Simulation of sample paths for Gauss-Markov processes in the presence of a reflecting boundary

Algorithms for the simulation of sample paths of Gauss–Markov processes, restricted from below by particular time-dependent reflecting boundaries, are proposed. These algorithms are used to build the histograms of first passage time density through specified boundaries and for the estimation of related moments. Particular attention is dedicated to restricted Wiener and Ornstein–Uhlenbeck processes due to their central role in the class of Gauss–Markov processes

The brain: What is critical about it?

We review the recent proposal that the most fascinating brain properties are related to the fact that it always stays close to a second order phase transition. In such conditions, the collective of neuronal groups can reliably generate robust and flexible behavior, because it is known that at the critical point there is the largest abundance of metastable states to choose from. Here we review the motivation, arguments and recent results, as well as further implications of this view of the functioning brain.Comment: Proceedings of BIOCOMP2007 - Collective Dynamics: Topics on Competition and Cooperation in the Biosciences. Vietri sul Mare, Italy (2007

Restricted Ornstein-Uhlenbeck process and applications in neuronal models with periodic input signals

Restricted Gauss-Markov processes are used to construct inhomogeneous leaky integrate-and-fire stochastic models for single neuron’s activity in the presence of a lower reflecting boundary and periodic input signals. The first-passage time problem through a time-dependent threshold is explicitly developed; numerical, simulation and asymptotic results for firing densities are provided

Paradossi della Probabilità condizionata: un possibile uso nella didattica della matematica dell’incerto

Per il tema “dati Previsioni” si propone l’impostazione didattica basata sui problemi. In particolare, si propone di utilizzare, in maniera appropriata e con la finalità di sollecitare le abilità comunicative ad argomentative, alcuni dei paradossi della probabilità condizionata che nel corso del tempo sono stati occasione di discussioni vivaci e intriganti. Qui, in particolare ci si sofferma sul paradosso dei tre prigionieri proponendo una rappresentazione grafica della classica soluzione algebrica basata sul teorema di Bayes

Indizi, Pre-giudizi e il Ragionamento Bayesiano

Attraverso tre diverse situazioni si illustrano gli ingrdienti basilari e il "motore inferenziale" per prendere decisioni in ondizione i incertezza. Tale modalità di ragionamento può essere d'aiuto agli insegnanti per sollecitare gli studenti sui processi metacognitivi molto spesso richimati nelle indicazioni nazionli

On some numerical and algorithmic problems in single neuron’s activity modelling

Neuronal firing is often viewed as a first passage time problem through a time dependend boundary for a diffusion process. In this paper we approach the study of features of the first passage time probability density function for the Wiener process and for a periodic boundary. This is expected to be of interest when neuronal models include oscillatory inputs or whenever the neuron's threshold oscillates as a consequence of internal or external periodic stimulations