Archives - Neuromathématiques
Retrouvez ici les archives du séminaire "Neuromathématiques" :
2021-2022
2020-2021
2017-2018
2016-2017
2015-2016
2014-2015
Année 2021-2022
Organisateurs : Giovanna Citti (University of Bologna), Jean-Pierre Nadal (CAMS – EHESS/CNRS & LPENS – ENS/CNRS/SU/Univ. de Paris, PSL), Jean Petitot (CAMS – EHESS), Jérôme Ribot (Collège de France), Alessandro Sarti (CAMS – EHESS/CNRS)
1er mardi du mois de 14h30 à 16h30 du 7 décembre 2021 au 3 mai 2022, en visio conférence.
Programme – année 2021-2022
7 décembre 2021
Davide Barbieri
Universidad Autonoma de Madrid
« Are cortical feature maps complete? »
Abstract: One of the most studied neural structures in brain’s visual cortex is area V1, where neurons perform a wavelet-like analysis that is generally considered to be associated with the group of rotations and translations of the plane. It is indeed possible to model part of the (classical) behavior of V1 cells in terms of a projection of the image onto one, or more, orbits of that group, and consequently to associate to each neuron in V1 a parameter of the group. However, as a consequence of the physical displacement of neurons onto the characteristic geometric structures of cortical feature maps, this modelling group is not fully represented in V1. A natural question arising from this model is whether the missing part of the group, and of the corresponding wavelet coefficients, has perceptual consequences, or if, on the contrary, it is possible to recover or estimate in some stable way the missing information. The purpose of this talk is to propose an iterative mechanism able to reconstruct the exact image, or equivalently the full group wavelet transform, starting from the knowledge of only the coefficients stored on pinwheel-shaped subsets of the group. The iteration is based on the group reproducing kernel, and on the projection onto the sampling surface. We will show an elementary proof of convergence in the finite setting, and discuss numerical simulations on natural images.
1 février 2022
Romain Brette
1er mars 2022
Remco Duits
5 avril 2022
Vasiliki Liontou.
Année 2020-2021
Organisateurs : Giovanna Citti (University of Bologna), Jean-Pierre Nadal (CAMS – EHESS/CNRS & LPENS – ENS/CNRS/SU/Univ. de Paris, PSL), Jean Petitot (CAMS – EHESS), Jérôme Ribot (Collège de France), Alessandro Sarti (CAMS – EHESS/CNRS)
1er mardi du mois de 14h à 16h (Collège de France, 11 Place Marcelin Berthelot 75005 Paris), du 1er décembre 2020 au 1er juin 2021 .
Programme
Mardi 1er décembre 2020
Jonathan Touboul (Brandeis University, Boston) and Jérôme Ribot (Collège de France)
Mardi 2 février 2020
Marcelo Bertalmio (Universitat Pompeu Fabra)
Mardi 2 mars, 14h30-16h30
en visio-conférence exclusivement
Inscription obligatoire sur https://listsem.ehess.fr/ (pour sélectionner le bon séminaire, saisir UE 225 – avec un espace entre UE et 225).
Emre Baspinar
Inria Sophia Antipolis Méditerranée, MathNeuro Team
« Biologically-inspired modeling for Poggendorff type illusions and frequency-phase sensitive cortical behavior applied to image enhancement »
Abstract: In this talk, we will see a geometric approach for cortical modeling which is in the same alignment following [1], [2] and [3]. In the first part, we will see a new biologically-inspired sub-Riemannian model employing Wilson-Cowan type mean field equations described in the model geometry proposed in [3], and in a similar fashion as in [4]. The model is applied to reproducing orientation-dependent Poggendorff-type illusions. The novelty of the model is that it embeds sub-Riemannian diffusion into the neuronal interaction term appearing in the mean field equations. This tunes the neuronal interactions in agreement with the functional architecture of the visual cortex. In the second part, we start with the sub-Riemannian model geometry proposed in [3], which is only orientation sensitive. We extend this model and provide a novel sub-Riemannian model of V1 which models orientation-frequency selective, phase shifted cortical cell behavior and the associated neural connectivity [5]. We develop an image enhancement algorithm using a multi-frequency Laplace-Beltrami procedure in this extended sub-Riemannian model framework. References
[1] W. C. Hoffman, “The visual cortex is a contact bundle,”Applied Mathemat-ics and Computation, vol. 32, no. 2-3, pp. 137–167, 1989.
