The Price of Cognition and Replicator Equations in Parallel Neural Networks

TL;DR

This paper introduces a mathematical model analyzing synaptic damage in neural networks using concepts like the price of cognition and replicator equations, to understand the impact of toxic neuropeptides on brain function.

Contribution

It proposes novel concepts of neuropeptide equilibrium and synapses optimum, integrating Wardrop's principles into neural network modeling, and introduces a replicator equation for synaptic damage analysis.

Findings

Defined the 'price of cognition' as the ratio of impairment to optimal synaptic state.

Established the concepts of neuropeptide equilibrium and synapses optimum.

Developed a replicator equation to identify the synapses optimum during neurotransmission.

Abstract

In this paper, we are aiming to propose a novel mathematical model that studies the dynamics of synaptic damage in terms of concentrations of toxic neuropeptides/neurotransmitters during neurotransmission processes. Our primary objective is to employ Wardrop's first and second principles within a neural network of the brain. In order to comprehensively incorporate Wardrop's first and second principles into the neural network of the brain, we introduce two novel concepts: \textit{neuropeptide's (neurotransmitter's) equilibrium} and \textit{synapses optimum}. The \textit{neuropeptide/neurotransmitter equilibrium} refers to \textit{a distribution of toxic neuropeptides/neurotransmitters that leads to uniform damage across all synaptic links}. Meanwhile, \textit{synapses optimum} is \textit{the most desirable distribution of toxic neuropeptides/neurotransmitters that minimizes the cumulative damage experienced by all synapses}. In the context of a neural network within the brain, an analogue of the price of anarchy is \textit{the price of cognition} which is \textit{the most unfavorable ratio between the overall impairment caused by toxic neuropeptide's (neurotransmitter's) equilibrium in comparison to the optimal state of synapses (synapses optimum)}. To put it differently, \textit{the price of cognition} measures \textit{the loss of cognitive ability resulting from increased concentrations of toxic neuropeptides/neurotransmitters}. Additionally, a replicator equation is proposed within this framework that leads to the establishment of the synapses optimum during the neurotransmission process.