The time to extinction for an SIS-household-epidemic model

We analyse a stochastic SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission

Angular Momentum Transport by MHD Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability

The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard alpha disk model. From our numerical experiments it is found that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength, and is unaffected by Ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly-isothermal calculations, where pressure varies little with time. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of non-steady magnetic reconnection.Comment: 45 pages, 5 tables, 17 figures, accepted for publication in Ap

The molecular size continuum of soil organic phosphorus and its chemical associations

The chemical nature of most organic P (Porg) in soil remains ‘unresolved’ but is accounted for by a broad signal in the phosphomonoester region of solution 31P nuclear magnetic resonance (NMR) spectra. The molecular size range of this broad NMR signal and its molecular structure remain unclear. The aim of this study was to elucidate the chemical nature of Porg with increasing molecular size in soil extracts combining size exclusion chromatography (SEC) with solution 31P NMR spectroscopy. Gel-filtration SEC was carried out on NaOH-EDTA extracts of four soils (range 238-1135 mg Porg/kgsoil) to collect fractions with molecular sizes of 70 kDa. These were then analysed by NMR spectroscopy. Organic P was detected across the entire molecular size continuum from 70 kDa. Concentrations of Porg in the >10kDa fraction ranged from 107 to 427 mg P/kgsoil and exhibited on average three to four broad signals in the phosphomonoester region of NMR spectra. These broad signals were most prominent in the 10-20 and 20-50 kDa fractions, accounting for on average 77 % and 74 % of total phosphomonoesters, respectively. Our study demonstrates that the broad signal is present in all investigated molecular size fractions and comprises on average three to four components of varying NMR peak line width (20 to 250 Hz). The stereoisomers myo- and scyllo-inositol hexakisphosphates (IP6) were also present across multiple molecular size ranges but were predominant in the 5-10 kDa fraction. The proportion of IP associated with large molecular size fractions >10 kDa was on average 23 % (SD=39 %) of total IP across all soils. These findings suggest that stabilisation of IP in soil includes processes associated with the organic phase

Influence of local carrying capacity restrictions on stochastic predator-prey models

We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained for site-restricted model variants. In accord with the classic Lotka-Volterra mean-field description, both species always coexist in two dimensions. Yet competing activity fronts generate complex, correlated spatio-temporal structures. As a consequence, finite systems display transient erratic population oscillations with characteristic frequencies that are renormalized by fluctuations. For large reaction rates, when the processes are rendered more local, these oscillations are suppressed. In contrast with site-restricted predator-prey model, we observe species coexistence also in one dimension. In addition, we report results on the steady-state prey age distribution.Comment: Latex, IOP style, 17 pages, 9 figures included, related movies available at http://www.phys.vt.edu/~tauber/PredatorPrey/movies

Sampling constrained probability distributions using Spherical Augmentation

Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained domains could be quite challenging for commonly used sampling algorithms. In this paper, we propose a novel augmentation technique that handles a wide range of constraints by mapping the constrained domain to a sphere in the augmented space. By moving freely on the surface of this sphere, sampling algorithms handle constraints implicitly and generate proposals that remain within boundaries when mapped back to the original space. Our proposed method, called {Spherical Augmentation}, provides a mathematically natural and computationally efficient framework for sampling from constrained probability distributions. We show the advantages of our method over state-of-the-art sampling algorithms, such as exact Hamiltonian Monte Carlo, using several examples including truncated Gaussian distributions, Bayesian Lasso, Bayesian bridge regression, reconstruction of quantized stationary Gaussian process, and LDA for topic modeling.Comment: 41 pages, 13 figure

Germline DNA Repair Gene Mutations in Young-onset Prostate Cancer Cases in the UK: Evidence for a More Extensive Genetic Panel

