Kadison-Kastler stable factors

A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations of one another. For n≥3 and a free, ergodic, probability measure-preserving action of SL<sub>n</sub>(Z) on a standard nonatomic probability space (X,μ), write M=(L<sup>∞</sup>(X,μ)⋊SL<sub>n</sub>(Z))⊗¯¯¯R, where R is the hyperfinite II1-factor. We show that whenever M is represented as a von Neumann algebra on some Hilbert space H and N⊆B(H) is sufficiently close to M, then there is a unitary u on H close to the identity operator with uMu∗=N. This provides the first nonamenable class of von Neumann algebras satisfying Kadison and Kastler’s conjecture. We also obtain stability results for crossed products L<sup>∞</sup>(X,μ)⋊Γ whenever the comparison map from the bounded to usual group cohomology vanishes in degree 2 for the module L<sup>2</sup>(X,μ). In this case, any von Neumann algebra sufficiently close to such a crossed product is necessarily isomorphic to it. In particular, this result applies when Γ is a free group

Energy density of foods and beverages in the Australian food supply: influence of macronutrients and comparison to dietary intake.

OBJECTIVES: The energy density (ED) of the diet is considered an important determinant of total energy intake and thus energy balance and weight change. We aimed to compare relationships between ED and macronutrient content in individual food and beverage items as well as population diet in a typical Western country. DESIGN: Nutrient data for 3673 food items and 247 beverage items came from the Australian Food and Nutrient database (AusNut). Food and beverage intake data came from the 1995 Australian National Nutrition Survey (a 24-h dietary recall survey in 13 858 people over the age of 2). Relationships between ED and macronutrient and water content were analysed by linear regression with 95% prediction bands. RESULTS: For both individual food items and population food intake, there was a positive relationship between ED and percent energy as fat and negative relationships between ED and percent energy as carbohydrate and percent water by weight. In all cases, there was close agreement between the slopes of the regression lines between food items and dietary intake. There were no clear relationships between ED and macronutrient content for beverage items. Carbohydrate (mostly sucrose) contributed 91, 47, and 25% of total energy for sugar-based, fat-based, and alcohol-based beverages respectively. CONCLUSIONS: The relationship between ED and fat content of foods holds true across both population diets and individual food items available in the food supply in a typical Western country such as Australia. As high-fat diets are associated with a high BMI, population measures with an overall aim of reducing the ED of diets may be effective in mediating the growing problem of overweight and obesity

Compact Modeling for a Double Gate MOSFET

MOSFETs (metal-oxide-silicon field-effect transistors) are an integral part of modern electronics. Improved designs are currently under investigation, and one that is promising is the double gate MOSFET. Understanding device characteristics is critical for the design of MOSFETs as part of design tools for integrated circuits such as SPICE. Current methods involve the numerical solution of PDEs governing electron transport. Numerical solutions are accurate, but do not provide an appropriate way to optimize the design of the device, nor are they suitable for use in chip simulation software such as SPICE. As chips contain more and more transistors, this problem will get more and more acute. There is hence a need for analytic solutions of the equations governing the performance of MOSFETs, even if these are approximate. Almost all solutions in the literature treat the long-channel case (thin devices) for which the PDEs reduce to ODEs. The goal of this problem is to produce analytical solutions based on the underlying PDEs that are rapid to compute (e.g. require solving only a small number of algebraic equations rather than systems of PDEs). Guided by asymptotic analysis, a fast numerical procedure has been developed to obtain approximate solutions of the governing PDEs governing MOSFET properties, namely electron density, Fermi potential and electrostatic potential. The approach depends on the channel’s being long enough, and appears accurate in this limit

A remark on the similarity and perturbation problems

In this note we show that Kadison's similarity problem for C*-algebras is equivalent to a problem in perturbation theory: must close C*-algebras have close commutants?Comment: 6 Pages, minor typos fixed. C. R. Acad. Sci. Canada, to appea

Effects of creatine supplementation on housekeeping genes in human skeletal muscle using real-time RT-PCR.

