The interspike interval spike trains of spontaneously active cortical neurons can display nonrandom internal structure. The degree of nonrandom structure can be quantified and was found to decrease during focal epileptic seizures. Greater statistical discrimination between the two physiological conditions (normal vs seizure) was obtained with measurements of context-free grammar complexity than...

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; an...

The mammalian retina deconstructs the visual world using parallel neural channels, embodied in the morphological and physiological types of ganglion cells. We sought distinguishing features of each cell type in the temporal pattern of their spikes. As a first step, conventional physiological properties were used to cluster cells in eight types by a statistical analysis. We then adapted a method...

This letter presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular...

Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. It is largely unknown how the spike train correlation structure is altered by ...

Neurons typically respond to a restricted number of stimulus features within the high-dimensional space of natural stimuli. Here we describe an explicit modelbased interpretation of traditional estimators for a neuron’s multi-dimensional feature space, which allows for several important generalizations and extensions. First, we show that traditional estimators based on the spike-triggered avera...