Quantum calcium-ion interactions with EEG

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.Comment: published in Sc

Path-integral evolution of multivariate systems with moderate noise

A non Monte Carlo path-integral algorithm that is particularly adept at handling nonlinear Lagrangians is extended to multivariate systems. This algorithm is particularly accurate for systems with moderate noise.Comment: 15 PostScript pages, including 7 figure

Probability tree algorithm for general diffusion processes

Motivated by path-integral numerical solutions of diffusion processes, PATHINT, we present a new tree algorithm, PATHTREE, which permits extremely fast accurate computation of probability distributions of a large class of general nonlinear diffusion processes

Statistical mechanics of neocortical interactions: large-scale EEG influences on molecular processes

Recent calculations further supports the premise that large-scale synchronous firings of neurons may affect molecular processes. The context is scalp electroencephalography (EEG) during short-term memory (STM) tasks. The mechanism considered is $\mathbf{\Pi} = \mathbf{p} + q \mathbf{A}$ (SI units) coupling, where $\mathbf{p}$ is the momenta of free $\mathrm{Ca}^{2+}$ waves $q$ the charge of $\mathrm{Ca}^{2+}$ in units of the electron charge, and $\mathbf{A}$ the magnetic vector potential of current $\mathbf{I}$ from neuronal minicolumnar firings considered as wires, giving rise to EEG. Data has processed using multiple graphs to identify sections of data to which spline-Laplacian transformations are applied, to fit the statistical mechanics of neocortical interactions (SMNI) model to EEG data, sensitive to synaptic interactions subject to modification by $\mathrm{Ca}^{2+}$ waves.Comment: Accepted for publication in Journal of Theoretical Biolog

Statistical mechanics of neocortical interactions: EEG eigenfunctions of short-term memory

This paper focuses on how bottom-up neocortical models can be developed into eigenfunction expansions of probability distributions appropriate to describe short-term memory in the context of scalp EEG. The mathematics of eigenfunctions are similar to the top-down eigenfunctions developed by Nunez, albeit they have different physical manifestations. The bottom-up eigenfunctions are at the local mesocolumnar scale, whereas the top-down eigenfunctions are at the global regional scale. However, as described in several joint papers, our approaches have regions of substantial overlap, and future studies may expand top-down eigenfunctions into the bottom-up eigenfunctions, yielding a model of scalp EEG that is ultimately expressed in terms of columnar states of neocortical processing of attention and short-term memory.Comment: 5 PostScript page

Electroencephalographic field influence on calcium momentum waves

Macroscopic EEG fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered are macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential $\mathbf{A}$. The bottom-up process considered are $\mathrm{Ca}^{2+}$ waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of $\mathbf{A}$ on $\mathrm{Ca}^{2+}$ momentum, $\mathbf{p}$. The canonical momentum of a charged particle in an electromagnetic field, $\mathbf{\Pi} = \mathbf{p} + q \mathbf{A}$ (SI units), is calculated, where the charge of $\mathrm{Ca}^{2+}$ is $q = - 2 e$, $e$ is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG $\mathbf{A}$ can be quite influential on the momentum $\mathbf{p}$ of $\mathrm{Ca}^{2+}$ ions, in both classical and quantum mechanics. Molecular scales of $\mathrm{Ca}^{2+}$ wave dynamics are coupled with $\mathbf{A}$ fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting $\mathbf{A}$ models to EEG data as reported here, building tripartite models to develop $\mathbf{A}$ models, and studying long coherence times of $\mathrm{Ca}^{2+}$ waves in the presence of $\mathbf{A}$ due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the $\mathbf{p} + q \mathbf{A}$ interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention.Comment: Final draft. http://ingber.com/smni14_eeg_ca.pdf may be updated more frequentl