Description

• CHAVEZ Mario (CNRS-UMR 7225, Institute for Brain and Spinal Cord, Paris, http://cogimage.dsi.cnrs.fr/oldsite/equipes/adn/index.htm),
• DEMONGEOT Jacques (AGIM CNRS/UJF 3405, Faculté de Médecine, Univ. J. Fourier Grenoble I, France, http://membres-timc.imag.fr/Jacques.Demongeot/),
• FRANCOISE Jean-Pierre (Prof. Laboratoire J.-L. Lions, UMR 7598 CNRS, Paris-6, http://www.ann.jussieu.fr/~francoise/),
• JIRSA Viktor, (DR-CNRS, Institut de Neurosciences des Systèmes, Aix-Marseille, http://ins.medecine.univmed.fr/research-teams/team-member/v.jirsa/)
• KRUPA (Martin) Maciej (INRIA, Paris Roquencourt Centre, https://who.rocq.inria.fr/Maciej.Krupa/index.html)
• POPOVIC Nikola (School of Math. & Maxwell Institute of Math.Sciences Univ. Edinburgh, UK, http://www.maths.ed.ac.uk/~npopovic/)

You are cordially invited to participate in this one-day workshop, scheduled on 16th May, 2013, (09h45 - 17h15).
The workshop is FREE, (Entrée libre : Pas de frais d'inscription).

Location of Le Havre University:
University of Le Havre, UFR-ST, LMAH (Applied Math Lab.), 25 Rue Philippe Lebon, Le Havre, France.
The university is located 5 minutes walk from the train station (plan to go to ULH university or Kyriad hotel HERE. See train schedules at the bottom of this page).

Main topics of interest (Dynamical Systems, PDE, ODE, SDE, ...) :

• Neuroscience (multidisciplinary approach, mainly theoretical, but also experimental)
• Brain dynamics and mathematical modeling,
• Brain network dynamics and complex systems

Program:

• 09h00 : Welcome, Coffee, (posters)

• 10h10-10h55, FRANCOISE Jean-Pierre (Lab. J.-L. Lions, UMR 7598 CNRS, Paris-6)
  
  Title: Dip and Buffering in a fast-slow system associated to Brain Lactate Kinetics
  
  Abstract: This is a joint work with M. Lahutte-Auboin, R. Costalat and R. Guillevin. This work is devoted to a mathematical analysis of a fast-slow impulsive system with control inspired by a physiological model introduced by A. Aubert, R. Costalat, P. Magistretti and L. Pellerin(2005). The model is based on transport theory through membranes from capillary to an extracellular compartment with a control term which yields the exchange with an intracellular compartment. The methods are quite classical (existence of a slow manifold, averaging theory) although they are applied to a less classical situation (perturbation of an integrable impulsive dynamics). It is interesting to note that the mathematical interpretation fits quite well the experimental results obtained by Hu and Wilson, further confirmed by IRMf imaging techniques.
  

• 10h55-11h40, JIRSA Viktor (DR-CNRS, Institut de Neurosciences des Systèmes, Aix-Marseille)
  
  Title: Invariances and bifurcations of epileptic seizures
  
  Abstract: Despite many decades of research to identify mechanisms and treatments for specific epileptic pathologies, many patients continue to have unpredictable and uncontrolled seizures. The lack of a clear understanding of the nature of seizures contributes to the challenge of improving clinical care. Here, we analyzed seizure dynamics mathematically to identify characteristics that are conserved across many different syndromes, brain regions, and species. We characterized the onset, time course, and offset of focal seizures in humans, rodents and zebrafish. We found that focal seizures necessitate a DC baseline shift at onset and logarithmic scaling of interspike intervals at offset. This enabled us to build a general phenomenological model of seizure dynamics composed of five state variables. We then identified possible biophysical correlates of these state variables, and verified the theoretical predictions experimentally. Finally, we found how seizure onset can be reached via very different routes, which may explain why seizures are difficult to treat and predict. Our results demonstrate that seizures are a simple form of activity, generic to different neuronal networks across species. Seizure threshold is defined by the interaction and distance between the current brain state and a permittivity variable, both of which are dynamic processes. Seizure susceptibility is thus affected by various internal and external factors that are present under many different conditions, a concept that may become central to the design of future anti-seizure strategies.
  

• 11h40-12h25, CHAVEZ Mario (CNRS-UMR 7225, Institut du Cerveau et de la Moelle Epinière, Institute for Brain and Spinal Cord, Paris)
  
  Title: Simple introduction to complex brain networks
  
  Abstract: In the last years, network science has became a comprehensive framework to investigate, model and understand the structure and function of the complex interaction patterns observed in diverse biological, physical, social and technological systems. In neurosciences, experimental works have recently suggested that brain connectivity can be modeled as networks, i.e. mathematical objects whose nodes represent different brain regions and links stand for functional or anatomical connections between them. I'll present provide a an overview of how this general framework, known as complex network theory, and I'll introduce various metrics to characterize the wiring structure at both local (the neighborhood of a node) and global (full network) level. I'll show how network theory provides a robust tool allows anyone to classify in a simple and straight way the functional brain network and to compare connectivity patterns obtained from different pathological and cognitive states.

