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# Zhi-Qin John Xu (Courant Institute of Mathematical Science, New York University), Applied Mathematics Colloquium

## February 10, 2017 @ 4:00 pm - 5:00 pm

**Title: **A Probability Polling State — the Maximum Entropy Principle in Neuronal Data Analysis

**Abstract: **How to extract information from exponentially growing recorded neuronal data is a great scientific challenge. It is urgent to develop methods to simplify the analysis of neuronal data. In this talk, we address what kind of dynamical states of neuronal networks allows us to have an effective description of coding schemes. For asynchronous neuronal networks, when considering the probability increment of a neuron spiking induced by other neurons, we found a probability polling (p-polling) state that captures the neuronal interactions which are affected by multiple factors, i.e., coupling structure, background input and external input. We show that this state is confirmed in some experiments in vitro and in vivo, and also confirmed through the simulation of Hodgkin-Huxley neuronal networks. We hypothesize that this p-polling state may be a general operating state of neuronal networks. For the p-polling state, we show that neuronal firing patterns can be well captured by the 2nd order maximum entropy model.