Statistical Mechanics Of Neocortical Interactions Research Articles

Hybrid Classical-quantum Computing: Applications to Statistical Mechanics of Neocortical Interactions

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the author. However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks in previous codes used to fit EEG data to the SMNI model, that included the analytic forms for the quantum processes but now replaced by qPATHINT. The author's Adaptive Simulated Annealing (ASA) importance-sampling optimization code is used for fitting the combined classical-quantum system. Gaussian Quadratures is used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

Quantum Calcium-Ion Affective Influences Measured by EEG

Background: Since circa 1980, a model of neocortical interactions, Statistical Mechanics of Neocortical Interactions (SMNI) has been successful in calculating many experimental phenomena, including fits to electroencephalographic (EEG) data in attention tasks, using an importance-sampling code Adaptive Simulated Annealing (ASA). The SMNI model is developed in the context of classical path-integrals, which affords intuitive insights as well as direct numerical benefits, e.g., using the effective Action as a a cost/objective function for parameter fits to data. Objective: Previous authors have fit affective EEG data to neural-network models. This project seeks to use models based on physics and biology to fit this same data. Previous work showed improvements in fits to EEG for attention states; this project extends these methods to affective states. Method: Path integrals are used in both classical and quantum contexts. Classical path integrals are used to define a cost/objective function to fit data, and quantum path integrals are used to derive a closed-form analytic expression for Ca-ion waves in the presence of a magnetic vector potential which is generated by highly synchronous neuronal firings which give rise to EEG. ASA is used to fit EEG data. Results: The mathematical-physics and computer parts of the study are successful, in that cost/objective functions used to fit EEG data using these models are consistent with previous work published by other authors. However, since the SMNI model includes these quantum effects, this is another reason to continue examining these issues. The results here are consistent, not better, than previous work using neural-network models, albeit only one parameter was used here, instead of multiple filters and kernels used previously on such data. Conclusion: Although these quantum effects are highly speculative, explicit calculations have shown them to be consistent with experimental data, at least to date. The current supercomputer project extends this model to affective/emotion data. Results from several authors using neural-network approaches at individual electrode sites show some predictive capabilities; the results given here are consistent with these other results. However, since the SMNI model includes these quantum effects, this is another reason to continue examining these issues.

Quantum Calcium-Ion Interactions with EEG

Background: 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. 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. 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. 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. Conclusions: 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.

Quantum Calcium-Ion Interactions with EEG

Background: 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. 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. 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. 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. Conclusions: 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.

Quantum Calcium-Ion Interactions with EEG

Background: 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. 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. 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. 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. Conclusions: 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.

Quantum Variables in Finance and Neuroscience II

Background: A path-integral algorithm, PATHINT used previously for several systems, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems into qPATHINT. Previous publications applied qPATHINT to two systems developed by the author, in neocortical interactions and financial options. Also, previous publications using classical PATHINT have developed a statistical mechanics of neocortical interactions (SMNI) that has been fitted to EEG data under attentional experimental paradigms. Classical PATHINT also has been published demonstrating development of Eurodollar options in industrial applications. Objective: A study is required to see if the qPATHINT algorithm can scale sufficiently to further develop real-world calculations in these two systems, requiring interactions between classical and quantum scales. A new algorithm is needed to develop interactions between classical and quantum scales. Method: Both systems are developed using mathematical-physics methods of path integrals in quantum spaces. Supercomputer pilot studies using XSEDE.org resources tested various dimensions for their scaling limits. For the financial options study, all traded Greeks are calculated for Eurodollar options in quantum-money spaces. For the neuroscience study, tripartite neuron-astrocyte-neuron Ca-ion waves are propagated for 100's of msec. For the neuroscience system, the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time, in the absence of shocks, that is used to calculate classical-physics interactions among scales. Results: The mathematical-physics and computer parts of the study are successful for both systems. A 3-dimensional path-integral propagation of qPATHINT for both systems is within normal computational bounds on supercomputers. The neuroscience quantum path-integral also has a closed solution at arbitrary time that tests the multiple-scale model including the quantum scale. Conclusion: Each of the two systems considered contribute insight into applications of qPATHINT to the other system, leading to new algorithms presenting time-dependent propagation of interacting quantum and classical scales. This can be achieved by propagating qPATHINT and PATHINT in synchronous time for the interacting systems, which is a future set of studies.

Options on Quantum Money: Quantum Path-Integral with Serial Shocks

The author previously developed a numerical multivariate path-integral algorithm, PATHINT, which has been applied to several classical physics systems, including statistical mechanics of neocortical interactions, options in financial markets, and other nonlinear systems including chaotic systems. A new quantum version, qPATHINT, has the ability to take into account nonlinear and time-dependent modifications of an evolving system. qPATHINT is shown to be useful to study some aspects of serial changes to systems. Applications to options on quantum money and blockchains in financial markets are discussed.

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

Calculations further support 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 Π=p+qA (SI units) coupling, where p is the momenta of free Ca2+ waves, q the charge of Ca2+ in units of the electron charge, and A the magnetic vector potential of current 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 Ca2+ waves.

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 II = p qA (SI units) coupling, where p is the momenta of free Ca2 waves q the charge of Ca2 in units of the electron charge, and A the magnetic vector potential of current I from neuronal minicolumnar firings considered as wires, giving rise to EEG. New data has been used and carefully 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 Ca2 waves.

Biological impact on military intelligence: application or metaphor?

Ideas by Statistical Mechanics (ISM) is a generic program to model evolution and propagation of ideas/patterns throughout populations subjected to endogenous and exogenous interactions. The program is based on the author's work in Statistical Mechanics of Neocortical Interactions (SMNI). This product can be used for decision support for projects ranging from diplomatic, information, military, and economic (DIME) factors of propagation/evolution of ideas, to commercial sales, trading indicators across sectors of financial markets, advertising and political campaigns, etc. It seems appropriate to base an approach for propagation of ideas on the only system so far demonstrated to develop and nurture ideas, i.e., the neocortical brain. The issue here is whether such biological intelligence is a valid application to military intelligence, or is it simply a metaphor?

Biological Impact on Military Intelligence: Application or Metaphor?

Ideas by Statistical Mechanics (ISM) is a generic program to model evolution and propagation of ideas/patterns throughout populations subjected to endogenous and exogenous interactions. The program is based on the author's work in Statistical Mechanics of Neocortical Interactions (SMNI). This product can be used for decision support for projects ranging from diplomatic, information, military, and economic (DIME) factors of propagation/evolution of ideas, to commercial sales, trading indicators across sectors of financial markets, advertising and political campaigns, etc. It seems appropriate to base an approach for propagation of ideas on the only system so far demonstrated to develop and nurture ideas, i.e., the neocortical brain. The issue here is whether such biological intelligence is a valid application to military intelligence, or is it simply a metaphor?

Electroencephalographic field influence on calcium momentum waves

Macroscopic electroencephalographic (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 is macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential A. The bottom-up process considered is Ca2+ 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 A on Ca2+ momentum, p. The canonical momentum of a charged particle in an electromagnetic field, Π=p+qA (SI units), is calculated, where the charge of Ca2+ is q=−2e, e is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG A can be quite influential on the momentum p of Ca2+ ions, in both classical and quantum mechanics. Molecular scales of Ca2+ wave dynamics are coupled with A fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting A models to EEG data as reported here, building tripartite models to develop A models, and studying long coherence times of Ca2+ waves in the presence of A due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the p+qA 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.

