Smooth double barriers in quantum mechanics

Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle energy, and their dependence on the barrier parameters are obtained for various cases. We also discuss the tunneling time, for which we obtain generalizations of the known results for rectangular barriers.Comment: 23 pages, 8 figures, a slightly reduced version to appear in American Journal of Physics, references correcte

Estimating correlation between multivariate longitudinal data in the presence of heterogeneity

Abstract Background Estimating correlation coefficients among outcomes is one of the most important analytical tasks in epidemiological and clinical research. Availability of multivariate longitudinal data presents a unique opportunity to assess joint evolution of outcomes over time. Bivariate linear mixed model (BLMM) provides a versatile tool with regard to assessing correlation. However, BLMMs often assume that all individuals are drawn from a single homogenous population where the individual trajectories are distributed smoothly around population average. Methods Using longitudinal mean deviation (MD) and visual acuity (VA) from the Ocular Hypertension Treatment Study (OHTS), we demonstrated strategies to better understand the correlation between multivariate longitudinal data in the presence of potential heterogeneity. Conditional correlation (i.e., marginal correlation given random effects) was calculated to describe how the association between longitudinal outcomes evolved over time within specific subpopulation. The impact of heterogeneity on correlation was also assessed by simulated data. Results There was a significant positive correlation in both random intercepts (ρ = 0.278, 95% CI: 0.121–0.420) and random slopes (ρ = 0.579, 95% CI: 0.349–0.810) between longitudinal MD and VA, and the strength of correlation constantly increased over time. However, conditional correlation and simulation studies revealed that the correlation was induced primarily by participants with rapid deteriorating MD who only accounted for a small fraction of total samples. Conclusion Conditional correlation given random effects provides a robust estimate to describe the correlation between multivariate longitudinal data in the presence of unobserved heterogeneity (NCT00000125)

Assessing the relative importance of psychological and demographic factors for predicting climate and environmental attitudes

In this paper, we seek to identify robust predictors of individuals’ attitudes towards climate change and environmental degradation. While much of the extant literature has been devoted to the individual explanatory potential of individuals’ characteristics, we focus on the extent to which these characteristics provide robust predictions of climate and environmental attitudes. Thereby, we adjudicate the relative predictive power of psychological and sociodemographic characteristics, as well as the predictive power of combinations of these attributes. To do so, we use a popular machine learning technique, Random Forests, on three surveys fielded in China, Switzerland, and the USA, using a variety of outcome variables. We find that a psychological construct, the consideration of future consequences (CFC) scale, performs well in predicting attitudes, across all contexts and better than traditional explanations of climate attitudes, such as income and education. Given recent advances suggesting potential psychological barriers of behavioural change Public (Weaver, Adm Rev 75:806–816, 2015) and the use of psychological constructs to target persuasive messages (Abrahamse et al., J Environ Psychol 265–276, 2007; Hirsh et al., Psychol Sci 23:578–581, 2012), identifying important predictors, such as the CFC may allow to better understand public’s appetite for climate and environmental policies and increase demand for these policies, in an area where existing efforts have shown to be lacking (Bernauer and McGrath, Nat Clim Chang 6:680–683, 2016; Chapman et al., Nat Clim Chang 7:850–852, 2017)

Parliament, people or technocrats? Explaining mass public preferences on delegation of policymaking authority

While delegation of policymaking authority from citizens to parliament is the most defining characteristic of representative democracy, public demand for delegating such authority away from legislature/government to technocrats or back to citizens appears to have increased. Drawing on spatial models of voting, we argue that the distance between individuals’ ideal policy points, the status quo, experts’ policy positions and aggregated societal policy preferences can help explain whether individuals prefer to delegate decision-making power away from parliament and, if so, to whom. The effects of individual’s preference distance from these ideal points are likely to be stronger the more salient the policy issue is for the respective individual. We test this argument using survey experiments in Germany, Switzerland and the United Kingdom. The analysis provides evidence for the empirical implications of our theoretical arguments. The research presented here contributes to better understanding variation in citizens’ support for representative democracy and preferences for delegating policymaking authority away from parliament

Working with simple machines

A set of examples is provided that illustrate the use of work as applied to simple machines. The ramp, pulley, lever and hydraulic press are common experiences in the life of a student and their theoretical analysis therefore makes the abstract concept of work more real. The mechanical advantage of each of these systems is also discussed so that students can evaluate their usefulness as machines.Comment: 9 pages, 4 figure

Association of metabolic dysregulation with volumetric brain magnetic resonance imaging and cognitive markers of subclinical brain aging in middle-aged adults: the Framingham Offspring Study.

