Plenary Talk - Dynamics of a population of neurons: underlying correlations at low and high frequencies

FERNANDO MONTANI

Conferencia; XX Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics; 2018

The presence of higher order correlations than two in the common inputs of neuronalpopulations and in the outputs of action potentials induces the need to develop a newtheoretical framework that could take into account the complexity of the synchronizedactivity patterns. It is well accepted that synchronized action potentials of many neuronscan for example modify substantially the information of the frequency components of thelocal field potentials (LFPs). In particular the electroencephalograms on the scalp, registeredby a single electrode are a softened version of the LFP spatiotemporally speaking. In thiswork we develop a formalism that allows us to quantify the amount of correlation higherthan two in the inputs and outputs of a population of neurons. This approach capturesthe dynamics produced by subtle changes in the inputs and outputs of neuronal populations quantifying all correlation moments. This permits us to investigate the behavior of thecritical fluctuations by means of the 4th-order Binder cumulant. We present an exhaustiveanalysis of how the statistics of the inputs transform the threshold process in the statisticsof the outputs, and we show under which conditions the higher correlation order may leadto a greater or lower number of synchronized action potentials in the neuronal population.Finally, at the low frequency level, we characterize the strength of the neuronal network fordifferent rhythmic oscillation in the brain.