10,376 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
Quantum affine Toda solitons
We review some of the progress in affine Toda field theories in recent years,
explain why known dualities cannot easily be extended, and make some
suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision
Prediction of the Atomization Energy of Molecules Using Coulomb Matrix and Atomic Composition in a Bayesian Regularized Neural Networks
Exact calculation of electronic properties of molecules is a fundamental step
for intelligent and rational compounds and materials design. The intrinsically
graph-like and non-vectorial nature of molecular data generates a unique and
challenging machine learning problem. In this paper we embrace a learning from
scratch approach where the quantum mechanical electronic properties of
molecules are predicted directly from the raw molecular geometry, similar to
some recent works. But, unlike these previous endeavors, our study suggests a
benefit from combining molecular geometry embedded in the Coulomb matrix with
the atomic composition of molecules. Using the new combined features in a
Bayesian regularized neural networks, our results improve well-known results
from the literature on the QM7 dataset from a mean absolute error of 3.51
kcal/mol down to 3.0 kcal/mol.Comment: Under review ICANN 201
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
Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice
We investigate the connection between local and global dynamics in the Fermi
-- Pasta -- Ulam (FPU) -- model from the point of view of stability of
its simplest periodic orbits (SPOs). In particular, we show that there is a
relatively high mode of the linear lattice, having one
particle fixed every two oppositely moving ones (called SPO2 here), which can
be exactly continued to the nonlinear case for and whose
first destabilization, , as the energy (or ) increases for {\it
any} fixed , practically {\it coincides} with the onset of a ``weak'' form
of chaos preceding the break down of FPU recurrences, as predicted recently in
a similar study of the continuation of a very low () mode of the
corresponding linear chain. This energy threshold per particle behaves like
. We also follow exactly the properties of
another SPO (with ) in which fixed and moving particles are
interchanged (called SPO1 here) and which destabilizes at higher energies than
SPO2, since . We find that, immediately after
their first destabilization, these SPOs have different (positive) Lyapunov
spectra in their vicinity. However, as the energy increases further (at fixed
), these spectra converge to {\it the same} exponentially decreasing
function, thus providing strong evidence that the chaotic regions around SPO1
and SPO2 have ``merged'' and large scale chaos has spread throughout the
lattice.Comment: Physical Review E, 18 pages, 6 figure
Scattering loss in electro-optic particulate composite materials
The effective permittivity dyadic of a composite material containing
particulate constituent materials with one constituent having the ability to
display the Pockels effect is computed, using an extended version of the
strong-permittivity-fluctuation theory which takes account of both the
distributional statistics of the constituent particles and their sizes.
Scattering loss, thereby incorporated in the effective electromagnetic response
of the homogenized composite material, is significantly affected by the
application of a low-frequency (dc) electric field
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
Fast and flexible selection with a single switch
Selection methods that require only a single-switch input, such as a button
click or blink, are potentially useful for individuals with motor impairments,
mobile technology users, and individuals wishing to transmit information
securely. We present a single-switch selection method, "Nomon," that is general
and efficient. Existing single-switch selection methods require selectable
options to be arranged in ways that limit potential applications. By contrast,
traditional operating systems, web browsers, and free-form applications (such
as drawing) place options at arbitrary points on the screen. Nomon, however,
has the flexibility to select any point on a screen. Nomon adapts automatically
to an individual's clicking ability; it allows a person who clicks precisely to
make a selection quickly and allows a person who clicks imprecisely more time
to make a selection without error. Nomon reaps gains in information rate by
allowing the specification of beliefs (priors) about option selection
probabilities and by avoiding tree-based selection schemes in favor of direct
(posterior) inference. We have developed both a Nomon-based writing application
and a drawing application. To evaluate Nomon's performance, we compared the
writing application with a popular existing method for single-switch writing
(row-column scanning). Novice users wrote 35% faster with the Nomon interface
than with the scanning interface. An experienced user (author TB, with > 10
hours practice) wrote at speeds of 9.3 words per minute with Nomon, using 1.2
clicks per character and making no errors in the final text.Comment: 14 pages, 5 figures, 1 table, presented at NIPS 2009 Mini-symposi
Counterposition and negative phase velocity in uniformly moving dissipative materials
The Lorentz transformations of electric and magnetic fields were implemented
to study (i) the refraction of linearly polarized plane waves into a half-space
occupied by a uniformly moving material, and (ii) the traversal of linearly
polarized Gaussian beams through a uniformly moving slab. Motion was taken to
occur tangentially to the interface(s) and in the plane of incidence. The
moving materials were assumed to be isotropic, homogeneous, dissipative
dielectric materials from the perspective of a co-moving observer. Two
different moving materials were considered: from the perspective of a co-moving
observer, material A supports planewave propagation with only positive phase
velocity, whereas material B supports planewave propagation with both positive
and negative phase velocity, depending on the polarization state. For both
materials A and B, the sense of the phase velocity and whether or not
counterposition occurred, as perceived by a nonco-moving observer, could be
altered by varying the observer's velocity. Furthermore, the lateral position
of a beam upon propagating through a uniformly moving slab made of material A,
as perceived by a nonco-moving observer, could be controlled by varying the
observer's velocity. In particular, at certain velocities, the transmitted beam
emerged from the slab laterally displaced in the direction opposite to the
direction of incident beam. The transmittances of a uniformly moving slab made
of material B were very small and the energy density of the transmitted beam
was largely concentrated in the direction normal to the slab, regardless of the
observer's velocity
Quantum signatures of breather-breather interactions
The spectrum of the Quantum Discrete Nonlinear Schr\"odinger equation on a
periodic 1D lattice shows some interesting detailed band structure which may be
interpreted as the quantum signature of a two-breather interaction in the
classical case. We show that this fine structure can be interpreted using
degenerate perturbation theory.Comment: 4 pages, 4 fig
- …