Lie algebra solution of population models based on time-inhomogeneous Markov chains

Many natural populations are well modelled through time-inhomogeneous stochastic processes. Such processes have been analysed in the physical sciences using a method based on Lie algebras, but this methodology is not widely used for models with ecological, medical and social applications. This paper presents the Lie algebraic method, and applies it to three biologically well motivated examples. The result of this is a solution form that is often highly computationally advantageous.Comment: 10 pages; 1 figure; 2 tables. To appear in Applied Probabilit

Prevalence of infection with human herpesvirus 8/Kaposi's sarcoma herpesvirus in rural South Africa

Objective. To determine prevalence of infection with human herpesvirus 8 (HHV-8)/Kaposi's sarcoma herpesvirus (KSHY) and to gain some insight into possible transmission dynamics of this novel virus in South Africa.Methods. Stored, anonymous serum from 50 patients with a ~ sexually transmitted disease (STD), 50 adult medical ward _. patients (25 male, 25 female), and 36 paediatric ward patients in Hlabisa Hospital, KwaZulu-Natal, was screened by enzyme-linked immunosorbent assay (ELISA) for antibodies to the small capsid-related protein encoded by HHV-8/KSHY orf65. Antibodies to the latency-associated nuclear antigen (LANA) were measured by immunofluorescence, and sera that were reactive in the ELISA but negative by immunofluorescence were re-tested by Western blot against the recombinant orf65 protein to exclude nonspecific reactivity.Results. Overall, 47 patients tested positive (34.6%), 76 tested negative (55.9%) and 13 (95%) had indeterminate results. Among those with a definite result, prevalence was similar among males (47.2%) and females (52.8%) and increased in later adulthood « 18 months 375%,19 -120 months 385%, 15 - 34 years 32.1%, 35 - 69 years 62.8%). Prevalence was highest among medical patients (58-1%); among those with an STD it was 31.1% (P = 0-01), and among children it was 22.8% (P = 0.001). When age-adjusted, prevalence among medical patients (23.7%) was similar to that among patients with an STD.Conclusion. Prevalence of HHV-8/KSHY is high in this setting and transmission appears to be occurring in childhood as well as among adults. Larger  population-based studies are required to detail the transmission dynamics of HHSV8/KSHv

Using Markov chain Monte Carlo methods for estimating parameters with gravitational radiation data

We present a Bayesian approach to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. By applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler, we demonstrate the potential that MCMC techniques may hold for the computation of posterior distributions of parameters of the binary system that created the gravity radiation signal. We describe the use of the Gibbs sampler method, and present examples whereby signals are detected and analyzed from within noisy data.Comment: 21 pages, 10 figure

Species abundance dynamics under neutral assumptions: a Bayesian approach to the controversy

1. Hubbell's 'Unified Neutral Theory of Biodiversity and Biogeography' (UNTB) has generated much controversy about both the realism of its assumptions and how well it describes the species abundance dynamics in real communities. 2. We fit a discrete-time version of Hubbell's neutral model to long-term macro-moth (Lepidoptera) community data from the Rothamsted Insect Survey (RIS) light-traps network in the United Kingdom. 3. We relax the assumption of constant community size and use a hierarchical Bayesian approach to show that the model does not fit the data well as it would need parameter values that are impossible. 4. This is because the ecological communities fluctuate more than expected under neutrality. 5. The model, as presented here, can be extended to include environmental stochasticity, density-dependence, or changes in population sizes that are correlated between different species

Joint analysis of X-ray and Sunyaev Zel'dovich observations of galaxy clusters using an analytic model of the intra-cluster medium

We perform a joint analysis of X-ray and Sunyaev Zel'dovich (SZ) effect data using an analytic model that describes the gas properties of galaxy clusters. The joint analysis allows the measurement of the cluster gas mass fraction profile and Hubble constant independent of cosmological parameters. Weak cosmological priors are used to calculate the overdensity radius within which the gas mass fractions are reported. Such an analysis can provide direct constraints on the evolution of the cluster gas mass fraction with redshift. We validate the model and the joint analysis on high signal-to-noise data from the Chandra X-ray Observatory and the Sunyaev-Zel'dovich Array for two clusters, Abell 2631 and Abell 2204.Comment: ApJ in pres

The clustering of massive galaxies at z~0.5 from the first semester of BOSS data

We calculate the real- and redshift-space clustering of massive galaxies at z~0.5 using the first semester of data by the Baryon Oscillation Spectroscopic Survey (BOSS). We study the correlation functions of a sample of 44,000 massive galaxies in the redshift range 0.4<z<0.7. We present a halo-occupation distribution modeling of the clustering results and discuss the implications for the manner in which massive galaxies at z~0.5 occupy dark matter halos. The majority of our galaxies are central galaxies living in halos of mass 10^{13}Msun/h, but 10% are satellites living in halos 10 times more massive. These results are broadly in agreement with earlier investigations of massive galaxies at z~0.5. The inferred large-scale bias (b~2) and relatively high number density (nbar=3e-4 h^3 Mpc^{-3}) imply that BOSS galaxies are excellent tracers of large-scale structure, suggesting BOSS will enable a wide range of investigations on the distance scale, the growth of large-scale structure, massive galaxy evolution and other topics.Comment: 11 pages, 12 figures, matches version accepted by Ap

Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge based potentials based on pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state -- a necessary component of these potentials -- is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities reference ratio distributions deriving from the application of the reference ratio method. This new view is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures