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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 ..."
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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.
Statistical mechanics of neocortical interactions. Dynamics of synaptic modification, Phys
 Rev. A
, 1983
"... A theory developed by the author to describe macroscopic neocortical interactions demonstrates that empirical values of chemical and electrical parameters of synaptic interactions establish several minima of the pathintegral Lagrangian as a function of excitatory and inhibitory columnar firings. Th ..."
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Cited by 37 (34 self)
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A theory developed by the author to describe macroscopic neocortical interactions demonstrates that empirical values of chemical and electrical parameters of synaptic interactions establish several minima of the pathintegral Lagrangian as a function of excitatory and inhibitory columnar firings. The number of possible minima, their time scales of hysteresis and probable reverberations, and their nearestneighbor columnar interactions are all consistent with wellestablished empirical rules of human shortterm memory. Thus, aspects of conscious experience are derived from neuronal firing patterns, using modern methods of nonlinear nonequilibrium statistical mechanics to develop realistic explicit synaptic interactions.
Statistical mechanics of multiple scales of neocortical interactions
 in Neocortical Dynamics and Human EEG Rhythms, (Edited by P.L. Nunez
, 1995
"... 14. Statistical mechanics of multiple scales of neocortical interactions ..."
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Cited by 36 (18 self)
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14. Statistical mechanics of multiple scales of neocortical interactions
Mathematical comparison of combat computer models to exercise data
 Mathl. Comput. Modelling
, 1991
"... The powerful techniques of modern nonlinear statistical mechanics are used to compare battalionscale combat computer models (including simulations and wargames) to exercise data. This is necessary if largescale combat computer models are to be extrapolated with confidence to develop battlemanagem ..."
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Cited by 35 (33 self)
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The powerful techniques of modern nonlinear statistical mechanics are used to compare battalionscale combat computer models (including simulations and wargames) to exercise data. This is necessary if largescale combat computer models are to be extrapolated with confidence to develop battlemanagement, C 3 and procurement decisionaids, and to improve training. This modeling approach to battalionlevel missions is amenable to reasonable algebraic and/or heuristic approximations to drive higherechelon computer models. Each data set is fit to several candidate shorttime probability distributions, using methods of ‘‘very fast simulated reannealing’ ’ with a Lagrangian (timedependent algebraic costfunction) derived from nonlinear stochastic rate equations. These candidate mathematical models are further tested by using pathintegral numerical techniques we have dev eloped to calculate longtime probability distributions spanning the combat scenario. We hav e demonstrated proofs of principle, that battalionlevel combat exercises can be well represented by the computer simulation JANUS(T), and that modern methods of nonlinear nonequilibrium statistical mechanics can well model these systems. Since only relatively simple drifts and diffusions were required, in larger systems, e.g., at brigade and division levels, it might be possible to ‘‘absorb’ ’ other important variables (C 3, human factors, logistics, etc.) into more nonlinear mathematical forms. Otherwise, this battalionlevel model should be supplemented with a ‘‘tree’ ’ of branches corresponding to estimated values of these variables.
Statistical mechanics of neocortical interactions. EEG dispersion relations
 IEEE Trans. Biomed. Eng
, 1985
"... Abstract—An approach is explicitly formulated to blend a local with a global theory to investigate oscillatory neocortical firings, to determine the source and the informationprocessing nature of the alpha rhythm. The basis of this optimism is founded on a statistical mechanical theory of neocortica ..."
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Cited by 29 (27 self)
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Abstract—An approach is explicitly formulated to blend a local with a global theory to investigate oscillatory neocortical firings, to determine the source and the informationprocessing nature of the alpha rhythm. The basis of this optimism is founded on a statistical mechanical theory of neocortical interactions which has had success in numerically detailing properties of shorttermmemory (STM) capacity at the mesoscopic scales of columnar interactions, and which is consistent with other theory deriving similar dispersion relations at the macroscopic scales of electroencephalographic (EEG) and magnetoencephalographic (MEG) activity.
Generic Mesoscopic Neural Networks Based on Statistical Mechanics of Neocortical Interactions
 Bull. Am. Phys. Soc
, 1992
"... able nonlinear stochastic development [113]. The basic approach of the SMNI has been to statistically aggregate synaptic and neuronal interactions, from microscopic systematics to mesoscopic interactions among minicolumns of hundreds of neurons, to macroscopic macrocolumnar interactions among thous ..."
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Cited by 28 (23 self)
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able nonlinear stochastic development [113]. The basic approach of the SMNI has been to statistically aggregate synaptic and neuronal interactions, from microscopic systematics to mesoscopic interactions among minicolumns of hundreds of neurons, to macroscopic macrocolumnar interactions among thousands of minicolumns, to approach regional spatial scales of several millimeters to several centimeters. The theory has been tested by verifying observations at the mesoscopic scale, e.g., shortterm memory phenomena [4,6], and at the macroscopic scale, e.g., electroencephalography (EEG) [4,5,13]. A current description of the theory to date is in Ref. [13], where extensions were made to the SMNI to correlate human behavioral states to circuitries measured by EEG electrode recordings, an ongoing project. While the experimental resolution of EEG typically is on the order of several centimeters, new work has shown that under some circumstances this resolution can be sharpened to several millimet
Extracting Oscillations: Neuronal Coincidence Detection with Noisy Periodic Spike Input
, 1998
"... How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integra ..."
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Cited by 19 (6 self)
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How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integrateandfire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code.
Pathintegral Riemannian contributions to nuclear Schrödinger equation
 REV. D
, 1984
"... Several studies in quantum mechanics and statistical mechanics have formally established that nonflat metrics induce a difference in the potential used to define the pathintegral Lagrangian from that used to define the differential Schrödinger Hamiltonian. Arecent study has described a statistical ..."
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Cited by 16 (16 self)
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Several studies in quantum mechanics and statistical mechanics have formally established that nonflat metrics induce a difference in the potential used to define the pathintegral Lagrangian from that used to define the differential Schrödinger Hamiltonian. Arecent study has described a statistical mechanical biophysical system in which this effect is large enough to be measurable. This study demonstrates that the nucleonnucleon velocitydependent interaction derived from meson exchanges is a quantum mechanical system in which this effect is also large enough to be measurable.
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.