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204
Simulated annealing: Practice versus theory
 Mathl. Comput. Modelling
, 1993
"... this paper "ergodic" is used in a very weak sense, as it is not proposed, theoretically or practically, that all states of the system are actually to be visited ..."
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Cited by 156 (20 self)
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this paper "ergodic" is used in a very weak sense, as it is not proposed, theoretically or practically, that all states of the system are actually to be visited
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 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 Mechanical Aids to Calculating Term Structure Models
 Rev. A
, 1990
"... This paper describes application of the very fast simulated reannealing and pathintegral methodologies to the estimation of the Brennan and Schwartz twofactor termstructure (timedependent) model of bond prices. It is shown that these methodologies can be utilized to estimate more complicated nf ..."
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Cited by 33 (30 self)
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This paper describes application of the very fast simulated reannealing and pathintegral methodologies to the estimation of the Brennan and Schwartz twofactor termstructure (timedependent) model of bond prices. It is shown that these methodologies can be utilized to estimate more complicated nfactor nonlinear models. Applications to other systems are stressed. Statistical mechanical aids2 Lester Ingber 1. INTRODUCTION
Application of statistical mechanics methodology to termstructure bondpricing models
 Mathl. Comput. Modelling
, 1991
"... Recent work in statistical mechanics has developed new analytical and numerical techniques to solve coupled stochastic equations. This paper applies the very fast simulated reannealing and pathintegral methodologies to the estimation of the Brennan and Schwartz twofactor term structure model. It ..."
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Cited by 32 (28 self)
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Recent work in statistical mechanics has developed new analytical and numerical techniques to solve coupled stochastic equations. This paper applies the very fast simulated reannealing and pathintegral methodologies to the estimation of the Brennan and Schwartz twofactor term structure model. It is shown that these methodologies can be utilized to estimate more complicated nfactor nonlinear models. 1. CURRENT MODELS OF TERM STRUCTURE The modern theory of term structure of interest rates is based on equilibrium and arbitrage models in which bond prices are determined in terms of a few state variables. The onefactor models of Cox, Ingersoll and Ross (CIR) [14], and the twofactor models of Brennan and Schwartz (BS) [59] have been instrumental in the development of the valuation of interest dependent securities. The assumptions of these models include: • Bond prices are functions of a number of state variables, one to several, that follow Markov processes. • Inv estors are rational and prefer more wealth to less wealth. • Inv estors have homogeneous expectations.
Harmonic analysis and propagators on homogeneous spaces
 Phys. Rep
, 1990
"... 2. The heat kernel and the Schwinger—DeWitt expansion 7 Riemann—Liouville integral 48 3. Example: the Einstein universe II 8.3. The heat kernel Ofl S~in terms of fractional deriva4. The eigenfunction expansion on a homogeneous space 14 tives 5)) ..."
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Cited by 24 (2 self)
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2. The heat kernel and the Schwinger—DeWitt expansion 7 Riemann—Liouville integral 48 3. Example: the Einstein universe II 8.3. The heat kernel Ofl S~in terms of fractional deriva4. The eigenfunction expansion on a homogeneous space 14 tives 5))
Statistical mechanics of neocortical interactions: Multiple scales of EEG
, 1993
"... The statistical mechanics of neocortical interactions (SMNI) approach derives a theoretical model for aggregated neuronal activity that defines the “dipole” assumed by many EEG researchers. This defines a nonlinear stochastic filter to extract EEG signals. ..."
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Cited by 19 (19 self)
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The statistical mechanics of neocortical interactions (SMNI) approach derives a theoretical model for aggregated neuronal activity that defines the “dipole” assumed by many EEG researchers. This defines a nonlinear stochastic filter to extract EEG signals.
Abelian magnetic monopole dominance in quark confinement
"... We prove Abelian magnetic monopole dominance in the string tension of QCD. Abelian and monopole dominance in low energy physics of QCD has been confirmed for various quantities by recent Monte Carlo simulations of lattice gauge theory. In order to prove this dominance, we use the reformulation of co ..."
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Cited by 18 (15 self)
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We prove Abelian magnetic monopole dominance in the string tension of QCD. Abelian and monopole dominance in low energy physics of QCD has been confirmed for various quantities by recent Monte Carlo simulations of lattice gauge theory. In order to prove this dominance, we use the reformulation of continuum YangMills theory in the maximal Abelian gauge as a deformation of a topological field theory of magnetic monopoles, which was proposed in the previous article by the author. This reformulation provides an efficient way for incorporating the magnetic monopole configuration as a topological nontrivial configuration in the functional integral. We derive a version of the nonAbelian Stokes theorem and use it to estimate the expectation value of the Wilson loop. This clearly exhibits the role played by the magnetic monopole as an origin of the Berry phase in the calculation of the Wilson loop in the manifestly gauge invariant manner. We show that the string tension derived from the diagonal (abelian) Wilson loop in the topological field theory (studied in the previous article) converges to that of the full nonAbelian Wilson loop in the limit of large Wilson loop. Therefore this result (together with the previous result) completes the proof of quark confinement in QCD based on the criterion of the area law of the full nonAbelian Wilson loop. Key words: quark confinement, topological field theory, magnetic monopole, non