[2] J. Petitot and Y. Tondut, “Vers une neurogeometrie. Fibrations corticales,structures de contact et contours subjectifs modaux,”Math ́ematiques et Sciences Humaines, vol. 145, pp. 5–101, 1999.
[3] G. Citti and A. Sarti, “A cortical based model of perceptual completion in the roto-translation space,”Journal of Mathematical Imaging and Vision,vol. 24, no. 3, pp. 307–326, 2006.
[4] M. Bertalmio, L. Calatroni, V. Franceschi, B. Franceschiello, and D. Prandi, “Cortical-inspired Wilson–Cowan type equations for orientation-dependent contrast perception modelling,”Journal of Mathematical Imaging and Vision, pp. 1–19, 2020.
[5] E.Baspinar, G.Citti, A.Sarti, A sub-Riemannian model of the visual cortex with frequency and phase, Journal of mathematical neuroscience, 2020.
Mardi 6 avril
Ugo Boscain
Année 2017-2018
Organisateurs : Giovanna Citti (University of Bologna), Jean-Pierre Nadal (CAMS – EHESS/CNRS & LPENS – ENS/CNRS/SU/Univ. de Paris, PSL), Jean Petitot (CAMS – EHESS), Alessandro Sarti (CAMS – EHESS/CNRS)
Le séminaire est hébergé par le Collège de France, 11, Place Marcelin-Berthelot, 75005, Paris
1er mardi du mois de 15h à 17h (Collège de France, 11 Place Marcelin Berthelot 75005 Paris), du 3 décembre 2019 au 5 mai 2020.
Le séminaire est hébergé par le Collège de France, 11, Place Marcelin-Berthelot, 75005, Paris
Mardi 9 janvier 2018, 14h30-16h30
salle D2.2, Collège de France, 11, Place Marcelin-Berthelot, 75005, Paris
Séance introductive du séminaire animée par Giovanna Citti (Université de Bologna) et Alessandro Sarti (CAMS-CNRS/EHESS) à partir de leurs objets d’étude au sujet de la neurogéometrie du cortex visuel.
Giovanna Citti et Alessandro Sarti: Séance introductive du séminaire
Mardi 6 février 2018
Daniel Bennequin
« Système visuo-vestibulaire, groupe de Galilée et champs récepteurs unitaires. Espace de l’action. »
Mardi 6 mars 2018
Jean Petitot
« Neurogéometrie des orientations et des directions dans le cortex visuel primaire »
Mardi 3 avril 2018
Agnes Desolneux, TBA
et
Kevin Berlemont, « Modélisation de la prise de décision perceptuelle à l’aide de réseaux attracteurs neuronaux
Mardi 5 juin 2018
Alexandre Afgoustidis
« Résultats d’analyse harmonique non-commutative inspiré par l’invariance euclidienne dans V1 »
Année 2016-2017
Mardi 2 mai 2017, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Peter Neri
Laboratoire systèmes perceptifs
Ecole Normale Supérieure, Paris
The basic facts of human vision are inconsistent with theoretically-driven accounts
In this talk I will play devil’s advocate in favour of data-driven characterization of sensory processing: I will present a number of instances where empirical measurements of human visual processing are inconsistent with, sometimes opposite to, what would be expected on the basis of purely theoretical considerations along the lines of ideal signal detection theory, Bayesian inference, redundancy reduction and related concepts. In the process of doing so, I will survey published research only superficially, and focus instead on unpublished data relating to elementary operations of human visual analysis. Overall, the empirical results urge caution when attempting to interpret human vision from the standpoint of theoretical constructs. Direct measurements of this phenomenon indicate that the actual constraints derive from basic architectural features of the system and their inherent limitations. More generally, the empirical results provide a compelling demonstration of how far we still are from securing an adequate computational account of even the most basic operations carried out by human vision.
