2021-03818 - Post-Doctoral Research Visit F/M Heterogeneity in Network of Interacting Neurons

Contract type : Fixed-term contract

Level of qualifications required : PhD or equivalent

Fonction : Post-Doctoral Research Visit

About the research centre or Inria department

The Inria Sophia Antipolis - Méditerranée center counts 34 research teams as well as 8 support departments. The center's staff (about 500 people including 320 Inria employees) is made up of scientists of different nationalities (250 foreigners of 50 nationalities), engineers, technicians and administrative staff. 1/3 of the staff are civil servants, the others are contractual agents. The majority of the center’s research teams are located in Sophia Antipolis and Nice in the Alpes-Maritimes. Four teams are based in Montpellier and two teams are hosted in Bologna in Italy and Athens. The Center is a founding member of Université Côte d'Azur and partner of the I-site MUSE supported by the University of Montpellier.

Context

Within the framework of a partnership

  • project/programme/European fund HBP SGA3

Supervision

Etienne Tanré and Romain Veltz, Permanent researcher Inria


Context

Olivier Faugeras is a member of the HBP project since the beginning.
His team, including Romain Veltz and Etienne Tanré, has developed and studied mathematical models with mean-field behaviors [1,2,3,4,5,6,7,8].
A common idea in most of these works is the following: an exchangeable interacting  particle system  has an asymptotic behavior as the number of particles tends to infinity.

Please, contact Etienne.Tanre@inria.fr and Romain.Veltz@inria.fr  for more details.

Assignment

Role of the Post-Doc

This position is related to the HBP project. As such, the post-doc student will investigate the effect of heterogeneous cell diversity (neuron parameters, synaptic weights, etc) on the dynamics of stochastic networks of spiking neurons. We no more consider that the synaptic weights are equal but we take into account biological variability in the interactions.

Some results have already been obtained [9,10,11,12] when the weights are static.
In this project, a precise comparison between heterogeneous and homogeneous networks will be done on the mean-field equation [12]. In addition, the finite size effects will also be investigated.


Research environment

The student will be advised by Etienne Tanré, Romain Veltz  and Olivier Faugeras. He/she will benefit from the environment of the HBP project. In particular, frequent meetings with the consortium are scheduled.

Additionally, the student will have the opportunity to interact with the members of the NeuroMod institute and the ChaMaNe ANR project.

Bibliography

[1] B. Aymard, F. Campillo, and R. Veltz. Mean-field limit of interacting 2D
nonlinear stochastic spiking neurons. 2019. https://arxiv.org/abs/1906.10232
[2] Q. Cormier, E. Tanré, and R. Veltz. Hopf bifurcation in a Mean-Field
model of spiking neurons. 2021.  https://arxiv.org/abs/2008.11116
[3] Q. Cormier, E. Tanré, and R. Veltz. Long time behavior of a mean-
field model of interacting neurons". In: Stochastic Process. Appl. 130.5
(2020), pp. 2553-2595. https://doi.org/10.1016/j‧spa.2019.07.010.
[4] F. Delarue, J. Inglis, S. Rubenthaler, and E. Tanré. Particle systems with
a singular mean-field self-excitation. Application to neuronal networks".
In: Stochastic Process. Appl. 125.6 (2015), pp. 2451-2492.  https://doi.org/10.1016/j.spa.2015.01.007.
[5] F. Delarue, J. Inglis, S. Rubenthaler, and E. Tanré. Global solvability of
a networked integrate-and-fire model of McKean-Vlasov type". In: Ann.
Appl. Probab. 25.4 (2015), pp. 2096-2133.  https://doi.org/10.1214/14-AAP1044.
[6] A. Drogoul and R. Veltz. Exponential stability of the stationary dis-
tribution of a mean-field of spiking neural network". In: J. Differential
Equations 270 (2021), pp. 809-842.  https://doi.org/10.1016/j.jde.2020.08.001
[7] A. Drogoul and R. Veltz. Hopf bifurcation in a nonlocal nonlinear trans-
port equation stemming from stochastic neural dynamics". In: Chaos 27.2
(2017), pp. 021101, 6.  https://doi.org/10.1063/1.4976510.
[8] P. Grazieschi, M. Leocata, C. Mascart, J. Chevallier, F. Delarue, and E‧Tanré. Network of interacting neurons with random synaptic weights". In: CEMRACS 2017|numerical methods for stochastic models: control, uncertainty quantification, mean-field. Vol. 65. ESAIM Proc. Surveys. 2019, pp. 445-475. https://doi.org/10.1051/proc/201965445.
[9] D. Lacker, K. Ramanan, and R. Wu. Locally interacting diffusions as space-time Markov random fields. 2020. https://arxiv.org/abs/1911.01300
[10] D. Lacker, K. Ramanan, and R. Wu. Marginal dynamics of interacting diffusions on unimodular Galton-Watson trees. 2020. https://arxiv.org/abs/2009.11667
[11] E. Luçon. Quenched asymptotics for interacting diffusions on inhomogeneous random graphs". In: Stochastic Process. Appl. 130.11 (2020), pp. 6783-6842.  https://doi.org/10.1016/j‧spa.2020.06.010.
[12] M. di Volo and A. Destexhe. Optimal responsiveness and collective oscillations emerging from the heterogeneity of inhibitory neurons".  https://arxiv.org/pdf/2005.05596.pdf

 

Main activities

Main activities:

Develop and study a mathematical model of heterogeneous network.

Skills

The student will use classical tools issued from stochastic calculus, dynamical systems and numerical methods.

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Remuneration

Gross Salary: 2653 € per month