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Forecasting with Importance-Sampling and Path-Integrals

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are described as being useful to detail such systems. Method: ASA and PATHINT/PATHTREE have been demonstrated as being effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Results: Not only can selected systems in these three disciplines be aptly modeled, but results of detailed calculations have led to new results and insights not previously obtained. Conclusion: While optimization and path-integral algorithms are now quite well-known (at least to many scientists), these applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.