Mardi 28 mars 2017, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Boris Gutkin
Ecole Normale Supérieure, Paris
Dynamics of dopamine neuron firing in normal and drug-modulated conditions
Dopaminergic neurons in the ventral tegmental area play a key role in signalling motivational information. Modulation of this signalling by drugs is also key to the development of addiction. These neurons have several firing modes ranging from periodic low frequency activity to higher frequency bursts. In vitro, intrinsically generated bursts are seen, while in vivo irregular high frequency alternates with periodic activity. Addictive drugs alter this firing patter towards high frequency bursting. In this talk i will discuss analysis of the mechanisms that lead to the various firing modes of the dopamine neurons and how addictive drugs alter them. Notably, I will present recent results on modelling effects of alcohol on dopaminergic dynamics and dopamine outflow. Here i will show how changes in the inhibitory input synchrony to the dopamine neurons may promote high frequency firing. Time permitting, I will show how inout structure to the dopamine neurons may control their excitabilty type and what that may imply for their ability to encode reward related signals.
Mardi 7 mars 2017, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Catherine Tallon-Baudry
Ecole Normale Supérieure, Paris
Visceral inputs, brain dynamics & subjectivity
Brain dynamics are usually considered to be constrained by brain-related parameters, such as anatomical connectivity and conduction delays, or by external factors, such as the stimulus to be processed. This classical point of view ignores the fact that the brain constantly monitors bodily inputs, in particular from life-supporting organs such as the heart or the stomach. I will present recent evidence that visceral inputs constrain brain dynamics, as measured with resting-state magneto-encephalography, functional MRI, or single-unit recordings, in humans. The neural monitoring of visceral inputs may play a fundamental role by generating an egocentric reference frame, from which first-person perspective, or subjectivity, can develop. I will present data showing that neural responses to heartbeats in the default-network play a functional role as they encode self-relevance in sontaneous thoughts but also predict subjective visual experience. Visceral-brain interactions might thus represent a core mechanism constraining both brain dynamics and « cold » cognitive processes.
Mardi 7 février 2017, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Romain Veltz
INRIA, Sophia Antipolis
Hopf bifurcation in the mean field of a stochastic spiking neural networks
In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearised equation. The second stems from the simulation of the full mean field. The third and last evidence comes from the simulation of the network for a large number of neurons. In passing, we provide a « recipe » to find such bifurcation. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronisation in excitatory globally pulse-coupled networks.
Mardi 6 décembre 2016, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
SEANCE ANNULEE : L’orateur Boris Gutkin ayant un ennui de santé, la séance de ce jour du séminaire du CAMS « Neuromathématiques », est annulée. En vous priant, de sa part et de la nôtre, de nous excuser pour cette annulation de dernière minute.
Boris Gutkin
Ecole Normale Supérieure, Paris
Dynamics of dopamine neuron firing in normal and drug-modulated conditions
Dopaminergic neurons in the ventral tegmental area play a key role in signalling motivational information. Modulation of this signalling by drugs is also key to the development of addiction. These neurons have several firing modes ranging from periodic low frequency activity to higher frequency bursts. In vitro, intrinsically generated bursts are seen, while in vivo irregular high frequency alternates with periodic activity. Addictive drugs alter this firing patter towards high frequency bursting. In this talk i will discuss analysis of the mechanisms that lead to the various firing modes of the dopamine neurons and how addictive drugs alter them. Notably, I will present recent results on modelling effects of alcohol on dopaminergic dynamics and dopamine outflow. Here i will show how changes in the inhibitory input synchrony to the dopamine neurons may promote high frequency firing. Time permitting, I will show how inout structure to the dopamine neurons may control their excitability type and what that may imply for their ability to encode reward related signals.
