59,237 research outputs found
Spike train statistics and Gibbs distributions
This paper is based on a lecture given in the LACONEU summer school,
Valparaiso, January 2012. We introduce Gibbs distribution in a general setting,
including non stationary dynamics, and present then three examples of such
Gibbs distributions, in the context of neural networks spike train statistics:
(i) Maximum entropy model with spatio-temporal constraints; (ii) Generalized
Linear Models; (iii) Conductance based Inte- grate and Fire model with chemical
synapses and gap junctions.Comment: 23 pages, submitte
An asymptotic shape theorem for random linear growth models
In this note, we generalize the asymptotic shape theorem proved in [Des14a]
for a class of random growth models whose growth is at least and at most
linear. In this way, we obtain asymptotic shape theorems conjectured for
several models: the contact process in a randomly evolving environment [SW08],
the oriented percolation with hostile immigration [GM12b] and the bounded
modified contact process [DS00]
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