# Heterogeneous gain distributions in neural networks I:The stationary case

## TL;DR

This paper models heterogeneous gain distributions in neural fields using quantum mechanics techniques, revealing how connectivity influences neural activity patterns and predicting testable phenomena.

## Contribution

It introduces a novel approach linking neural gain distributions to quantum mechanics, specifically the Schrödinger equation, to explain neural field behaviors.

## Key findings

- Connectivity-gain relationships explain neural activity patterns.
- Predictions include gating, propagation, and bump formation in neural fields.
- Results are testable in vivo or in vitro experiments.

## Abstract

We study heterogeneous distribution of gains in neural fields using techniques of quantum mechanics by exploiting a relationship of our model and the time-independent Schr\"{o}dinger equation. We show that specific relationships between the connectivity kernel and the gain of the population can explain the behavior of the neural field in simulations. In particular, we show this relationships for the gating of activity between two regions (step potential), the propagation of activity throughout another region (barrier) and, most importantly, the existence of bumps in gain-contained regions (gain well). Our results constitute specific predictions that can be tested in vivo or in vitro.