Semester on

OCTOBER - NOVEMBER - DECEMBER 2011

CIRM - Marseille

		Neuroscience and its applications are greatly developing world-wide and Europe is one of the important contributors to the advancement of this discipline. Because of the variety of topics that it has to address, it is characterized by a very broad inter-disciplinarity and requires the cooperation of actors in several fields of knowledge. In this context, the need for developing new theoretical, mathematical, and computational tools can be clearly identified and must be addressed. The purpose of this semester is to present some of the relevant modern mathematical tools through short courses and to explore several facets of the current research through workshops.
Program committee:   P. Bressloff (University of Utah), N. Brunel (Université Paris 5), P. Chossat (CNRS - INRIA), O. Faugeras (ENS - INRIA), W. Gerstner (EPFL), V. Jirsa (CNRS - Université de la Méditerranée).

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WORKSHOPS

03-07/10/2011 - Organizers : N. Brunel, O. Faugeras (Schedule - presentations - Portfolio pdf)
Mean-field methods and multiscale analysis of neuronal populations

24-28/10/2011 - Organizers : P. Bressloff, S. Coombes
Spatio-temporal evolution equations and neural fields

07-11/11/2011 - Organizers : N. Brunel, W. Gerstner, J. Sjostrom, H. Markram
Learning and Plasticity

5-9/12/2011- Organizers : V. Jirsa, G. Deco
Mathematical Models of Cognitive Architectures

COURSES

10/10-12/10 - Denis Talay (INRIA), Samuel Herrmann (Ecole des Mines - INRIA), Etienne Tanré (INRIA)
Stochastic models and simulations in neuroscience

Lecture 1:	Diffusion processes hitting times. Application to spike trains modelling.
Lecture 2:	Stochatic differential equations with non-Lipschitz coefficients: analysis and simulation, applications to models in Neuroscience.
Lecture 3:	Links between Partial Differential Equations (PDEs) and Stochatic Differential Equations (SDEs).
Lecture 4:	Analysis of stochastic numerical methods for SDEs and PDEs. Applications in Neuroscience.
Lecture 5:	Probabilistic numerical methods for diffusion processes hitting times and spike trains.

13/10-14/10 & 17/10-19/10 - Fred Wolf (MPI Göttingen)
Self-organisation in the development of visual cortical circuits

Lecture 1:	Overview
	Singularities in the Brain: Understanding Network Self-Organization from Homotopy, Symmetries, and Fields.
Lecture 2:	Pattern selection of aperiodic solutions
	Visual Cortical Architecture: A Living Pomeau-Newel-Turbulent-Cristal.
Lecture 3:	Pattern selection of aperiodic solutions:
	Quantitative Universality in Brain Evolution.
Lecture 4:	Structure and Function:
	Euclidean Symmetry Correctly Predicts the Strategic Positioning of Orientation Columns.
Lecture 5:	Guiding in vivo experiments by theory
	Moving the Wheels: Testing Massive Multi Stability of Circuit Self-Organization.

17/10-21/10 - Nils Berglund (Université d’Orléans)
Bifurcations in stochastic systems with multiple timescales

Lecture 1:	Deterministic fast-slow systems
	Examples from neuroscience - conduction-based models; slowmanifolds,
	Fenichel theory; dynamic bifurcations: dynamic saddle- node, pitchfork and Hopf bifurcation; example: canards in the Fitzhugh-Nagumo equations
Lecture 2:	One-dimensional slowly time-dependent stochasticsystems
	Dynamics near stable equilibrium branches; dynamic saddle-node bifurcation; dynamic pitchfork bifurcation; example: stochastic resonance
Lecture 3:	Multidimensional fast-slow systems with noise
	Dynamics near stable slow manifolds; dynamic Hopf bifurcation; example: elliptic bursting
Lecture 4:	Excitable systems
	Excitability of type I: SNIC bifurcation, Morris-Lecar model, interspike time statistics; excitability of type II: singular Hopf bifurcation, Fitzhugh-Nagumo model, interspike time statistics
Lecture 5:	Mixed-mode oscillations
	Deterministic models: folded node singularity, canards; stochastic case: effect of noise on mixed-mode patterns; Hodgkin-Huxley model

02/11-04/11 - Stephen Coombes (Université de Nottingham)
Neural field modelling

Lecture 1:	Tissue level firing rate models with axo-dendritic connections I
	Turing instability analysis
Lecture 2:	Tissue level firing rate models with axo-dendritic connections II
	Amplitude equations
	Brain wave equations
Lecture 3:	Travelling waves and localised states
	Construction and stability (Evans functions)
	Interface dynamics
Lecture 4:	Waves in random neural media
Lecture 5:	Tissue level spiking models: the dynamics of the continuum Lighthouse model

14/11-18/11 - Pascal Chossat (CNRS - INRIA)
Dynamical systems in the presence of symmetry in the biological context

Lecture 1:	Introduction to the general concepts of symmetry and equivariant bifurcations
Lecture 2:	Symmetry breaking bifurcations, a non trivial example: Turing patterns
Lecture 3:	Equivariant Hopf bifurcation, example: oscillatory patterns in coupled oscillators
Lecture 4:	Symmetry-induced intermittency: the concept of heteroclinic cycles, example: multi-species competition
Lecture 5:	Symmetry-induced unsteady patterns in spatially extended system, example: spiral waves.

28/11-02/12 - Jean Petitot (Ecole Polytechnique - CREA)
Neurogeometry of functional architectures for visual perception

Lecture 1:	Functional architecture of V1
Lecture 2:	Implementing the contact structure of the 1-jet space of planar curves
Lecture 3:	The E(2) group of planar isometries, sub-Riemannian geometry and illusory contours
Lecture 4:	Non-commutative harmonic analysis
Lecture 5:	Open problems in neurogeometry