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We propose a generalisation of the existing maximum entropy models used for spike trains statistics analysis, based on the thermodynamic formalism from ergodic theory, and allowing one to take into account memory effects in dynamics. We propose a spectral method which provides directly the “free-energy” density and the Kullback-Leibler divergence between… (More)
“Spikes are the neural code”: this claim is about 15 years old (Shadlen & Newsome, 1994; Rieke, Warland, Steveninck, & Bialek, 1996), preceded by theoretical studies on the underlying mathematical processes (e.g., (Gerstein & Mandelbrot, 1964)), and followed by many developments regarding biological modelling or computational paradigms, or both (e.g.,… (More)
We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed.