L2-invariants of nonuniform lattices in semisimple Lie groups

We compute L2-invariants of certain nonuniform lattices in semisimple Lie groups by means of the Borel-Serre compactification of arithmetically defined locally symmetric spaces. The main results give new estimates for Novikov-Shubin numbers and vanishing L2-torsion for lattices in groups with even deficiency. We discuss applications to Gromov's Zero-in-the-Spectrum Conjecture as well as to a proportionality conjecture for the L2-torsion of measure equivalent groups.Comment: 35 pages, 2 figure

Approximating Novikov-Shubin numbers of virtually cyclic coverings

We assign real numbers to finite sheeted coverings of compact CW complexes designed as finite counterparts to the Novikov-Shubin numbers. We prove an approximation theorem in the case of virtually cyclic fundamental groups employing methods from Diophantine approximation.Comment: Final version to appear in Groups Geom. Dyn., 17 page

The shrinkage type of knots

We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated with ratios of logarithms of algebraic numbers determined by the first two Alexander polynomials. From this point of view it is natural to subdivide all knots into three different types. We show that examples of all types abound and discuss what happens for twist and torus knots as well as knots with few crossings.Comment: Final version to appear in Bull. Lond. Math. Soc., 19 pages, 2 figure

Cerebral fat embolism syndrome mimicking thrombotic thrombocytopenic purpura in a patient with Hemoglobin SC disease

Case Presentation A 54 year‐old man with hemoglobin SC disease (HbSC) and a history of substance abuse presented to the Emergency Department from a nursing home with two days of progressive weakness, shortness of breath, and lower back pain. He developed a fever, hypoxia, and tachycardia on the day of admission. He did not have any recent changes in medications, and his family as well as the nursing home staff denied any access to illicit drugs

Improved accuracies for satellite tracking

A charge coupled device (CCD) camera on an optical telescope which follows the stars can be used to provide high accuracy comparisons between the line of sight to a satellite, over a large range of satellite altitudes, and lines of sight to nearby stars. The CCD camera can be rotated so the motion of the satellite is down columns of the CCD chip, and charge can be moved from row to row of the chip at a rate which matches the motion of the optical image of the satellite across the chip. Measurement of satellite and star images, together with accurate timing of charge motion, provides accurate comparisons of lines of sight. Given lines of sight to stars near the satellite, the satellite line of sight may be determined. Initial experiments with this technique, using an 18 cm telescope, have produced TDRS-4 observations which have an rms error of 0.5 arc second, 100 m at synchronous altitude. Use of a mosaic of CCD chips, each having its own rate of charge motion, in the focal place of a telescope would allow point images of a geosynchronous satellite and of stars to be formed simultaneously in the same telescope. The line of sight of such a satellite could be measured relative to nearby star lines of sight with an accuracy of approximately 0.03 arc second. Development of a star catalog with 0.04 arc second rms accuracy and perhaps ten stars per square degree would allow determination of satellite lines of sight with 0.05 arc second rms absolute accuracy, corresponding to 10 m at synchronous altitude. Multiple station time transfers through a communications satellite can provide accurate distances from the satellite to the ground stations. Such observations can, if calibrated for delays, determine satellite orbits to an accuracy approaching 10 m rms

The Use of Absolute-Value Terms in Regression Modeling of Multi-Piece Force Balances

Different aspects of the use of absolute-value terms in regression models of the electrical outputs of multi-piece force balance calibration data are discussed. First, characteristics of a variety of regression model term combinations with absolute-value terms are reviewed that are currently used in the aerospace testing community to fit the gage outputs of a balance. Then, a semi-empirical test is presented that quantifies bidirectional characteristics of the balance bridge outputs. Several diagnostic methods are discussed to assess the severity of near-linear dependencies between regressors of models with absolute-value terms. In particular, connections between the linear, absolute-value, quadratic, signed quadratic, and cubic terms are studied in greater detail. Data from an automated calibration of NASAs MK29B force balance are used to illustrate the most important observations and results. Rules of thumb that variance-inflation factors be less than 10 must be relaxed when using absolute-value terms to describe bidirectional balances

Turnover Processes in a Temporal Context: It's About Time

To better understand the process of organizational withdrawal, a turnover model incorporating dynamic predictors measured at five distinct points in time was examined by following a large, occupationally diverse sample over a two-year period. Results demonstrated that turnover can be predicted by perceived costs of turnover, organizational commitment, and critical events measured soon after entry into the organization, and unemployment rates, job satisfaction, and search for alternative jobs also become significant predictors when measured over time. Critical events also predicted turnover in a manner distinct from the operation of attitudes, consistent with the unfolding model (Lee & Mitchell, 1994). The path to turnover was marked by consistently low perceived costs of turnover and satisfaction, decreases in commitment, and increases in job search over time.