Influence of Macrocolumnar EEG on Ca Waves

A smoking gun for explicit top-down neocortical mechanisms that directly drive bottom-up processes that describe memory, attention, etc. 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 A. The bottom-up process considered are C2 waves prominent in synaptic and extracellar processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of A C2 momentum, p. The canonical momentum of a charged particle in an electromagnetic field, Pi=p qA (SI units), is calculated, where the charge of C2 is q=2e, e is the magnitude of the charge of an electron, valid in both classical and quantum mechanics. It is shown that A is large enough to influence p. This suggests that, instead of the common assumption that C2 waves contribute to neuronal activity, they may in fact at times be caused by the influence of A of larger-scale EEG.

Electroencephalographic Field Influence on Calcium Momentum Waves

Macroscopic electroencephalographic (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.

Computational Algorithms Derived from Multiple Scales of Neocortical Processing

A statistical mechanics of neocortical interactions of columnar activity and the vector potential of minicolumnar electromagnetic activity provide a context to explore neocortical information processes and influences on cognitive processing at multiple scales, i.e., mesoscopic (columnar scales), macroscopic (mesoscopic influences at regional scales), and microscopic (mesoscopic influences of ions affecting interactions between and among neurons and astrocytes). Even within this confined context, a case has been made that it should not be expected that the proposed Holy Grail of neuroscience, i.e., to ultimately explain all brain processing in terms of a nonlinear science at molecular scales, is at all realistic. As with many Crusades for some truths, other truths can be trampled.

Columnar Electromagnetic Influences on Short-Term Memory at Multiple Scales

For several decades the stated Holy Grail of chemical, biological and biophysical research into neocortical information processing has been to reduce such neocortical phenomena into specific bottom-up molecular and smaller-scale processes. Over the past three decades, with regard to short-term memory (STM) and long-term memory (LTM) phenomena, which themselves are likely components of other phenomena like attention and consciousness, a statistical mechanics of neocortical interactions (SMNI) approach has yielded specific details of STM capacity, duration and stability not present in molecular approaches, but it is clear that most molecular approaches consider it inevitable that their reductionist approaches at molecular and possibly even quantum scales will yet prove to be causal explanations of such phenomena. The SMNI approach is a bottom-up aggregation from synaptic scales to columnar and regional scales of neocortex, and has been merged with larger non-invasive EEG scales with other colleagues – all at scales much coarser than molecular scales. As with many Crusades for some truths, other truths can be trampled. It is proposed that an SMNI vector potential (SMNI-VP) constructed from magnetic fields induced by neuronal electrical firings, at thresholds of collective minicolumnar activity with laminar specification, can give rise to causal top-down mechanisms that effect molecular excitatory and inhibitory processes in STM and LTM. A specific example might be causal influences on momentum $\mathbf{p}$ of Ca$^{2 }$ ions by the SMNI-VP $\mathbf{A}$, as calculated by the canonical momentum $\mathbf{q}$, $\mathbf{q} = \mathbf{p} - e \mathbf{A}$, where $e$ is the electron coulomb charge and $c$ is the speed of light, which may be applied either classically or quantum-mechanically. Such a smoking gun for top-down effects awaits forensic in vivo experimental verification, requiring appreciating the necessity and due diligence of including true multiple-scale interactions across orders of magnitude in the complex neocortical environment.

Neocortical dynamics at multiple scales: EEG standing waves, statistical mechanics, and physical analogs

The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the importance of myelinated axon propagation delays and periodic boundary conditions in the cortical-white matter system, which is topologically close to a spherical shell. By contrast, the proposed local mechanisms are multiscale interactions between cortical columns via short-ranged non-myelinated fibers. A mechanical model consisting of a stretched string with attached nonlinear springs demonstrates the general idea. The string produces standing waves analogous to large-scale coherent EEG observed in some brain states. The attached springs are analogous to the smaller (mesoscopic) scale columnar dynamics. Generally, we expect string displacement and EEG at all scales to result from both global and local phenomena. A statistical mechanics of neocortical interactions (SMNI) calculates oscillatory behavior consistent with typical EEG, within columns, between neighboring columns via short-ranged non-myelinated fibers, across cortical regions via myelinated fibers, and also derives a string equation consistent with the global EEG model.

