in Concurrent and Countercurrent
Flows, A.

Gabrielli, J. Talbot and P. Viot Phys. Rev. Lett,  110, 170601 (2013)

[2]   Stochastic   model   of   single­file   flow   with   reversible
blockage,  Chloé   Barré, Julian Talbot and Pascal Viot EPL, 104 60005
(2013)

[3] Irreversible Blocking in Single­File Concurrent and Countercurrent
articulate Flows, J. Talbot, A. Gabrielli  and P. Viot J. Stat.Mech
P01027 (2015)

10/04/2015 - Guillaume Dhont, (LPCA, Université du Littoral Côte d'Opale)

Structures combinatoires, algébriques et topologiques en physique

Résumé:

L'analyse qualitative de systèmes moléculaires vise à obtenir
une description globale de leurs propriétés et amène à étudier
des structures mathématiques qui relèvent de la combinatoire, de
l'algèbre ou de la topologie. En particulier, les fonctions
génératrices sont un outil mathématique efficace pour encoder de
l'information sous une forme compacte. Nous présenterons dans
cet exposé l'application des fonctions génératrices à l'étude des
invariants et des covariants sous l'action du groupe SO(2) d'une
part et au dénombrement des niveaux d'énergie dans les polyades
vibrationnelles de molécules d'autre part.

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Vendredi 20/11/2015  à 11h en salle de conférences

Mohammed-Salah Abdelouahab (Laboratory of Mathematics and their
interactions, Mila University Center, Mila, Algeria)

"Hopf Bifurcation and Chaos in Simplest Fractional-order Memristor-based Electrical Circuit"

Résumé : We investigate the bifurcation and the onset of chaos in a
fractional-order simplest memristor-based electrical circuit
composed of only three circuit elements: a linear passive capacitor,
a linear passive inductor and a nonlinear active memristor with two
degree polynomial memristance and a second order exponent internal
state. It is shown that this fractional circuit can exhibit a very
rich nonlinear dynamics such as a Hopf bifurcation, coexistence of
two, three and four limit cycles, double-scroll chaotic attractor,
four-scroll chaotic attractor, coexistence of one (or two) chaotic
attractors with one limit cycle and new chaotic attractor which is
not observed in the integer case. Finally, the presence of chaos is
confirmed by the application of the recently introduced 0-1 test.
(Email: m.abdelouahab@centre-univ-mila.dz)
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Mardi 24/11/2015  à 11h en salle 3

Tidjani Menacer, (Université Mohamed Khider de Biskra, Algérie)

"Bifurcations cachées dans les attracteurs multi-spiral de type Chua"

Résumé : La recherche « d’attracteurs cachés » dans les systèmes
dynamiques (c’est-à-dire d’attracteurs caractérisés par un bassin
d'attraction très petit qui n’est relié à aucun point d'équilibre,
de sorte qu’il ne peut pas être localisée par des procédures de
calcul standard) a été initiée depuis quelques années par Kuznetsov
et Leonov [1] qui ont proposé une méthode analytique-numérique pour
les localiser (localisation basée sur la méthode des fonctions de
description). Dans le cas des attracteurs chaotiques multi-spiral de
type Chua qui dépendent d’un paramètre discret, nous détournons la
méthode de Kuznetsoz et Leonov pour trouver des « bifurcations
cachées » en faisant apparaître par cette méthode détournée un
paramètre de bifurcation continu.
[1] http://www.worldscientific.com/doi/abs/10.1142/S0218127413300024

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jeudi 10 décembre 2015 à 14h en salle de conférences

soutenance d'Amine ILMANE

" Développements autour de la méthode d'interactions de configurations en champ moyen "