The present study examined the validity and reliability of measuring the expression of various genes in human skeletal muscle using quantitative real-time RT-PCR on a GeneAmp 5700 sequence detection system with SYBR Green 1 chemistry. In addition, the validity of using some of these genes as endogenous controls (i.e., housekeeping genes) when human skeletal muscle was exposed to elevated total creatine levels and exercise was also examined. For all except 28S, linear relationships between the logarithm of the starting RNA concentrations and the cycle threshold (C(T)) values were established for beta-actin, beta2-microglobulin (beta2M), cyclophilin (CYC), and glyceraldehyde-3-phosphate dehydrogenase (GAPDH). We found a linear response between C(T) values and the logarithm of a given amount of starting cDNA for all the genes tested. The overall intra-assay coefficient of variance for these genes was 1.3% and 21% for raw C(T) values and the linear value of 2(-C(T)), respectively. Interassay variability was 2.3% for raw C(T) values and 34% for the linear value of 2(-C(T)). We also examined the expression of various housekeeping genes in human skeletal muscle at days 0, 1, and 5 following oral supplementation with either creatine or a placebo employing a double-blind crossover study design. Treatments were separated by a 5-wk washout period. Immediately following each muscle sampling, subjects performed two 30-s all-out bouts on a cycle ergometer. Creatine supplementation increased (P < 0.05) muscle total creatine content above placebo levels; however, there were no changes (P > 0.05) in C(T) values across the supplementation periods for any of the genes. Nevertheless, 95% confidence intervals showed that GAPDH was variable, whereas beta-actin, beta2M, and CYC were the least varying genes. Normalization of the data to these housekeeping genes revealed variable behavior for beta2M with more stable expressions for both beta-actin and CYC. We conclude that, using real-time RT-PCR, beta-actin or CYC may be used as housekeeping genes to study gene expression in human muscle in experiments employing short-term creatine supplementation combined with high-intensity exercise

Discovery of a z=4.93, X-ray selected quasar by the Chandra Multiwavelength Project (ChamP)

We present X-ray and optical observations of CXOMP J213945.0-234655, a high redshift (z=4.93) quasar discovered through the Chandra Multiwavelength Project (ChaMP). This object is the most distant X-ray selected quasar published, with an X-ray luminosity of L(X)=5.9x10^44 erg/s (measured in the 0.3-2.5 keV band and corrected for Galactic absorption). CXOMP J213945.0-234655 is a g' dropout object (>26.2), with r'=22.87 and i'=21.36. The rest-frame X-ray to optical flux ratio is similar to quasars at lower redshifts and slightly X-ray bright relative to z>4 optically-selected quasars observed with Chandra. The ChaMP is beginning to acquire significant numbers of high redshift quasars to investigate the unobscured X-ray luminosity function out to z~5.Comment: Published in ApJ Letters; 4 pages; 3 figures; http://hea-www.harvard.edu/CHAMP

The Luminosity Function of X-ray Selected Active Galactic Nuclei: Evolution of Supermassive Black Holes at High Redshift

We present a measure of the hard (2-8 keV) X-ray luminosity function (XLF) of Active Galactic Nuclei up to z~5. At high redshifts, the wide area coverage of the Chandra Multiwavength Project is crucial to detect rare and luminous (Lx > 10^44 erg s^-1) AGN. The inclusion of samples from deeper published surveys, such as the Chandra Deep Fields, allows us to span the lower Lx range of the XLF. Our sample is selected from both the hard (z 6.3x10^-16 erg cm^-2 s^-1) and soft (z > 3; f(0.5-2.0 keV) > 1.0x10^-16 erg cm^-2 s^-1) energy band detections. Within our optical magnitude limits (r',i' < 24), we achieve an adequate level of completeness (>50%) regarding X-ray source identification (i.e., redshift). We find that the luminosity function is similar to that found in previous X-ray surveys up to z~3 with an evolution dependent upon both luminosity and redshift. At z > 3, there is a significant decline in the numbers of AGN with an evolution rate similar to that found by studies of optically-selected QSOs. Based on our XLF, we assess the resolved fraction of the Cosmic X-ray Background, the cumulative mass density of Supermassive Black Holes (SMBHs), and the comparison of the mean accretion rate onto SMBHs and the star formation history of galaxies as a function of redshift. A coevolution scenario up to z~2 is plausible though at higher redshifts the accretion rate onto SMBHs drops more rapidly. Finally, we highlight the need for better statistics of high redshift AGN at z > 3, which is achievable with the upcoming Chandra surveys.Comment: Accepted for publication in ApJ; 25 pages, 18 figure