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Register a new userStatistical mechanics of neocortical interactions: Portfolio of Physiological Indicators
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Added by
Lester Ingber
Publication date
2006
fields
Informatics Engineering
and research's language is
English
Authors
Lester Ingber
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There are several kinds of non-invasive imaging methods that are used to collect data from the brain, e.g., EEG, MEG, PET, SPECT, fMRI, etc. It is difficult to get resolution of information processing using any one of these methods. Approaches to integrate data sources may help to get better resolution of data and better correlations to behavioral phenomena ranging from attention to diagnoses of disease. The approach taken here is to use algorithms developed for the authors Trading in Risk Dimensions (TRD) code using modern methods of copula portfolio risk management, with joint probability distributions derived from the authors model of statistical mechanics of neocortical interactions (SMNI). The authors Adaptive Simulated Annealing (ASA) code is for optimizations of training sets, as well as for importance-sampling. Marginal distributions will be evolved to determine their expected duration and stability using algorithms developed by the author, i.e., PATHTREE and PATHINT codes.
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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 Mechanics of Neocortical Interactions (SMNI), and uses the authors Adaptive Simulated Annealing (ASA) code for optimizations of training sets, as well as for importance-sampling to apply the authors copula financial risk-management codes, Trading in Risk Dimensions (TRD), for assessments of risk and uncertainty. 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. A statistical mechanical model of neocortical interactions, developed by the author and tested successfully in describing short-term memory and EEG indicators, is the proposed model. Parameters with a given subset of macrocolumns will be fit using ASA to patterns representing ideas. Parameters of external and inter-regional interactions will be determined that promote or inhibit the spread of these ideas. Tools of financial risk management, developed by the author to process correlated multivariate systems with differing non-Gaussian distributions using modern copula analysis, importance-sampled using ASA, will enable bona fide correlations and uncertainties of success and failure to be calculated. Marginal distributions will be evolved to determine their expected duration and stability using algorithms developed by the author, i.e., PATHTREE and PATHINT codes.
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.
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 Algorithm 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).
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 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.
We provide an Information-Geometric formulation of Classical Mechanics on the Riemannian manifold of probability distributions, which is an affine manifold endowed with a dually-flat connection. In a non-parametric formalism, we consider the full set of positive probability functions on a finite sample space, and we provide a specific expression for the tangent and cotangent spaces over the statistical manifold, in terms of a Hilbert bundle structure that we call the Statistical Bundle. In this setting, we compute velocities and accelerations of a one-dimensional statistical model using the canonical dual pair of parallel transports and define a coherent formalism for Lagrangian and Hamiltonian mechanics on the bundle. Finally, in a series of examples, we show how our formalism provides a consistent framework for accelerated natural gradient dynamics on the probability simplex, paving the way for direct applications in optimization, game theory and neural networks.
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