Résumé :  Dans
cette thèse ont été développés  de nouveaux  outils de calcul théorique
de spectres moléculaires rovibrationnels qui permettent de mieux
traiter les états vibrationnels  très excités ainsi que les mouvements
de grandes amplitudes avec la méthode d’interactions de configurations
en champ moyen. Dans un premier temps, nous avons discuté la question du
choix des bases modales et les différents compromis à trouver afin de
pallier aux défauts possibles des surfaces d'énergie potentielle.  Dans
ce cadre nous avons également développé un critère de sélection visant à
améliorer la qualité des fonctions d'ondes rovibrationnelles de base.
Ces approches ont été appliquées avec succés à la molécule de méthane
CH4.Dans un second temps, nous avons  implémenté un algorithme de calcul
formel des opérateurs d'énergie cinétique en coordonnées quelconques
qui permet d'avoir des expressions exactes ainsi que leurs
développements en série de Taylor  ou Fourier, qui exploite au mieux les
potentialité du logiciel MATHEMATICA et a permis d'obtenir des
hamiltoniens rovibrationnels en coordonnées de valence de façon
particulièrement efficace. Enfin, nous avons généralisé la méthode
d’interactions de configurations en champ moyen en ajoutant de façon
perturbative un champ effectif d'ordre deux. Nous avons appliqué cette
généralisation à la molécule de  péroxyde d'hydrogène HOOH, ce qui a
permis de montrer son intérêt tant pour l'amélioration des niveaux
d'énergie que des fonctions d'onde associées, lorsqu'on a affaire à des
groupes de degrés de liberté bien séparés énergétiquement.

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26/02/2016

Magnetic anisotropy in mono- and bi-nuclear complexes: theoretical insight and prospects

Renaud Ruamps;A R. Maurice;B C. de Graaf,C and Nathalie GuihéryA

A Université de Toulouse 3, Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France;

B SUBATECH, UMR CNRS 6457, IN2P3/EMN Nantes/Université de Nantes, 4 rue A. Kastler, BP 20722, 44307 Nantes Cedex 3, France;

C Universitat Rovira i Virgili, Marcel-li Domingo s:n, 43007 Tarragona, Spain

Magnetic anisotropy is the origin of the single molecule magnet (SMM) behavior
which is manifested by a slow relaxation of the magnetization and a
blocking of the magnetization for low enough temperatures. Since this
bistable behavior may lead to possible technological applications in
the domain of data storage and quantum computing, the understanding
of the microscopic origin of magnetic anisotropy has received a
considerable interest during the last two decades.

Mono-nuclear complexes having exotic coordination of the metal ion have recently
been shown to exhibit a very large magnetic anisotropy. A first study
will be devoted to the rationalization of the magnitude and nature of
single ion anisotropy from theoretical calculations. It will be shown
that the competition between relativistic effects and Jahn Teller
distortion may lead to very large magnetic anisotropy (see figure 1).

The overall magnetic anisotropy of a poly-nuclear complex comes from both
the local anisotropies of paramagnetic ions and their interactions.
The second part of this presentation will focus on the understanding
of synergistic effects between local anisotropies in bi-nuclear
species for which we have both tuned the local anisotropies by
imposing peculiar geometries and combined various types of local
anisotropies (see figure 2, values are in cm
-1).

The method used here was successfully confronted to experimental values in series of mono- and bi-nuclear complexes.[1]

References:

[1] J. of Chem. Theo. Comp., 2009 5, 11 2977; J Chem. Theor. Chem 2010 6 1, 55; J. Chem. Theor. Chem. 2010 6 10, 3092; Phys. Rev. B, 2010 81 21, 214427;  J. Chem. Phys. 2010 133, 084307; Inorg. Chem. 2011 50 13, 6229; Phys. Rev. B 2012, 85, 014409;
Phys. Rev. B 2012, 86, 024411; Chem. Euro. J. 2013, 19, 950; R. Ruamps et al. J. Am. Chem. Soc.
2013, 135, 3017A, Phys. Chem. Chem. Phys., 2013, 15 (43), 18784.

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18/03/2016

Kurusch Ebrahimi-Fard,

"Saving a species in a Lotka-Volterra model via an Hopf algebra antipode"

Abstract: Lotka-Volterra systems can be viewed as nonlinear input-output systems when
time-varying parameters are taken as system inputs and the population
levels are the system outputs. By varying some of these inputs, an
open-loop control problem results, and one objective may be to determine
appropriate inputs to produce desired system profiles. This is known as
the left inversion problem. In this talk we outline the general left
inversion problem for multivariable input-output systems that can be
represented in terms of Fliess operators (aka Chen-Fliess series) using
concepts from combinatorial Hopf algebras. The antipode plays a central
role in this context. This is then applied to a three
species Lotka-Volterra system. The aim is to change the population
dynamics of the top-level predator species in a food chain in such a way
as to prevent extinction.

