Marginal distributions in (2N)(\bf 2N)-dimensional phase space and the quantum (N+1)(\bf N+1) marginal theorem

We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e. depending on a (complete) commuting set of $N$ variables, are considered. A diagrammatic or graph theoretic formulation of the problem is developed. We then exactly determine the set of ``admissible'' data, i.e. those types of data for which the problem always admits solutions. This is done in the case where the joint distributions originate from quantum mechanics as well as in the case where this constraint is not imposed. In particular, it is shown that a necessary (but not sufficient) condition for the existence of solutions is $n\leq N+1$. When the data are admissible and the quantum constraint is not imposed, the general solution for the phase space density is determined explicitly. For admissible data of a quantum origin, the general solution is given in certain (but not all) cases. In the remaining cases, only a subset of solutions is obtained.Comment: 29 pages (Work supported by the Indo-French Centre for the Promotion of Advanced Research, Project Nb 1501-02). v2 to add a report-n

Bell Inequalities in Phase Space and their Violation in Quantum Mechanics

We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there exist quantum states for which more than three of the quantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and $(p_1,q_2)$ cannot be reproduced as marginals of a positive $\rho(\overrightarrow{q},\overrightarrow{p})$''. We also construct the most general positive $\rho(\overrightarrow{q},\overrightarrow{p})$ which reproduces any three of the above quantum probability densities for arbitrary quantum states. This is crucial for the construction of a maximally realistic quantum theory.Comment: 11 pages, latex, no figure

An Analysis of Pricing Strategy and Price Dispersion on the Internet

Using prices obtained from shopbots, we test several hypotheses regarding the economics of information and optimal search. We find that price dispersion is positively (negatively) related to product price and the number of sellers in cross-sectional (time series) analysis. Price dispersion increases over time when the sample includes new entrants, but decreases in the absence of entry. Controlling for shipping charges and seller heterogeneity reduces, but does not eliminate, price dispersion. Finally, prices appear to be correlated across products and over time – low price sellers for one product (time period) generally charge low prices for all items (time periods).

Prevalence and causes of dysphonia in a large treatment-seeking population

Journal ArticleObjective: To determine the prevalence and common causes of dysphonia as diagnosed by primary care physicians (PCPs) and otolaryngologists, and to evaluate differences in etiologies offered by these providers. Study Design: Retrospective analysis of data from a large, nationally representative administrative U.S. claims database. Methods: Patients were identified as dysphonic based on ICD-9-CM codes from January 1, 2004 to December 31, 2008. Data regarding age, gender, geographic location, and type of physician providing the dysphonia diagnosis were collected. Overall and age-related prevalence rates, as well as frequency of specific etiologies by provider type were calculated. Results: Of the almost 55 million individuals in the database, 536,943 patients, ages 0 to > 65 years, were given a dysphonia diagnosis (point prevalence rate of 0.98%). The prevalence rate was higher among females as compared to males (1.2% versus 0.7%) and among those > 70 years of age (2.5%). The most frequent diagnoses overall were acute laryngitis, non-specific dysphonia, benign vocal fold lesions, and chronic laryngitis. PCPs more commonly diagnosed acute laryngitis, whereas otolaryngologists more commonly diagnosed non-specific dysphonia and laryngeal pathology. Gastro-esophageal reflux was more commonly diagnosed as a comorbid condition by otolaryngologists than by PCPs. Overall laryngeal cancer prevalence in this treatment-seeking population was 2.2% and was greatest among males > 70 years of age. Conclusion: This analysis of insurance claims data from a nationally representative database represents the largest study of its kind. Important differences in dysphonia prevalence related to age, gender, diagnosis, and physician type were identified. Word count: 248, Evidence level: level 2b. Introduction: The public health impact of vocal dysfunction is becoming increasingly recognized. Dysphonia adversely impacts communication with physical, social, and workrelated effects. Patients suffer social isolation, depression, impaired disease-specific and general quality of life, and work absenteeism.1-4 Thus, voice disorders negatively impact individuals and burden society

Predictive value of grade point average (GPA), Medical College Admission Test (MCAT), internal examinations (Block) and National Board of Medical Examiners (NBME) scores on Medical Council of Canada qualifying examination part I (MCCQE-1) scores

Background: To determine whether the pre-medical Grade Point Average (GPA), Medical College Admission Test (MCAT), Internal examinations (Block) and National Board of Medical Examiners (NBME) scores are correlated with and predict the Medical Council of Canada Qualifying Examination Part I (MCCQE-1) scores.Methods: Data from 392 admitted students in the graduating classes of 2010-2013 at University of Manitoba (UofM), College of Medicine was considered. Pearson’s correlation to assess the strength of the relationship, multiple linear regression to estimate MCCQE-1 score and stepwise linear regression to investigate the amount of variance were employed.Results: Complete data from 367 (94%) students were studied. The MCCQE-1 had a moderate-to-large positive correlation with NBME scores and Block scores but a low correlation with GPA and MCAT scores. The multiple linear regression model gives a good estimate of the MCCQE-1 (R2 =0.604). Stepwise regression analysis demonstrated that 59.2% of the variation in the MCCQE-1 was accounted for by the NBME, but only 1.9% by the Block exams, and negligible variation came from the GPA and the MCAT.Conclusions: Amongst all the examinations used at UofM, the NBME is most closely correlated with MCCQE-1