Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Altered distribution of interstitial cells and innervation in the rat urinary bladder following spinal cord injury

Introduction Changes in the distribution of interstitial cells (IC) are reportedly associated with dysfunctional bladder. The present study investigated whether spinal cord injury (SCI) resulted in changes to IC subpopulations (vimentin-positive with the ultrastructural profile of IC), smooth muscle and nerves within the bladder wall and correlated cellular remodelling with functional properties. Methods Bladders from SCI (T8/9 transection) and sham-operated rats five-weeks post-injury were used for ex vivo pressure-volume experiments or processed for morphological analysis with transmission electron microscopy (TEM) and light/confocal microscopy. Results Pressure-volume relationships revealed low-pressure, hypercompliance in SCI bladders indicative of decompensation. Extensive networks of vimentin-positive IC were typical in sham lamina propria and detrusor but were markedly reduced post-SCI; semi-quantitative analysis showed significant reduction. Nerves labelled with anti-neurofilament and anti-vAChT were notably decreased post-SCI. TEM revealed lamina propria IC and detrusor IC which formed close synaptic-like contacts with vesicle-containing nerve varicosities in shams. Lamina propria and detrusor IC were ultrastructurally damaged post-SCI with retracted/lost cell processes and were adjacent to areas of cellular debris and neuronal degradation. Smooth muscle hypertrophy was common to SCI tissues. Conclusions IC populations in bladder wall were decreased five weeks post-SCI, accompanied with reduced innervation, smooth muscle hypertrophy and increased compliance. These novel findings indicate that bladder wall remodelling post-SCI affects the integrity of interactions between smooth muscle, nerves and IC, with compromised IC populations. Correlation between IC reduction and a hypercompliant phenotype suggests that disruption to bladder IC contribute to pathophysiological processes underpinning the dysfunctional SCI bladder.

The velocity distribution of solar photospheric magnetic bright points.

We use high spatial resolution observations and numerical simulations to study the velocity distribution of solar photospheric magnetic bright points. The observations were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope, while the numerical simulations were undertaken with the MURaM code for average magnetic fields of 200 G and 400 G. We implemented an automated bright point detection and tracking algorithm on the data set and studied the subsequent velocity characteristics of over 6000 structures, finding an average velocity of approximately 1 km s(-1), with maximum values of 7 km s(-1). Furthermore, merging magnetic bright points were found to have considerably higher velocities, and significantly longer lifetimes, than isolated structures. By implementing a new and novel technique, we were able to estimate the background magnetic flux of our observational data, which is consistent with a field strength of 400 G.

The spatial distribution of Holocene cryptotephras in north-west Europe since 7 ka: implications for understanding ash fall events from Icelandic eruptions

We present distribution maps for all cryptotephras (distal volcanic ash layers) younger than 7 ka that have been reported from three or more lakes or peatlands in north-west Europe. All but one of the tephras originates from Iceland; the exception has been attributed to Jan Mayen. We find strong spatial patterning in tephra occurrence at the landscape scale; most, but not all of the tephra occurrences are significantly spatially clustered, which likely reflects atmospheric and weather patterns at the time of the eruptions. Contrary to expectations based on atmospheric modelling studies, tephras appear to be at least as abundant in Ireland and northern Scotland as in Scandinavia. Rhyolitic and other felsic tephras occur in lakes and peatlands throughout the study region, but andesitic and basaltic tephras are largely restricted to lake sites in the Faroe Islands and Ireland. Explanations of some of these patterns will require further research on the effects of different methodologies for locating and characterizing cryptotephras. These new maps will help to guide future investigations in tephrochronology and volcanic hazard analysis.

Polar distribution of ablated atomic material during the pulsed laser deposition of Cu in vacuum: Dependence on focused laser spot size and power density

Experiments have been carried out to investigate the polar distribution of atomic material ablated during the pulsed laser deposition of Cu in vacuum. Data were obtained as functions of focused laser spot size and power density. Thin films were deposited onto flat glass substrates and thickness profiles were transformed into polar atomic flux distributions of the form f(theta)=cos(n) theta. At constant focused laser power density on target, I=4.7+/-0.3X10(8) W/cm(2), polar distributions were found to broaden with a reduction in the focused laser spot size. The polar distribution exponent n varied from 15+/-2 to 7+/-1 for focused laser spot diameter variation from 2.5 to 1.4 mm, respectively, with the laser beam exhibiting a circular aspect on target. With the focused laser spot size held constant at phi=1.8 mm, polar distributions were observed to broaden with a reduction in the focused laser power density on target, with the associated polar distribution exponent n varying from 13+/-1.5 to 8+/-1 for focused laser power density variation from 8.3+/-0.3X10(8) to 2.2+/-0.1X10(8) W/cm(2) respectively. Data were compared with an analytical model available within the literature, which correctly predicts broadening of the polar distribution with a reduction in focused laser spot size and with a reduction in focused laser power density, although the experimentally observed magnitude was greater than that predicted in both cases. (C) 1996 American Institute of Physics.