Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

Modeling the Measurements of Cochlear Microcirculation and Hearing Function after Loud Noise

Objective: Recent findings support the crucial role of microcirculatory disturbance and ischemia for hearing impairment especially after noise-induced hearing loss (NIHL). The aim of this study was to establish an animal model for in vivo analysis of cochlear microcirculation and hearing function after a loud noise to allow precise measurements of both parameters in vivo. Study Design: Randomized controlled trial. Setting: Animal study. Subjects and Methods: After assessment of normacusis (0 minutes) using evoked auditory brainstem responses (ABRs), noise (106-dB sound pressure level [SPL]) was applied to both ears in 6 guinea pigs for 30 minutes while unexposed animals served as controls. In vivo fluorescence microscopy of the stria vascularis capillaries was performed after surgical exposure of 1 cochlea. ABR measurements were derived from the contralateral ear. Results: After noise exposure, red blood cell velocity was reduced significantly by 24.3% (120 minutes) and further decreased to 44.5% at the end of the observation (210 minutes) in contrast to stable control measurements. Vessel diameters were not affected in both groups. A gradual decrease of segmental blood flow became significant (38.1%) after 150 minutes compared with controls. Hearing thresholds shifted significantly from 20.0 ± 5.5 dB SPL (0 minutes) to 32.5 ± 4.2dB SPL (60 minutes) only in animals exposed to loud noise. Conclusion: With regard to novel treatments targeting the stria vascularis in NIHL, this standardized model allows us to analyze in detail cochlear microcirculation and hearing function in vivo

Searches for Gravitational Waves from Binary Neutron Stars: A Review

A new generation of observatories is looking for gravitational waves. These waves, emitted by highly relativistic systems, will open a new window for ob- servation of the cosmos when they are detected. Among the most promising sources of gravitational waves for these observatories are compact binaries in the final min- utes before coalescence. In this article, we review in brief interferometric searches for gravitational waves emitted by neutron star binaries, including the theory, instru- mentation and methods. No detections have been made to date. However, the best direct observational limits on coalescence rates have been set, and instrumentation and analysis methods continue to be refined toward the ultimate goal of defining the new field of gravitational wave astronomy.Comment: 30 pages, 5 Figures, to appear in "Short-Period Binary Stars: Observations, Analyses, and Results", Ed.s Eugene F. Milone, Denis A. Leahy, David W. Hobil

Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity

Calibration of photomultiplier arrays

A method is described that allows calibration and assessment of the linearity of response of an array of photomultiplier tubes. The method does not require knowledge of the photomultiplier single photoelectron response model and uses science data directly, thus eliminating the need for dedicated data sets. In this manner all photomultiplier working conditions (e.g. temperature, external fields, etc.) are exactly matched between calibration and science acquisitions. This is of particular importance in low background experiments such as ZEPLIN-III, where methods involving the use of external light sources for calibration are severely constrained

Search for Gravitational Waves from Primordial Black Hole Binary Coalescences in the Galactic Halo

We use data from the second science run of the LIGO gravitational-wave detectors to search for the gravitational waves from primordial black hole (PBH) binary coalescence with component masses in the range 0.2--$1.0 M_\odot$. The analysis requires a signal to be found in the data from both LIGO observatories, according to a set of coincidence criteria. No inspiral signals were found. Assuming a spherical halo with core radius 5 kpc extending to 50 kpc containing non-spinning black holes with masses in the range 0.2--$1.0 M_\odot$, we place an observational upper limit on the rate of PBH coalescence of 63 per year per Milky Way halo (MWH) with 90% confidence.Comment: 7 pages, 4 figures, to be submitted to Phys. Rev.

Does involvement in a cohort study improve health and affect health inequalities? A natural experiment

Abstract Background Evidence suggests that the process of taking part in health research can improve participants\u2019 health, independent of any intended intervention. However, no research has yet explored whether these effects differ across socioeconomic groups. If the effect of mere participation in health research also has a social gradient this could increase health inequalities and bias research results. This study used the Born in Bradford family cohort (BIB) to explore whether simply taking part in BIB had improved participants\u2019 health and, if so, whether this effect was mediated by socioeconomic status. Methods Survey data on self-reported health behaviours were collected between 2007 and 2010 as part of BIB. These were augmented by clinical data on birth weight. Pregnant women on their second pregnancy, joining BIB for the first time formed the control group. Their health was compared to women on their second pregnancy who had both pregnancies within the study, who formed the exposed group. In order to limit the inherent bias in a non-randomised study, propensity score analysis was used, matching on age, ethnicity, education and date of questionnaire. The results were then compared according to mothers' education. Results Of six outcomes tested, only alcohol consumption showed a statistically significant reduction with exposure to BIB (OR: 0.35, 95% CIs 0.13, 0.92). Although effect estimates were larger for women with higher education compared to lower education, these effects were not statistically significant. Conclusions Despite one significant finding, these results overall are insufficient to conclude that simply taking part in BIB affected participants\u2019 health. We recommend that socioeconomic status is considered in future studies testing effects of research participation, and that randomised studies with larger sample sizes are conducted

Limits on the spin-dependent WIMP-nucleon cross-sections from the first science run of the ZEPLIN-III experiment

We present new experimental constraints on the WIMP-nucleon spin-dependent elastic cross-sections using data from the first science run of ZEPLIN-III, a two-phase xenon experiment searching for galactic dark matter WIMPs based at the Boulby mine. Analysis of $\sim$450 kg$\cdot$days fiducial exposure revealed a most likely signal of zero events, leading to a 90%-confidence upper limit on the pure WIMP-neutron cross-section of $\sigma_n=1.8\times 10^{-2}$ pb at 55 GeV/$c^2$ WIMP mass. Recent calculations of the nuclear spin structure based on the Bonn CD nucleon-nucleon potential were used for the odd-neutron isotopes $^{129}$Xe and $^{131}$Xe. These indicate that the sensitivity of xenon targets to the spin-dependent WIMP-proton interaction is much lower than implied by previous calculations, whereas the WIMP-neutron sensitivity is impaired only by a factor of $\sim$2

Physics, Astrophysics and Cosmology with Gravitational Waves

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.Comment: 137 pages, 16 figures, Published version <http://www.livingreviews.org/lrr-2009-2