(Joint work with W. S. Gray and L. Duffaut Espinosa.)

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10/05/2016 à 14h en Salle de conf., Séminaire commun avec Proba-Stat (attention jour et horaire exceptionnel)

Eric Guerci, "Why do we need “quantum-like” models for cognition"

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20/05/2016 à 11h en Salle de conf., Séminaire commun avec Proba-Stat

Claire Guerrier, (ENS Ulm) "Modélisation mathématique et simulations multi-échelles pour l'étude de la relâche vésiculaire dans les synapses neuronales."

	Nous avons étudié plusieurs structures neuronales à différentes
échelles allant des  synapses aux réseaux neuronaux. Notre objectif était de développer et analyser des modèles mathématiques, afin de déterminer comment les propriétés des synapses au niveau moléculaire façonnent leur activité, et se propagent au niveau du réseau. Ce changement d’échelle peut être formulé et analysé à l’aide de plusieurs outils tels que les équations aux dérivées partielles, les processus stochastiques ou les simulations numériques. Dans un premier temps, nous avons calculé le temps moyen pour qu’une particule brownienne arrive à une petite ouverture définie comme le cylindre faisant la jonction entre deux sphères tangentes. La méthode repose sur une transformation conforme de Möbius appliquée à l’équation de Laplace. Nous avons également estimé, lorsque la particule se trouve dans un voisinage de l’ouverture, la probabilité d’atteindre l’ouverture avant de quitter le voisinage. De nouveau, cette probabilité est exprimée à l’aide d’une équation de Laplace, avec des conditions aux limites mixtes. En utilisant ces résultats, nous développons un modèle et des simulations stochastiques pour étudier la libération vésiculaire au niveau des synapses, en tenant compte de leur géométrie particulière. En nous appuyant sur ces résultats, nous avons développer un modèle pour le terminal pré-synaptique, qui couple un système d’équations d’action de masse à un ensemble d’équations de Markov, ce qui permet d’obtenir des résultats analytiques et de réaliser des simulations stochastiques rapides.


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27/05/2016

Rachel Sparks, Tomsk State University, Russia

"Nanotechnology: Small Science, Big Ideas"

Nanoscience studies the world of very small objects, it aims to shape the world
atom by atom, to create new artificial structures with improved
properties, due entirely to their size.
Nanotechnology
enables the development of new materials, devices, or other useful
structures. Applications include; electronics, automotive, sports,
textiles, construction, energy, medicine and environment, to name a
few. Nanotechnology is producing revolutions in these areas by making
devices smaller, lighter, cheaper and faster with better performance.

Electronic devices at the nano scale have now become an essential feature of
modern technology and the field of molecular electronics is
continuously striving towards ever smaller electronic devices.
Understanding what is happening on such a small scale is becoming
increasingly more important. The rapid increase in computing power
available and the advancement of the modelling tools available have
led to theory that now reflects reality. Theoretical tools such as
Density Functional Theory (DFT), enable scientists to make accurate
explanation of experimental results.

Molecular switches are a desirable concept in molecular electronics. The aim is
to have the ability to manipulate, control and fully understand the
process that enables the molecule to switch reversibly at room
temperature, a goal that has not yet been reached.

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08/07/2016

Faith Chiu, UCL, UK

"An analysis of coupling and decoupling neural activity in speech perception"

Speech perception relies on the
accurate identification of phonemes within an auditory string. These
phonemes have been argued to be the smallest of meaningfully contrastive
units in speech ; a change in phoneme will concurrently induce a change
in meaning. Previous modelling efforts implicate that a change in word
meaning (caused by a change in phoneme) causes a change in coupling
activity in the cortical hierarchy (Schofield et al., 2009). However,
MMN has been shown to reflect language-specific phonemic representations
regardless of word meaning, even in non-words (Näätänen et al., 1997).
To disentangle this phoneme-meaning relationship, I present preliminary
results from a current study which applies Dynamic Causal Modelling
(Kiebel et al., 2006) on elicited Mismatch Negativity responses to
categorical speech sound changes. We notice condition-specific
significant changes in effective connectivity for connection strengths
involving the superior temporal gyri (STG) which are located within
higher levels of the auditory cortical hierarchy.

