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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents 35Q89 5 results

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The mean-field limit of non-exchangeable integrate and fire systems - Jabin, Pierre-Emmanuel (Author of the conference) | CIRM H

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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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The mean-field limit of non-exchangeable integrate and fire systems (continued) - Jabin, Pierre-Emmanuel (Author of the conference) | CIRM H

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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 ; 49N80 ; 92B20 ; 65N75 ; 65N75

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Mean Field Games - lecture 1 - Cardaliaguet, Pierre (Author of the conference) | CIRM H

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The lecture is a short presentation of the theory of Mean Field Games (MFG) and Mean Field Control (MFC). After explaining how to derive these models from optimal control problems and games with a large number of players, we will describe the basic results of MFG (existence, uniqueness of the solution) and MFC, writing in the later case the associated infinite dimensional Hamilton-Jacobi equation and the optimality conditions.

35Q89 ; 49J55 ; 49K20

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Mean Field Games - lecture 2 - Cardaliaguet, Pierre (Author of the conference) | CIRM H

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The lecture is a short presentation of the theory of Mean Field Games (MFG) and Mean Field Control (MFC). After explaining how to derive these models from optimal control problems and games with a large number of players, we will describe the basic results of MFG (existence, uniqueness of the solution) and MFC, writing in the later case the associated infinite dimensional Hamilton-Jacobi equation and the optimality conditions.

35Q89 ; 93E20 ; 49K20

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Mean Field Games - lecture 3 - Cardaliaguet, Pierre (Author of the conference) | CIRM H

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The lecture is a short presentation of the theory of Mean Field Games (MFG) and Mean Field Control (MFC). After explaining how to derive these models from optimal control problems and games with a large number of players, we will describe the basic results of MFG (existence, uniqueness of the solution) and MFC, writing in the later case the associated infinite dimensional Hamilton-Jacobi equation and the optimality conditions.

35Q89 ; 93E20 ; 49K20

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