ObjectiveDiabetic and prediabtic states, including insulin resistance, fasting hyperglycemia, and hyperinsulinemia, are associated with metabolic dysregulation. These components have been individually linked to increased risks of cognitive decline and Alzheimer's disease. We aimed to comprehensively relate all of the components of metabolic dysregulation to cognitive function and brain magnetic resonance imaging (MRI) in middle-aged adults.Research design and methodsFramingham Offspring participants who underwent volumetric MRI and detailed cognitive testing and were free of clinical stroke and dementia during examination 7 (1998-2001) constituted our study sample (n = 2,439; 1,311 women; age 61 ± 9 years). We related diabetes, homeostasis model assessment of insulin resistance (HOMA-IR), fasting insulin, and glycohemoglobin levels to cross-sectional MRI measures of total cerebral brain volume (TCBV) and hippocampal volume and to verbal and visuospatial memory and executive function. We serially adjusted for age, sex, and education alone (model A), additionally for other vascular risk factors (model B), and finally, with the inclusion of apolipoprotein E-ε4, plasma homocysteine, C-reactive protein, and interleukin-6 (model C).ResultsWe observed an inverse association between all indices of metabolic dysfunction and TCBV in all models (P < 0.030). The observed difference in TCBV between participants with and without diabetes was equivalent to approximately 6 years of chronologic aging. Diabetes and elevated glycohemoglobin, HOMA-IR, and fasting insulin were related to poorer executive function scores (P < 0.038), whereas only HOMA-IR and fasting insulin were inversely related to visuospatial memory (P < 0.007).ConclusionsMetabolic dysregulation, especially insulin resistance, was associated with lower brain volumes and executive function in a large, relatively healthy, middle-aged, community-based cohort

Genetic Correlates of Brain Aging on MRI and Cognitive Test Measures: A Genome-Wide Association and Linkage Analysis in the Framingham Study

BACKGROUND: Brain magnetic resonance imaging (MRI) and cognitive tests can identify heritable endophenotypes associated with an increased risk of developing stroke, dementia and Alzheimer's disease (AD). We conducted a genome-wide association (GWA) and linkage analysis exploring the genetic basis of these endophenotypes in a community-based sample. METHODS: A total of 705 stroke- and dementia-free Framingham participants (age 62 +9 yrs, 50% male) who underwent volumetric brain MRI and cognitive testing (1999–2002) were genotyped. We used linear models adjusting for first degree relationships via generalized estimating equations (GEE) and family based association tests (FBAT) in additive models to relate qualifying single nucleotide polymorphisms (SNPs, 70,987 autosomal on Affymetrix 100K Human Gene Chip with minor allele frequency ≥ 0.10, genotypic call rate ≥ 0.80, and Hardy-Weinberg equilibrium p-value ≥ 0.001) to multivariable-adjusted residuals of 9 MRI measures including total cerebral brain (TCBV), lobar, ventricular and white matter hyperintensity (WMH) volumes, and 6 cognitive factors/tests assessing verbal and visuospatial memory, visual scanning and motor speed, reading, abstract reasoning and naming. We determined multipoint identity-by-descent utilizing 10,592 informative SNPs and 613 short tandem repeats and used variance component analyses to compute LOD scores. RESULTS: The strongest gene-phenotype association in FBAT analyses was between SORL1 (rs1131497; p = 3.2 × 10-6) and abstract reasoning, and in GEE analyses between CDH4 (rs1970546; p = 3.7 × 10-8) and TCBV. SORL1 plays a role in amyloid precursor protein processing and has been associated with the risk of AD. Among the 50 strongest associations (25 each by GEE and FBAT) were other biologically interesting genes. Polymorphisms within 28 of 163 candidate genes for stroke, AD and memory impairment were associated with the endophenotypes studied at p < 0.001. We confirmed our previously reported linkage of WMH on chromosome 4 and describe linkage of reading performance to a marker on chromosome 18 (GATA11A06), previously linked to dyslexia (LOD scores = 2.2 and 5.1). CONCLUSION: Our results suggest that genes associated with clinical neurological disease also have detectable effects on subclinical phenotypes. These hypothesis generating data illustrate the use of an unbiased approach to discover novel pathways that may be involved in brain aging, and could be used to replicate observations made in other studies.National Institutes of Health National Center for Research Resources Shared Instrumentation grant (ISI0RR163736-01A1); National Heart, Lung, and Blood Institute's Framingham Heart Study (N01-HC-25195); National Institute of Aging (5R01-AG08122, 5R01-AG16495); National Institute of Neurological Disorders and Stroke (5R01-NS17950

A Research-Based Curriculum for Teaching the Photoelectric Effect

Physics faculty consider the photoelectric effect important, but many erroneously believe it is easy for students to understand. We have developed curriculum on this topic including an interactive computer simulation, interactive lectures with peer instruction, and conceptual and mathematical homework problems. Our curriculum addresses established student difficulties and is designed to achieve two learning goals, for students to be able to (1) correctly predict the results of photoelectric effect experiments, and (2) describe how these results lead to the photon model of light. We designed two exam questions to test these learning goals. Our instruction leads to better student mastery of the first goal than either traditional instruction or previous reformed instruction, with approximately 85% of students correctly predicting the results of changes to the experimental conditions. On the question designed to test the second goal, most students are able to correctly state both the observations made in the photoelectric effect experiment and the inferences that can be made from these observations, but are less successful in drawing a clear logical connection between the observations and inferences. This is likely a symptom of a more general lack of the reasoning skills to logically draw inferences from observations.Comment: submitted to American Journal of Physic