##### Department of Mathematics,

University of California San Diego

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

## Professor Henry Abarbanel

#### Physics and SIO, UCSD

## Reduced, Biophysically Based, Models for Neurons to Use as Computationally Efficient Elements of Large Functional Biological

##### Abstract:

Using a combination of methods from applied mathematics and nonlinear dynamics, we present a constructive way to give a discrete time dynamical rule that accurately forecasts the voltage across a neuron cell membrane. This is the only quantity required to build a biological network of realistic neurons. The construction uses simulated 'data' or observed biophysical data alone to develop the dynamical map. We call this data driven forecasting (DDF). The method is described in detail at first using 'data' from simple neuron models and then using observed neurobiological data from laboratory experiments. It provides accurate forecasting of observed quantities in each setting.

In an example where a detailed Hodgkin-Huxley (HH) model was developed using data assimilation for observed laboratory observations the DDF neuron runs an order of magnitude faster than the HH version in forecasting the important neuron voltage time course. As the computation required for a network of N nodes will be faster by about a factor of 10N using DDF neurons, this will permit building and analyzing the very large networks desired to address realistic biological questions using elements determined via the biophysics of the component neurons.

If time permits, we will describe how one may use the DDF idea to substantially reduce the geophysical computations required for regional numerical weather forecasting.

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

### March 10, 2022

### 2:00 PM

Contact Bo Li at bli@math.ucsd.edu for the Zoom info

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