511 research outputs found
Circuit Based Quantification: Back to State Set Manipulation within Unbounded Model Checking
In this paper a non-canonical circuit-based state set representation is used to efficiently perform quantifier elimination. The novelty of this approach lies in adapting equivalence checking and logic synthesis techniques, to the goal of compacting circuit based state set representations resulting from existential quantification. The method can be efficiently combined with other verification approaches such as inductive and SAT-based pre-image verifications
Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
In this article, we consider the stochastic wave equation on , driven by a linear multiplicative space-time homogeneous
Gaussian noise whose temporal and spatial covariance structures are given by
locally integrable functions (in time) and (in space), which are
the Fourier transforms of tempered measures on , respectively
on . Our main result shows that the law of the solution
of this equation is absolutely continuous with respect to the Lebesgue
measure.Comment: This is a major revision of the previous version of the paper, where
we have corrected an important erro
Estimating exit rate for rare event dynamical systems by extrapolation
In this article we present an idea to speed up the sampling exit of rates from
metastable molecular conformations. The idea is based on flattening the energy
landscape by a global transformation which decreases the energy barrier. In this
matter we create different energy surfaces in which we sample the exit rate and use these to extrapolate the exit rate for the original potential. Because of the lower energy barrier the sampling is computationally cheaper and also the variance of the estimators for the exit rate in the transformed energy landscape is smaller
Non elliptic SPDEs and ambit fields: existence of densities
Relying on the method developed in [debusscheromito2014], we prove the
existence of a density for two different examples of random fields indexed by
(t,x)\in(0,T]\times \Rd. The first example consists of SPDEs with Lipschitz
continuous coefficients driven by a Gaussian noise white in time and with a
stationary spatial covariance, in the setting of [dalang1999]. The density
exists on the set where the nonlinearity of the noise does not vanish.
This complements the results in [sanzsuess2015] where is assumed to be
bounded away from zero. The second example is an ambit field with a stochastic
integral term having as integrator a L\'evy basis of pure-jump, stable-like
type.Comment: 23 page
An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates
In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov’s theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate
the potential accordingly. Our method circumvents this problem by using an
assimilated version of the Metadynamics algorithm and thus creates a nonequilibrium dynamics which is used to sample the equilibrium quantities
Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
In this article, we consider the stochastic wave equation on R × R, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally integrable functions γ (in time) and f (in space), which are the Fourier transforms of tempered measures ν on R, respectively µ on R. Our main result shows that the law of the solution u(t, x) of this equation is absolutely continuous with respect to the Lebesgue measure
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