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Computational Neuroscience Journal Club

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If you have a question about this talk, please contact Dr Jean-Pascal Pfister.

Jean-Pascal will present a paper by A.G. Hawkes

Point Spectra of Some Mutually Exciting Point Processes

Journal of the Royal Statistical Society. Series B (Methodological), Vol. 33, No. 3 (1971), pp. 438

URL : http://www.jstor.org/stable/2984686

Although slightly technical, this elegant paper is very relevant for the study of the dynamics  of recurrent neural networks. In particular it calculates explicitly the autocorrelation function for a family of recurrent networks.

Abstract:

In contagious processes, the occurrence of events increases the probability of further events occurring in the near future. Also several series of events may interact with each other, for example on might consider notifications of some disease in a number of adjacent regions which would interact through infectives or carriers moving between the regions, In this paper, we postulate a model for such processes and derive a general expression for the point spectral matrices. These theoretical spectra are useful for comparison with spectra estimated from data and thus provide a means of evaluating the fit of such a model in the madder of Barlett (1963). The model studied was put forward in an earlier paper (Hawkes, 1971) but the solution was obtained only in special cases. In this paper, an elegant solution is obtained for the general case.

This talk is part of the Computational Neuroscience series.

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