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08/09/2016

14h Salles des Séminaires

Paulo Amorim (Univ. fédérale de Rio)

Ant foraging dynamics: From reaction-diffusion to individual-based models

15h30 Salles des Séminaires

Collective dynamics in sheeps herds

Jeudi 22 / 09 / 2016 à 14h00 en salle de séminaires

[Séminaire commun edp-an / mecaflu/ interfaces]

Ana Maria Alonso Rodriguez (univ. Trento )

Finite Element Potentials

The
aim of this talk is to furnish a simple and efficient way for
constructing finite elements with assigned gradient, or curl, or
divergence. Clearly in numerical computations this is important any time
one has to reduce a given problem to an associated one with vanishing
data. Some simple notions of homology theory and graph theory applied to
the finite element mesh are basic tools for devising the solution
algorithm.

Vendredi 23 / 09 / 2016 à 11h30 en salle de séminaires

Igor Aranson, Prof. Invité au Lab. Dieudonné

Ferromagnetic swimmers, spinners and rollers

This
is a colloidal system of self-propelled particles, similar to the
Quincke Rollers (but not identical).  The active particles exhibit
various collective patterns.

Vendredi 30 / 09 / 2016 à 11h30 en salle de séminaires

Igor Aranson, Prof. Invité au Lab. Dieudonné

Living nematic: linking motility and liquid crystallinity

By
letting bacteria swim in a suspension of liquid crystals, Igor and
collaborators managed to see how the swimming of bacteria distorted
nematic order around them, which allowed them to learn about the
swimming of bacteria.

Vendredi 14 Octobre 2016 à 14h00 en salle de conférences

Gabriela Petrungaro (Buenos aires)

Titre:  Dynamics of mobile, delayed-coupled oscillators

Résumé :

	The vertebrate body is provided with a repetitive structure of
segments, which originate sequentially -one by one- during embryonic
development, with a definite rhythm. This rhythm is controlled by a
biological clock, known as the vertebrate segmentation clock, which
relies on synchronization of cellular oscillators. It is thought that
each of the cells involved in the process acts as an independent
genetic oscillator. A local communication mechanism between cells
couple their dynamics giving rise to synchronization. Two key
components of this mechanism are communication delays and cell
movement. Intercellular communication involves synthesis and transport
of macromolecules which act as ligands and receptors. This aspect can
be described by incorporating delays in the coupling between
oscillators. Furthermore, cell mobility in the context of coupled
oscillators could promote synchronization by extending the effective
range of the coupling. Motivated by this mechanism we study the
dynamics of a system of coupled oscillators that includes these two
fundamental aspects of cell communication. We find that the system
exhibits complex spatio-temporal patterns on its way towards
synchronization.

Vendredi 14 Octobre 2016 à 10h30 en salle de conférences

André Galligo (LJAD)  [travail effectué en collaboration avec Didier Clamond (LJAD)  et Jean Rajchenbach (LPMC)].

Titre: Modélisation de la compression d'un matériau polycarbonate en nids d'abeilles.

Résumé :

Les
solides cellulaires (e.g. en nids d'abeilles) sont fréquemment
rencontrés aussi bien dans la nature que dans l'industrie, où ils sont
appréciés pour leurs propriétés mécaniques et leur légerté.  Nous
étudions le cas d'un polycarbonate formé en thermocollant un amas de
cylindres circulaires. En réponse à des compressions latérales, il
montre des comportements inattendus qui dépendent de  l'orientation.
Pour les expliquer, nous présentons une modélisation avec deux échelles
de grandeurs: celle des petits interstices et celle de la plaque
entière de polycarbonate. On peut alors, dans ce cadre, préciser les
différentes notions d'elasticité et d'inélassticité et les comparer aux
comportements de nos composants locaux (triangles elasticae) et de notre
matériau global.  L'originalité de notre approche consiste à
privilégier les déformations des interstices et à souligner l'intér\^et
(théorique et pratique) du concept de triangle elastica.  La
présentation  et l'explication seront largement illustrées avec des
images et des diagrammes.

