The Role of Schwartz Measures in Human Tri-Color Vision

The human tri-color vision process may be characterized as follows: 1. A requirement of three scalar quantities to fully define a color (for example, intensity, hue, and purity), with 2. These scalar measures linear in the intensity of the incident light, allowing in general any specific color to be duplicated by an additive mixture of light from three standardized (basis) colors, 3. The exception being that the spectral colors are unique, in that they cannot be duplicated by any positive mixture of other colors. These characteristics strongly suggest that human color vision makes use of Schwartz measures in processing color data. This hypothesis is subject to test. In this brief paper, the results of this hypothesis are shown to be in good agreement with measured data

An Infrared Study of the Circumstellar Material Associated with the Carbon Star R Sculptoris

The asymptotic giant branch (AGB) star R Sculptoris (R Scl) is one of the most extensively studied stars on the AGB. R Scl is a carbon star with a massive circumstellar shell ($M_{shell}\sim 7.3\times10^{-3}~M_{\odot}$) which is thought to have been produced during a thermal pulse event $\sim2200$ years ago. To study the thermal dust emission associated with its circumstellar material, observations were taken with the Faint Object InfraRed CAMera for the SOFIA Telescope (FORCAST) at 19.7, 25.2, 31.5, 34.8, and 37.1 $\mu$m. Maps of the infrared emission at these wavelengths were used to study the morphology and temperature structure of the spatially extended dust emission. Using the radiative transfer code DUSTY and fitting the spatial profile of the emission, we find that a geometrically thin dust shell cannot reproduce the observed spatially resolved emission. Instead, a second dust component in addition to the shell is needed to reproduce the observed emission. This component, which lies interior to the dust shell, traces the circumstellar envelope of R Scl. It is best fit by a density profile with $n \propto r^{\alpha}$ where $\alpha=0.75^{+0.45}_{-0.25}$ and dust mass of $M_d=9.0^{+2.3}_{-4.1}\times10^{-6}~M_{\odot}$. The strong departure from an $r^{-2}$ law indicates that the mass-loss rate of R Scl has not been constant. This result is consistent with a slow decline in the post-pulse mass-loss which has been inferred from observations of the molecular gas.Comment: 10 pages, 10 figures, accepted to Ap

Force and energy dissipation variations in non-contact atomic force spectroscopy on composite carbon nanotube systems

UHV dynamic force and energy dissipation spectroscopy in non-contact atomic force microscopy were used to probe specific interactions with composite systems formed by encapsulating inorganic compounds inside single-walled carbon nanotubes. It is found that forces due to nano-scale van der Waals interaction can be made to decrease by combining an Ag core and a carbon nanotube shell in the Ag@SWNT system. This specific behaviour was attributed to a significantly different effective dielectric function compared to the individual constituents, evaluated using a simple core-shell optical model. Energy dissipation measurements showed that by filling dissipation increases, explained here by softening of C-C bonds resulting in a more deformable nanotube cage. Thus, filled and unfilled nanotubes can be discriminated based on force and dissipation measurements. These findings have two different implications for potential applications: tuning the effective optical properties and tuning the interaction force for molecular absorption by appropriately choosing the filling with respect to the nanotube.Comment: 22 pages, 6 figure

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

Development of a composite model derived from cardiopulmonary exercise tests to predict mortality risk in patients with mild-to-moderate heart failure

Objective: Cardiopulmonary exercise testing (CPET) is used to predict outcome in patients with mild-to-moderate heart failure (HF). Single CPET-derived variables are often used, but we wanted to see if a composite score achieved better predictive power. Methods: Retrospective analysis of patient records at the Department of Cardiology, Castle Hill Hospital, Kingston-upon-Hull. 387 patients [median (25th-75th percentile)] [age 65 (56-72) years; 79% males; LVEF 34 (31-37) %] were included. Patients underwent a symptomlimited, maximal CPET on a treadmill. During a median follow up of 8.6 ± 2.1 years in survivors, 107 patients died. Survival models were built and validated using a hybrid approach between the bootstrap and Cox regression. Nine CPET-derived variables were included. Z-score defined each variable's predictive strength. Model coefficients were converted to a risk score. Results: Four CPET-related variables were independent predictors of all-cause mortality in the survival model: the presence of exertional oscillatory ventilation (EOV), increasing slope of the relation between ventilation and carbon dioxide production (VE/VCO2 slope), decreasing oxygen uptake efficiency slope (OUES), and an increase in the lowest ventilatory equivalent for carbon dioxide (VEqCO2 nadir). Individual predictors of mortality ranged from 0.60 to 0.71 using Harrell’s C-statistic, but the optimal combination of EOV + VE/VCO2 slope + OUES + VEqCO2 nadir reached 0.75. The Hull CPET risk score had a significantly higher area under the curve (0.78) when compared to the Heart Failure Survival Score (AUC=0.70;

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity

This is the published version, also available here: http://dx.doi.org/10.1137/S1064827595291984.The work presented here describes a method of coordinate transformation that enables spectral methods to be applied efficiently to differential problems with steep solutions. The approach makes use of the adaptive finite difference method presented by Huang and Sloan [SIAM J. Sci. Comput., 15 (1994), pp. 776--797]. This method is applied on a coarse grid to obtain a rough approximation of the solution and a suitable adapted mesh. The adaptive finite difference solution permits the construction of a smooth coordinate transformation that relates the computational space to the physical space. The map between the spaces is based on Chebyshev polynomial interpolation. Finally, the standard pseudospectral (PS) method is applied to the transformed differential problem to obtain highly accurate, nonoscillatory numerical solutions. Numerical results are presented for steady problems in one and two space dimensions

Glueball matrix elements on anisotropic lattices

We describe a lattice calculation of the matrix elements relevant for glueball production in $J / \psi$ radiative decays. The techniques for such a calculation on anisotropic lattices with an improved action are outlined. We present preliminary results showing the efficacy of the computational method.Comment: 3 pages (LaTeX), 3 figures (PostScript), Presented at Lattice '9