Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Cosmological parameters from SDSS and WMAP

We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a ``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1 sigma constraints on the Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt figures available at http://www.hep.upenn.edu/~max/sdsspars.htm

Abacavir, efavirenz, didanosine, with or without hydroxyurea, in HIV-infected adults failing initial nucleoside/protease inhibitor-containing regimens

Background: Hydroxyurea (HU) is an immunomodulatory agent that has been documented to enhance the antiretroviral activity of nucleoside reverse transcriptase inhibitors, such as abacavir (ABC) and didanosine (ddI), and would be expected to improve virologic efficacy. Methods: A 48-week, phase IV, multicenter, open-label, proof-of-concept clinical trial was conducted to evaluate second-line, protease inhibitor (PI)-sparing therapy with ABC/efavirenz (EFV)/ddl plus HU or without HU in HIV-infected subjects failing to achieve HIV-1 RNA ≤ 400 copies/mL after ≥ 16 weeks of treatment with lamivudine /zidovudine or lamivudine/stavudine, plus 1 or 2 Pls. Subjects were assigned to ABC (300 mg twice daily)/ EFV (600 mg once daily)/ ddI (400 mg once daily) plus HU (500 mg twice daily) (n = 30) or this regimen without HU (n = 24). Results: Baseline mean HIV-1 RNA was 3.86 log10 copies/mL and CD4+ cell count was 345 cells/mm3. A similar percentage of subjects in the non-HU arm (58%) and HU arm (53%) completed the study. Intent-to-treat: missing = failure analysis showed no differences in proportions of subjects in the non-HU and HU arms achieving undetectable plasma HIV-1 RNA levels at week 24 (&lt;400 copies/mL: 58% [14/24] vs 57% [17/30], P = 0.899; &lt;50 copies/mL (50% [12/24] vs 47% [14/30], P = 0.780). Median change from baseline in CD4+ cell count in the non-HU and HU arms at week 48 was +114 cells/mm3 and -63 cells/mm3 (P = 0.007), respectively. Both regimens were generally well tolerated, although more subjects in the HU arm withdrew prematurely from the study due to adverse events (23% vs 4%). Four cases of possible ABC-related hypersensitivity were observed. Conclusion: ABC/EFV/ddI was an effective and well-tolerated second-line regimen for nucleoside/PI-experienced HIV-infected subjects. The addition of HU blunted the CD4+ cell response, did not appear to enhance antiviral activity, and resulted in more treatment-limiting adverse events

Hamstring muscles: Architecture and innervation

Knowledge of the anatomical organization of the hamstring muscles is necessary to understand their functions, and to assist in the development of accurate clinical and biomechanical models. The hamstring muscles were examined by dissection in six embalmed human lower limbs with the purpose of clarifying their gross morphology. In addition to obtaining evidence for or against anatomical partitioning ( as based on muscle architecture and pattern of innervation), data pertaining to architectural parameters such as fascicular length, volume, physiological cross-sectional area, and tendon length were collected. For each muscle, relatively consistent patterns of innervation were identified between specimens, and each was unique with respect to anatomical organization. On the basis of muscle architecture, three regions were identified within semimembranosus. However, this was not completely congruent with the pattern of innervation, as a primary nerve branch supplied only two regions, with the third region receiving a secondary branch. Semitendinosus comprised two distinct partitions arranged in series that were divided by a tendinous inscription. A singular muscle nerve or a primary nerve branch innervated each partition. In the biceps femoris long head the two regions were supplied via a primary nerve branch which divided into two primary branches or split into a series of branches. Being the only muscle to cross a single joint, biceps femoris short head consisted of two distinct regions demarcated by fiber direction, with each innervated by a separate muscle nerve. Architecturally, each muscle differed with respect to parameters such as physiological cross-sectional area, fascicular length and volume, but generally all partitions within an individual muscle were similar in fascicular length. The long proximal and distal tendons of these muscles extended into the muscle bellies thereby forming elongated musculotendinous junctions. Copyright (C) 2005 S. Karger AG, Basel

TIC 172900988: A transiting circumbinary planet detected in one sector of TESS data

We report the first discovery of a transiting circumbinary planet detected from a single sector of Transiting Exoplanet Survey Satellite (TESS) data. During Sector 21, the planet TIC 172900988b transited the primary star and then five days later it transited the secondary star. The binary is itself eclipsing, with a period P ≈ 19.7 days and an eccentricity e ≈ 0.45. Archival data from ASAS-SN, Evryscope, KELT, and SuperWASP reveal a prominent apsidal motion of the binary orbit, caused by the dynamical interactions between the binary and the planet. A comprehensive photodynamical analysis of the TESS, archival and follow-up data yields stellar masses and radii of M1 = 1.2384 ± 0.0007 Me and R1 = 1.3827 ± 0.0016 Re for the primary and M2 = 1.2019 ± 0.0007 Me and R2 = 1.3124 ± 0.0012 Re for the secondary. The radius of the planet is R3 = 11.25 ± 0.44 R (1.004 ± 0.039RJup). The planet's mass and orbital properties are not uniquely determined-there are six solutions with nearly equal likelihood. Specifically, we find that the planet's mass is in the range of 824 M3 981 M (2.65 M3 3.09MJup), its orbital period could be 188.8, 190.4, 194.0, 199.0, 200.4, or 204.1 days, and the eccentricity is between 0.02 and 0.09. At V = 10.141 mag, the system is accessible for high-resolution spectroscopic observations, e.g., the Rossiter-McLaughlin effect and transit spectroscopy

Shielding studies at Mound Laboratory

Neutron shielding is done to protect workers from excessive radiation and to keep a low neutron background for research in neutron counting. To meet health standards the total neutron flux allowable is 150 n/cm/sec per eight hours, or 50 n/cm/sec per twenty-four hours. Literature values for the absorption coefficients of paraffin and water are considered, and some experimental data is presented which approximately confirm them. A description of barriers at Mound Laboratory is given. Plans for future work on slowing-down of fast nautrons and capture of slow neutrons are included

THE EFFECT OF ENVIRONMENTAL TEMPERATURES ON THE RETENTION OF CESIUMsup137sup 137 BY MICE

Three groups of 12 mice each were maintained at environmental temperatures of 34, 22, and 5 deg C for a period of about 7 weeks after an intraperitoneal injection of Cs/sup 137/. Periodic assay of the activity in the whole body and excreta showed that as environmental temperature decreases the excretion of Cs/sup 137/ increases, probably as a result of the increased metabolic rates associated with low temperatures. (auth