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At the crossroad between invariant manifolds and the role of noise

Banff International Research Station for Mathematical Innovation and Discovery

I will drift along several topics in which we are currently involved. They all contain some treatment of recent tools from dynamical systems, mainly related to invariant manifolds, intertwined with the role of stochasticity. We aim at sharing our research interests to boost discussion and eventual collaborations. The first example will be on bistable perception where we are exploring up to which extent noise is necessary to explain data obtained from psycophysical experiments, as opposed to the information provided assuming quasi-periodic forcing. Second, we will focus on phase response curves (PRC) for oscillating neurons, a well-known tool to study the effectiveness of information transmission between cells; we have extended the notion of PRC to that of phase response field/function (PRF), also valid away from pure periodic behaviour. Stochastic PRCs have been already studied but PRFs constitute a more natural setting when neurons are subject to noisy inputs; we have neither explored the impact of noise on PRFs nor the extension of the concept to stochastic processes yet and, moreover, we also seek for experimental tests of our theoretical findings. Therefore, we think it can be interesting to address these open questions in this audience. If time allows, we will comment on some other issues (estimation of conductances and short-term synaptic depression) that combine concepts of dynamical systems with the presence of noise.

Mathematics; Statistics; Probability theory and stochastic processes; Applied statistics

video/mp4

Author affiliation: Universitat Politèchnica de Calatunya

2019-03-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68567

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/