9,368 research outputs found
An extended space approach for particle Markov chain Monte Carlo methods
In this paper we consider fully Bayesian inference in general state space
models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an
augmented model that takes into account all the variable sampled in a
sequential Monte Carlo algorithm. This paper describes an approach that also
uses sequential Monte Carlo to construct an approximation to the state space,
but generates extra states using MCMC runs at each time point. We construct an
augmented model for our extended space with the marginal distribution of the
sampled states matching the posterior distribution of the state vector. We show
how our method may be combined with particle independent Metropolis-Hastings or
particle Gibbs steps to obtain a smoothing algorithm. All the Metropolis
acceptance probabilities are identical to those obtained in existing
approaches, so there is no extra cost in term of Metropolis-Hastings rejections
when using our approach. The number of MCMC iterates at each time point is
chosen by the used and our augmented model collapses back to the model in
Olsson and Ryden (2011) when the number of MCMC iterations reduces. We show
empirically that our approach works well on applied examples and can outperform
existing methods.Comment: 35 pages, 2 figures, Typos corrected from Version
Generalization of the density-matrix method to a non-orthogonal basis
We present a generalization of the Li, Nunes and Vanderbilt density-matrix
method to the case of a non-orthogonal set of basis functions. A representation
of the real-space density matrix is chosen in such a way that only the overlap
matrix, and not its inverse, appears in the energy functional. The generalized
energy functional is shown to be variational with respect to the elements of
the density matrix, which typically remains well localized.Comment: 11 pages + 2 postcript figures at the end (search for -cut here
The Decay Properties of the Finite Temperature Density Matrix in Metals
Using ordinary Fourier analysis, the asymptotic decay behavior of the density
matrix F(r,r') is derived for the case of a metal at a finite electronic
temperature. An oscillatory behavior which is damped exponentially with
increasing distance between r and r' is found. The decay rate is not only
determined by the electronic temperature, but also by the Fermi energy. The
theoretical predictions are confirmed by numerical simulations
Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models
Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where a graph means the configuration of nonzero offdiagonal elements in the inverse of the covariance matrix. Our prior for the covariance matrix is such that the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We give empirical results that show the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix. The advantage is greatest when the number of observations is small relative to the dimension of the covariance matrix. The article also shows empirically that there is minimal change in statistical efficiency in using the mixture over decomposable graphs prior for estimating a general covariance compared to the Bayesian estimator by Wong et al. (2003), even when the graph of the covariance matrix is nondecomposable. However, our approach has some important advantages over that of Wong et al. (2003). Our method requires the number of decomposable graphs for each graph size. We show how to estimate these numbers using simulation and that the simulation results agree with analytic results when such results are known. We also show how to estimate the posterior distribution of the covariance matrix using Markov chain Monte Carlo with the elements of the covariance matrix integrated out and give empirical results that show the sampler is computationally efficient and converges rapidly. Finally, we note that both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.Covariance selection; Graphical models; Reduced conditional sampling; Variable selection
Total energy global optimizations using non orthogonal localized orbitals
An energy functional for orbital based calculations is proposed, which
depends on a number of non orthogonal, localized orbitals larger than the
number of occupied states in the system, and on a parameter, the electronic
chemical potential, determining the number of electrons. We show that the
minimization of the functional with respect to overlapping localized orbitals
can be performed so as to attain directly the ground state energy, without
being trapped at local minima. The present approach overcomes the multiple
minima problem present within the original formulation of orbital based
methods; it therefore makes it possible to perform calculations for an
arbitrary system, without including any information about the system bonding
properties in the construction of the input wavefunctions. Furthermore, while
retaining the same computational cost as the original approach, our formulation
allows one to improve the variational estimate of the ground state energy, and
the energy conservation during a molecular dynamics run. Several numerical
examples for surfaces, bulk systems and clusters are presented and discussed.Comment: 24 pages, RevTex file, 5 figures available upon reques
Lower bounds for the conductivities of correlated quantum systems
We show how one can obtain a lower bound for the electrical, spin or heat
conductivity of correlated quantum systems described by Hamiltonians of the
form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by
conservation laws which lead to an infinite conductivity for g=0. The small
perturbation g H1, however, renders the conductivity finite at finite
temperatures. For example, H0 could be a continuum field theory, where momentum
is conserved, or an integrable one-dimensional model while H1 might describe
the effects of weak disorder. In the limit g to 0, we derive lower bounds for
the relevant conductivities and show how they can be improved systematically
using the memory matrix formalism. Furthermore, we discuss various applications
and investigate under what conditions our lower bound may become exact.Comment: Title changed; 9 pages, 2 figure
Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights
There is an ongoing debate on the therapeutic potential of vaso-modulatory
interventions against glioma invasion. Prominent vasculature-targeting
therapies involve functional tumour-associated blood vessel deterioration and
normalisation. The former aims at tumour infarction and nutrient deprivation
medi- ated by vascular targeting agents that induce occlusion/collapse of
tumour blood vessels. In contrast, the therapeutic intention of normalising the
abnormal structure and function of tumour vascular net- works, e.g. via
alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and
radiation therapy efficacy. Although both strategies have shown therapeutic
potential, it remains unclear why they often fail to control glioma invasion
into the surrounding healthy brain tissue. To shed light on this issue, we
propose a mathematical model of glioma invasion focusing on the interplay
between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells
and modulations of the functional tumour vasculature. Vaso-modulatory
interventions are modelled by varying the degree of vaso-occlusion. We
discovered the existence of a critical cell proliferation/diffusion ratio that
separates glioma invasion re- sponses to vaso-modulatory interventions into two
distinct regimes. While for tumours, belonging to one regime, vascular
modulations reduce the tumour front speed and increase the infiltration width,
for those in the other regime the invasion speed increases and infiltration
width decreases. We show how these in silico findings can be used to guide
individualised approaches of vaso-modulatory treatment strategies and thereby
improve success rates
- …