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Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography
 PHYS. REV. A
, 1991
"... A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electricalchemical properties of synaptic interactions. While not useful to yield insights at the single neuron lev ..."
Abstract

Cited by 47 (41 self)
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A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electricalchemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing largescale properties of shortterm memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numerical algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG and evoked potential data being collected to investigate genetic predispositions to alcoholism and to extract brain “signatures” of shortterm memory. Using the numerical algorithm of Very Fast Simulated ReAnnealing, it is demonstrated that SMNI can indeed fit this data within experimentally observed ranges of its underlying neuronalsynaptic parameters, and use the quantitative modeling results to examine physical neocortical mechanisms to discriminate between highrisk and lowrisk populations genetically predisposed to alcoholism. Since this first study is a control to span relatively long time epochs, similar to earlier attempts to establish such correlations, this discrimination is inconclusive because of other neuronal activity which can mask such effects. However, the SMNI model is shown to be consistent
Statistical Mechanics of Nonlinear Nonequilibrium Financial Markets: Applications to Optimized Trading
 MATH. MODELLING
, 1996
"... A paradigm of statistical mechanics of financial markets (SMFM) using nonlinear nonequilibrium algorithms, first published in L. Ingber, Mathematical Modelling, 5, 343361 (1984), is fit to multivariate financial markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to p ..."
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Cited by 41 (34 self)
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A paradigm of statistical mechanics of financial markets (SMFM) using nonlinear nonequilibrium algorithms, first published in L. Ingber, Mathematical Modelling, 5, 343361 (1984), is fit to multivariate financial markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical momenta are thereby derived and used as technical indicators in a recursive ASA optimization process to tune trading rules. These trading rules are then used on outofsample data, to demonstrate that they can profit from the SMFM model, to illustrate that these markets are likely not efficient.
structure, and role of background EEG activity. Part 4. Neural frame simulation
 Clin. Neurophysiol
, 2006
"... spatial power spectral density (PSD X), volume conduction ..."
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Cited by 41 (16 self)
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spatial power spectral density (PSD X), volume conduction
A neurobiological theory of meaning in perception. Part 1. Information and meaning in nonconvergent and nonlocal brain dynamics
 Int. J. Bifurc. Chaos
, 2003
"... Synchrony among multicortical EEGs 2 Freeman, Gaál & Jörnsten Information transfer and integration among functionally distinct areas of cerebral cortex of oscillatory activity requires some degree of phase synchrony of the trains of action potentials that carry the information prior to the integrati ..."
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Cited by 28 (14 self)
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Synchrony among multicortical EEGs 2 Freeman, Gaál & Jörnsten Information transfer and integration among functionally distinct areas of cerebral cortex of oscillatory activity requires some degree of phase synchrony of the trains of action potentials that carry the information prior to the integration. However, propagation delays are obligatory. Delays vary with the lengths and conduction velocities of the axons carrying the information, causing phase dispersion. In order to determine how synchrony is achieved despite dispersion, we recorded EEG signals from multiple electrode arrays on five cortical areas in cats and rabbits, that had been trained to discriminate visual or auditory conditioned stimuli. Analysis by timelagged correlation, multiple correlation and PCA, showed that maximal correlation was at zero lag and averaged.7, indicating that 50 % of the power in the gamma range among the five areas was at zero lag irrespective of phase or frequency. There were no stimulusrelated episodes of transiently increased phase locking among the areas, nor EEG "bursts " of transiently increased amplitude above the sustained level of synchrony. Three operations were identified to account for the sustained correlation. Cortices broadcast their outputs over divergentconvergent axonal
Nonlinear brain dynamics as macroscopic manifestation of underlying manybody dynamics
, 2006
"... ..."
Canonical momenta indicators of financial markets and neocortical
 EEG.” InInternational Conference on Neural Information Processing (ICONIP’96
, 1996
"... Abstract—A paradigm of statistical mechanics of financial markets (SMFM) is fit to multivariate financial markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabi ..."
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Cited by 16 (16 self)
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Abstract—A paradigm of statistical mechanics of financial markets (SMFM) is fit to multivariate financial markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical momenta are thereby derived and used as technical indicators in a recursive ASA optimization process to tune trading rules. These trading rules are then used on outofsample data, to demonstrate that they can profit from the SMFM model, to illustrate that these markets are likely not efficient. This methodology can be extended to other systems, e.g., electroencephalography. This approach to complex systems emphasizes the utility of blending an intuitive and powerful mathematicalphysics formalism to generate indicators which are used by AItype rulebased models of management. 1.