Vendredi 18 Novembre 2016 à 11 heures en salles de séminaires

Ophelie Guinaudeau (i3s)

Titre: Abstraction de la structure et de la dynamique du neurone biologique pour une étude formelle de l'intégration dendritique

Résumé:

Le neurone possède des dendrites qui sont des prolongements ramifiés au
niveau desquelles il reçoit des messages nerveux provenant de milliers
d'autres neurones. Ces messages se propagent dans l'arborescence
dendritique en direction du corps cellulaire du neurone qui permet, sous
certaines conditions, la transmission du message résultant aux neurones
adjacents. Notre apport est de modéliser le traitement et la
transmission des messages en faisant collaborer une modélisation
discrète et une modélisation continue: le neurone peut être vu comme un
système complexe qui reçoit des entrées discrètes, les convertit en un
signal continu le long de l'arborescence dendritique et le re-discrétise
à la sortie du corps cellulaire. La complexité réside notamment dans le
fait que les entrées qui sont distribuées sur l'arborescence
dendritique interagissent dans le temps et dans l'espace lors de leur
propagation. De plus, cette propagation est accompagnée d'une
atténuation du signal qui est décrite par la théorie des câbles. En se
basant sur cette théorie, nous avons développé un modèle de neurone
individuel permettant d'étudier l'influence de la topologie des
dendrites sur la fonction du neurone. Les abstractions que nous
proposons conservent la précision biophysique tout en réduisant le
nombre de paramètres impliqués. Ceci nous a permis de démontrer un
théorème qui définit des classes d'équivalence de comportements. Il
implique que la topologie des dendrites est, de manière surprenante,
assez peu déterminante dans la fonction d'entrée-sortie du neurone. Il
en résulte que la forme de l'arbre dendritique est probablement
essentiellement dictée par la géométrie du cerveau.

==================================================

Vendredi 2 décembre 2016 en Salle 2 du LJAD à 11 heures

M. Krupa (Inria)

"Heteroclinic chains as a model of priming"

Priming is the ability of the brain to more quickly activate a target concept
in response to a related stimulus (prime). Experiments point to the
existence of an overlap between the populations of the neurons coding
for di erent stimuli. Other experiments show that prime-target relations
arise in the process of long term memory formation. The classical
modelling paradigm is that long term memories correspond to stable
steady states of a Hop eld network with Hebbian connectivity.
Experiments show that short term synaptic depression plays an important
role in the processing of memories. This leads naturally to a
computational model of priming, called latching dynamics; a stable state
(prime) can become unstable and the system may converge to another
transiently stable steady state (target). We show that in the context of
Hop eld networks latching dynamics is closely approximated by (robust)
heteroclinic chains and discuss the role of sparse connectivity,
inhibition and noise in the approximation. Further, we derive necessary
conditions for the existence of heteroclinic chains in Hop eld networks
with synaptic depression and show how a Hop eld network supporting a
heteroclinic chain can be extended to a larger network in which the
weights are derived from a Hebbian learning rule.

Jeudi 9 février 2017 en Salle de Conférences du LJAD à 11 heures

Jacques Féjoz (Dauphine)

"Théorème KAM, symétrie et dégénérescence"

La persistence de solutions quasipériodiques dans les systèmes hamiltoniens presque
intégrables dépend de conditions de non-dégénérescences. Nous analyserons comment ces
conditions et leurs conséquences sont modifiées en présence de symétries, avec le problème
des trois corps en guise d'application.



