The vast majority of neurons in the brain communicate with one another using discrete impulses known as spikes. Modeling studies have demonstrated that systems constituted of spiking neurons can have dynamics that are starkly different from those of systems whose constituent units interact via continuously varying quantities. This project is aimed at deciphering the core dynamical and computational properties of networks of spiking neurons, a formal understanding of which is necessary to comprehend how the brain, or any part thereof, works.
A prerequisite for such a program is the choice of a mathematical model for networks of spiking neurons that is at once biologically realistic and is amenable to formal analysis. In prior work, Arunava Banerjee has formulated one such model that is founded on the observation that a neuron is in essence a device that transforms multiple input sequences of spikes arriving at its various afferent synapses into an output sequence of spikes on its axon. Building on this model, this project aims to answer a broad set of interrelated questions concerning the nature of computation in feed-forward and recurrent networks of spiking neurons.
For continuous input-output systems, the Volterra/Wiener approach to system identification has led to a highly successful account of the levels of complexity inherent to transforming functionals. This project will formulate and analyze a corresponding framework that is applicable to feed-forward networks whose inputs and outputs are both spike trains. Next, the relationship between the input-output transformation of a feed-forward network and its information transmission capacity, as well as the nature of the recoding of information, will be analyzed. Networks driven by artificially generated realistic input spike trains shall be used to address this issue. The educational aspect of the project will focus on achieving two simultaneous objectives: attracting undergraduate women with an interest in the Biological Sciences to the field of Computer Science, and introducing senior undergraduate and beginning graduate Computer Science students to the basic neurobiology of the brain.
