Normalizers of Irreducible Subfactors

We consider normalizers of an irreducible inclusion $N\subseteq M$ of $\mathrm{II}_1$ factors. In the infinite index setting an inclusion $uNu^*\subseteq N$ can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these normalizers of $N$ in $M$ to projections in the basic construction and show that every trace one projection in the relative commutant $N'\cap$ is of the form $u^*e_Nu$ for some unitary $u\in M$ with $uNu^*\subseteq N$. This enables us to identify the normalizers and the algebras they generate in several situations. In particular each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of irreducible subfactors arising from subgroup--group inclusions $H\subseteq G$. Here the normalizers are the normalizing group elements modulo a unitary from $L(H)$. We are also able to identify the finite trace $L(H)$-bimodules in $\ell^2(G)$ as double cosets which are also finite unions of left cosets.Comment: 33 Page

MCMC methods for functions modifying old algorithms to make\ud them faster

Many problems arising in applications result in the need\ud to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems

Evaluation of the angiotensin II receptor blocker azilsartan medoxomil in African-American patients with hypertension

The efficacy and safety of azilsartan medoxomil (AZL-M) were evaluated in African-American patients with hypertension in a 6-week, double-blind, randomized, placebo-controlled trial, for which the primary end point was change from baseline in 24-hour mean systolic blood pressure (BP). There were 413 patients, with a mean age of 52years, 57% women, and baseline 24-hour BP of 146/91mmHg. Treatment differences in 24-hour systolic BP between AZL-M 40mg and placebo (-5.0mmHg; 95% confidence interval, -8.0 to -2.0) and AZL-M 80mg and placebo (-7.8mmHg; 95% confidence interval, -10.7 to -4.9) were significant (P.001 vs placebo for both comparisons). Changes in the clinic BPs were similar to the ambulatory BP results. Incidence rates of adverse events were comparable among the treatment groups, including those of a serious nature. In African-American patients with hypertension, AZL-M significantly reduced ambulatory and clinic BPs in a dose-dependent manner and was well tolerated

Summer Habitat Selection and Range Expansion of Non-Native Mountain Goats in the Greater Yellowstone Area

The ongoing expansion of non-native mountain goat populations throughout the mountainous regions of the greater Yellowstone area (GYA) may pose a threat to species native to this ecosystem, particularly native and restored bighorn sheep populations with a history of vulnerability to overexploitation, habitat loss, and disease die-offs. To inform future management actions and policy on the breadth of mountain goat expansion, we used unique occupancy methodologies to rigorously survey two study areas with established bighorn sheep and mountain goat populations over three summer field seasons (2011-2013), modeled patterns of scale-specific habitat selection, and predicted the ultimate distribution of suitable habitat and abundance of mountain goats for the entire GYA. We recorded 505 mountain goat detections for 53,098 sampling units. Mountain goat occupancy was most strongly related to slope, slope variance, canopy cover, heat load, and NDVI. We predicted extensive suitable habitat for the GYA covering 10,745 km2 and extending throughout the South Absaroka, Teton, Gros Ventre, Wind River, and Wyoming Ranges. We estimated the GYA to support 5,372-8,918 total mountain goats, or about 2.5-4.2 times the current abundance estimate of 2,104. The potential implications to management and conservation of bighorn sheep and mountain goats are addressed

Experimental results for nulling the effective thermal expansion coefficient of fused silica fibres under a static stress

We have experimentally demonstrated that the effective thermal expansion coefficient of a fused silica fibre can be nulled by placing the fibre under a particular level of stress. Our technique involves heating the fibre and measuring how the fibre length changes with temperature as the stress on the fibre was systematically varied. This nulling of the effective thermal expansion coefficient should allow for the complete elimination of thermoelastic noise and is essential for allowing second generation gravitational wave detectors to reach their target sensitivity. To our knowledge this is the first time that the cancelation of the thermal expansion coefficient with stress has been experimentally observed

Groupoid normalizers of tensor products

We consider an inclusion B [subset of or equal to] M of finite von Neumann algebras satisfying B′∩M [subset of or equal to] B. A partial isometry vset membership, variantM is called a groupoid normalizer if vBv*,v*Bv[subset of or equal to] B. Given two such inclusions B<sub>i</sub> [subset of or equal to] M<sub>i</sub>, i=1,2, we find approximations to the groupoid normalizers of [formula] in [formula], from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis [formula], i=1,2. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries vset membership, variantM satisfying vBv*[subset of or equal to] B and v*v,vv*[set membership, variant] B

Inverse Compton Scattering as the Source of Diffuse EUV Emission in the Coma Cluster of Galaxies

