Optimizing condition numbers

In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite $n\times n$ matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function. We prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program. This asymptotic analysis provides a valuable tool for designing an implementable algorithm for solving the problem of minimizing condition numbers

Reliability of measuring thoracic kyphosis angle, lumbar lordosis angle and straight leg raise with an inclinometer

Licensed under the terms of the Creative Commons Attribution non-commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, providing that the work is properly citedPurpose: Several non-invasive measurement methods have been described in the literature for recording thoracic kyphosis, lumbar lordosis and straight leg raise (SLR). However, attempts to quantify the reliability of the inclinometer in these measurements are scarce. In addition, existing reliability studies within the literature were found to use small sample sizes. The aim of this investigation was to examine the intra-rater reliability of the chief investigator (SM), in order to provide clinicians with data that will allow them to better measure sagittal spinal posture and SLR. A blinded test-retest design was performed to determine the intra-rater reliability of thoracic kyphosis, lumbar lordosis and SLR when assessed using an Isomed inclinometer in normals. Methods. Thirty asymptomatic subjects were assessed on two occasions separated by a time interval of 1 hour to reduce investigator memory bias. Thoracic and lumbar measurements were recorded in a relaxed standing position using an inclinometer; SLR of the dominant leg was assessed with subjects in the supine position. Intraclass correlation coefficients (ICC), 95% confidence intervals (CI), and standard errors of measurement (SEM) were analysed to determine measurement reliability. Results. The chief investigator demonstrated excellent intra-rater reliability in the measurements of thoracic kyphosis, lumbar lordosis and SLR. ICC (2,3) values for all three variables exceeded the 0.90 threshold suggesting that the reliability of these measures are acceptable for clinical application. Conclusions. The inclinometer technique employed in this study to record thoracic kyphosis, lumbar lordosis and SLR is a reliable measurement method.Peer reviewe

Prox-regularity of rank constraint sets and implications for algorithms

We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank exactly equal to $s$. The normal cone formula appears to be new. This allows for easy application of prior results guaranteeing local linear convergence of the fundamental alternating projection algorithm between sets, one of which is a rank constraint set. We apply this to show local linear convergence of another fundamental algorithm, approximate steepest descent. Our results apply not only to linear systems with rank constraints, as has been treated extensively in the literature, but also nonconvex systems with rank constraints.Comment: 12 pages, 24 references. Revised manuscript to appear in the Journal of Mathematical Imaging and Visio

Acebutolol in cardiac arrhythmiaa

Acebutolol (Sectral), a new beta-adrenoceptor antagonist, was used in 44 patients with cardiac arrhythmias (53 episodes). It was used intravenously (12,5 and 25 mg), orally (100 mg every 8 hours) or in combination with quinidine. Acebutolol was most effective in supraventricular tachyarrhythmias, to control the ventricular response when digital's was ineffective, as a synergist with quinidine to convert patients to sinus rhythm, or prophylactically to prevent relapse to atrial fibrillation. It also terminated ventricular tachycardia in two patients. Side-effects occurred in three ill patients.S. Afr. Med. J., 48, 821 (1974

Motives of some Fano varieties

We study the Fano varieties of projective k-planes lying in hypersurfaces and investigate the associated motives. © 2008 Springer-Verlag

Semidefinite Representation of the kk-Ellipse

The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if $k$ is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted $k$-ellipses and $k$-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure

The effects of respiratory muscle strength training on individuals with Parkinson\u27s disease

The purpose of this study was to determine if respiratory muscle strength training (RMST) results in increased measures of respiratory function, improved vocal quality, and improved quality of life as perceived by the participants. Data obtained by this study adds to the body of knowledge regarding clinical use of RMST for SLPs working with patients with Parkinson\u27s disease (PD). The study was comprised of a 13-week ABAB within-subject design with a baseline period, five weeks of respiratory training (Phase 1), three weeks without training (Detraining Phase), and five weeks with training (Phase 2). Three individuals with moderate PD (1M, 2F) participated. They were taught to use the PowerLung® respiratory training device and completed twice daily sessions of expiratory and inspiratory muscle training, five days per week. Outcome measures included maximum inspiratory and expiratory pressures (MIP and MEP, respectively); forced vital capacity (FVC), percent predicted forced vital capacity (FVC%), and forced expiratory volume in 1 second (FEV1); and sustained vowel phonation. Measurements were taken at baseline, before and after detraining (where applicable), and at the end of the study. Results indicated improved maximum respiratory pressures for all participants from baseline to end of study. No participant showed significant changes in FVC, FVC%, and FEV 1, and results of sustained vowel phonation varied. Participants\u27 vocal quality was evaluated by three independent raters as well as the subjects themselves and two conversation partners. Two CSD graduate students and one certified SLP rated subjects\u27 voices at baseline and at the end of treatment using recorded conversation samples and the GRBAS Voice Rating Scale (Hirano, 1981). Improvement in vocal quality was perceived in two participants, and no change was seen in the other. Participants and two conversation partners completed the Perceptual Rating Form to report on vocal quality. Participants noted improvement in vocal quality; conversation partners reported both improvement and decline in various aspects of two participants\u27 vocal quality. Participants completed two surveys regarding the impact of their voice on overall communication and quality of life. These surveys, completed at the start of the study and at completion of each phase, were the Voice Handicap Index (VHI) (Jacobson, et al., 1997) and The Communicative Participation Item Bank General Short Form (Baylor et al. [under review]). Responses from participants revealed inconsistent effects of RMST on quality of life. Results of this study demonstrate that the combination of inspiratory and expiratory muscle strength training in individuals with moderate Parkinson\u27s disease may be a beneficial treatment to improve respiratory function and positively impact vocal quality and overall quality of life as it relates to communicative participation. Results from this study revealed the potential for additional research on the effects of RMST on pulmonary functions such as vital capacity (VC) and total lung capacity (TLC), which are not dependent on maximum speed and effort. Additionally, further investigation of RMST on quality of life is warranted in areas related to voice and communication, as well as overall physical and emotional wellbeing

Psychotic experiences, working memory, and the developing brain: a multimodal neuroimaging study

Psychotic experiences (PEs) occur in the general population, especially in children and adolescents, and are associated with poor psychosocial outcomes, impaired cognition, and increased risk of transition to psychosis. It is unknown how the presence and persistence of PEs during early adulthood affects cognition and brain function. The current study assessed working memory as well as brain function and structure in 149 individuals, with and without PEs, drawn from a population cohort. Observer-rated PEs were classified as persistent or transient on the basis of longitudinal assessments. Working memory was assessed using the n-back task during fMRI. Dynamic causal modeling (DCM) was used to characterize frontoparietal network configuration and voxel-based morphometry was utilized to examine gray matter. Those with persistent, but not transient, PEs performed worse on the n-back task, compared with controls, yet showed no significant differences in regional brain activation or brain structure. DCM analyses revealed greater emphasis on frontal connectivity within a frontoparietal network in those with PEs compared with controls. We propose that these findings portray an altered configuration of working memory function in the brain, potentially indicative of an adaptive response to atypical development associated with the manifestation of PEs

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201