Statistical Mechanics of Neocortical Interactions: Columnar EEG

It is demonstrated that local columnar firings of neocortex, as modeled by a Statistical Mechanics of Neocortical Interactions (SMNI), supports multiple firing regions of multiple oscillatory processing, at frequencies consistent with observed regional electroencephalography (EEG). Direct calculations of the nonlinear multivariate Euler-Lagrange (EL) equations of the SMNI Lagrangian, giving most likely states of the system, are performed for three prototypical cases, predominately excitatory columnar firings, predominately inhibitory columnar firings, and in between balanced columnar firings, with and without a centering mechanism (based on observed changes in stochastic background of presynaptic interactions) which pulls more stable states into the physical firings ranges. These calculations are repeated for the visual neocortex, which has twice as many neurons/minicolumn as other neocortical regions. The nonlinearities lead to very long codes, and so the EL equations are presented here as graphs over the firing space.

Statistical Mechanics of Neocortical Interactions: Nonlinear Columnar Electroencephalography

Columnar firings of neocortex, modeled by a statistical mechanics of neocortical interactions (SMNI), are investigated for conditions of oscillatory processing at frequencies consistent with observed electroencephalography (EEG). A strong inference is drawn that physiological states of columnar activity receptive to selective attention support oscillatory processing in observed frequency ranges. Direct calculations of the Euler-Lagrange (EL) equations which are derived from functional variation of the SMNI probability distribution, giving most likely states of the system, are performed for three prototypical Cases, dominate excitatory columnar firings, dominate inhibitory columnar firings, and in-between balanced columnar firings, with and without a Centering mechanism (CM) (based on observed changes in stochastic background of presynaptic interactions) which pulls more stable states into the physical firings ranges. Only states with the CM exhibit robust support for these oscillatory states. These calculations are repeated for the visual neocortex, which has twice as many neurons/minicolumn as other neocortical regions. These calculations argue that robust columnar support for common EEG activity requires the same columnar presynaptic parameter necessary for ideal short-term memory (STM). It is demonstrated at this columnar scale, that both shifts in local columnar presynaptic background as well as local or global regional oscillatory interactions can effect or be affected by attractors that have detailed experimental support to be considered states of STM. Including the CM with other proposed mechanisms for columnar-glial interactions and for glial-presynaptic background interactions, a path for future investigations is outlined to test for quantum interactions, enhanced by magnetic fields from columnar EEG, that directly support cerebral STM and computation by controlling presynaptic noise. This interplay can provide mechanisms for information processing and computation in mammalian neocortex.

Statistical Mechanics of Neocortical Interactions: Nonlinear Columnar Electroencephalography

Columnar firings of neocortex, modeled by a statistical mechanics of neocortical interactions (SMNI), are investigated for conditions of oscillatory processing at frequencies consistent with observed electroencephalography (EEG). A strong inference is drawn that physiological states of columnar activity receptive to selective attention support oscillatory processing in alpha, beta and theta ranges. Direct calculations of the Euler-Lagrange (EL) equations which are derived from functional variation of the SMNI probability distribution, giving most likely states of the system, are performed for three prototypical Cases, predominately excitatory columnar firings, predominately inhibitory columnar firings, and in-between balanced columnar firings, with and without a Centering mechanism (based on observed changes in stochastic background of presynaptic interactions) which pulls more stable states into the physical firings ranges. Only states with the Centering mechanism exhibit robust support for these oscillatory states. These calculations are repeated for the visual neocortex, which has twice as many neurons/minicolumn as other neocortical regions. Including the Centering mechanism with other proposed mechanisms for columnar-glial magnetic interactions and for glial-presynaptic background interactions, a path for future investigations is outlined to test for quantum-classical interactions that directly support cerebral memory and computation.