Tridiagonal realization of the anti-symmetric Gaussian β\beta-ensemble

The Householder reduction of a member of the anti-symmetric Gaussian unitary ensemble gives an anti-symmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter $\beta$, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of $\{q_i\}$, the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the anti-symmetric tridiagonal matrices. This proof uses the Dixon-Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real anti-symmetric tridiagonal matrices, its eigenvalues and $\{q_i\}$. The third proof maps matrices from the anti-symmetric Gaussian $\beta$-ensemble to those realizing particular examples of the Laguerre $\beta$-ensemble. In addition to these proofs, we note some simple properties of the shooting eigenvector and associated Pr\"ufer phases of the random matrices.Comment: 22 pages; replaced with a new version containing orthogonal transformation proof for both cases (Method III

Band Distributions for Quantum Chaos on the Torus

Band distributions (BDs) are introduced describing quantization in a toral phase space. A BD is the uniform average of an eigenstate phase-space probability distribution over a band of toral boundary conditions. A general explicit expression for the Wigner BD is obtained. It is shown that the Wigner functions for {\em all} of the band eigenstates can be reproduced from the Wigner BD. Also, BDs are shown to be closer to classical distributions than eigenstate distributions. Generalized BDs, associated with sets of adjacent bands, are used to extend in a natural way the Chern-index characterization of the classical-quantum correspondence on the torus to arbitrary rational values of the scaled Planck constant.Comment: 12 REVTEX page

Effects of Electron Correlations on Hofstadter Spectrum

By allowing interactions between electrons, a new Harper's equation is derived to examine the effects of electron correlations on the Hofstadter energy spectra. It is shown that the structure of the Hofstadter butterfly ofr the system of correlated electrons is modified only in the band gaps and the band widths, but not in the characteristics of self-similarity and the Cantor set.Comment: 13 pages, 5 Postscript figure

“I wish I’d told them”: a qualitative study examining the unmet psychosexual needs of prostate cancer patients during follow-up after treatment

<b>Objective</b> To gain insight into patients' experiences of follow-up care after treatment for prostate cancer and identify unmet psychosexual needs.<p></p> <b>Methods</b> Semi-structured interviews were conducted with a purposive sample of 35 patients aged 59-82 from three UK regions. Partners were included in 18 interviews. Data were analyzed using constant comparison. <p></p> <b>Results</b> (1) Psychosexual problems gained importance over time, (2) men felt they were rarely invited to discuss psychosexual side effects within follow-up appointments and lack of rapport with health care professionals made it difficult to raise problems themselves, (3) problems were sometimes concealed or accepted and professionals' attempts to explore potential difficulties were resisted by some, and (4) older patients were too embarrassed to raise psychosexual concerns as they felt they would be considered 'too old' to be worried about the loss of sexual function.<p></p> <b>Conclusion</b> Men with prostate cancer, even the very elderly, have psychosexual issues for variable times after diagnosis. These are not currently always addressed at the appropriate time for the patient.Practice implications Assessments of psychosexual problems should take place throughout the follow-up period, and not only at the time of initial treatment. Further research examining greater willingness or reluctance to engage with psychosexual interventions may be particularly helpful in designing future intervention

Challenges of ultra large scale integration of biomedical computing systems

The NCRI Informatics Initiative is overseeing the implementation of an informatics framework for the UK cancer research community. The framework advocates an integrated multidisciplinary method of working between scientific and medical communities. Key to this process is community adoption of high quality acquisition, storage, sharing and integration of diverse data elements to improve knowledge of the causes, prevention and treatment of cancer. The integration of the complex data and meta-data used by these multiple communities is a significant challenge and there are technical, resource-based and sociological issues to be addressed. In this paper we review progress aimed at establishing the framework and outline key challenges in ultra large scale integration of biomedical computing systems

Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results.Comment: 9 pages, 6 figure

Evaluation of nonmetallic thermal protection materials for the manned space shuttle. Volume 1, task 1: Assessment of technical risks associated with utilization of nonmetallic thermal protection system

Technical problems of design and flight qualification of the proposed classes of surface insulation materials and leading edge materials were reviewed. A screening test plan, a preliminary design data test plan and a design data test plan were outlined. This program defined the apparent critical differences between the surface insulators and the leading edge materials, structuring specialized screening test plans for each of these two classes of materials. Unique testing techniques were shown to be important in evaluating the structural interaction aspects of the surface insulators and a separate task was defined to validate the test plan. In addition, a compilation was made of available information on proposed material (including metallic TPS), previous shuttle programs, pertinent test procedures, and other national programs of merit. This material was collected and summarized in an informally structured workbook

Small phase pattern 2D beam steering and a single LCOS design of 40 1 × 12 stacked wavelength selective switches

Two-dimensional beam steering by small, square, phase patterns as small as 50 × 50 pixels on a phase-only liquid crystal on silicon (LCOS) device is experimentally verified as suitable for the application of wavelength selective switches (WSSs), in terms of the diffraction efficiency and steering accuracy. This enables a proposed highly functional and versatile stacked switch architecture, where 40 independent 1 × 12 WSSs can be realised on a single 4k LCOS device. They can be configured to support a 1 × N WSSs with N≤144, or an N × N wavelength crossconnect with N≤12.This is the accepted manuscript. It is currently embargoed pending publication

'Datafication': Making sense of (big) data in a complex world

This is a pre-print of an article published in European Journal of Information Systems. The definitive publisher-authenticated version is available at the link below. Copyright @ 2013 Operational Research Society Ltd.No abstract available (Editorial