Hopf bifurcation in a Mean-Field model of spiking neurons

Autor: Etienne Tanré, Romain Veltz, Quentin Cormier

Publikováno v: Electronic Journal of Probability
Electronic Journal of Probability, 2021, 26, ⟨10.1214/21-EJP688⟩
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2021, 26, ⟨10.1214/21-EJP688⟩

International audience; We study a family of non-linear McKean-Vlasov SDEs driven by a Poisson measure, modelling the mean-field asymptotic of a network of generalized Integrate-and-Fire neurons.We give sufficient conditions to have periodic solution

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ff88bacaee7aa779a6318247cb9f023f
http://arxiv.org/abs/2008.11116

On a toy network of neurons interacting through their dendrites

Autor: Nicolas Fournier, Etienne Tanré, Romain Veltz

Publikováno v: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2020, 56 (2), pp.1041-1071. ⟨10.1214/19-AIHP993⟩
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2020, 56 (2), pp.1041-1071. ⟨10.1214/19-AIHP993⟩
Ann. Inst. H. Poincaré Probab. Statist. 56, no. 2 (2020), 1041-1071
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2020, 56 (2), pp.1041-1071

Consider a large number $n$ of neurons, each being connected to approximately $N$ other ones, chosen at random. When a neuron spikes, which occurs randomly at some rate depending on its electric potential, its potential is set to a minimum value $v_{

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e13e7d679237ad555c914390adf4ebc0
https://doi.org/10.1214/19-aihp993

Network of interacting neurons with random synaptic weights

Autor: Etienne Tanré, Cyrille Mascart, Julien Chevallier, François Delarue, Paolo Grazieschi, Marta Leocata

Publikováno v: ESAIM: Proceedings and Surveys
ESAIM: Proceedings and Surveys, EDP Sciences, 2019, CEMRACS 2017-Numerical methods for stochastic models: control, uncertainty quantification, mean-field, 65, pp.445-475. ⟨10.1051/proc/201965445⟩
ESAIM: Proceedings and Surveys, Vol 65, Pp 445-475 (2019)
ESAIM: Proceedings and Surveys, 2019, CEMRACS 2017-Numerical methods for stochastic models: control, uncertainty quantification, mean-field, 65, pp.445-475. ⟨10.1051/proc/201965445⟩

Since the pioneering works of Lapicque [17] and of Hodgkin and Huxley [16], several types of models have been addressed to describe the evolution in time of the potential of the membrane of a neuron. In this note, we investigate a connected version o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::35bf2136e8317640f8bbb70dea226783
https://hal.inria.fr/hal-01928990

Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size

Autor: Etienne Tanré, Pierre Guiraud

Publikováno v: Discrete and Continuous Dynamical Systems-Series B
Discrete and Continuous Dynamical Systems-Series B, 2019, 24 (9), pp.5183--5201. ⟨10.3934/dcdsb.2019056⟩
Discrete and Continuous Dynamical Systems-Series B, American Institute of Mathematical Sciences, 2019, 24 (9), pp.5183--5201. ⟨10.3934/dcdsb.2019056⟩

International audience; In the present paper, we study the synchronization in a model of neural network which can be considered as a noisy version of the model of \citet{mirollo1990synchronization}, namely, fully-connected and totally excitatory inte

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94ebdd3cff9960610b294d0fac6a42e0
http://arxiv.org/abs/1609.07103

Liquidity costs: a new numerical methodology and an empirical study

Autor: Etienne Tanré, Christophe Michel, Denis Talay, Victor Reutenauer

Publikováno v: Applied Mathematical Finance
Applied Mathematical Finance, 2016, ⟨10.1080/1350486X.2016.1164608⟩
Applied Mathematical Finance, Taylor & Francis (Routledge): SSH Titles, 2016, ⟨10.1080/1350486X.2016.1164608⟩

International audience; We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit optimal strategy minimizing a risk measure of the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::84891e18121db6f71440b3949d62c490
http://arxiv.org/abs/1501.07404