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The mean-field limit of non-exchangeable integrate and fire systems (continued)

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Authors : Jabin, Pierre-Emmanuel (Author of the conference)
CIRM (Publisher )

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Abstract : We investigate the mean-field limit of large networks of interacting biological neurons. The neurons are represented by the so-called integrate and fire models that follow the membrane potential of each neuron and captures individual spikes. However we do not assume any structure on the graph of interactions but consider instead any connection weights between neurons that obey a generic mean-field scaling. We are able to extend the concept of extended graphons, introduced in Jabin-Poyato-Soler, by introducing a novel notion of discrete observables in the system. This is a joint work with D. Zhou.

Keywords : multi-agent systems; many-particle systems; integrate & fire models

MSC Codes :
05C90 - Applications of graph theory
60G09 - Exchangeability
92B20 - Neural networks, artificial life and related topics
35Q83 - Vlasov-like equations
35Q70 - PDEs in connection with mechanics of particles and systems
65N75 - Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs
35R02 - PDEs on graphs and networks (ramified or polygonal spaces)
35Q89 - PDEs in connection with mean field game theory
35Q49 - Transport equations
49N80 - Mean field games and control
35R06 - PDEs with measure

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 22/07/2024
    Conference Date : 27/06/2024
    Subseries : Research School
    arXiv category : Probability ; Analysis of PDEs
    Mathematical Area(s) : Analysis and its Applications ; PDE ; Mathematics in Science & Technology ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 01:08:54
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-06-27_jabin_2.mp4

Information on the Event

Event Title : Research School - Jean Morlet Chair - Frontiers in Interacting Particle Systems, Aggregation-Diffusion Equations & Collective Behavior / Ecole - Chaire Jean Morlet - Frontières dans les équations de systèmes de particules en interaction. Equations d'agrégation-diffusion et comportement collectif
Event Organizers : Carrillo, José Antonio ; Nouri, Anne
Dates : 24/06/2024 - 28/06/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/3050.html

Citation Data

DOI : 10.24350/CIRM.V.20194703
Cite this video as: Jabin, Pierre-Emmanuel (2024). The mean-field limit of non-exchangeable integrate and fire systems (continued). CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20194703
URI : http://dx.doi.org/10.24350/CIRM.V.20194703

See Also

Bibliography

  • JABIN, Pierre-Emmanuel, POYATO, David, et SOLER, Juan. Mean-field limit of non-exchangeable systems. arXiv preprint arXiv:2112.15406, 2021. - https://arxiv.org/abs/2112.15406

  • JABIN, Pierre-Emmanuel et ZHOU, Datong. The mean-field limit of sparse networks of integrate and fire neurons. arXiv preprint arXiv:2309.04046, 2023. - https://arxiv.org/abs/2309.04046



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