El Col·loqui del Departament de Matemàtiques, novembre 2014
Colloqui 07.11.2014 Divulgació  -  El proper dimecres 26 de novembre a les 12h, a la Sala de Graus I de les Facultats de Ciències i Biociències, hi haurà el Col·loqui del Departament de Matemàtiques titulat Kinetic Theory for Neuronal Networks, a càrrec d'Alexander Roxin (Centre de Recerca Matemàtica).
Resum:  
             
The mammalian cerebral cortex is highly recurrent in its connectivity. This makes understanding the dynamical states which arise in cortical tissue a difficult computational problem. One way to address this problem, which has proven fruitful, is to consider a statistical ensemble of neurons bombarded by a large number of inputs.  Therefore one recasts the problem in terms of a probability distribution over the internal states of the neurons, and enforces self-consistency in the network by matching inputs and outputs. If each input is small compared to the distance to the firing threshold of the neurons then the problem is equivalent to a Fokker-Planck equation with appropriate boundary conditions. I will discuss how to derive the Fokker-Planck equation as well as some stationary solutions for simple neuron models. Finally, I will discuss a new approach which works only for all-to-all connected networks of model neurons.  The advantage of the new approach is that is gives an exact solution for the probability distribution at all times in a particularly simple form.
 
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Departament de Matemàtiques
Edifici C Facultat de Ciències
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