Testing a Simplified Version of Einstein's Equations for Numerical Relativity

Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation work well if we are to believe its predictions for more complicated systems like binaries. Our results are very encouraging.Comment: 9 pages (RevTeX 3.0 with 6 uuencoded figures), CRSR-107

New information reported under HMDA and its application in fair lending enforcement

In 2002 the Federal Reserve Board amended its Regulation C, which implements the Home Mortgage Disclosure Act of 1975, to expand the types of information that lenders covered by the law must disclose to the public about their home-lending activities. The amendments are intended to improve the quality, consistency, and utility of the reported data and to keep the regulation in step with recent developments in home-loan markets. Data reported for 2004 are the first to reflect the changes in the reporting rules. ; This article presents a first look at these greatly expanded data and considers some of their implications for the continuing concerns about fair lending. The analysis highlights some key relationships revealed in an initial review of the types of data that are new for 2004. Some parts of the analysis focus on nationwide statistics, and others examine patterns across groups of lenders, loan products, and various groupings of applicants, borrowers, and neighborhoods. The authors explore, in particular and in some depth, the strengths and limitations of the information on loan pricing. They also describe how the new data are being used to enhance fair lending enforcement activities.Regulation C: Home Mortgage Disclosure ; Home Mortgage Disclosure Act

New CP-violation and preferred-frame tests with polarized electrons

We used a torsion pendulum containing $\sim 9 \times 10^{22}$ polarized electrons to search for CP-violating interactions between the pendulum's electrons and unpolarized matter in the laboratory's surroundings or the sun, and to test for preferred-frame effects that would precess the electrons about a direction fixed in inertial space. We find $|g_{\rm P}^e g_{\rm S}^N|/(\hbar c)< 1.7 \times 10^{-36}$ and $|g_{\rm A}^e g_{\rm V}^N|/(\hbar c) < 4.8 \times 10^{-56}$ for $\lambda > 1$AU. Our preferred-frame constraints, interpreted in the Kosteleck\'y framework, set an upper limit on the parameter $|\bm{\tilde {b}}^e| \leq 5.0 \times 10^{-21}$ eV that should be compared to the benchmark value $m_e^2/M_{\rm Planck}= 2 \times 10^{-17}$ eV.Comment: 4 figures, accepted for publication in Physical Review Letter

Verifying proofs in constant depth

In this paper we initiate the study of proof systems where verification of proofs proceeds by NC circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct NC proof systems for a variety of languages ranging from regular to NP-complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit NC proof systems. We also present a general construction of proof systems for regular languages with strongly connected NFA's

Black hole evolution by spectral methods

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast to finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.Comment: 20 pages, 17 figures, submitted to PR

Intranasal Inhalation of Oxytocin Improves Face Processing in Developmental Prosopagnosia

Developmental prosopagnosia (DP) is characterised by a severe, lifelong impairment in face recognition. Little work has attempted to improve face processing in these individuals, but intriguingly, recent evidence suggests oxytocin can improve face processing in both healthy participants and individuals with autism. This study examined whether oxytocin could also improve face processing in individuals with DP. Ten adults with the condition and 10 matched controls were tested using a randomized placebo-controlled double-blind within-subject experimental design (AB-BA). Each participant took part in two testing sessions where they inhaled 24IU of oxytocin or placebo spray and completed two face processing tests: one assessing face memory and the other face perception. Results showed main effects of both participant group and treatment condition in both face processing tests, but the two did not interact. Specifically, the performance of DP participants was significantly lower than control performance under both oxytocin and placebo conditions, but oxytocin improved processing to a similar extent in both groups

Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions

We construct a sequence of binary black hole puncture data derived under the assumptions (i) that the ADM mass of each puncture as measured in the asymptotically flat space at the puncture stays constant along the sequence, and (ii) that the orbits along the sequence are quasi-circular in the sense that several necessary conditions for the existence of a helical Killing vector are satisfied. These conditions are equality of ADM and Komar mass at infinity and equality of the ADM and a rescaled Komar mass at each puncture. In this paper we explicitly give results for the case of an equal mass black hole binary without spin, but our approach can also be applied in the general case. We find that up to numerical accuracy the apparent horizon mass also remains constant along the sequence and that the prediction for the innermost stable circular orbit is similar to what has been found with the effective potential method.Comment: 6 pages, 3 figures, 1 tabl

Proving Termination Starting from the End

We present a novel technique for proving program termination which introduces a new dimension of modularity. Existing techniques use the program to incrementally construct a termination proof. While the proof keeps changing, the program remains the same. Our technique goes a step further. We show how to use the current partial proof to partition the transition relation into those behaviors known to be terminating from the current proof, and those whose status (terminating or not) is not known yet. This partition enables a new and unexplored dimension of incremental reasoning on the program side. In addition, we show that our approach naturally applies to conditional termination which searches for a precondition ensuring termination. We further report on a prototype implementation that advances the state-of-the-art on the grounds of termination and conditional termination.Comment: 16 page

Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale

We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 micrometers, probing distances less than the dark-energy length scale $\lambda_{\rm d}=\sqrt[4]{\hbar c/\rho_{\rm d}}\approx 85 \mu$m. We find with 95% confidence that the inverse-square law holds ($|\alpha| \leq 1$) down to a length scale $\lambda = 56 \mu$m and that an extra dimension must have a size $R \leq 44 \mu$m.Comment: 4 pages, 6 figure