Microscopic Black Hole Pairs in Highly-Excited States

We consider the quantum mechanics of a system consisting of two identical, Planck-size Schwarzschild black holes revolving around their common center of mass. We find that even in a very highly-excited state such a system has very sharp, discrete energy eigenstates, and the system performs very rapid transitions from a one stationary state to another. For instance, when the system is in the 100th excited state, the life times of the energy eigenstates are of the order of $10^{-30}$ s, and the energies of gravitons released in transitions between nearby states are of the order of $10^{22}$ eV.Comment: 22 pages, 3 figures, uses RevTe

Twisted reductions of integrable lattice equations, and their Lax representations

It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize the periodicity condition by adding a symmetry transformation and apply this idea to autonomous and non-autonomous lattice equations. As results of this approach, we obtain new reductions of the discrete potential Korteweg–de Vries (KdV) equation, discrete modified KdV equation and the discrete Schwarzian KdV equation. We will also describe a direct method for obtaining Lax representations for the reduced equations

S-Nitrosothiols modulate G protein-coupled receptor signaling in a reversible and highly receptor-specific manner

BACKGROUND: Recent studies indicate that the G protein-coupled receptor (GPCR) signaling machinery can serve as a direct target of reactive oxygen species, including nitric oxide (NO) and S-nitrosothiols (RSNOs). To gain a broader view into the way that receptor-dependent G protein activation – an early step in signal transduction – might be affected by RSNOs, we have studied several receptors coupling to the G(i )family of G proteins in their native cellular environment using the powerful functional approach of [(35)S]GTPγS autoradiography with brain cryostat sections in combination with classical G protein activation assays. RESULTS: We demonstrate that RSNOs, like S-nitrosoglutathione (GSNO) and S-nitrosocysteine (CysNO), can modulate GPCR signaling via reversible, thiol-sensitive mechanisms probably involving S-nitrosylation. RSNOs are capable of very targeted regulation, as they potentiate the signaling of some receptors (exemplified by the M2/M4 muscarinic cholinergic receptors), inhibit others (P2Y(12 )purinergic, LPA(1)lysophosphatidic acid, and cannabinoid CB(1 )receptors), but may only marginally affect signaling of others, such as adenosine A(1), μ-opioid, and opiate related receptors. Amplification of M2/M4 muscarinic responses is explained by an accelerated rate of guanine nucleotide exchange, as well as an increased number of high-affinity [(35)S]GTPγS binding sites available for the agonist-activated receptor. GSNO amplified human M4 receptor signaling also under heterologous expression in CHO cells, but the effect diminished with increasing constitutive receptor activity. RSNOs markedly inhibited P2Y(12 )receptor signaling in native tissues (rat brain and human platelets), but failed to affect human P2Y(12 )receptor signaling under heterologous expression in CHO cells, indicating that the native cellular signaling partners, rather than the P2Y(12 )receptor protein, act as a molecular target for this action. CONCLUSION: These in vitro studies show for the first time in a broader general context that RSNOs are capable of modulating GPCR signaling in a reversible and highly receptor-specific manner. Given that the enzymatic machinery responsible for endogenous NO production is located in close proximity with the GPCR signaling complex, especially with that for several receptors whose signaling is shown here to be modulated by exogenous RSNOs, our data suggest that GPCR signaling in vivo is likely to be subject to substantial, and highly receptor-specific modulation by NO-derived RSNOs

Spacetime Foam Model of the Schwarzschild Horizon

We consider a spacetime foam model of the Schwarzschild horizon, where the horizon consists of Planck size black holes. According to our model the entropy of the Schwarzschild black hole is proportional to the area of its event horizon. It is possible to express geometrical arguments to the effect that the constant of proportionality is, in natural units, equal to one quarter.Comment: 16 pages, 2 figures, improved and extended version with some significant changes. Accepted for publication in Phys.Rev.

Effects of 2-year physical activity and dietary intervention on adrenarchal and pubertal development: the PANIC study.

CONTEXT Childhood overweight has been linked to earlier development of adrenarche and puberty, but it remains unknown if lifestyle interventions influence sexual maturation in general populations. OBJECTIVE To investigate if a 2-year lifestyle intervention influences circulating androgen concentrations and sexual maturation in a general population of children. DESIGN AND PARTICIPANTS A 2-year intervention study in which 421 prepubertal and mostly normal-weight 6-9-year-old children were allocated either to a lifestyle intervention group (119 girls, 132 boys) or a control group (84 girls, 86 boys). INTERVENTION A 2-year physical activity and dietary intervention. MAIN OUTCOME MEASURES Serum dehydroepiandrosterone, dehydroepiandrosterone sulfate, androstenedione, and testosterone concentrations, and clinical adrenarchal and pubertal signs. RESULTS The intervention and control groups had no differences in body size and composition, clinical signs of androgen action, and serum androgens at baseline. The intervention attenuated the increase of dehydroepiandrosterone (p = 0.032), dehydroepiandrosterone sulfate (p = 0.001), androstenedione (p = 0.003), and testosterone (p = 0.007) and delayed pubarche (p = 0.038) in boys but it only attenuated the increase of dehydroepiandrosterone (p = 0.013) and dehydroepiandrosterone sulfate (p = 0.003) in girls. These effects of lifestyle intervention on androgens and the development of pubarche were independent of changes in body size and composition but the effects of intervention on androgens were partly explained by changes in fasting serum insulin. CONCLUSIONS A combined physical activity and dietary intervention attenuates the increase of serum androgen concentrations and sexual maturation in a general population of prepubertal and mostly normal-weight children, independently of changes in body size and composition

