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

12 30

Neural fields with rebound currents: novel routes to patterning

By Sunil Modhara

The understanding of how spatio-temporal patterns of neural activity may arise in the cortex of the brain has advanced with the development and analysis of neural field models. To replicate this success for sub-cortical tissues, such as the thalamus, requires an extended approach which includes relevant ionic currents that are able to further shape firing response. Here we advocate for one such approach that can accommodate slow currents. By way of illustration we focus on incorporating a T-type calcium current into the standard neural field framework. Direct numerical simulations are used to show that the resulting tissue model has many of the properties seen in more biophysically detailed model studies, and most importantly the generation of oscillations, waves, and patterns that arise from rebound firing. To explore the emergence of such solutions we focus on one- and two-dimensional spatial models and show that exact solutions describing homogeneous oscillations can be constructed in the limit that the firing rate nonlinearity is a Heaviside function. A linear stability analysis, using techniques from non-smooth dynamical systems, is used to determine the points at which bifurcations from synchrony can occur. Furthermore, we construct periodic travelling waves and investigate their stability with the use of an appropriate Evans function. The stable branches of the dispersion curve for periodic travelling waves are found to be in excellent agreement with simulations initiated from an unstable branch of the synchronous solution.

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.WS2.012
Cite this video Modhara, Sunil (02/02/2022). Neural fields with rebound currents: novel routes to patterning. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.012
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.012

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