• 12h25 - 14h10 : lunch (at your expense, except for speakers, but the brewery's canteen is very good and cheap)

• 14h10-14h55, DEMONGEOT Jacques (AGIM CNRS/UJF 3405, Faculté de Médecine, Grenoble)
  
  Title: Robustness in Neural and Genetic Regulatory Networks: Mathematical Approach and Biological Applications
  
  Abstract: Numerous indices of complexity are used in biological networks like the number of their components, their connectivity, or the number of the strong connected components of their interaction graph. Concerning the stability and robustness of a biological network, they correspond to its ability to respectively recover the same asymptotic dynamics or keep invariant the number and nature of attractors, from dynamical or structural disturbances. The complexity will be quantified here by the evolutionary entropy, which describes the way the asymptotic presence distribution (or equilibrium invariant measure) of a dynamical system is spread over the state space and the stability (or robustness) will be characterized by the rate at which the system returns to its equilibrium distribution (or the distance at which the system remains from its anterior dynamics) after a dynamical (or structural) perturbation. Mathematical relationships between evolutionary entropy, stability rate and robustness index will be given in the general framework of Markov chains and in the specific case of Markov chains related to the genetic threshold Boolean random regulatory networks (getBren). It is proved that in certain circumstances of particular connectivity, the entropy of the invariant measure can be considered both as a complexity, stability and robustness index, by exploiting the links between these notions, fundamental to characterize the resistance of a biological system against endogenous or exogenous perturbations. Examples of biological networks (like m-switch or cell cycle control for different species) show the practical interest of this approach in biology and evolution.
  

• 14h55-15h40, POPOVIC Nikola (School of Math. & Maxwell Institute of Math.Sciences, Univ. Edinburgh, UK) ,
  
  Title: Three Time-Scales in an Extended Bonhoeffer-van der Pol Oscillator
  
  We consider a three-dimensional extension of the classical Bonhoeffer-van der Pol oscillator which exhibits dynamics on three different time-scales in certain parameter regimes. We characterise the resulting mixed-mode oscillations in the context of a canonical three time-scale system which was described in detail by Krupa et al. [SIAM J. Applied Dynamical Systems 7(2), 361-420, 2008]. Our asymptotics complements numerical results obtained by Sekikawa et al. in earlier work [Phys. Lett. A 374(36), 3745-3751, 2010]; in particular, we recover the period-doubling bifurcations of canards reported by them.
  

• 15h40-16h00 : Coffee break (posters)

• 16h00-16h45, KRUPA (Martin) Maciej (INRIA Paris Roquencourt Centre)
  
  Title: Rhythmic oscillations in clusters
  
  Abstract: Rhythmic oscillations in the gamma or beta frequency range are a prominent phenomenon related to a number of brain functions. Data show that individual pyramidal neurons can fire at very low frequency with the population showing clear gamma oscillations and synchrony. An idealized model of such weak gamma is when pyramidal neurons fire in clusters. In this talk we explain a mechanism of cluster formation in PING (pyramidal-interneuron gamma) models with strong inhibition and weaker excitation. We also discuss in detail how adaptation of pyramidal neurons and inhibition coming from interneurons influence cluster formation.
  

• 16h45 : Closing.

• Ambrosio Benjamin, LMAH
• Aziz-Alaoui M.A., LMAH
• Corson Nathalie, LMAH
• Krupa Martin, INRIA
• Lanza Valentina, LMAH
• Verdiere Nathalie, LMAH

Location of Le Havre University:
University of Le Havre, UFR-ST, LMAH (Applied Math Lab.), 25 Rue Philippe Lebon, Le Havre, France.
The university is located 5 minutes walk from the train station, See also HERE

Schedules of trains running between Paris and Le Havre (wednesday May 15 and thursday May 16, 2013, about 2 hours trip):
PARIS SAINT-LAZARE ---> LE HAVRE, departure from Paris at : 06h53 ; 07h53 ; 08h53 ; 10h50 ; 12h50 ; 14h50 ; 15h50 ; 16h50 ; 17h25 ; 17h50 ; 18h50 ; 19h50 ; 20h50.
LE HAVRE ---> PARIS SAINT-LAZARE, departure from LeHavre at : 05h29 ; 06h29 ; 07h02 ; 08h01 ; 09h03 ; 10h02 ; 12h01 ; 13h02 ; 14h00 ; 16h02 ; 17h00 ; 18h02 ; 19h11 ; 20h02.

Accomodation: If you wish, we can book a hotel room for you, contact us by email : aziz.alaoui@univ-lehavre.fr or claire.roussin@univ-lehavre.fr

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