Chaos in the one-dimensional gravitational three-body problem

We have investigated the appearance of chaos in the 1-dimensional Newtonian gravitational three-body system (three masses on a line with $-1/r$ pairwise potential). We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change (with negative total energy). For two mass choices we have calculated 18000 full orbits (with initial states on a $100\times 180$ lattice on the Poincar\'e section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincar\'e maps for $10\times 18$ starting points. Our results show that the Poincar\'e section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: 1) There is a region of fast scattering, with a minimum of pairwise collisions and smooth dependence on initial values. 2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincar\'e section. For both 1) and 2) the initial and final states consists of a binary + single particle. 3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is the periodic Schubart orbit, whose stability turns out to correlate strongly with the global behavior.Comment: 24 pages of text (REVTEX 3.0) + 21 pages of figures. Figures are only available in paper form, ask for a preprint from the author

Soliton Solutions for ABS Lattice Equations II: Casoratians and Bilinearization

In Part I [arXiv:0902.4873 [nlin.SI]] soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by reductions. In that work central role was played by a Cauchy matrix. In this work we use a different approach, we derive the $N$-soliton solutions following Hirota's direct and constructive method. This leads to Casoratians and bilinear difference equations. We give here details for the H-series of equations and for Q1; the results for Q3 have been given earlier.Comment: 36 page

Improved Imputation of Common and Uncommon Single Nucleotide Polymorphisms (SNPs) with a New Reference Set

Statistical imputation of genotype data is an important technique for analysis of genome-wide association studies (GWAS). We have built a reference dataset to improve imputation accuracy for studies of individuals of primarily European descent using genotype data from the Hap1, Omni1, and Omni2.5 human SNP arrays (Illumina). Our dataset contains 2.5-3.1 million variants for 930 European, 157 Asian, and 162 African/African-American individuals. Imputation accuracy of European data from Hap660 or OmniExpress array content, measured by the proportion of variants imputed with R^2^>0.8, improved by 34%, 23% and 12% for variants with MAF of 3%, 5% and 10%, respectively, compared to imputation using publicly available data from 1,000 Genomes and International HapMap projects. The improved accuracy with the use of the new dataset could increase the power for GWAS by as much as 8% relative to genotyping all variants. This reference dataset is available to the scientific community through the NCBI dbGaP portal. Future versions will include additional genotype data as well as non-European populations

Painleve equations from Darboux chains - Part 1: P3-P5

We show that the Painleve equations P3-P5 can be derived (in a unified way) from a periodic sequence of Darboux transformations for a Schrodinger problem with quadratic eigenvalue dependency. The general problem naturally divides into three different branches, each described by an infinite chain of equations. The Painleve equations are obtained by closing the chain periodically at the lowest nontrivial level(s). The chains provide ``symmetric forms'' for the Painleve equations, from which Hirota bilinear forms and Lax pairs are derived. In this paper (Part 1) we analyze in detail the cases P3-P5, while P6 will be studied in Part 2.Comment: 23 pages, 1 reference added + minor change

Quantum-mechanical model of the Kerr-Newman black hole

We consider a Hamiltonian quantum theory of stationary spacetimes containing a Kerr-Newman black hole. The physical phase space of such spacetimes is just six-dimensional, and it is spanned by the mass $M$, the electric charge $Q$ and angular momentum $J$ of the hole, together with the corresponding canonical momenta. In this six-dimensional phase space we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Kerr-Newman black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator and an eigenvalue equation for the Arnowitt-Deser-Misner (ADM) mass of the hole, from the point of view of a distant observer at rest, is obtained. In a certain very restricted sense, this eigenvalue equation may be viewed as a sort of "Schr\"odinger equation of black holes". Our "Schr\"odinger equation" implies that the ADM mass, electric charge and angular momentum spectra of black holes are discrete, and the mass spectrum is bounded from below. Moreover, the spectrum of the quantity $M^2-Q^2-a^2$, where $a$ is the angular momentum per unit mass of the hole, is strictly positive when an appropriate self-adjoint extension is chosen. The WKB analysis yields the result that the large eigenvalues of $M$, $Q$ and $a$ are of the form $\sqrt{2n}$, where $n$ is an integer. It turns out that this result is closely related to Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 30 pages, 3 figures, RevTe