Bernstein Center Freiburg

Bernstein Seminar

December 6, 2018
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Bernstein Seminar
MATTHIEU GILSON ►

Center for Brain and Cognition | Universitat Pompeu Fabra | Barcelona, Spain

Propagation of moments in Hawkes networks

Thursday, December 6, 2018

17:15 h

The talk is open to the public.
Guests are cordially invited!

Hosted by Stefan Rotter

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Bernstein Center Freiburg
Lecture Hall (ground floor)
Hansastr. 9a
79104 Freiburg


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Abstract

The present study provides a mathematical description of high-order moments of spiking activity in a recurrently-connected network of Hawkes processes. It extends previous studies that have explored the case of a (linear) Hawkes network driven by deterministic rate functions to the case of a stimulation by external inputs (rate functions or spike trains) with arbitrary correlation structure. Our approach describes the spatio-temporal filtering induced by the afferent and recurrent connectivities using operators of the input moments. This algebraic viewpoint provides intuition about how the network ingredients shape the input-output mapping for moments, as well as cumulants. This mathematical framework provides a basis for the study of learning in recurrently connected networks when high-order spiking statistics are involved (e.g., triplet STDP).

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