Introduction

This work studies acitivities of neurons on both individual and group level. We aim to establish and analyze a time-varying network. The central objective is how to infer a dynamic network on the bottom from multiple point processes on the top in the following figure.

Conditional intensity function

First, we can convert a point process into a real-valued function for further analysis. Let be the conditional intensity function of a spike sequence at time t, such thatwhere is the time of last spike and is the time of next one. After some computations, we can obtain

Establish a network and inferences

A time-varying directed network is then established based on intensity functions given a group of 12 neurons. The gist is to consider that the changes in spiking activities of $g$-th neuron depends on others in the group throughwhere we can consider are the regulation effects of l-th neuron on g-gh. A dynamic network can be inferred by using 12 models in the above form so that we use regulation effects to illustrate the directed connectivity between neurons. If is large, then l-th neuron has strong effects on g-th neuron at time t, for g, l = 1,..., 12. By assuming are sparse functions, either or for some time t, we can select significant connections across neurons in the group. The below figure is the regulation functions on one of the neurons.