Lundi 27 février 2017 en Salle de Conférences du LJAD à 11 heures

Tarcísio M. Rocha Filho (Brasília)

"Equilibrium and Non-Equilibrium Statistical Mechanics of Systems with Long-Range Interactions"

I
will presente some recent developments on equilibrium and
non-equilibrium Statistical  Mechanics of systems with long-range
interactions. Our results concern mainly kinetic theory, chaos, ensemble
inequivalence and the classical analogue of Goldstone modes excited by
thermal fluctuations

Vendredi 10 mars 2017 en Salle de Conférences du LJAD à 11 heures

Andreas Deutsch (Dresden)

Collective effects in cancer growth and invasion: insights from
mathematical models
Cancer growth and  invasion can be interpreted as  collective behaviour arising in migrating
and interacting cell populations. Here, we demonstrate how cellular automaton models allow
for prediction and analysis of emerging properties (e.g. invasion speed) arising from particularly
chosen cell migration and interaction scenarios (especially go or grow“ and „go and grow“
dynamics). We use our models for the interpretation of data from in vitro cancer cell invasion
assays and will also discuss implications of the „go or grow“ dichotomy for cancer growth and
persistence.
Reference:
A. Deutsch, S. Dormann:  Cellular Automaton Modeling of Biological Pattern Formation: Characterization,
Applications, and Analysis. Birkhäuser, Boston, 2005 (2nd ed. 2016)



Mercredi 10 mai 2017 en Salle de Conférences du LJAD à 11 heures

Antonio Celani (ICTP, Trieste)

"Learning to navigate in dynamic environments: animal behavior and artificial intelligence"

I will discuss two examples of difficult navigation tasks in highly
dynamical environments. The first one is thermal soaring in birds. Birds
and gliders piggyback ascending currents to fly with a reduced
expenditure of energy, for example, during migration, and to extend
their flying range. Flow in the thermals is highly turbulent, which
poses the challenge of the orientation in strongly fluctuating
environments. The second one is gravitaxis by smart
microswimmers. These are self-propelled particles that can sense basic
mechanical cues from their surroundings and respond to them in order to
reach the highest altitude within some time horizon. We
combine numerical simulations of fluid flow with reinforcement learning
methods to identify strategies of navigation that can cope with
potentially dangerous flow configurations and exploit favorable ones.

Jeudi 11 mai 2017 en Salle de Conférences du LJAD à 11 heures

Stijn de Baerdemacker (Université de Gent)

"Richardson-Gaudin integrability for strongly correlated quantum systems"
One of the most intriguing problems in quantum many-particle physics
is the emergence of strong quantum correlations and complexity.
Theoretical physics is tasked with explaining, understanding, and even
predicting these complex phenomena starting from fundamental premises.
Unfortunately, this is an unsurmountable task due to the size-explosion of the
Hilbert space, limiting exact computations to few-particle systems only.
Interestingly, for the class of integrable systems, an exact solution can be
obtained in the form of a Bethe Ansatz wavefunction, even when the
correlations are strong.  In this presentation, I will discuss and present the class
of Richardson-Gaudin integrable systems, and show how they can be used as an
optimal starting point for realistic quantum many-particle systems.

Vendredi 12 mai 2017 en Salle de Conférences du LJAD à 11 heures

Boris Nectoux (Cermics and INRIA)

"Metastability and the Eyring Kramer’s law"

In materials science, biology and chemistry, atomistic models are now used
in order to predict the macroscopic properties from a microscopic description of
matter. The basic ingredient is a potential energy function f : R d → R which
associates to a set of coordinates of particles the energy of the system. Using
this function f , two types of models are built:
1. continuous state space Markov models such as the Langevin dynamics or
the overdamped Langevin dynamics and,
2. discrete state space Markov models (jump Markov processes). One major issue for the sampling of the trajectories of the Langevin dynamics
is the possible metastable behaviour of this dynamics. Metastability refers to
the case when the typical time to observe transitions between some regions of
the configuration space is much longer than the typical timestep of vibrations
of the system. To deal with this issue, kinetic Monte Carlo methods are used
to design an underlying jump Markov process between metastable states. The
ingredient in kinetic Monte Carlo algorithms is the collection of transition rates
which are computed in practize with the help of the Eyring-Kramers law.
I will present recent results which aim at justifying rigorously the use of the
Eyring Kramers law in the small temperature regime. The proofs are based on
tools from semi-classical analysis.