Vous pouvez retrouver l’affiche de cette séance ici
Mardi 8 novembre 2016, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Romain Brette
Institut de la Vision, Paris
Neuronal geometry and excitability
Most theoretical studies on neural excitability have dealt with either isopotential membranes, for example the space-clamped squid axon, or homogeneous axons. However, in most vertebrate neurons, action potentials are initiated in a small region of the axon, the axonal initial segment (AIS), packed with sodium channels and placed very close to the soma. Thus there is a spatial discontinuity in channel properties and geometry (large soma, thin axon). In addition, both the length and position of the AIS can vary with activity. In this presentation, I will show how neuron and AIS geometry impact the initiation of action potentials and their backpropagation to the soma. Géométrie neuronale et excitabilité
La plupart des études théoriques sur l’excitabilité neuronale ont porté sur des membranes isopotentielles, comme par example l’axone géant du calamar dans lequel une tige métallique est insérée, ou sur des axones homogènes. Cependant, dans la plupart des neurones des vertébrés, les potentiels d’action sont initiés dans une petite région de l’axone appelée le segment initial axonal (SIA), qui contient une forte densité de canaux sodiques et est placé très proche du soma. Ainsi il y a une discontinuité spatiale dans les propriétés des canaux et la géométrie (grand soma, petit axone). De plus, la position et la longueur du SIA varient avec l’activité. Dans cette présentation, je montrerai l’effet de la géométrie du neurone et du SIA sur l’initiation des potentiels d’action et leur rétropropagation au soma.
Année 2015-2016
Mardi 3 mai 2016, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Florent Meyniel
CEA, Neurospin Center, France
A normative account of the sense of confidence during probabilistic learning
The sense of confidence has been studied by psychologists over the past century. It has been under scrutiny only recently in the field of neuroscience. I will briefly review the topic and present the idea that the viewpoints of psychology and neuroscience on confidence can be unified by a definition of confidence as Bayesian probability. After this general introduction, I will present a focused investigation of the sense of confidence in a learning context. Learning in an environment that is both stochastic and changing consists of estimating a model from a limited amount of noisy data. Learning is therefore inherently uncertain, and at least in humans, the learning process is accompanied by a “feeling of knowing” or confidence in what has been learned. The talk will address the characteristics, the origin and the functional role of subjective confidence during learning using behavioral and functional MRI data in humans.
To this end, we developed a probabilistic learning task in which human subjects estimated the transition probabilities between two stimuli in a sequence of observations. The true probabilities changed unexpectedly over time and from time to time, subjects reported their probability estimates as well as their confidence in those estimates. We computed the optimal solution for this learning problem and we used it to analyze subjects’ data from a normative viewpoint. Behavioral data showed that humans not only infer a model of their environment, but they also accurately track the likelihood that their inferences are correct. Several characteristics of these confidence reports support that learning and estimating confidence in what has been learned may arise from the same, close-to-optimal probabilistic inference. Functional MRI data showed that the brain may resort to a hierarchical inference to solve this learning problem, and that confidence may be used in the learning algorithm to weight optimally the previously acquired knowledge against and the new incoming evidence.
Vous pouvez retrouver l’affiche de ce séminaire ici
Mardi 5 avril 2016, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Bertrand Thirion
INRIA Saclay-Ile-de-France
Seeing it all: Convolutional network layers map the function of the human visual system
How to demonstrate and analyze the complexity of visual experiences in a brain mapping framework? The key to this seems to reside in using natural stimulation while increasing the capacity of the analysis system. In this presentation we discuss a predictive model of brain activity following visual stimulation using the layers of a contest-winning object recognition convolutional network. We find that it explains both high-level and low-level visual areas well and that it can serve as a reliable predictor of brain activity for previously unseen stimuli. We use it to synthesize classical contrast-driven fMRI experiments and analyze the synthetic activity in a conventional way, revealing that the synthesis model captures the known details of the visual system. It is possible to recover classical contrast maps from this model on unseen images. To expose the brain mapping implicit in the model, we assess how well each contributing layer of the convolutional net fits each voxel. Visualizing these predictive scores reveals a profound correspondence between convolutional net layer depth and known hierarchy of visual cortical regions.
