2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Collection 2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Organizer(s) Ditlevsen, Susanne ; Faugeras, Olivier ; Galves, Antonio ; Reynaud-Bouret, Patricia ; Salort, Delphine ; Shinomoto, Shigeru

Date(s) 31/01/2022 - 04/02/2022

linked URL https://indico.math.cnrs.fr/event/6532/

00:00:00 / 00:00:00

17 30

Some recent results on a mean field of a network of 2d spiking neurons

By Romain Veltz

In this talk, I will present some results regarding the dynamics of a network of stochastic spiking neurons akin to the "generalized linear model" connected with a mean-field coupling. This network is an elaboration of the one introduced in [De Masi et al. 2014] by generalizing the dynamics of the individual neurons. This allows to capture most of the known intrinsic neuronal spiking, like bursting for example, and thus to study the effect of the intrinsic neuron dynamics on the macroscopic one.

I will study the property of the mean-field limit. In effect, it is a nonlinear Piecewise Deterministic Markov process with explosive flow and unbounded total rate function. I will first present some theoretical results regarding the solution of the linearized SDE which is shown to be regular and has mean firing rate characterized by an integral equation. I will then show that the solution is ergodic and give many quantitative properties of its invariant distribution. I will then extend some of these results (well posedness, stationary distributions) to the nonlinear case.

Information about the video

Date of recording 02/02/2022
Date of publication 02/02/2022
Institution IHP
Language English
Audience Researchers
Director(s) Mandarine Audiovisuel
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2022.T1.WS2.017
Cite this video Veltz, Romain (02/02/2022). Some recent results on a mean field of a network of 2d spiking neurons. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.017
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.017

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

All the collection videos

58:30

published on January 31, 2022

Retrieving the structure of probabilistic sequences of auditory stimuli from electroencephalographic (EEG) signals

By Claudia Vargas , Guilherme Ost

34:36

published on January 31, 2022

Inferring monosynaptic connections from a cross-correlogram of neuronal spike trains

By Shigeru Shinomoto

38:18

published on January 31, 2022

Marked Point Process Modeling and Estimation Problems in Neural Data Analysis

By Uri Eden

47:44

published on January 31, 2022

Neural networks in the replica-mean field limits

By Thibault Taillefumier

25:17

published on January 31, 2022

Statistical Models of Interaction Across Brain Regions from Multi-Electrode Recordings

By Rob Kass

23:58

published on February 1, 2022

Self-organized criticality hierarchical modular networks of Galves-Löcherbach neurons

By Flavio Rusch

18:59

published on February 1, 2022

A new method to simulate Hawkes processes

By Tien Cuong Phi

24:46

published on February 1, 2022

Maximally predictive ensemble dynamics from data

By Antonio Carlos Costa

32:25

published on February 1, 2022

Multi-scale modeling of vesicular release at neuronal synapses

By Claire Guerrier

53:45

published on February 1, 2022

Graph rules and topological insights for inhibitory network dynamics

By Carina Curto

01:06:27

published on February 1, 2022

Topological insights on neuronal morphologies

By Lida Kanari , Kathryn Hess

22:56

published on February 2, 2022

Neural fields with rebound currents: novel routes to patterning

By Sunil Modhara

24:30

published on February 2, 2022

Beyond Blow-Up for Nonlinear Noisy Leaky Integrate and Fire neuronal models: numerical approach to the "plateau" state

By Alejandro Ramos Lora

01:01:45

published on February 2, 2022

System of interacting neurons with short term synaptic facilitation

By Eva Löcherbach , Christophe Pouzat

38:38

published on February 2, 2022

Spontaneous oscillations in a pure excitatory mean field networks of neurons

By Etienne Tanré

39:59

published on February 2, 2022

Fluctuation limits for mean-field interacting nonlinear Hawkes processes

By Wilhelm Stannat

28:14

published on February 2, 2022

Some recent results on a mean field of a network of 2d spiking neurons

By Romain Veltz

20:52

published on February 3, 2022

Time averages of a metastable system of spiking neurons

By Morgan André

21:23

published on February 3, 2022

Metastable spiking networks in the replica-mean-field limit

By Luyan Yu

25:10

published on February 3, 2022

Propagation of Chaos and Poisson Hypothesis for Replica Mean-Field Models

By Michel Davydov

01:03:32

published on February 3, 2022

Understanding Synaptic Mechanisms: Why a Multi-disciplinary Approach is Important

By Afia Ali , Mathieu Desroches

44:59

published on February 3, 2022

Projection methods for spatially-extended neurobiological models

By Daniele Avitabile

41:44

published on February 3, 2022

Front initiation in continuous neural fields

By Grégory Faye

41:50

published on February 3, 2022

Noise-driven bifurcations in a neural field system modelling networks of grid cells

By José A. Carillo

38:03

published on February 3, 2022

The non linear dynamics of retinal waves

By Bruno Cessac

24:34

published on February 4, 2022

Towards understanding the time periodic solutions in a kinetic model for neuron networks

By Zhennan Zhou

24:01

published on February 4, 2022

Theoretical study of the emergence of periodic solutions for the inhibitory NNLIF neuron model with synaptic delay

By Kota Ikeda

25:03

published on February 4, 2022

A multiple time renewal equation for neural assemblies with elapsed time model

By Nicolas Torres

20:29

published on May 7, 2024

A new synaptic rule to unify experimental heterogeneity

By Yuri Rodrigues

44:26

published on May 7, 2024

A neural mass model for abnormal beta-rebound in schizophrenia

By Stephen Coombes , Peter Liddle

Copyright Carmin.tv 2024

Give feedback