On the relationship of synaptic activity to macroscopic measurements: does coregistration of EEG with fMRI make sense?
 BRAIN TOPOGR
, 2000
"... A twoscale theoretical description outlines relationships between brain current sources and the resulting extracranial electric field, recorded as EEG. Finding unknown sources of EEG, the socalled "inverse problem", is discussed in general terms, with emphasis on the fundamental nonuniqueness of ..."
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Cited by 15 (0 self)
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A twoscale theoretical description outlines relationships between brain current sources and the resulting extracranial electric field, recorded as EEG. Finding unknown sources of EEG, the socalled "inverse problem", is discussed in general terms, with emphasis on the fundamental nonuniqueness of inverse solutions. Hemodynamic signatures, measured with fMRI, are expressed as voxel integrals to facilitate comparisons with EEG. Two generally distinct cell groups (1 and 2), generating EEG and fMRI signals respectively, are embedded within the much broader class of synaptic action fields. Cell groups 1 and 2 may or may not overlap in specific experiments. Implications of this incomplete overlap for coregistration studies are considered. Each experimental measure of brain function is generally sensitive to a different kind of source activity and to different spatial and temporal scales. Failure to appreciate such distinctions can exacerbate conflicting views of brain function that emphasize either global integration or functional localization.
Pathintegral evolution of chaos embedded in noise: Duffing neocortical analog. Mathl Computer Modelling 1996;23(3):43–53. Available from http://www.ingber.com/path96 duffing.pdf
"... Abstract—A two dimensional timedependent Duffing oscillator model of macroscopic neocortex exhibits chaos for some ranges of parameters. We embed this model in moderate noise, typical of the context presented in real neocortex, using PATHINT, anonMonteCarlo pathintegral algorithm that is particu ..."
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Cited by 13 (13 self)
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Abstract—A two dimensional timedependent Duffing oscillator model of macroscopic neocortex exhibits chaos for some ranges of parameters. We embed this model in moderate noise, typical of the context presented in real neocortex, using PATHINT, anonMonteCarlo pathintegral algorithm that is particularly adept in handling nonlinear FokkerPlanck systems. This approach shows promise to investigate whether chaos in neocortex, as predicted by such models, can survive in noisy contexts. Keywords: chaos, path integral, Fokker Planck, Duffing equation, neocortexPathintegral of Duffing model2 Ingber, Srinivasan and Nunez 1.
Statistical mechanics of neocortical interactions: Training and testing canonical momenta indicators of EEG
 Mathl. Computer Modelling
, 1998
"... Abstract—A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electricalchemical properties of synaptic interactions. While not useful to yield insights at the single ne ..."
Abstract

Cited by 13 (10 self)
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Abstract—A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electricalchemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing largescale properties of shortterm memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. Sets of EEG and evoked potential data were fit, collected to investigate genetic predispositions to alcoholism and to extract brain “signatures ” of shortterm memory. Adaptive Simulated Annealing (ASA), a global optimization algorithm, was used to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical momenta indicators (CMI) are thereby derived for individual’s EEG data. The CMI give better signal recognition than the raw data, and can be used to advantage as correlates of behavioral states. These results give strong quantitative support for an accurate intuitive picture, portraying neocortical interactions as having common algebraic or physics mechanisms that scale across quite disparate spatial scales and functional or behavioral phenomena, i.e., describing interactions among neurons, columns of neurons, and regional masses of neurons. This paper adds to these previous investigations two important aspects, a description of how the CMI may be used in source localization, and calculations using previously ASAfitted parameters in outofsample data.
Platonic Model of Mind as an Approximation to Neurodynamics
, 1997
"... Hierarchy of approximations involved in simplification of microscopic theories, from subcellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platoniclike model of mind based on psychological spaces. Objects and events in these spaces co ..."
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Cited by 12 (10 self)
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Hierarchy of approximations involved in simplification of microscopic theories, from subcellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platoniclike model of mind based on psychological spaces. Objects and events in these spaces correspond to quasistable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view.