Neuromathématiques : année 2014/2015
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Mardi 3 novembre 2015, 15h00-16h30, salle de conférence de l’European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris.
Daniel Bennequin
Institut Mathématique de Jussieu & Université Paris 7
Cohomology for adaptation
Adaptation is a fundamental property of life. We will give examples of rapid adaptation in the sensory system of mammals (visual, vestibular, auditory, …). Then we will show how in these examples a kind of ternary structure appears, involving transfers, parameters and modular strategies. The notion of co-homology in mathematics will be presented, with examples related to geometry, probability and sensory systems. Then we will show how this notion should enlight the functioning of ternary structures for adaptation.The particular case of color space, color adaptation and color constancy will be discussed in this context.
Vous pouvez retrouver l’affiche de ce séminaire ici
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Mardi 16 juin 2015, 14h30-16h30, salle de conférence de l’European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris.
Gabriel Peyré
CNRS & CEREMADE, Université Paris-Dauphine
Dynamical texture synthesis to probe visual perception
In this talk, I will review statistical models of dynamical textures, targeting applications to computer graphics synthesis and stimulations to probe the visual cortex. I will focus in particular my attention to Gaussian texture models. Despite their simplicity, they are surprisingly effective at capturing micro-textural patterns and simple dynamics. These models can be parameterized as linear stochastic partial differential equations, which makes them easy to learn from exemplar videos and fast to synthesize on the fly. This also opens the door to both Fourier analysis (power-spectrum parameterization) and an interpretation as an infinite superposition of translated/rotated/scaled elementary « textons ». Both interpretations are crucial to allow formalizing psychophysical studies in term of an optimal Bayesian observer. I will show how this explains some psychophysical findings about the influence of texture statistics to bias human speed discrimination (joint work with J. Vacher, L. Perrinet and A. Meso).
Vous pouvez retrouver l’affiche de ce séminaire ici
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Mardi 5 mai 2015, 14h30-16h30, salle de conférence de l’European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris.
Alexandre Afgoustidis
Institut Mathématique de Jussieu & Université Paris 7
Orientation maps in the primary visual cortex, gaussian random fields and group representations.
I will first describe some experimental facts on the geometry of orientation maps in the primary visual cortex (area V1) of mammals; this will include the intriguing measurement of a pinwheel (topological singularity) density close to π in very distinct species. The aim of my talk is to identify a few principles that seem necessary for reconstructing this geometry in abstract fashion, and – as a test for their relevance – to use them to introduce V1-like geometries on non-Eucldean spaces. I will focus on theoretical maps which are sampled from Gaussian Random Fields : here the geometrical principles have a simple probabilistic expression, and a natural interpretation in terms of the unitary representations of the Euclidean group of rigid plane motions. Using representations of other groups to shift to non Euclidean geometries might help us understand the conceptual significance of the experimental observations on pinwheel densities.
Vous pouvez retrouver l’affiche de ce séminaire ici
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Mardi 31 mars 2015, 14h30-16h30, salle de conférence de l’European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris.
Khashayar Pakdaman
Institut Jacques Monod, Groupe biologie computationnelle et biomathématiques
On some aspects of synchronization and spontaneous activity in neuronal
Spontaneous activity is ubiquitous in neuronal assemblies and takes on a variety of forms. Motivated by experimental studies on such activity in brain stem slices, this presentation will review modelling aspects and their theoretical analysis with specific emphasis on the emergence of synchrony.
Vous pouvez retrouver l’affiche de ce séminaire ici
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Mardi 3 février 2015, 14h30-16h30, salle de conférence de l’European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris.
Gregory Faye
ERC ReaDi, CAMS – EHESS
Traveling pulses in neural field equations
In this seminar, I will present some recent work on traveling pulses in neural field equations. More precisely, we explore how local negative feedbacks (linear adaptation or synaptic depression) impact the generation of traveling pulses. We will use techniques ranging from singular perturbation theory, Fredholm operators and Evans functions to study the existence and stability of such traveling waves.
Vous pouvez retrouver l’affiche de ce séminaire ici
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Mardi 2 décembre 2014, 14h30-16h30, salle de conférence de l’European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris.
Davide Barbieri
Mathematics Department, Universidad Autonoma de Madrid
Simple cells receptive fields and orientation preference maps : A Lie group approach for the analysis of fundamental morphologies of V1
Work in collaboration with G. Citti, G. Sanguinetti and A. Sarti
Simple cells classical receptive fields can be accurately modeled by Gaussian Gabor functions. However, this a-priori 6 parameters family (including positions, frequencies and scales) is represented on an essentially two dimensional cortical layer. This implies that only a subset of the parameter space is actually available to the linear filtering of visual stimuli performed by V1.
We will first discuss a fundamental property of the family of implemented parameters, namely the distribution of the shape index, which measures the number of on and off regions of receptive fields by relating frequencies to scales. We will show that it can be effectively quantified in terms of the uncertainty principle associated to the complementary symmetries of the parameter space, that are given by the group of translations and rotations of the Euclidean plane SE(2). The main argument is the effort to keep the highest possible resolution in the detection of position and orientation allowed by the dimensional constraint.
Then we will enter a more detailed study of the SE(2) group, and show that its irreducible representations can be used to provide an accurate model for orientation preference maps. In particular, we will see that the associated continuous wavelet transform allows to effectively reproduce the maps of activation of V1 in response to gratings, whenever the mother wavelet is a fundamental minumum of the uncertainty principle and the analyzed signal is white noise. In this case we can also prove that the wavelet transform is injective, which implies uniqueness of the white noise source, despite not being square integrable. Moreover, its complex regularity inherited by the uncertainty principle allows to obtain it as the two dimensional Bargmann transform of a purely directional signal, hence characterizing all possible configurations of such activated regions.
