6,256 research outputs found
Efficient spatial modelling using the SPDE approach with bivariate splines
Gaussian fields (GFs) are frequently used in spatial statistics for their
versatility. The associated computational cost can be a bottleneck, especially
in realistic applications. It has been shown that computational efficiency can
be gained by doing the computations using Gaussian Markov random fields (GMRFs)
as the GFs can be seen as weak solutions to corresponding stochastic partial
differential equations (SPDEs) using piecewise linear finite elements. We
introduce a new class of representations of GFs with bivariate splines instead
of finite elements. This allows an easier implementation of piecewise
polynomial representations of various degrees. It leads to GMRFs that can be
inferred efficiently and can be easily extended to non-stationary fields. The
solutions approximated with higher order bivariate splines converge faster,
hence the computational cost can be alleviated. Numerical simulations using
both real and simulated data also demonstrate that our framework increases the
flexibility and efficiency.Comment: 26 pages, 7 figures and 3 table
Lookahead Strategies for Sequential Monte Carlo
Based on the principles of importance sampling and resampling, sequential
Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with
complex stochastic dynamic systems. Many of these systems possess strong
memory, with which future information can help sharpen the inference about the
current state. By providing theoretical justification of several existing
algorithms and introducing several new ones, we study systematically how to
construct efficient SMC algorithms to take advantage of the "future"
information without creating a substantially high computational burden. The
main idea is to allow for lookahead in the Monte Carlo process so that future
information can be utilized in weighting and generating Monte Carlo samples, or
resampling from samples of the current state.Comment: Published in at http://dx.doi.org/10.1214/12-STS401 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Symmetry Reduction and Boundary Modes for Fe-Chains on an s-wave Superconductor
We investigate the superconducting phase diagram and boundary modes for a
quasi-1D system formed by three Fe-Chains on an s-wave superconductor,
motivated by the recent Princeton experiment. The onsite
spin-orbit term, inter-chain diagonal hopping couplings, and magnetic disorders
in the Fe-chains are shown to be crucial for the superconducting phases, which
can be topologically trivial or nontrivial in different parameter regimes. For
the topological regime a single Majorana and multiple Andreew bound modes are
obtained in the ends of the chain, while for the trivial phase only low-energy
Andreev bound states survive. Nontrivial symmetry reduction mechanism induced
by the term, diagonal hopping couplings, and magnetic
disorder is uncovered to interpret the present results. Our study also implies
that the zero-bias peak observed in the recent experiment may or may not
reflect the Majorana zero modes in the end of the Fe-chains.Comment: 5 pages, 4 figures; some minor errors are correcte
- …