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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.[-]

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 ...[+]

35Q49 ; 35Q83 ; 35R02 ; 35Q70 ; 05C90 ; 60G09 ; 35R06 ; 35Q89 ; 35Q92 ; 49N80 ; 92B20 ; 65N75

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We consider a general time-periodic linear transport equation with integral source term and we prove the existence of a Floquet principal eigenvalue, namely a real number such that the equation rescaled by this number admits positive periodic solutions. We also prove the exponential attractiveness of these solutions. The method relies on general spectral results about positive operators.

35B10 ; 35B40 ; 35Q92 ; 35R01 ; 47B65

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We provide an asymptotic analysis of a nonlinear integro-differential equation which describes the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is modeled via a nonlinear integral term, known as the 'infinitesimal model'. We consider a regime of small segregational variance, where a parameter in the infinitesimal operator, which measures the deviation between the trait of the offspring and the mean parental trait, is small. We prove that in this regime the phenotypic distribution remains close to a Gaussian profile with a fixed small variance and we characterize the dynamics of the mean phenotypic trait via an ordinary differential equation. We also briefly discuss the extension of the method to the study of steady solutions and their stability.[-]

We provide an asymptotic analysis of a nonlinear integro-differential equation which describes the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is modeled via a nonlinear integral term, known as the 'infinitesimal model'. We consider a regime of small segregational variance, where a parameter in the infinitesimal operator, which measures the deviation ...[+]

35B40 ; 35Q92 ; 92D15 ; 47G20

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35K57 ; 92D25 ; 35Q92

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35K57 ; 92D25 ; 35Q92

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92D25 ; 35Q92 ; 60J85 ; 60H30 ; 35K57 ; 35K55

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92D25 ; 35Q92 ; 60J85 ; 60H30 ; 35K57 ; 35K55

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In this talk we overview some of the challenges of cardiac modeling and simulation of the electrical depolarization of the heart. In particular, we will present a strategy allowing to avoid the 3D simulation of the thin atria depolarization but only solve an asymptotic consistent model on the mid-surface. In a second part, we present a strategy for estimating a cardiac electrophysiology model from front data measurements using sequential parallel data assimilation strategy.[-]

In this talk we overview some of the challenges of cardiac modeling and simulation of the electrical depolarization of the heart. In particular, we will present a strategy allowing to avoid the 3D simulation of the thin atria depolarization but only solve an asymptotic consistent model on the mid-surface. In a second part, we present a strategy for estimating a cardiac electrophysiology model from front data measurements using sequential ...[+]

92C30 ; 35Q92 ; 65C20

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Tumour vascular is highly disordered and has been the subject of intense interest both clinically (anti-angiogenesis therapies) and theoretically (many models have been proposed). In this talk, I will review aspects of modelling tumour angiogenesis and how different modelling assumptions impact conclusions on oxygen delivery and, therefore, predictions on the possible effects of radiation treatments.

93A30 ; 92C50 ; 92C37 ; 92C17 ; 65C20 ; 35Q92

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35B40 ; 35Q20 ; 35K40 ; 35Q92 ; 35A01 ; 92D15

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Documents 35Q92 20 résultats

The mean-field limit of non-exchangeable integrate and fire systems - Jabin, Pierre-Emmanuel (Auteur de la conférence) | CIRM H Nouveau

The principal eigenvalue of time-periodic nonlocal equations with drift - Gabriel, Pierre (Auteur de la conférence) | CIRM H Nouveau

A moment-based approach for the analysis of the infinitesimal model - Mirrahimi, Sepideh (Auteur de la conférence) | CIRM H Nouveau

Spatially structured population dynamics: the point of view of PDEs - Part 1 - Desvillettes, Laurent (Auteur de la conférence) | CIRM H Nouveau

Spatially structured population dynamics: the point of view of PDEs - Part 2 - Desvillettes, Laurent (Auteur de la conférence) | CIRM H Nouveau

Non-local Lokta-Volterra cross diffusion systems - Part 1 - Fontbona, Joaquin (Auteur de la conférence) | CIRM H Nouveau

Non-local Lokta-Volterra cross diffusion systems - Part 2 - Fontbona, Joaquin (Auteur de la conférence) | CIRM H Nouveau

Modeling and data assimilation in cardiac electrophysiology - Collin, Annabelle (Auteur de la conférence) | CIRM H Nouveau

Mathematical modelling of angiogenesis - Maini, Philip (Auteur de la conférence) | CIRM H Nouveau

Macroscopic limit from a structured population model to the Kirkpatrick-Barton model - Raoul, Gaël (Auteur de la conférence) | CIRM H Nouveau