Buongiorno a tutti,

abbiamo il piacere di annunciare i prossimi Webinars promossi dal Gruppo UMI-PRISMA:

Lunedi’ 2 maggio 2022

ore 16-17 LAURA SACERDOTE

TITOLO: Input-output consistency in Integrate and Fire neuronal networks

ABSTRACT: Models of neurons aim to describe the information transmission within a neural network. Some models are mathematically tractable with the introduction of strong simplifications, ignoring the involved biophysicalfeatures of the single units. Others are very faithful to reality at the price of very complex mathematical descriptions. Models are then used to describe networks, often through simulations. The appearance of particular patterns in the trains of spikes is then used to compare with observed data or to switch from microscopic to macroscopic analysis. In this framework, it is essential to guarantee the reliability of the output of the model and often scientists compare the output of the models with real data. However, when the models are used to reproduce networks the output of some neurons becomes the input of a successive layer of neurons. This fact opens a problem of consistency between input and output of layers of neurons. To the best of our knowledge, this problem has not yet been deeply investigated. Here, we consider the simplest Stochastic Integrate and Fire model and we try to characterize the features of its input in such a way to re-obtain the same features in the output. In particular, we focus on the tail properties of ISIs distribution. Observed data suggest the presence of heavy tails for this distribution. Using the Stochastic Integrate and Fire paradigm for the neurons of the network we study how such features can be transmitted from the network. In this framework we introduce a particular class of multivariate distributions, i.e. the regularly varying distributions. We show that assuming that the input to a neuron is a regularly varying random vector and that successive ISIs of a neuron are asymptotically independent thenthe resulting output is a regularly varying random variable. The talk is based on a joint work with Petr Lansky and Federico Polito.

Ore 17-18 BRUNO TOALDO

TITLE: Semi-Markov processes, their exit times and non-local equations

ABSTRACT: We introduce the theory of semi-Markov processes and their interplay with non-local equations. Particular attention will be devoted to the theory of exit times from sets and the connection with boundary value problems, e.g., on a time-dependent parabolic domain.

Collegamento Teams:

https://teams.microsoft.com/l/meetup-join/19%3ad685b25ed15f4821ac5168e63cf98...

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Grazie per l’attenzione, Claudia Ceci e Domenico Marinucci

Claudia Ceci Dipartimento di Economia Universita' "G. d'Annunzio" di Chieti-Pescara V.le Pindaro 42 65127, Pescara, ITALY c.ceci@unich.it