8,951 research outputs found
Towards gravitationally assisted negative refraction of light by vacuum
Propagation of electromagnetic plane waves in some directions in
gravitationally affected vacuum over limited ranges of spacetime can be such
that the phase velocity vector casts a negative projection on the time-averaged
Poynting vector. This conclusion suggests, inter alia, gravitationally assisted
negative refraction by vacuum.Comment: 6 page
The Loss Rank Principle for Model Selection
We introduce a new principle for model selection in regression and
classification. Many regression models are controlled by some smoothness or
flexibility or complexity parameter c, e.g. the number of neighbors to be
averaged over in k nearest neighbor (kNN) regression or the polynomial degree
in regression with polynomials. Let f_D^c be the (best) regressor of complexity
c on data D. A more flexible regressor can fit more data D' well than a more
rigid one. If something (here small loss) is easy to achieve it's typically
worth less. We define the loss rank of f_D^c as the number of other
(fictitious) data D' that are fitted better by f_D'^c than D is fitted by
f_D^c. We suggest selecting the model complexity c that has minimal loss rank
(LoRP). Unlike most penalized maximum likelihood variants (AIC,BIC,MDL), LoRP
only depends on the regression function and loss function. It works without a
stochastic noise model, and is directly applicable to any non-parametric
regressor, like kNN. In this paper we formalize, discuss, and motivate LoRP,
study it for specific regression problems, in particular linear ones, and
compare it to other model selection schemes.Comment: 16 page
Depolarization volume and correlation length in the homogenization of anisotropic dielectric composites
In conventional approaches to the homogenization of random particulate
composites, both the distribution and size of the component phase particles are
often inadequately taken into account. Commonly, the spatial distributions are
characterized by volume fraction alone, while the electromagnetic response of
each component particle is represented as a vanishingly small depolarization
volume. The strong-permittivity-fluctuation theory (SPFT) provides an
alternative approach to homogenization wherein a comprehensive description of
distributional statistics of the component phases is accommodated. The
bilocally-approximated SPFT is presented here for the anisotropic homogenized
composite which arises from component phases comprising ellipsoidal particles.
The distribution of the component phases is characterized by a two-point
correlation function and its associated correlation length. Each component
phase particle is represented as an ellipsoidal depolarization region of
nonzero volume. The effects of depolarization volume and correlation length are
investigated through considering representative numerical examples. It is
demonstrated that both the spatial extent of the component phase particles and
their spatial distributions are important factors in estimating coherent
scattering losses of the macroscopic field.Comment: Typographical error in eqn. 16 in WRM version is corrected in arxiv
versio
Depolarization regions of nonzero volume in bianisotropic homogenized composites
In conventional approaches to the homogenization of random particulate
composites, the component phase particles are often treated mathematically as
vanishingly small, point-like entities. The electromagnetic responses of these
component phase particles are provided by depolarization dyadics which derive
from the singularity of the corresponding dyadic Green functions. Through
neglecting the spatial extent of the depolarization region, important
information may be lost, particularly relating to coherent scattering losses.
We present an extension to the strong-property-fluctuation theory in which
depolarization regions of nonzero volume and ellipsoidal geometry are
accommodated. Therein, both the size and spatial distribution of the component
phase particles are taken into account. The analysis is developed within the
most general linear setting of bianisotropic homogenized composite mediums
(HCMs). Numerical studies of the constitutive parameters are presented for
representative examples of HCM; both Lorentz-reciprocal and
Lorentz-nonreciprocal HCMs are considered. These studies reveal that estimates
of the HCM constitutive parameters in relation to volume fraction, particle
eccentricity, particle orientation and correlation length are all significantly
influenced by the size of the component phase particles
Clustering of solutions in the random satisfiability problem
Using elementary rigorous methods we prove the existence of a clustered phase
in the random -SAT problem, for . In this phase the solutions are
grouped into clusters which are far away from each other. The results are in
agreement with previous predictions of the cavity method and give a rigorous
confirmation to one of its main building blocks. It can be generalized to other
systems of both physical and computational interest.Comment: 4 pages, 1 figur
Surface-plasmon-polariton wave propagation supported by anisotropic materials: multiple modes and mixed exponential and linear localization characteristics
The canonical boundary-value problem for surface-plasmon-polariton (SPP)
waves guided by the planar interface of a dielectric material and a plasmonic
material was solved for cases wherein either partnering material could be a
uniaxial material with optic axis lying in the interface plane.Numerical
studies revealed that two different SPP waves, with different phase speeds,
propagation lengths, and penetration depths, can propagate in a given direction
in the interface plane; in contrast, the planar interface of isotropic
partnering materials supports only one SPP wave for each propagation direction.
Also, for a unique propagation direction in each quadrant of the interface
plane, it was demonstrated that a new type of SPP wave--called a
surface-plasmon-polariton-Voigt (SPP-V) wave--can exist. The fields of these
SPP-V waves decay as the product of a linear and an exponential function of the
distance from the interface in the anisotropic partnering material; in
contrast, the fields of conventional SPP waves decay only exponentially with
distance from the interface. Explicit analytic solutions of the dispersion
relation for SPP-V waves exist and help establish constraints on the
constitutive-parameter regimes for the partnering materials that support
SPP-V-wave propagation
Estimating the Expected Value of Partial Perfect Information in Health Economic Evaluations using Integrated Nested Laplace Approximation
The Expected Value of Perfect Partial Information (EVPPI) is a
decision-theoretic measure of the "cost" of parametric uncertainty in decision
making used principally in health economic decision making. Despite this
decision-theoretic grounding, the uptake of EVPPI calculations in practice has
been slow. This is in part due to the prohibitive computational time required
to estimate the EVPPI via Monte Carlo simulations. However, recent developments
have demonstrated that the EVPPI can be estimated by non-parametric regression
methods, which have significantly decreased the computation time required to
approximate the EVPPI. Under certain circumstances, high-dimensional Gaussian
Process regression is suggested, but this can still be prohibitively expensive.
Applying fast computation methods developed in spatial statistics using
Integrated Nested Laplace Approximations (INLA) and projecting from a
high-dimensional into a low-dimensional input space allows us to decrease the
computation time for fitting these high-dimensional Gaussian Processes, often
substantially. We demonstrate that the EVPPI calculated using our method for
Gaussian Process regression is in line with the standard Gaussian Process
regression method and that despite the apparent methodological complexity of
this new method, R functions are available in the package BCEA to implement it
simply and efficiently
Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs
Belief propagation -- a powerful heuristic method to solve inference problems
involving a large number of random variables -- was recently generalized to
quantum theory. Like its classical counterpart, this algorithm is exact on
trees when the appropriate independence conditions are met and is expected to
provide reliable approximations when operated on loopy graphs. In this paper,
we benchmark the performances of loopy quantum belief propagation (QBP) in the
context of finite-tempereture quantum many-body physics. Our results indicate
that QBP provides reliable estimates of the high-temperature correlation
function when the typical loop size in the graph is large. As such, it is
suitable e.g. for the study of quantum spin glasses on Bethe lattices and the
decoding of sparse quantum error correction codes.Comment: 5 pages, 4 figure
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