The outburst radial velocity curve of X-Ray Nova Scorpii 1994 (=GRO J1655--40)

We present a reanalysis of the outburst radial velocity data for X-Ray Nova Scorpii 1994. Using a model based on X-ray heating of the secondary star we suggest a more realistic treatment of the radial velocity data. Solutions are obtained in the (K_2,q) plane which, when combined with the published value for the binary mass ratio and inclination, constrain the mass of the black hole to within the region 4.1<M_1<6.6 Msun (90 per cent confidence), which is significantly lower than the value obtained by Orosz & Bailyn (1997). This reduced lower bound for the black hole mass together with the high space velocity of the system is consistent with the idea that it was formed by the post-supernova collapse of a neutron star.Comment: Accepted for MNRAS, 4 pages Latex, 4 figure

A direct proof of Z-stability for AH algebras of bounded topological dimension

We prove that a unital simple approximately homogeneous (AH) C*-algebra with no dimension growth absorbs the Jiang-Su algebra tensorially without appealing to the classification theory of these algebras. Our main result continues to hold under the slightly weaker hypothesis of exponentially slow dimension growth.Comment: 15 pages, no figure

Solving Tree Problems with Category Theory

Artificial Intelligence (AI) has long pursued models, theories, and techniques to imbue machines with human-like general intelligence. Yet even the currently predominant data-driven approaches in AI seem to be lacking humans' unique ability to solve wide ranges of problems. This situation begs the question of the existence of principles that underlie general problem-solving capabilities. We approach this question through the mathematical formulation of analogies across different problems and solutions. We focus in particular on problems that could be represented as tree-like structures. Most importantly, we adopt a category-theoretic approach in formalising tree problems as categories, and in proving the existence of equivalences across apparently unrelated problem domains. We prove the existence of a functor between the category of tree problems and the category of solutions. We also provide a weaker version of the functor by quantifying equivalences of problem categories using a metric on tree problems.Comment: 10 pages, 4 figures, International Conference on Artificial General Intelligence (AGI) 201

Vortex Glass is a Metal: Unified Theory of the Magnetic Field and Disorder-Tuned Bose Metals

We consider the disordered quantum rotor model in the presence of a magnetic field. We analyze the transport properties in the vicinity of the multicritical point between the superconductor, phase glass and paramagnetic phases. We find that the magnetic field leaves metallic transport of bosons in the glassy phase in tact. In the vicinity of the vicinity of the superconductivity-to-Bose metal transition, the resistitivy turns on as $(H-H_c)^{2}$ with $H_c$. This functional form is in excellent agreement with the experimentally observed turn-on of the resistivity in the metallic state in MoGe, namely $R\approx R_c(H-H_c)^\mu$, $1<\mu<3$. The metallic state is also shown to presist in three spatial dimensions. In addition, we also show that the metallic state remains intact in the presence of Ohmic dissipation in spite of recent claims to the contrary. As the phase glass in $d=3$ is identical to the vortex glass, we conclude that the vortex glass is, in actuality, a metal rather than a superconductor at T=0. Our analysis unifies the recent experiments on vortex glass systems in which the linear resistivity remained non-zero below the putative vortex glass transition and the experiments on thin films in which a metallic phase has been observed to disrupt the direct transition from a superconductor to an insulator.Comment: Published version with an appendix showing that the claim in cond-mat/0510380 (and cond-mat/0606522) that Ohmic dissipation in the phase glass leads to a superconducting state is false. A metal persists in this case as wel

Supersymmetry with Grand Unification

Supersymmetry (SUSY) has many well known attractions, especially in the context of Grand Unified Theories (GUTs). SUSY stabilizes scalar mass corrections (the hierarchy problem), greatly reduces the number of free parameters, facilitates gauge coupling unification, and provides a plausible candidate for cosmological dark matter. In this conference report we survey some recent examples of progress in SUSY-GUT applications.Comment: Talk V. Barger at the Workshop on Physics at Current Accelerators and the Supercollider, Argonne, June 1993, 15 pages + 12 PS figures included (uuencoded), (correct author list in header) MAD/PH/78

Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB Anisotropy

We use simulated maps of the cosmic microwave background anisotropy to quantify the ability of different statistical tests to discriminate between Gaussian and non-Gaussian models. Despite the central limit theorem on large angular scales, both the genus and extrema correlation are able to discriminate between Gaussian models and a semi-analytic texture model selected as a physically motivated non-Gaussian model. When run on the COBE 4-year CMB maps, both tests prefer the Gaussian model. Although the bispectrum has comparable statistical power when computed on the full sky, once a Galactic cut is imposed on the data the bispectrum loses the ability to discriminate between models. Off-diagonal elements of the bispectrum are comparable to the diagonal elements for the non-Gaussian texture model and must be included to obtain maximum statistical power.Comment: Accepted for publication in ApJ; 20 pages, 6 figures, uses AASTeX v5.