We have examined the hypothesis that the majority of the diffuse EUV flux in the Coma cluster is due to inverse Compton scattering of low energy cosmic ray electrons (0.16 < epsilon < 0.31 GeV) against the 3K black-body background. We present data on the two-dimensional spatial distribution of the EUV flux and show that these data provide strong support for a non-thermal origin for the EUV flux. However, we show that this emission cannot be produced by an extrapolation to lower energies of the observed synchrotron radio emitting electrons and an additional component of low energy cosmic ray electrons is required.Comment: 11 pages, 5 figure

The Density Matrix Renormalization Group for finite Fermi systems

The Density Matrix Renormalization Group (DMRG) was introduced by Steven White in 1992 as a method for accurately describing the properties of one-dimensional quantum lattices. The method, as originally introduced, was based on the iterative inclusion of sites on a real-space lattice. Based on its enormous success in that domain, it was subsequently proposed that the DMRG could be modified for use on finite Fermi systems, through the replacement of real-space lattice sites by an appropriately ordered set of single-particle levels. Since then, there has been an enormous amount of work on the subject, ranging from efforts to clarify the optimal means of implementing the algorithm to extensive applications in a variety of fields. In this article, we review these recent developments. Following a description of the real-space DMRG method, we discuss the key steps that were undertaken to modify it for use on finite Fermi systems and then describe its applications to Quantum Chemistry, ultrasmall superconducting grains, finite nuclei and two-dimensional electron systems. We also describe a recent development which permits symmetries to be taken into account consistently throughout the DMRG algorithm. We close with an outlook for future applications of the method.Comment: 48 pages, 17 figures Corrections made to equation 19 and table

Assessment of the Water Quality in the Salt River Prior to Its Impoundment in Anderson and Spencer Counties, Kentucky

Monthly water samples were taken and analyzed to determine the water quality of the Salt River in Anderson and Spencer counties Kentucky prior to the river\u27s impoundment. Sediments from the area watershed were analyzed to total acid digestion, barium chloride extraction, and aqueous extraction methods. Rainwater and runoff water were collected and analyzed for major cations and anions from two sites in the watershed. The Salt River at Taylorsville is characterized by hard water with high levels of calcium (33.5-74.8 mg/1), bicarbonate (136-236 mg/l), specific conductance (200-535 μmhos/cm), and sulfate (16.5-71.5 mg/l). Nitrates (0.6-5.7 mg/l), phosphates (0.2-2.4 mg/l), sodium (3.2-20.3 mg/l), and potassium (1.3-5.6 mg/l), are moderate. Iron, manganese, copper, and nitrites are less than 0.5 mg/1. Suspended solids in the river (4.0-l ,684.0 mg/l) are highly variable and directly related to fluctuations in discharge. Sediments from the Salt River Basin are high in potassium (12.4-213.3 mg/g) and iron (23.4-135.1 mg/g), with moderate levels of calcium (0.8-45.7 mg/g), sodium (4.5-10.5 mg/g), magnesium (3.2-6.3 mg/g), and phosphate (1.3-15.3 mg/g). Approximately 10% of the total ionic composition of these sediments is exchangeable and may be extracted with barium chloride. Calcium (309-3,292 μg/g), was the most readily adsorbed cation, with lower levels of potassium (17.6-490.5 μg/g), sodium (12.9-458.1 μg/g), and magnesium (89.4-266.2 μg/g). In the aqueous extractions, calcium (18-486 μg/g), potassium (16.6-69.5 μg/g), sodium (11.1-30.8 μg/g), and magnesium (6.6-68.7 μg/g) comprised about 10% of the exchangeable fraction. Ranges of rainwater ions from the Salt River Basin were: sulfate (8.3-27.8 mg/l), calcium (0.3-10.7 mg/l), potassium (0.4-15.4 mg/l), sodium (0.0-0.7 mg/l), and magnesium (0.1-2.8 mg/l). Ionic composition and sediment yield of runoff water was variable and was related to magnitude of rainfall and runoff sampler placement. Ranges for selected constituents at the two samplers near Taylorsville were: suspended solids (44.0-8,808.0 mg/l), potassium (1.1-84.0 mg/l), magnesium (l.5-7.1 mg/l), calcium (9.5-33.0 mg/l), and sodium (0.6-3.0 mg/l). Calcium and bicarbonate in the Salt River originate from weathering of calcite, although mole ratios of these two ions greater than 1:2 suggest that weathering of magnesium carbonates also contributes bicarbonate to the water. Carbonate equilibrium calculations using field pH and ionic strength suggest calcium is at saturation in the Salt River. High levels of sulfate in rainwater indicate some of this anion may be introduced into the area watershed by atmospheric precipitation