M.F. Wehner and W.G. Wolfer, Numerical evaluation of path integral solutions to FokkerPlanck equations. III. Time and functionally dependent coefficients, Phys. Rev. A 35, 1795-1801 (1987).  Home/Search   Document Not in Database   Summary   APS   Related Articles   Check

.... a systematic numerical procedure has been developed for fitting parameters in such stochastic nonlinear systems to data using methods of very fast simulated re annealing [58] and then integrating the path integral using a non Monte Carlo technique especially suited for nonlinear systems [123 125]. This methodology has been applied with success to military modeling [36,126] and to financial markets [41,42] and we will be using it in this neocortical system to correlate EEG to behavioral states [24] The key issue is that Riemannian geometry is not required to derive the mathematics of ....

....The second code develops the long time probability distribution from the Lagrangian fit by the first code. A robust and accurate histogram based (non Monte Carlo) path integral algorithm to calculate the long time probability distribution has been developed to handle nonlinear Lagrangians [123 125], which was extended to two dimensional problems [36] The histogram procedure recognizes that the distribution can be numerically approximated to a high degree of accuracy as sum of rectangles at points M i of height P i and width M i . For convenience, just consider a one dimensional system. ....

M.F. Wehner and W.G. Wolfer, "Numerical evaluation of path integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients," Phys. Rev. A 35, 1795-1801 (1987).

.... a systematic numerical procedure has been developed for fitting parameters in such stochastic nonlinear systems to data using methods of very fast simulated re annealing [58] and then integrating the path integral using a non Monte Carlo technique especially suited for nonlinear systems [123 125]. This methodology has been applied with success to military modeling [36,126] and to financial markets [41,42] and we will be using it in this neocortical system to correlate EEG to behavioral states [24] The key issue is that Riemannian geometry is not required to derive the mathematics of ....

....Most important contributions to the probability distribution P come from ranges of the time slice 6 and the action NL, such that 6 NL 1. By considering the contributions to the first and second moments of M for small time slices 6 , conditions on the time and variable meshes can be derived [123]. The time slice is determined by 6 (NL) throughout the ranges of M giving the most important contributions to the probability distribution P. The variable mesh, a function of M , is optimally chosen such that M is measured by the covariance g (diagonal in the neocortex due to ....

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M.F. Wehner and W.G. Wolfer, "Numerical evaluation of path-integral solutions to Fokker-Planck equations. I.," Phys. Rev. A 27, 2663-2670 (1983).

....second code, PATHINT, develops the long time probability distribution from the Lagrangian fit by the first code. A robust and accurate histogram based (non Monte Carlo) path integral algorithm to calculate the long time probability distribution has been developed to handle nonlinear Lagrangians [44,50,66 70], The histogram procedure recognizes that the distribution can be numerically approximated to a high degree of accuracy as sum of rectangles at points M i of height P i and width #M i . For convenience, just consider a one dimensional system. The above path integral representation can be ....

....differential equation. The coarser resolution is appropriate, typically required, for numerical solution of the time dependent pathintegral: By considering the contributions to the first and second moments of #M for small time slices # , conditions on the time and variable meshes can be derived [66]. The time slice essentially is determined by # # L ,where L is the static Lagrangian with dM d#=0, throughout the ranges of M giving the most important contributions to the probability distribution P. The variable mesh, a function of M is optimally chosen such that #M is ....

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. I., Phys. Rev. A 27, 2663-2670 (1983).

....a given physical system as a nonlinear multivariate GaussianMarkovian system. Standard Monte Carlo techniques typically fail for highly nonlinear problems. Only recently has it been possible to accurately calculate the evolution of a nonlinear path integral with complex boundary conditions [19]. We are currently extending these algorithms to two dimensions, and hope to extend them even further. Thus, the cost function L in the form in Eq. 20) is statistically fit to data by inserting a simulated temperature T 1 into the short time probability distribution with Lagrangian L given in ....

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path integral solutions to FokkerPlanck equations. III. Time and functionally dependent coefficients, Phys. Rev. A 35, 1795-1801 (1987).

....starting with 0 t t = In the step by step calculation, values of the probability density ) t p l are obtained at discrete points, and its values between two neighboring points can be obtained with a suitable interpolation scheme. The above procedure is known as path integration (see, e.g. Wehner and Wolfer 1983, Yu et al. 1997) The structure fails if either ) 0 t q exceeds c 0 q or ) 1 t q exceeds c 1 q . Equivalently, it fails when the average energy ) t L exceeds the corresponding critical level c l , determined from = c x c c c dx x f x f x x U 0 1 0 2 2 0 ) 2 1 ) n w l ....

Wehner, M. F. and Wolfer, W. G. (1983). "Numerical Evaluation of Path-Integral Solution to Fokker-Planck Equations." Physical Review A, 27(5), 2663-2670.

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M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes, Phys. Rev. A 28, 3003-3011 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. I., Phys. Rev. A 27, 2663-2670 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients, Phys. Rev. A 35, 1795-1801 (1987).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path integral solutions to FokkerPlanck equations. III. Time and functionally dependent coefficients, Phys. Rev. A 35, 1795-1801 (1987).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients, Phys. Rev. A 35, 1795-1801 (1987).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes, Phys. Rev. A 28, 3003-3011 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. I., Phys. Rev. A 27, 2663-2670 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients, Phys. Rev. A 35, 1795-1801 (1987).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes, Phys. Rev. A 28, 3003-3011 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. I., Phys. Rev. A 27, 2663-2670 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients, Phys. Rev. A 35, 1795-1801 (1987).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes, Phys. Rev. A 28, 3003-3011 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. I., Phys. Rev. A 27, 2663-2670 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, "Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes," Phys. Rev. A 28, 3003-3011 (1983).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients, Phys. Rev. A 35, 1795-1801 (1987).

No context found.

M.F. Wehner and W.G. Wolfer, Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes, Phys. Rev. A 28, 3003-3011 (1983).

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