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42
Very Fast Simulated ReAnnealing
, 1989
"... This paper contributes to this methodology by presenting an improvement over previous algorithms. Sections II and III give a short outline of previous Boltzmann annealing (BA) and fast Cauchy fast annealing (FA) algorithms. Section IV presents the new very fast algorithm. Section V enhances this alg ..."
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Cited by 196 (33 self)
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This paper contributes to this methodology by presenting an improvement over previous algorithms. Sections II and III give a short outline of previous Boltzmann annealing (BA) and fast Cauchy fast annealing (FA) algorithms. Section IV presents the new very fast algorithm. Section V enhances this algorithm with a reannealing modification found to be extremely useful for multidimensional parameterspaces. This method will be referred to here as very fast reannealing (VFR)
Noisy Time Series Prediction using a Recurrent Neural Network and Grammatical Inference
 Machine Learning
, 2001
"... Financial forecasting is an example of a signal processing problem which is challenging due to small sample sizes, high noise, nonstationarity, and nonlinearity. Neural networks have been very successful in a number of signal processing applications. We discuss fundamental limitations and inherent ..."
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Cited by 49 (0 self)
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Financial forecasting is an example of a signal processing problem which is challenging due to small sample sizes, high noise, nonstationarity, and nonlinearity. Neural networks have been very successful in a number of signal processing applications. We discuss fundamental limitations and inherent difficulties when using neural networks for the processing of high noise, small sample size signals. We introduce a new intelligent signal processing method which addresses the difficulties. The method proposed uses conversion into a symbolic representation with a selforganizing map, and grammatical inference with recurrent neural networks. We apply the method to the prediction of daily foreign exchange rates, addressing difficulties with nonstationarity, overfitting, and unequal a priori class probabilities, and we find significant predictability in comprehensive experiments covering 5 different foreign exchange rates. The method correctly predicts the direction of change for th...
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 48 (42 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 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 38 (35 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
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 33 (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.
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.
Adaptive Simulated Annealing (ASA)
"... Adaptive Simulated Annealing (ASA) is a Clanguage code developed to statistically find the best global fit of a nonlinear constrained nonconvex costfunction over aDdimensional space. This algorithm permits an annealing schedule for “temperature ” T decreasing exponentially in annealingtime k, T ..."
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Cited by 25 (2 self)
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Adaptive Simulated Annealing (ASA) is a Clanguage code developed to statistically find the best global fit of a nonlinear constrained nonconvex costfunction over aDdimensional space. This algorithm permits an annealing schedule for “temperature ” T decreasing exponentially in annealingtime k, T = T 0 exp(−ck 1/D). The introduction of reannealing also permits adaptation to changing sensitivities in the multidimensional parameterspace. This annealing schedule is faster than fast Cauchy annealing, where T = T 0/k, and much faster than Boltzmann annealing, where T = T 0/lnk. ASA has over 100 OPTIONS to provide robust tuning over many classes of nonlinear stochastic systems.
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.