Lester Ingber

Genetic Algorithms and Very Fast Simulated Reannealing: A comparison

We compare Genetic Algorithms (GA) with a functional search method, Very Fast Simulated Reannealing (VFSR), that not only is efficient in its search strategy, but also is statistically guaranteed to find the function optima. GA previously has been demonstrated to be competitive with other standard Boltzmann-type simulated annealing techniques. Presenting a suite of six standard test functions to GA and VFSR codes from previous studies, without any additional fine tuning, strongly suggests that VFSR can be expected to be orders of magnitude more efficient than GA.

Statistical mechanics of neocortical interactions: I. Basic formulation

An approach to collective aspects of the neocortical system is formulated by methods of modern nonlinear nonequilibrium statistical mechanics. Microscopic neuronal synaptic interactions, consistent with anatomical observations, are first spatially averaged over columnar domains. These spatially ordered domains retain contact with the original physical synaptic parameters, are consistent with observed columnar physiology, and are a suitable substrate for macroscopic spatial-temporal regions described by a Lagrangian formalism. Long-ranged influences from extrinsic and inter-regional afferents drive these short-ranged interactions, giving rise to several columnar mechanisms affecting macroscopic activity.

Multiple scales of statistical physics of the neocortex: Application to electroencephalography

The human neocortex is a complex physical and biological system that processes information at multiple spatial and temporal scales. This paper describes a statistical physics methodology to bridge several of these scales which are of current experimental interest. We propose specific algorithms to calculate neuronal processes underlying electroencephalographic and evoked potential data.

Statistical mechanics of nonlinear nonequilibrium financial markets

Abstract An approach to understanding the nature of markets is modelled using methods of modern nonlinear nonequilibrium statistical mechanics. This permits examination of the premise that markets can be described by nonlinear nonequilibrium Markovian distributions. Corrections to previous nonlinear continuous time models are explicitly presented. A quite general microscopic model is presented of individual agents operating on a market, and explicit relationships are derived between variables describing these agents and the macroscopic market.

Adaptive Simulated Annealing

Adaptive Simulated Annealing (ASA) is a C-language code that finds the best global fit of a nonlinear cost-function over a D-dimensional space. ASA has over 100 OPTIONS to provide robust tuning over many classes of nonlinear stochastic systems. These many OPTIONS help ensure that ASA can be used robustly across many classes of systems.

Statistical Mechanics of Neocortical Interactions: EEG Dispersion Relations

An approach is explicitly formulated to blend a local with a global theory to investigate oscillatory neocortical firings to determine the source and the information-processing 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 short-term memory (STM) capacity at the mesoscopic scales of columnar interactions, and which is consistent with other theories deriving similar dispersion relations at the macroscopic scales of electroencephalographic (EEG) and magnetoencephalographic (MEG) activity.

Application of statistical mechanics methodology to term-structure bond-pricing models

Recent work in statistical mechanics has developed new analytical and numerical techniques to solve coupled stochastic equations. This paper applies the very fast simulated re-annealing and path-integral methodologies to the estimation of the Brennan and Schwartz two-factor term structure model. It is shown that these methodologies can be utilized to estimate more complicated n-factor nonlinear models.

Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing - Volume 35

Stochastic global optimization is a very important subject, that hasapplications in virtually all areas of science and technology. Therefore there is nothing more opportune than writing a book about a successful and mature algorithm that turned out to be a good tool in solving difficult problems. Here we present some techniques for solving several problems by means of Fuzzy Adaptive Simulated Annealing (Fuzzy ASA), a fuzzy-controlled version of ASA, and by ASA itself. ASA is a sophisticated global optimization algorithm that is based upon ideas of the simulated annealing paradigm, coded in the C programming language and developed to statistically find the best global fit of a nonlinear constrained, non-convex cost function over a multi-dimensional space. By presenting detailed examples of its application we want to stimulate the readers intuition and make the use of Fuzzy ASA (or regular ASA) easier for everyone wishing to use these tools to solve problems. We kept formal mathematical requirements to a minimum and focused on continuous problems, although ASA isable to handle discrete optimization tasks as well. This book can be used by researchers and practitioners in engineering and industry, in courses on optimization for advanced undergraduate and graduate levels, and also for self-study.

Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading

A paradigm of statistical mechanics of financial markets (SMFM) using nonlinear non-equilibrium algorithms, first published in [1], 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 out-of-sample data, to demonstrate that they can profit from the SMFM model, to illustrate that these markets are likely not efficient.

Path-integral evolution of chaos embedded in noise: Duffing neocortical analog

A two-dimensional time-dependent 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, a non-Monte-Carlo path-integral algorithm that is particularly adept in handling nonlinear Fokker-Planck systems. This approach shows promise to investigate whether chaos in neocortex, as predicted by such models, can survive in noisy contexts.