Understanding the Random Displacement Model: From Ground-State Properties to Localization

We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.Comment: 31 pages, 7 figures, final version, to appear in Proceedings of "Spectral Days 2010", Santiago, Chile, September 20-24, 201

Growth differentiation factor-15 predicts mortality and morbidity after cardiac resynchronization therapy

The aim of this study was to determine whether growth differentiation factor-15 (GDF-15) predicts mortality and morbidity after cardiac resynchronization therapy (CRT). Growth differentiation factor-15, a transforming growth factor-beta-related cytokine which is up-regulated in cardiomyocytes via multiple stress pathways, predicts mortality in patients with heart failure treated pharmacologically

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

The impact of adolescent exposure to medical marijuana laws on high school completion, college enrollment and college degree completion

Background: There is concern that medical marijuana laws (MMLs) could negatively affect adolescents. To better understand these policies, we assess how adolescent exposure to MMLs is related to educational attainment. Methods: Data from the 2000 Census and 2001-2014 American Community Surveys were restricted to individuals who were of high school age (14-18) between 1990 and 2012 (n = 5,483,715). MML exposure was coded as: (i) a dichotomous any MML indicator, and (ii) number of years of high school age exposure. We used logistic regression to model whether MMLs affected: (a) completing high school by age 19; (b) beginning college, irrespective of completion; and (c) obtaining any degree after beginning college. A similar dataset based on the Youth Risk Behavior Survey (YRBS) was also constructed for confirmatory analyses assessing marijuana use. Results: MMLs were associated with a 0.40 percentage point increase in the probability of not earning a high school diploma or GED after completing the 12th grade (from 3.99% to 4.39%). High school MML exposure was also associated with a 1.84 and 0.85 percentage point increase in the probability of college non-enrollment and degree non-completion, respectively (from 31.12% to 32.96% and 45.30% to 46.15%, respectively). Years of MML exposure exhibited a consistent dose response relationship for all outcomes. MMLs were also associated with 0.85 percentage point increase in daily marijuana use among 12th graders (up from 1.26%). Conclusions: Medical marijuana law exposure between age 14 to 18 likely has a delayed effect on use and education that persists over time. (C) 2016 Elsevier Ireland Ltd. All rights reserved

Comparison of techniques for handling missing covariate data within prognostic modelling studies: a simulation study

Background: There is no consensus on the most appropriate approach to handle missing covariate data within prognostic modelling studies. Therefore a simulation study was performed to assess the effects of different missing data techniques on the performance of a prognostic model. Methods: Datasets were generated to resemble the skewed distributions seen in a motivating breast cancer example. Multivariate missing data were imposed on four covariates using four different mechanisms; missing completely at random (MCAR), missing at random (MAR), missing not at random (MNAR) and a combination of all three mechanisms. Five amounts of incomplete cases from 5% to 75% were considered. Complete case analysis (CC), single imputation (SI) and five multiple imputation (MI) techniques available within the R statistical software were investigated: a) data augmentation (DA) approach assuming a multivariate normal distribution, b) DA assuming a general location model, c) regression switching imputation, d) regression switching with predictive mean matching (MICE-PMM) and e) flexible additive imputation models. A Cox proportional hazards model was fitted and appropriate estimates for the regression coefficients and model performance measures were obtained. Results: Performing a CC analysis produced unbiased regression estimates, but inflated standard errors, which affected the significance of the covariates in the model with 25% or more missingness. Using SI, underestimated the variability; resulting in poor coverage even with 10% missingness. Of the MI approaches, applying MICE-PMM produced, in general, the least biased estimates and better coverage for the incomplete covariates and better model performance for all mechanisms. However, this MI approach still produced biased regression coefficient estimates for the incomplete skewed continuous covariates when 50% or more cases had missing data imposed with a MCAR, MAR or combined mechanism. When the missingness depended on the incomplete covariates, i.e. MNAR, estimates were biased with more than 10% incomplete cases for all MI approaches. Conclusion: The results from this simulation study suggest that performing MICE-PMM may be the preferred MI approach provided that less than 50% of the cases have missing data and the missing data are not MNAR