Author
Herbert Goldstein
Bio: Herbert Goldstein is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 10662 citations.
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TL;DR: The Weighted Histogram Analysis Method (WHAM) as mentioned in this paper is an extension of Ferrenberg and Swendsen's multiple histogram technique for complex biomolecular Hamiltonians.
Abstract: The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built-in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free-energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.
5,784 citations
TL;DR: Quantitative-diffusion-tensor MRI consists of deriving and displaying parameters that resemble histological or physiological stains, i.e., that characterize intrinsic features of tissue microstructure and microdynamics that are objective, and insensitive to the choice of laboratory coordinate system.
4,064 citations
TL;DR: In this article, the authors demonstrate the mechanism for a universal instability, the Arnold diffusion, which occurs in the oscillating systems having more than two degrees of freedom, which results in an irregular, or stochastic, motion of the system as if the latter were influenced by a random perturbation even though, in fact, the motion is governed by purely dynamical equations.
3,527 citations
TL;DR: Extended Theories of Gravity as discussed by the authors can be considered as a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales, which is an approach that, by preserving the undoubtedly positive results of Einstein's theory, is aimed to address conceptual and experimental problems recently emerged in astrophysics, cosmology and High Energy Physics.
2,776 citations
TL;DR: In this article, the authors examined viscosity solutions of Hamilton-Jacobi equations, and proved the existence assertions by expanding on the arguments in the introduction concerning the relationship of the vanishing-viscosity method and the notion of viscoity solutions.
Abstract: Publisher Summary This chapter examines viscosity solutions of Hamilton–Jacobi equations. The ability to formulate an existence and uniqueness result for generality requires the ability to discuss non differential solutions of the equation, and this has not been possible before. However, the existence assertions can be proved by expanding on the arguments in the introduction concerning the relationship of the vanishing viscosity method and the notion of viscosity solutions, so users can adapt known methods here. The uniqueness is then the main new point.
2,407 citations