##### Department of Mathematics,

University of California San Diego

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### Math 218 - Seminars on Mathematics for Complex Biological Systems

## Gabriel Silva

#### UCSD

## Exploring Categorical Models of Generative Neural Properties from Computable Local Dynamics

##### Abstract:

We recently described the construction and theoretical analysis of a framework (competitive-refractory dynamics model) derived from the canonical neurophysiological principles of spatial and temporal summation. The framework models the competing interactions of signals incident on a target downstream node (e.g. a neuron) along directed edges coming from other upstream nodes that connect into it. The model takes into account how temporal latencies produce offsets in the timing of the summation of incoming discrete events due to the geometry (physical structure) of the network, and how this results in the activation of the target node. It provides a computable representation of how local computations result in global network dynamics. Grounded in this neurophysiological model, we are beginning to explore the use some aspects of category theory and related ideas in order to abstract up and understand how the brain might produce generative (emergent) non-trivial computational properties. In particular, we are interested in understanding the emergence of creativity and imagination.

https://mathweb.ucsd.edu/~bli/research/mathbiosci/MBBseminar/

Organizer: Li-Tien Cheng, Bo Li, and Ruth Williams

### May 26, 2022

### 2:00 PM

https://ucsd.zoom.us/j/

Meeting ID: 932 7622 5058

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