asa01_lecture

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%A L. Ingber

%T Adaptive Simulated Annealing (ASA) and Path-Integral (PATHINT) Algorithms: Generic Tools for Complex Systems

%R ASA-PATHINT Lecture Plates

%I Physical Studies Institute

%D 2001

%O URL https://www.ingber.com/asa01_lecture.pdf

path01_lecture.pdf is a link to asa01_lecture.pdf.

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 COVER PAGE

 CONTENTS-1

 CONTENTS-2

 ADAPTIVE SIMULATED ANNEALING (ASA)

      Applications

      Hills and Valleys

      Outline of ASA Algorithm

      Index of Pre-Compile Tuning Parameters

      Index of Adaptive Tuning Parameters

      Reannealing Example

 MATHEMATICAL PHYSICS

      Nonlinear Nonequilibrium Multivariate Stochastic Aggregation

      Stochastic Differential Equation (SDE)

      Partial Differential Equation (PDE)

      Lagrangian Probability Distribution Function (PDF)

      Path-Integral Riemannian Geometry

           Fitting Variance With ASA

      Information

      Transformations Without Ito Calculus

      Intuitive Variables

           Euler-Lagrange Variational Equations

           Canonical Momenta Indicators (CMI)

 NUMERICAL PATH INTEGRATION (PATHINT)

      Applications

      Outline of PATHINT Algorithm

           Boundary Condition Sensitivity

           Mesh Limitations

      Probability Tree (PATHTREE)

           Standard Binomial Tree

           Deficiency of Standard Algorithm to Order sqrt(dt)

           Problems Generalizing The Standard Tree

           Probability PATHTREE

           Construction of PATHTREE

           Direct Calculation of Probability

                Numerical Derivatives of Expectation of Probability

                Alternative First Derivative Calculation of Probability

           PATHTREE vs PATHINT

           Black-Scholes (BS) and Ornstein-Uhlenbeck (OU) Examples

 GENERIC MESOSCOPIC NEURAL NETWORKS (MNN)

      Applications

      MNN Learning

      MNN Prediction

      MNN Parallel Processing

 SOME APPLICATIONS

      Statistical Mechanics of Financial Markets (SMFM)

           2-Factor Interest-Rate Model

                Lagrangian Representation

                ASA Fits

                Bond PDE/PATHINT

           Power-Law Model

                Multi-Factor Volatility Model

                PATHINT Options

                PATHINT Two-Factor

                x Market Indicators

           S&P Interday Futures-Cash

           Tick Resolution CMI Trading

      Statistical Mechanics of Combat (SMC)

           National Training Center -- Janus(T)

           Basic Equations of Aggregated Units

           Long-Time Correlations Test Short-Time Models

           CMI

      Statistical Mechanics of Neocortical Interactions (SMNI)

           Multiple Scales

                Microscopic Aggregation

           Short-Term Memory (STM)

           Electroencephalography (EEG)

                ASA Fits of CMI

           Chaos in SMNI

                Duffing Analog

                Noise Washes Out Chaos/PATHINT

      

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