Inferência da conectividade neuronal e o modelo de Galves e Löcherbach

Abstract

One of the most important issues in neuroscience is to understand the dynamics of animal behavior, that is, the joint action of large numbers of neurons, body parts, and the environment. The relationship between this behavior and the way that neurons interact with each other is a challenging question, since real experiments only have access to a small part of the neural system. Alternatively, generic mathematical models are considered to describe this phenomenon. In this work, the activity of each neuron is represented by a discrete-time stochastic process, whose random variables indicate whether or not there was a neuronal spike at a given instant of time. For each neuron, the probability of observing a neuronal spike at a given instant of time depends on the evolution of presynaptic neurons since their last spiking time. We use the Galves-Löcherbach model to model this spike probability. When a neuron spikes, its membrane potential is reset to its resting potential and electrical signals are generated, modifying the membrane potential of all postsynaptic neurons. The relationship between a neuron and its presynaptic and postsynaptic neurons defines a weighted oriented graph. The objective of this work is studying, from a computation point of view, the performance of the estimation process of the connectivity graph from the observation of the neuronal activity of a finite set of neurons over a limited time interval, considering the Galves-Löcherbach model as underlying model.