1,003 research outputs found
Gamma Limit for Transition Paths of Maximal Probability
Chemical reactions can be modelled via diffusion processes conditioned to
make a transition between specified molecular configurations representing the
state of the system before and after the chemical reaction. In particular the
model of Brownian dynamics - gradient flow subject to additive noise - is
frequently used. If the chemical reaction is specified to take place on a given
time interval, then the most likely path taken by the system is a minimizer of
the Onsager-Machlup functional. The Gamma limit of this functional is
determined in the case where the temperature is small and the transition time
scales as the inverse temperatur
Eigenfactor : Does the Principle of Repeated Improvement Result in Better Journal Impact Estimates than Raw Citation Counts?
Eigenfactor.org, a journal evaluation tool which uses an iterative algorithm
to weight citations (similar to the PageRank algorithm used for Google) has
been proposed as a more valid method for calculating the impact of journals.
The purpose of this brief communication is to investigate whether the principle
of repeated improvement provides different rankings of journals than does a
simple unweighted citation count (the method used by ISI).Comment: bibliographic information correcte
Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions
In this paper we study algorithms to find a Gaussian approximation to a
target measure defined on a Hilbert space of functions; the target measure
itself is defined via its density with respect to a reference Gaussian measure.
We employ the Kullback-Leibler divergence as a distance and find the best
Gaussian approximation by minimizing this distance. It then follows that the
approximate Gaussian must be equivalent to the Gaussian reference measure,
defining a natural function space setting for the underlying calculus of
variations problem. We introduce a computational algorithm which is
well-adapted to the required minimization, seeking to find the mean as a
function, and parameterizing the covariance in two different ways: through low
rank perturbations of the reference covariance; and through Schr\"odinger
potential perturbations of the inverse reference covariance. Two applications
are shown: to a nonlinear inverse problem in elliptic PDEs, and to a
conditioned diffusion process. We also show how the Gaussian approximations we
obtain may be used to produce improved pCN-MCMC methods which are not only
well-adapted to the high-dimensional setting, but also behave well with respect
to small observational noise (resp. small temperatures) in the inverse problem
(resp. conditioned diffusion).Comment: 28 page
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