Reference:

Interplay of random and nonnormally structured connectivity in the dynamics of neural networks
Yashar Ahmadian (U. Columbia)

Neuronal networks exhibit significant randomness in their synaptic connectivity. But importantly, alongside randomness, the synaptic connectivity of most neural networks also features ordered structure on various levels, depending on the network's function. Investigating the interplay of these two features of connectivity and their respective role in the dynamics of neural networks and the computations they perform constitutes a general theoretical problem in neuroscience. Of particular interest are connectivity structures that can be described by a nonnormal matrix. In this case the network can be described as having a hidden feedforward connectivity structure between orthogonal activity patterns, each of which can also excite or inhibit itself. Such networks arise naturally from the separation of excitatory and inhibitory neurons and yield large transient amplification of patterns without any dynamical slowing. This latter effect has been used to explain the similarity of the fluctuating patterns of spontaneous activity in primary visual cortex (V1) to patterns of activity evoked by visual stimuli.

In my first talk, I will give a general overview of the early visual system, review some of the relevant literature bearing on the above problems and topics, including the experimental observations of the spontaneous activity in V1, and two different theoretical approaches to modeling them.