Vendredi 19 mai 2017 en Salle de Conférences du LJAD de 11 à 15 heures

Suivi des thèses de l'équipe IMSC

 Nom Prénom Directeur Titre comité de suivi 11:00 Gomez Nava Luis Alberto F. Peruani Modelling and controlling collective behavior in animal groups F. Peruani, B. Marcos, P. Cassam-Chenaï 11:25 Perez Thomas P. Cassam-Chenaï Problèmes d’algèbre multilinéaire liés à l’intrication quantique des fonctions d’onde moléculaires F. Patras, P. Cassam-Chenaï 11:50 Métivier David J. Barré Interactions à longue portée et physique statistique hors équilibre J. Barré, B. Marcos, P. Cassam-Chenaï 12:15 Buffet déjeunatoire 14:15 Stephano Jonathan B. Mauroy Propriétés du transport de l'oxygène et du dioxyde de carbone chez les mammifères et sélection naturelle B. Mauroy, P. Biwole, P. Cassam-Chenaï

Mercredi 14 juin 2017 à 16h (salle de conférences du LJAD)

Roberto Benzi (Università di Roma "Tor Vergata") https://scholar.google.com/citations?user=QJeFmVEAAAAJ&hl=en

"Earthquake statistics and plastic events in soft-glassy materials"

We propose a new approach for generating synthetic earthquakes based on the physics of soft
glasses. The continuum approach produces yield-stress materials based on Lattice–Boltzmann
simulations. We show that if the material is stimulated below yield stress, plastic events occur,
which have strong similarities to seismic events. Based on a suitable definition of displacement
in the continuum, we show that the plastic events obey a Gutenberg–Richter law with exponents
similar to those for real earthquakes. We also find that the average acceleration, energy release,
stress drop and interoccurrence times scale with the same exponent. Furthermore, choosing
a suitable definition for aftershocks, we show that they follow Omori’s law. Finally, the far
field power spectra of elastic waves generated by these plastic events decay as ω −2 similar to
those observed for seismic waves. Our approach is fully self-consistent and all quantities can
be calculated at all scales without the need of ad hoc friction or statistical assumptions. We
therefore suggest that our approach may lead to new insights into the physics connecting the
micro- and macroscales of earthquakes.

Vendredi 23 juin 2017 à 11h (salle 2 du LJAD)

Mathias Legrand (McGill)

"Equation des ondes en une dimension et contraintes unilatérales"

Ce
travail concerne le calcul des modes de vibration non-linéaires d'une
structure mécanique simplifiée, une barre, encastrée à une extrémité et
sujette à des conditions de contact unilatéral, à l'autre.
Mathématiquement, il s'agit de chercher des familles continues de
trajectoires périodiques satisfaisant l'équation d'onde en une dimension
d'espace sur le domaine de la barre ainsi que la condition de
complémentarité traduisant le contact unilatéral. Ces familles forment
alors l'extension de la notion de "modes de vibration" bien connus dans
le cadre de la dynamique des structures linéaires. La méthode des
éléments finis introduit des difficultés numériques qui peuvent être
levées grâce à une variante d'un schéma de type "volumes finis". La
résolution numérique permet de dégager des solutions exactes. Le lien
entre solutions forcées périodiquement et solutions modales sera
illustré à l'aide de diagrammes "Energie-Fréquence".

Vendredi 30 juin 2017 à 11h (salle de conférences du LJAD)

Séminaire commun ATG / Interfaces

Elena Magliaro (Mines - Paritech)

"Overview of Loop Quantum Gravity"

La relativité générale et la mécanique quantique sont les deux théories
révolutionnaires qui ont changé la physique au siècle dernier. La
recherche d’une théorie qui fonde ceux deux théories dans un cadre
cohérent est la recherche d’une théorie de la gravité quantique, ou de
l’espace-temps quantique.

Aujourd’hui, un programme de recherche prometteur est la gravité quantique à boucles (Loop Quantum Gravity), développée désormais depuis 30 ans. Dans ce séminaire je présenterai les bases de cette théorie, dans sa version hamiltonienne et covariante (mousse de spin) en mentionnant les résultats les plus significatifs.