Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include

Asymptotic corrections to the eigenvalue density of the GUE and LUE

We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N by N matrices, both in the bulk of the spectrum and near the spectral edge. This is achieved by using the well known orthogonal polynomial expression for the kernel to construct a double contour integral representation for the density, to which we apply the saddle point method. The main correction to the bulk density is oscillatory in N and depends on the distribution function of the limiting density, while the corrections to the Airy kernel at the soft edge are again expressed in terms of the Airy function and its first derivative. We demonstrate numerically that these expansions are very accurate. A matching is exhibited between the asymptotic expansion of the bulk density, expanded about the edge, and the asymptotic expansion of the edge density, expanded into the bulk.Comment: 14 pages, 4 figure

Effect of Magnetic Fields on Drug Induced Contractility and Mortality in Spirostomum

The influence of homogeneous magnetic fields up to 5.5 T on contractile frequency and mortality in the ciliate protozoan spirostomum ambiguum stimulated by 2,2′ PDS is reported. Magnetic fields are observed to decrease contractile frequency and to significantly increase mortality

International capital mobility in an era of globalisation: adding a political dimension to the 'Feldstein–Horioka Puzzle'

The debate about the scope of feasible policy-making in an era of globalisation continues to be set within the context of an assumption that national capital markets are now perfectly integrated at the international level. However, the empirical evidence on international capital mobility contradicts such an assumption. As a consequence, a significant puzzle remains. Why is it, in a world in which the observed pattern of capital flows is indicative of a far from globalised reality, that public policy continues to be constructed in line with more extreme variants of the globalisation hypothesis? I attempt to solve this puzzle by arguing that ideas about global capital market integration have an independent causal impact on political outcomes which extends beyond that which can be attributed to the extent of their actual integration

Impact of a brief faculty training to improve patient-centered communication while using electronic health records

Objective Despite rapid EHR adoption, few faculty receive training in how to implement patient-centered communication skills while using computers in exam rooms. We piloted a patient-centered EHR use training to address this issue. Methods Faculty received four hours of training at Cleveland Clinic and a condensed 90-minute version at the University of Chicago. Both included a lecture and a Group-Objective Structured Clinical Exam (GOSCE) experience. Direct observations of 10 faculty in their clinical practices were performed pre- and post-workshop. Results Thirty participants (94%) completed a post-workshop evaluation assessing knowledge, attitude, and skills. Faculty reported that training was important, relevant, and should be required for all providers; no differences were found between longer versus shorter training. Participants in the longer training reported higher GOSCE efficacy, however shorter workshop participants agreed more with the statement that they had gained new knowledge. Faculty improved their patient-centered EHR use skills in clinical practice on post- versus pre-workshop ratings using a validated direct-observation rating tool. Conclusion A brief lecture and GOSCE can be effective in training busy faculty on patient-centered EHR use skills. Practice Implications Faculty training on patient-centered EHR skills can enhance patient-doctor communication and promotes positive role modeling of these skills to learners

Aircraft and avionic related research required to develop an effective high-speed runway exit system

Research was conducted to increase airport capacity by studying the feasibility of the longitudinal separation between aircraft sequences on final approach. The multidisciplinary factors which include the utility of high speed exits for efficient runway operations were described along with recommendations and highlights of these studies

We Could, but Should We? Ethical Considerations for Providing Access to GeoCities and Other Historical Digital Collections

We live in an era in which the ways that we can make sense of our past are evolving as more artifacts from that past become digital. At the same time, the responsibilities of traditional gatekeepers who have negotiated the ethics of historical data collection and use, such as librarians and archivists, are increasingly being sidelined by the system builders who decide whether and how to provide access to historical digital collections, often without sufficient reflection on the ethical issues at hand. It is our aim to better prepare system builders to grapple with these issues. This paper focuses discussions around one such digital collection from the dawn of the web, asking what sorts of analyses can and should be conducted on archival copies of the GeoCities web hosting platform that dates to 1994.This research was supported by the Natural Sciences and Engineering Research Council of Canada, the Social Sciences and Humanities Research Council of Canada, the US National Science Foundation (grants 1618695 and 1704369), the Andrew W. Mellon Foundation, Start Smart Labs, and Compute Canada