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) $\beta$ -- model from the point of view of stability of its simplest periodic orbits (SPOs). In particular, we show that there is a relatively high $q$ mode $(q=2(N+1)/{3})$ 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 $N=5+3m, m=0,1,2,...$ and whose first destabilization, $E_{2u}$, as the energy (or $\beta$) increases for {\it any} fixed $N$, 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 ($q=3$) mode of the corresponding linear chain. This energy threshold per particle behaves like $\frac{E_{2u}}{N}\propto N^{-2}$. We also follow exactly the properties of another SPO (with $q=(N+1)/{2}$) in which fixed and moving particles are interchanged (called SPO1 here) and which destabilizes at higher energies than SPO2, since $\frac{E_{1u}}{N}\propto N^{-1}$. 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 $N$), 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

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

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

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