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 authors work in Statistical Mechanic
s 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?
It is proposed to apply modern methods of nonlinear nonequilibrium statistical mechanics to develop software algorithms that will optimally respond to targets within short response times with minimal computer resources. This Statistical Mechanics Alg
orithm for Response to Targets (SMART) can be developed with a view towards its future implementation into a hardwired Statistical Algorithm Multiprocessor (SAM) to enhance the efficiency and speed of response to targets (SMART_SAM).
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 $math
bf{Pi} = mathbf{p} + q mathbf{A}$ (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.
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 neocor
tex, 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.
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 my
elinated 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 coherence 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 derive a string equation consistent with the global EEG model.
Previous work, mostly published, developed two-shell recursive trading systems. An inner-shell of Canonical Momenta Indicators (CMI) is adaptively fit to incoming market data. A parameterized trading-rule outer-shell uses the global optimization code
Adaptive Simulated Annealing (ASA) to fit the trading system to historical data. A simple fitting algorithm, usually not requiring ASA, is used for the inner-shell fit. An additional risk-management middle-shell has been added to create a three-shell recursive optimization/sampling/fitting algorithm. Portfolio-level distributions of copula-transformed multivariate distributions (with constituent markets possessing different marginal distributions in returns space) are generated by Monte Carlo samplings. ASA is used to importance-sample weightings of these markets. The core code, Trading in Risk Dimensions (TRD), processes Training and Testing trading systems on historical data, and consistently interacts with RealTime trading platforms at minute resolutions, but this scale can be modified. This approach transforms constituent probability distributions into a common space where it makes sense to develop correlations to further develop probability distributions and risk/uncertainty analyses of the full portfolio. ASA is used for importance-sampling these distributions and for optimizing system parameters.
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-dimensio
nal 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.
Real Options for Project Schedules (ROPS) has three recursive sampling/optimization shells. An outer Adaptive Simulated Annealing (ASA) optimization shell optimizes parameters of strategic Plans containing multiple Projects containing ordered Tasks.
A middle shell samples probability distributions of durations of Tasks. An inner shell samples probability distributions of costs of Tasks. PATHTREE is used to develop options on schedules.. Algorithms used for Trading in Risk Dimensions (TRD) are applied to develop a relative risk analysis among projects.
