$p+^{4,6,8}He elastic scattering at intermediate energies

Using a relativistic nuclear optical potential consisting of a Lorentz scalar, $V_{s}$, and the time-like component of a four-vector potential, $V_{0}$, we calculate elastic scattering differential cross sections and polarizations for $p+^{4}$He at intermediate energies for which experimental data are available. We also calculate the differential cross sections and analyzing powers for $p+^{6,8}$He at intermediate energies and compare with the few available experimental data.Comment: 09 pages, 04 figure

The predictive receiver operating characteristic curve for the joint assessment of the positive and negative predictive values

Binary test outcomes typically result from dichotomizing a continuous test variable, observable or latent. The effect of the threshold for test positivity on test sensitivity and specificity has been studied extensively in receiver operating characteristic (ROC) analysis. However, considerably less attention has been given to the study of the effect of the positivity threshold on the predictive value of a test. In this paper we present methods for the joint study of the positive (PPV) and negative predictive values (NPV) of diagnostic tests. We define the predictive receiver operating characteristic (PROC) curve that consists of all possible pairs of PPV and NPV as the threshold for test positivity varies. Unlike the simple trade-off between sensitivity and specificity exhibited in the ROC curve, the PROC curve displays what is often a complex interplay between PPV and NPV as the positivity threshold changes. We study the monotonicity and other geometric properties of the PROC curve and propose summary measures for the predictive performance of tests. We also formulate and discuss regression models for the estimation of the effects of covariates

Adjustment for energy intake in nutritional research: a causal inference perspective

Background Four models are commonly used to adjust for energy intake when estimating the causal effect of a dietary component on an outcome: 1) the “standard model” adjusts for total energy intake, 2) the “energy partition model” adjusts for remaining energy intake, 3) the “nutrient density model” rescales the exposure as a proportion of total energy, and 4) the “residual model” indirectly adjusts for total energy by using a residual. It remains underappreciated that each approach evaluates a different estimand and only partially accounts for confounding by common dietary causes. Objectives We aimed to clarify the implied causal estimand and interpretation of each model and evaluate their performance in reducing dietary confounding. Methods Semiparametric directed acyclic graphs and Monte Carlo simulations were used to identify the estimands and interpretations implied by each model and explore their performance in the absence or presence of dietary confounding. Results The “standard model” and the mathematically identical “residual model” estimate the average relative causal effect (i.e., a “substitution” effect) but provide biased estimates even in the absence of confounding. The “energy partition model” estimates the total causal effect but only provides unbiased estimates in the absence of confounding or when all other nutrients have equal effects on the outcome. The “nutrient density model” has an obscure interpretation but attempts to estimate the average relative causal effect rescaled as a proportion of total energy. Accurate estimates of both the total and average relative causal effects may instead be derived by simultaneously adjusting for all dietary components, an approach we term the “all-components model.” Conclusions Lack of awareness of the estimand differences and accuracy of the 4 modeling approaches may explain some of the apparent heterogeneity among existing nutritional studies. This raises serious questions regarding the validity of meta-analyses where different estimands have been inappropriately pooled

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Turbulent luminance in impassioned van Gogh paintings

We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation

Computation of the winding number diffusion rate due to the cosmological sphaleron

A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solution for a sphaleron model in $3+1$ spacetime dimensions.Comment: Some style corrections suggested by the referee are introduced (mainly in Sec.II), one reference added. To appear in Phys.Rev.D 29 pages, LaTeX, 3 Postscript figures, uses epsf.st

A complete parton level analysis of boson-boson scattering and ElectroWeak Symmetry Breaking in lv + four jets production at the LHC

A complete parton level analysis of lv + four jets production at the LHC is presented, including all processes at order O(alpha^6), O(alpha^4*alpha_s^2) and O(alpha^2*alpha_s^4). The infinite Higgs mass scenario, which is considered as a benchmark for strong scattering theories and is the limiting case for composite Higgs models, is confronted with the Standard Model light Higgs predictions in order to determine whether a composite Higgs signal can be detected as an excess of events in boson--boson scattering.Comment: More detailed discussion of the effects of the reconstruction of the longitudinal neutrino momentum. Improved figures. To be published in JHE

Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn

The Cassini spacecraft collects high resolution images of the saturnian satellites and reveals the surface of these new worlds. The shape and rotation of the satellites can be determined from the Cassini Imaging Science Subsystem data, employing limb coordinates and stereogrammetric control points. This is the case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of new rotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011). Especially, Epimetheus is characterized by its horseshoe shape orbit and the presence of the swap is essential to introduce explicitly into rotational models. During its journey in the saturnian system, Cassini spacecraft accumulates the observational data of the other satellites and it will be possible to determine the rotational parameters of several of them. To prepare these future observations, we built rotational models of the coorbital (also called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 and L_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital of Dione. The goal of this study is to understand how the departure from the Keplerian motion induced by the perturbations of the coorbital body, influences the rotation of these satellites. To this aim, we introduce explicitly the perturbation in the rotational equations by using the formalism developed by Erdi (1977) to represent the coorbital motions, and so we describe the rotational motion of the coorbitals, Janus and Epimetheus included, in compact form

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure