253,734 research outputs found
High order recombination and an application to cubature on Wiener space
Particle methods are widely used because they can provide accurate
descriptions of evolving measures. Recently it has become clear that by
stepping outside the Monte Carlo paradigm these methods can be of higher order
with effective and transparent error bounds. A weakness of particle methods
(particularly in the higher order case) is the tendency for the number of
particles to explode if the process is iterated and accuracy preserved. In this
paper we identify a new approach that allows dynamic recombination in such
methods and retains the high order accuracy by simplifying the support of the
intermediate measures used in the iteration. We describe an algorithm that can
be used to simplify the support of a discrete measure and give an application
to the cubature on Wiener space method developed by Lyons and Victoir [Proc. R.
Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004) 169-198].Comment: Published in at http://dx.doi.org/10.1214/11-AAP786 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The human ECG - nonlinear deterministic versus stochastic aspects
We discuss aspects of randomness and of determinism in electrocardiographic
signals. In particular, we take a critical look at attempts to apply methods of
nonlinear time series analysis derived from the theory of deterministic
dynamical systems. We will argue that deterministic chaos is not a likely
explanation for the short time variablity of the inter-beat interval times,
except for certain pathologies. Conversely, densely sampled full ECG recordings
possess properties typical of deterministic signals. In the latter case,
methods of deterministic nonlinear time series analysis can yield new insights.Comment: 6 pages, 9 PS figure
Model Reduction for Multiscale Lithium-Ion Battery Simulation
In this contribution we are concerned with efficient model reduction for
multiscale problems arising in lithium-ion battery modeling with spatially
resolved porous electrodes. We present new results on the application of the
reduced basis method to the resulting instationary 3D battery model that
involves strong non-linearities due to Buttler-Volmer kinetics. Empirical
operator interpolation is used to efficiently deal with this issue.
Furthermore, we present the localized reduced basis multiscale method for
parabolic problems applied to a thermal model of batteries with resolved porous
electrodes. Numerical experiments are given that demonstrate the reduction
capabilities of the presented approaches for these real world applications
Bayesian analysis of hierarchical multi-fidelity codes
This paper deals with the Gaussian process based approximation of a code
which can be run at different levels of accuracy. This method, which is a
particular case of co-kriging, allows us to improve a surrogate model of a
complex computer code using fast approximations of it. In particular, we focus
on the case of a large number of code levels on the one hand and on a Bayesian
approach when we have two levels on the other hand. The main results of this
paper are a new approach to estimate the model parameters which provides a
closed form expression for an important parameter of the model (the scale
factor), a reduction of the numerical complexity by simplifying the covariance
matrix inversion, and a new Bayesian modelling that gives an explicit
representation of the joint distribution of the parameters and that is not
computationally expensive. A thermodynamic example is used to illustrate the
comparison between 2-level and 3-level co-kriging
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