Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

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

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

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Evaluation of clinical prediction models (part 1):from development to external validation

Evaluating the performance of a clinical prediction model is crucial to establish its predictive accuracy in the populations and settings intended for use. In this article, the first in a three part series, Collins and colleagues describe the importance of a meaningful evaluation using internal, internal-external, and external validation, as well as exploring heterogeneity, fairness, and generalisability in model performance

The melanoma-specific graded prognostic assessment does not adequately discriminate prognosis in a modern population with brain metastases from malignant melanoma

The melanoma-specific graded prognostic assessment (msGPA) assigns patients with brain metastases from malignant melanoma to 1 of 4 prognostic groups. It was largely derived using clinical data from patients treated in the era that preceded the development of newer therapies such as BRAF, MEK and immune checkpoint inhibitors. Therefore, its current relevance to patients diagnosed with brain metastases from malignant melanoma is unclear. This study is an external validation of the msGPA in two temporally distinct British populations.Performance of the msGPA was assessed in Cohort I (1997-2008, n=231) and Cohort II (2008-2013, n=162) using Kaplan-Meier methods and Harrell's c-index of concordance. Cox regression was used to explore additional factors that may have prognostic relevance.The msGPA does not perform well as a prognostic score outside of the derivation cohort, with suboptimal statistical calibration and discrimination, particularly in those patients with an intermediate prognosis. Extra-cerebral metastases, leptomeningeal disease, age and potential use of novel targeted agents after brain metastases are diagnosed, should be incorporated into future prognostic models.An improved prognostic score is required to underpin high-quality randomised controlled trials in an area with a wide disparity in clinical care

Centerscope

Centerscope, formerly Scope, was published by the Boston University Medical Center "to communicate the concern of the Medical Center for the development and maintenance of improved health care in contemporary society.

Relationship Between Time in Therapeutic Range and Comparative Treatment Effect of Rivaroxaban and Warfarin: Results From the ROCKET AF Trial

Background: Time in therapeutic range (TTR) is a standard quality measure of the use of warfarin. We assessed the relative effects of rivaroxaban versus warfarin at the level of trial center TTR (cTTR) since such analysis preserves randomized comparisons. Methods and Results: TTR was calculated using the Rosendaal method, without exclusion of international normalized ratio (INR) values performed during warfarin initiation. Measurements during warfarin interruptions >7 days were excluded. INRs were performed via standardized finger‐stick point‐of‐care devices at least every 4 weeks. The primary efficacy endpoint (stroke or non‐central nervous system embolism) was examined by quartiles of cTTR and by cTTR as a continuous function. Centers with the highest cTTRs by quartile had lower‐risk patients as reflected by lower CHADS2 scores (P<0.0001) and a lower prevalence of prior stroke or transient ischemic attack (P<0.0001). Sites with higher cTTR were predominantly from North America and Western Europe. The treatment effect of rivaroxaban versus warfarin on the primary endpoint was consistent across a wide range of cTTRs (P value for interaction=0.71). The hazard of major and non‐major clinically relevant bleeding increased with cTTR (P for interaction=0.001), however, the estimated reduction by rivaroxaban compared with warfarin in the hazard of intracranial hemorrhage was preserved across a wide range of threshold cTTR values. Conclusions: The treatment effect of rivaroxaban compared with warfarin for the prevention of stroke and systemic embolism is consistent regardless of cTTR

American Head and Neck Society Endocrine Section clinical consensus statement: North American quality statements and evidence‐based multidisciplinary workflow algorithms for the evaluation and management of thyroid nodules

BackgroundCare for patients with thyroid nodules is complex and multidisciplinary, and research demonstrates variation in care. The objective was to develop clinical guidelines and quality metrics to reduce unwarranted variation and improve quality.MethodsMultidisciplinary expert consensus and modified Delphi approach. Source documents were workflow algorithms from Kaiser Permanente Northern California and Cancer Care of Ontario based on the 2015 American Thyroid Association management guidelines for adult patients with thyroid nodules and differentiated thyroid cancer.ResultsA consensus‐based, unified preoperative, perioperative, and postoperative workflow was developed for North American use. Twenty‐one panelists achieved consensus on 16 statements about workflow‐embedded process and outcomes metrics addressing safety, access, appropriateness, efficiency, effectiveness, and patient centeredness of care.ConclusionA panel of Canadian and United States experts achieved consensus on workflows and quality metric statements to help reduce unwarranted variation in care, improving overall quality of care for patients diagnosed with thyroid nodules.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148340/1/hed25526_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148340/2/hed25526.pd

Prediction of two month modified Rankin Scale with an ordinal prediction model in patients with aneurysmal subarachnoid haemorrhage

Background. Aneurysmal subarachnoid haemorrhage (aSAH) is a devastating event with a frequently disabling outcome. Our aim was to develop a prognostic model to predict an ordinal clinical outcome at two months in patients with aSAH. Methods. We studied patients enrolled in the International Subarachnoid Aneurysm Trial (ISAT), a randomized multicentre trial to compare coiling and clipping in aSAH patients. Several models were explored to estimate a patient's outcome according to the modified Rankin Scale (mRS) at two months after aSAH. Our final model was validated internally with bootstrapping techniques. Results. The study population comprised of 2,128 patients of whom 159 patients died within 2 months (8%). Multivariable proportional odds analysis identified World Federation of Neurosurgical Societies (WFNS) grade as the most important predictor, followed by age, sex, lumen size of the aneurysm, Fisher grade, vasospasm on angiography, and treatment modality. The model discriminated moderately between those with poor and good mRS scores (c statistic = 0.65), with minor optimism according to bootstrap re-sampling (optimism corrected c statistic = 0.64). Conclusion. We presented a calibrated and internally validated ordinal prognostic model to predict two month mRS in aSAH patients who survived the early stage up till a treatment decision.