Neurons in nervous systems interact with each other to form complex networks. It is important to understand how the connectivity leads to dynamics or activity patterns across neurons, which are thought to be the basis of various neural computations. Recent experiments reveal that certain connection patterns, or motifs, occur at markedly different frequencies than would be expected if neurons were randomly connected. This motivates us to study how motifs may impact neural dynamics. We show that population-averaged spike correlation, a widely studied aspect of collective dynamics, is determined by the statistical prevalence of two classes of motifs. Our theory is able to predict the average correlation efficiently based on statistics of only a few small size motifs by removing redundancy from composing motifs. The developed motif-based method can also be used to characterize how the filtering of temporal signals through a recurrent network depends on the statistics of motifs which correspond to a hierarchy of effective feedbacks. Neural activity is studied at multiple scales and experimental data are often collected at a coarser level, for example, through spatial averaging or sub-sampling over neurons. It is thus important to connect dynamics and network models across scales. To this end, we develop a principled framework that maps neuron-level networks with linear dynamics to effective network models which describe the coarse-grained (CGed) dynamics. We show that the connectivity in the CGed model can deviate from the usual mean-field theory with additional functional connectivity and perform detailed analyses of widely used neural network architectures including ring networks and random networks. The theoretical study of multi-scale neural dynamics is synergistic with emerging experiments of large-scale simultaneous neuron-level recordings. I will discuss a collaboration on analyzing wholebrain data in larval zebrafish and our first steps of identifying functional clusters of neurons based on their on-going activity.
Yu Hu received his BS in mathematics from Peking University in 2009. He then studied at the Applied Mathematics Department at University of Washington advised by Dr Eric Shea-Brown and received his PhD in 2014. He then began his current position of a postdoctoral fellow at the Center for Brain Science at Harvard University, working with Dr Haim Sompolinsky.