Quantum Probes of Spacetime Singularities

It is shown that there are static spacetimes with timelike curvature singularities which appear completely nonsingular when probed with quantum test particles. Examples include extreme dilatonic black holes and the fundamental string solution. In these spacetimes, the dynamics of quantum particles is well defined and uniquely determined.Comment: 12 pages, RevTeX, no figures, A few breif comments added and typos correcte

Learning Poisson Binomial Distributions

We consider a basic problem in unsupervised learning: learning an unknown \emph{Poisson Binomial Distribution}. A Poisson Binomial Distribution (PBD) over $\{0,1,\dots,n\}$ is the distribution of a sum of $n$ independent Bernoulli random variables which may have arbitrary, potentially non-equal, expectations. These distributions were first studied by S. Poisson in 1837 \cite{Poisson:37} and are a natural $n$-parameter generalization of the familiar Binomial Distribution. Surprisingly, prior to our work this basic learning problem was poorly understood, and known results for it were far from optimal. We essentially settle the complexity of the learning problem for this basic class of distributions. As our first main result we give a highly efficient algorithm which learns to \eps-accuracy (with respect to the total variation distance) using \tilde{O}(1/\eps^3) samples \emph{independent of $n$}. The running time of the algorithm is \emph{quasilinear} in the size of its input data, i.e., \tilde{O}(\log(n)/\eps^3) bit-operations. (Observe that each draw from the distribution is a $\log(n)$-bit string.) Our second main result is a {\em proper} learning algorithm that learns to \eps-accuracy using \tilde{O}(1/\eps^2) samples, and runs in time (1/\eps)^{\poly (\log (1/\eps))} \cdot \log n. This is nearly optimal, since any algorithm {for this problem} must use \Omega(1/\eps^2) samples. We also give positive and negative results for some extensions of this learning problem to weighted sums of independent Bernoulli random variables.Comment: Revised full version. Improved sample complexity bound of O~(1/eps^2

Genomic Relationships, Novel Loci, and Pleiotropic Mechanisms across Eight Psychiatric Disorders

Genetic influences on psychiatric disorders transcend diagnostic boundaries, suggesting substantial pleiotropy of contributing loci. However, the nature and mechanisms of these pleiotropic effects remain unclear. We performed analyses of 232,964 cases and 494,162 controls from genome-wide studies of anorexia nervosa, attention-deficit/hyper-activity disorder, autism spectrum disorder, bipolar disorder, major depression, obsessive-compulsive disorder, schizophrenia, and Tourette syndrome. Genetic correlation analyses revealed a meaningful structure within the eight disorders, identifying three groups of inter-related disorders. Meta-analysis across these eight disorders detected 109 loci associated with at least two psychiatric disorders, including 23 loci with pleiotropic effects on four or more disorders and 11 loci with antagonistic effects on multiple disorders. The pleiotropic loci are located within genes that show heightened expression in the brain throughout the lifespan, beginning prenatally in the second trimester, and play prominent roles in neurodevelopmental processes. These findings have important implications for psychiatric nosology, drug development, and risk prediction.Peer reviewe

Dissecting the Shared Genetic Architecture of Suicide Attempt, Psychiatric Disorders, and Known Risk Factors

Background Suicide is a leading cause of death worldwide, and nonfatal suicide attempts, which occur far more frequently, are a major source of disability and social and economic burden. Both have substantial genetic etiology, which is partially shared and partially distinct from that of related psychiatric disorders. Methods We conducted a genome-wide association study (GWAS) of 29,782 suicide attempt (SA) cases and 519,961 controls in the International Suicide Genetics Consortium (ISGC). The GWAS of SA was conditioned on psychiatric disorders using GWAS summary statistics via multitrait-based conditional and joint analysis, to remove genetic effects on SA mediated by psychiatric disorders. We investigated the shared and divergent genetic architectures of SA, psychiatric disorders, and other known risk factors. Results Two loci reached genome-wide significance for SA: the major histocompatibility complex and an intergenic locus on chromosome 7, the latter of which remained associated with SA after conditioning on psychiatric disorders and replicated in an independent cohort from the Million Veteran Program. This locus has been implicated in risk-taking behavior, smoking, and insomnia. SA showed strong genetic correlation with psychiatric disorders, particularly major depression, and also with smoking, pain, risk-taking behavior, sleep disturbances, lower educational attainment, reproductive traits, lower socioeconomic status, and poorer general health. After conditioning on psychiatric disorders, the genetic correlations between SA and psychiatric disorders decreased, whereas those with nonpsychiatric traits remained largely unchanged. Conclusions Our results identify a risk locus that contributes more strongly to SA than other phenotypes and suggest a shared underlying biology between SA and known risk factors that is not mediated by psychiatric disorders.Peer reviewe

SLOW INTRAMOLECULAR VIBRATIONAL REDISTRIBUTION (IVR) IN ISOLATED BENZENE MOLECULES

$^{1}$ K. V. Reddy. D. F. Heller and M. J. Berry, J. Chem. Phys. 76. 2814 (1982). Address of Chernoff and Pruett: Corporate Research Center. The Standard Oil Company (Ohio). 4440 Warrensville Center Road. Warrensville Heights. Ohio 44128. Address of Myers: Dept. of Chemistry. U. of Calif., Berkeley, CA 94720.Author Institution:We report small homogeneous widths of high overtones of mode 1 (C-C ring breathing) in benzene and $benzene-d_{6}$, in contrast with much larger widths of C-H stretch overtones at similar energies. From the uncertainty principle, these widths provide an upper bound to the potential rate of IVR. We used a tunable. nsec UV laser to excite benzene molecules seeded in a supersonic free jet to the $6^{1}1^{2}$ vibrational level in the $S_{1}$ electronic state. We recorded emission spectra including transitions terminating at various levels up to ca. $10,000 cm^{-1}$ in the $S_{0}$ state. With the same upper state, any changes in transition linewidth would be characteristic of the lower state. Our emission spectra consist of several hundred sharp vibrational bands and a congested background which breaks into many additional bands at higher resolution. Our major finding is that the sharp structure persists throughout the spectrum. Most of these bands can be assigned readily: in particular, we have located members of the $6^{1}_{0}1^{2}_{n}$ progression. A comparison of the band shapes in this progression indicates little or no change in width. Considering our limiting spectral resolution of $13.5 cm^{-1}$, we estimate that the homogeneous linewidths of the highest levels we observe are probably less than $5 cm^{-1}$ for both benzene and $benzene-d_{6}$. This result is significantly different from that found by Reddy and co-workers for the C-H and C-D stretching overtones (homogeneous widths of $23 cm^{-1}$ for $3v_{CH}$ at $8786 cm^{-1}$ in benzene and $53 cm^{-1}$ for $4\nu_{cp}$ at $8734 cm^{-1}$ in $benzene-d_{6}$). [1] Clearly, the couplings of the C-C ring breathing mode to other modes are much different