Vous pouvez retrouver l’affiche de ce séminaire ici
Mardi 1er mars 2016, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Laurent Perrinet
Institut de Neuroscience de la Timone
Towards understanding the inferential processes underlying the representation of trajectories in the primary visual cortex
Neural computations in the early visual system are optimized by evolution to efficiently process the trajectory of visual objects in natural scenes and in particular to modulate local mechanisms by the surrounding visual context. In the primary visual cortex, these computations are often characterized by the so-called association field, that is, by the set of rules that combine neighboring visual contour elements to refine more global visual processes. I will first show a simple method to compute the statistics of neighboring contour elements in static images. Surprisingly, we will show that this statistics are sufficient to characterize the category an image belongs to (for instance if it contains an animal), a function usually attributed to higher visual areas. Extending this endeavor to the temporal trajectory of a moving oriented bar, I will present results of a maximum likelihood decoding strategy applied to extracellular activity recorded in the primary visual cortex of behaving macaque monkeys (V1). The orientation and direction decoded in neural activity exhibits the signature of an anticipatory inferential processes optimizing the representation of the bar’s trajectory in V1. I will discuss these results in light of a probabilistic model of V1 integrating an explicit knowledge of sensory delays and minimizing its free-energy. This will allow to discuss the implications of these neuronal solutions to the representation of time in the brain, which is essential for the proper fusion of information in the central nervous system.
Vous pouvez retrouver l’affiche de ce séminaire ici
Mardi 2 février 2016, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris.
Jonathan Touboul
Collège de France & INRIA
The pinwheel-dipole structure of orientation and spatial frequency, and their common organizing principles
In the early visual cortex of higher mammals, information is processed within functional maps whose layout is thought to underlie visual perception. Here, I will present a few theoretical thoughts together with experimental data on the possible principles at the basis of their architecture, as well as their role in perception. Using new optical imaging data with high resolution, I will show that spatial frequency preference representation exhibits singularities, precisely co-located with pinwheels, and around which the spatial frequency map organizes as an electric dipole potential. This is particularly interesting theoretically: I will demonstrate that both pinwheel and dipoles are the unique topologies ensuring exhaustive representation of both attributes while being optimally parsimonious. Eventually, I will raise the question of the functional advantages and drawbacks of the topology. I will show that the pinwheel dipole topology leaves room for a balanced detection of both attributions. But simulations predict that selectivity shall be sharper near singularity to ensure balanced detection, which I will confirm on biological data. This is a joint work with J. Ribot, A. Romagnoni, C. Milleret and D. Bennequin.
Vous pouvez retrouver l’affiche de ce séminaire ici
Mardi 1er décembre 2015, 14h30-16h30
salle de conférence de l’European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris.
Sophie Deneve
Laboratoire de Neurosciences Cognitives, ENS
Efficiency turns the table on neural encoding, decoding and noise
Sensory neurons are usually described with an encoding model, e.g. a function that predicts their response from the sensory stimulus, e.g. with receptive field (RF) or a tuning curve. However, central to theories of sensory processing is the notion of « efficient coding ». We argue here that efficient coding implies a completely different neural coding strategy. Instead of a fixed encoding model, neural populations would be described by a fixed decoding model (i.e. a model reconstructing the stimulus from the neural responses). Because the population solves a global optimization problem, individual neurons are variable, but not noisy, and have no truly invariant tuning curve or receptive field. We review recent experimental evidence and implications for neural noise correlations, robustness and adaptation.
Vous pouvez retrouver l’affiche de ce séminaire ici
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
Année 2014-2015
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
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
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
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
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.