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.
Deep Dive into 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 a
This project calculates quantum Ca 2+ interactions with EEG. In this paper, EEG is synonymous with large-scale neocortical firings during attentional tasks as measured by large-amplitude electroencephalographic (EEG) recordings. In this paper, only very specific calcium ions, Ca 2+ , are considered, those arising from regenerative calcium waves generated at tripartite neuron-astrocyteneuron synapses. Indeed, it is important to note that Ca 2+ ions, and specifically Ca 2+ waves, influence many processes in the brain, but this study focuses on free waves generated at tripartite synapses because of their calculated direct interactions with large synchronous neuronal firings.
Section 2 reviews the background of the main model used, Statistical Mechanics of Neocortical Interactions (SMNI).
Section 3 reviews the code Adaptive Simulated Annealing (ASA), used for optimization of many systems -fitting models to real data, e.g., fits to EEG data reported here.
Section 4 reviews the development of path-integral codes, PATHINT and qPATHINT, used for propagation of conditional probabilities and quantum-mechanical wave-functions, as reported here.
Section 5 gives new results of inclusion of quantum-mechanical interactions of Ca 2+ wave-packets with EEG.
Section 6 reviews some applications of this project. Section 7 gives the conclusion. The theory and codes for ASA and [q]PATHINT have been well tested across many disciplines by multiple users. This particular project most certainly is speculative, but it is testable. As reported here, fitting such models to EEG tests some aspects of this project. This is a somewhat indirect path, but not novel to many physics paradigms that are tested by experiment or computation. A detailed future path is described in the [q]PATHINT review Section.
While SMNI has been developed since 1981, and been confirmed by many tests, this evolving model including ionic scales has been part of multiple papers relatively recently, since 2012. Classical physics calculations support these extended SMNI models and are consistent with experimental data. Quantum physics calculations also support these extended SMNI models and, while they too are consistent with experimental data, it is quite speculative that they can persist in neocortex. Admittedly, it is surprising that detailed calculations continue to support this model, and so it is worth continued examination it until it is theoretically or experimentally proven to be false.
SMNI has been developed since 1981, scaling aggregate synaptic interactions to neuronal firings, up to minicolumnar-macrocolumnar columns of neurons to mesocolumnar dynamics, up to columns of neuronal firings, up to regional macroscopic sites (Ingber, 1981(Ingber, , 1982(Ingber, , 1983(Ingber, , 1984(Ingber, , 1985a(Ingber, , 1994)).
SMNI has calculated agreement/fits with experimental data from various aspects of neocortical interactions, e.g., properties of short-term memory (STM) (Ingber, 2012a), including its capacity (auditory 7 ± 2 and visual 4 ± 2) (Ericsson and Chase, 1982;Zhang and Simon, 1985), duration, stability, primacy versus recency rule, as well other phenomenon, e.g., Hick’s law (Hick, 1952;Ingber, 1999;Jensen, 1987), interactions within macrocolumns calculating mental rotation of images, etc (Ingber, 1982(Ingber, , 1983(Ingber, , 1984(Ingber, , 1985a(Ingber, , 1994)). SMNI scaled mesocolumns across neocortical regions to fit EEG data (Ingber, 1997a(Ingber, ,b, 2012a)). Fig. 1 depicts this model (Ingber, 1983).
Figure 1 illustrates three SMNI biophysical scales (Ingber, 1982(Ingber, , 1983))
The short-time conditional probability distribution of firing of a given neuron firing given justprevious firings of other neurons is calculated from chemical and electrical intra-neuronal interactions (Ingber, 1982(Ingber, , 1983)). Given its previous interactions with k neurons within τ j of 5-10 msec, the conditional probability that neuron j fires (σ j = +1) or does not fire (σ j = -1) is
The contribution to polarization achieved at an axon given activity at a synapse, taking into account averaging over different neurons, geometries, etc., is given by Γ, the “intra-neuronal” probability distribution. Ψ is the “inter-neuronal” probability distribution, of thousands of quanta of neurotransmitters released at one neuron’s presynaptic site effecting a (hyper-)polarization at another neuron’s postsynaptic site, taking into account interactions with neuromodulators, etc. This development holds for Γ Poisson, and for Ψ Poisson or Gaussian.
V j is the depolarization threshold in the somatic-axonal region. v jk is the induced synaptic polarization of E or I type at the axon, and φ jk is its variance. The efficacy a jk is a sum of A jk from the connectivity between neurons, activated if the impinging k-neuron fires, and B jk from spontaneous background noise. The efficacy is related to the impedance across synaptic gaps.
Aggregation up to the mesoscopic scale from th
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