4,683 research outputs found
Informed Proposal Monte Carlo
Any search or sampling algorithm for solution of inverse problems needs
guidance to be efficient. Many algorithms collect and apply information about
the problem on the fly, and much improvement has been made in this way.
However, as a consequence of the the No-Free-Lunch Theorem, the only way we can
ensure a significantly better performance of search and sampling algorithms is
to build in as much information about the problem as possible. In the special
case of Markov Chain Monte Carlo sampling (MCMC) we review how this is done
through the choice of proposal distribution, and we show how this way of adding
more information about the problem can be made particularly efficient when
based on an approximate physics model of the problem. A highly nonlinear
inverse scattering problem with a high-dimensional model space serves as an
illustration of the gain of efficiency through this approach
Inertial Motions of a Rigid Body with a cavity filled with a viscous liquid
We study inertial motions of the coupled system, S, constituted by a rigid
body containing a cavity that is completely filled with a viscous liquid. We
show that for data of arbitrary size (initial kinetic energy and total angular
momentum) every weak solution (a la Leray-Hopf) converges, as time goes to
infinity, to a uniform rotation, thus proving a famous "conjecture" of
Zhukovskii. Moreover we show that, in a wide range of initial data, this
rotation must occur along the central axis of inertia of S that has the largest
moment of inertia. Furthermore, necessary and sufficient conditions for the
rigorous nonlinear stability of permanent rotations are provided, which improve
and/or generalize results previously given by other authors under different
types of approximation of the original equations and/or suitable symmetry
assumptions on the shape of the cavity. Finally, we present a number of results
obtained by a targeted numerical simulation that, on the one hand, complement
the analytical findings, whereas, on the other hand, point out new features
that the analysis is yet not able to catch, and, as such, lay the foundation
for interesting and challenging future investigation.Comment: Some of the main results proved in this paper were previously
announced in Comptes Rendus Mecanique, Vol. 341, 760--765 (2013
Efficient Finite Difference Method for Computing Sensitivities of Biochemical Reactions
Sensitivity analysis of biochemical reactions aims at quantifying the
dependence of the reaction dynamics on the reaction rates. The computation of
the parameter sensitivities, however, poses many computational challenges when
taking stochastic noise into account. This paper proposes a new finite
difference method for efficiently computing sensitivities of biochemical
reactions. We employ propensity bounds of reactions to couple the simulation of
the nominal and perturbed processes. The exactness of the simulation is
reserved by applying the rejection-based mechanism. For each simulation step,
the nominal and perturbed processes under our coupling strategy are
synchronized and often jump together, increasing their positive correlation and
hence reducing the variance of the estimator. The distinctive feature of our
approach in comparison with existing coupling approaches is that it only needs
to maintain a single data structure storing propensity bounds of reactions
during the simulation of the nominal and perturbed processes. Our approach
allows to computing sensitivities of many reaction rates simultaneously.
Moreover, the data structure does not require to be updated frequently, hence
improving the computational cost. This feature is especially useful when
applied to large reaction networks. We benchmark our method on biological
reaction models to prove its applicability and efficiency.Comment: 29 pages with 6 figures, 2 table
Experimental confirmation of long-memory correlations in star-wander data
In this letter we have analyzed the temporal correlations of the
angle-of-arrival fluctuations of stellar images. Experimentally measured data
were carefully examined by implementing multifractal detrended fluctuation
analysis. This algorithm is able to discriminate the presence of fractal and
multifractal structures in recorded time sequences. We have confirmed that
turbulence-degraded stellar wavefronts are compatible with a long-memory
correlated monofractal process. This experimental result is quite significant
for the accurate comprehension and modeling of the atmospheric turbulence
effects on the stellar images. It can also be of great utility within the
adaptive optics field.Comment: 4 pages, 5 figures, 23 references. Minor grammatical changes to match
the published version. Comments and suggestions are welcome
A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model
We study a finite element computational model for solving the coupled problem
arising in the interaction between a free fluid and a fluid in a poroelastic
medium. The free fluid is governed by the Stokes equations, while the flow in
the poroelastic medium is modeled using the Biot poroelasticity system.
Equilibrium and kinematic conditions are imposed on the interface. A mixed
Darcy formulation is employed, resulting in continuity of flux condition of
essential type. A Lagrange multiplier method is employed to impose weakly this
condition. A stability and error analysis is performed for the semi-discrete
continuous-in-time and the fully discrete formulations. A series of numerical
experiments is presented to confirm the theoretical convergence rates and to
study the applicability of the method to modeling physical phenomena and the
sensitivity of the model with respect to its parameters
- …