##### Department of Mathematics,

University of California San Diego

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

## Johnatan (Yonatan) Aljadeff

#### Neurobiology, UCSD

## Multiplicative Shot Noise: A New Route to Stability of Plastic Networks

##### Abstract:

Fluctuations of synaptic-weights, among many other physical, biological and ecological quantities, are driven by coincident events originating from two 'parent' processes. We propose a multiplicative shot-noise model that can capture the behavior of a broad range of such natural phenomena, and analytically derive an approximation that accurately predicts its statistics. We apply our results to study the effects of a multiplicative synaptic plasticity rule that was recently extracted from measurements in physiological conditions. Using mean-field theory analysis and network simulations we investigate how this rule shapes the connectivity and dynamics of recurrent spiking neural networks. We show that the multiplicative plasticity rule, without fine-tuning, gives a stable, unimodal synaptic-weight distribution with a large fraction of strong synapses. The strong synapses remain stable over long times but do not `run away'. Our results suggest that the multiplicative plasticity rule offers a new route to understand the tradeoff between flexibility and stability in neural circuits and other dynamic networks. Joint work with Bin Wang.

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

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

### February 3, 2022

### 2:00 PM

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

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