Abstract: Neurons in cortex are connected in intricate patterns, with local- and long-range connections and distance-dependent time delays for transmitting signals. In recent work, we have found that spontaneous and stimulus-driven waves of neural activity travel over these networks, sparsely modulating the spiking activity of the local network as they pass. The waves represent changes in the moment-by-moment activity state of these networks, which in turn directly shapes neuronal responses to incoming visual input and causes measurable effects in visual perception.

Understanding how the networks of cortex generate these sophisticated dynamics, however, remains an open problem. This is due, in part, to the fact that connecting the specific structure of networks to the resulting nonlinear dynamics is a difficult problem in general. Experiments suggest one mechanism for these waves could be the distance-dependent time delays due to transmitting spikes along the axons connecting neurons across these networks. Analyzing the underlying network mechanism for these waves thus represents an additional mathematical challenge, as we need to consider systems with many time delays.

In this talk, I will present recent results from my group connecting the structure of individual networks to the resulting dynamics in systems of nonlinear Kuramoto oscillators. We introduce a complex-valued approach that allows linking the precise structure of connections in the network to the spatiotemporal patterns that will occur in individual simulations. This approach allows understanding these activity patterns in terms of a modification of the eigenspectrum of the graph adjacency matrix. This, in turn, leads to analytical predictions for the precise traveling wave patterns that will emerge in these systems. Finally, I will present our latest efforts to understand computation with spatiotemporal dynamics in neural systems using these nonlinear network models.

Contact: Guanhua Sun