22,320 research outputs found
Resampling methods for spatial regression models under a class of stochastic designs
In this paper we consider the problem of bootstrapping a class of spatial
regression models when the sampling sites are generated by a (possibly
nonuniform) stochastic design and are irregularly spaced. It is shown that the
natural extension of the existing block bootstrap methods for grid spatial data
does not work for irregularly spaced spatial data under nonuniform stochastic
designs. A variant of the blocking mechanism is proposed. It is shown that the
proposed block bootstrap method provides a valid approximation to the
distribution of a class of M-estimators of the spatial regression parameters.
Finite sample properties of the method are investigated through a moderately
large simulation study and a real data example is given to illustrate the
methodology.Comment: Published at http://dx.doi.org/10.1214/009053606000000551 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A general approach to the sign problem - the factorization method with multiple observables
The sign problem is a notorious problem, which occurs in Monte Carlo
simulations of a system with the partition function whose integrand is not real
positive. The basic idea of the factorization method applied on such a system
is to control some observables in order to determine and sample efficiently the
region of configuration space which gives important contribution to the
partition function. We argue that it is crucial to choose appropriately the set
of the observables to be controlled in order for the method to work
successfully in a general system. This is demonstrated by an explicit example,
in which it turns out to be necessary to control more than one observables.
Extrapolation to large system size is possible due to the nice scaling
properties of the factorized functions, and known results obtained by an
analytic method are shown to be consistently reproduced.Comment: 6 pages, 3 figures, (v2) references added (v3) Sections IV, V and VI
improved, final version accepted by PR
A Study of the Complex Action Problem in a Simple Model for Dynamical Compactification in Superstring Theory Using the Factorization Method
The IIB matrix model proposes a mechanism for dynamically generating four
dimensional space--time in string theory by spontaneous breaking of the ten
dimensional rotational symmetry . Calculations using the
Gaussian expansion method (GEM) lend support to this conjecture. We study a
simple invariant matrix model using Monte Carlo simulations
and we confirm that its rotational symmetry breaks down, showing that lower
dimensional configurations dominate the path integral. The model has a strong
complex action problem and the calculations were made possible by the use of
the factorization method on the density of states of properly
normalized eigenvalues of the space--time moment of inertia
tensor. We study scaling properties of the factorized terms of and
we find them in agreement with simple scaling arguments. These can be used in
the finite size scaling extrapolation and in the study of the region of
configuration space obscured by the large fluctuations of the phase. The
computed values of are in reasonable agreement with GEM
calculations and a numerical method for comparing the free energy of the
corresponding ansatze is proposed and tested.Comment: 7 pages, 4 figures, Talk presented at the XXVIII International
Symposium on Lattice Field Theory, Lattice2010, Villasimius, Italy, June 201
Recent Progress of Multiferroic Perovskite Manganites
Many multiferroic materials, with various chemical compositions and crystal
structures, have been discovered in the past years. Among these multiferroics,
some perovskite manganites with ferroelectricity driven by magnetic orders are
of particular interest. In these multiferroic perovskite manganites, not only
their multiferroic properties are quite prominent, but also the involved
physical mechanisms are very plenty and representative. In this Brief Review,
we will introduce some recent theoretical and experimental progress on
multiferroic manganites.Comment: 24 pages, 17 figures. A brief revie
- …