Quantum calcium-ion interactions with EEG

TL;DR

This paper develops a quantum path-integral model for calcium ions to analyze their interactions with classical EEG-based neural models, showing modest improvements in fitting EEG data and proposing future directions for detailed quantum-classical neural simulations.

Contribution

It introduces a closed-form quantum path-integral solution for calcium ions and integrates it with classical SMNI models to improve EEG data fitting.

Findings

Modest improvement in EEG data fit using quantum calcium interactions.

Successful derivation of a closed-form quantum path-integral solution for calcium.

Proposes future quantum-classical neural modeling with synchronized wave propagation.

Abstract

Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. \textbf{Objective}: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. \textbf{Method}: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. \textbf{Results}: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. \textbf{Conclusion}: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.