Background Rare germline mutations in DNA repair genes are associated with prostate cancer (PCa) predisposition and prognosis. Objective To quantify the frequency of germline DNA repair gene mutations in UK PCa cases and controls, in order to more comprehensively evaluate the contribution of individual genes to overall PCa risk and likelihood of aggressive disease. Design, setting, and participants We sequenced 167 DNA repair and eight PCa candidate genes in a UK-based cohort of 1281 young-onset PCa cases (diagnosed at ≤60 yr) and 1160 selected controls. Outcome measurements and statistical analysis Gene-level SKAT-O and gene-set adaptive combination of p values (ADA) analyses were performed separately for cases versus controls, and aggressive (Gleason score ≥8, n = 201) versus nonaggressive (Gleason score ≤7, n = 1048) cases. Results and limitations We identified 233 unique protein truncating variants (PTVs) with minor allele frequency <0.5% in controls in 97 genes. The total proportion of PTV carriers was higher in cases than in controls (15% vs 12%, odds ratio [OR] = 1.29, 95% confidence interval [CI] 1.01–1.64, p = 0.036). Gene-level analyses selected NBN (pSKAT-O = 2.4 × 10−4) for overall risk and XPC (pSKAT-O = 1.6 × 10−4) for aggressive disease, both at candidate-level significance (p < 3.1 × 10−4 and p < 3.4 × 10−4, respectively). Gene-set analysis identified a subset of 20 genes associated with increased PCa risk (OR = 3.2, 95% CI 2.1–4.8, pADA = 4.1 × 10−3) and four genes that increased risk of aggressive disease (OR = 11.2, 95% CI 4.6–27.7, pADA = 5.6 × 10−3), three of which overlap the predisposition gene set. Conclusions The union of the gene-level and gene-set-level analyses identified 23 unique DNA repair genes associated with PCa predisposition or risk of aggressive disease. These findings will help facilitate the development of a PCa-specific sequencing panel with both predictive and prognostic potential. Patient summary This large sequencing study assessed the rate of inherited DNA repair gene mutations between prostate cancer patients and disease-free men. A panel of 23 genes was identified, which may improve risk prediction or treatment pathways in future clinical practice

KINETIC AND SUBJECTIVE ANALYSIS OF KNEE ROLLERS, HANDS FREE CRUTCH, AND CONVENTIONAL CRUTCHES

This study assessed the kinetic demands of ambulatory assistance devices and the subject’s perceptions of each. Twelve subjects used a knee roller (KR), a hands free crutch (HFC), and conventional axillary crutches (CC), while walking over a force platform. Ground reaction forces (GRF) were obtained for each device for the unaffected and the affected limb. Significant differences in GRF for each device were found for each limb (p ≤ 0.001). No gender interaction was found (p \u3e 0.05). The GRF of the un-affected limb was highest for the CC and lowest for the KR (p ≤ 0.05). The GRF of the affected limb was higher for the KR compared to the HFC (p =.045). For the unaffected limb, the CC produced 45% more kinetic demand than the KR, and 11% more than the HFC. However, the qualitative analysis suggested that the CC and KR were favored over the HFC

Fast Differentially Private Matrix Factorization

Differentially private collaborative filtering is a challenging task, both in terms of accuracy and speed. We present a simple algorithm that is provably differentially private, while offering good performance, using a novel connection of differential privacy to Bayesian posterior sampling via Stochastic Gradient Langevin Dynamics. Due to its simplicity the algorithm lends itself to efficient implementation. By careful systems design and by exploiting the power law behavior of the data to maximize CPU cache bandwidth we are able to generate 1024 dimensional models at a rate of 8.5 million recommendations per second on a single PC

Metabolic Syndrome Derived from Principal Component Analysis and Incident Cardiovascular Events: The Multi Ethnic Study of Atherosclerosis (MESA) and Health, Aging, and Body Composition (Health ABC).

Background. The NCEP metabolic syndrome (MetS) is a combination of dichotomized interrelated risk factors from predominantly Caucasian populations. We propose a continuous MetS score based on principal component analysis (PCA) of the same risk factors in a multiethnic cohort and compare prediction of incident CVD events with NCEP MetS definition. Additionally, we replicated these analyses in the Health, Aging, and Body composition (Health ABC) study cohort. Methods and Results. We performed PCA of the MetS elements (waist circumference, HDL, TG, fasting blood glucose, SBP, and DBP) in 2610 Caucasian Americans, 801 Chinese Americans, 1875 African Americans, and 1494 Hispanic Americans in the multiethnic study of atherosclerosis (MESA) cohort. We selected the first principal component as a continuous MetS score (MetS-PC). Cox proportional hazards models were used to examine the association between MetS-PC and 5.5 years of CVD events (n = 377) adjusting for age, gender, race, smoking and LDL-C, overall and by ethnicity. To facilitate comparison of MetS-PC with the binary NCEP definition, a MetS-PC cut point was chosen to yield the same 37% prevalence of MetS as the NCEP definition (37%) in the MESA cohort. Hazard ratio (HR) for CVD events were estimated using the NCEP and Mets-PC-derived binary definitions. In Cox proportional models, the HR (95% CI) for CVD events for 1-SD (standard deviation) of MetS-PC was 1.71 (1.54-1.90) (P &lt; 0.0001) overall after adjusting for potential confounders, and for each ethnicity, HRs were: Caucasian, 1.64 (1.39-1.94), Chinese, 1.39 (1.06-1.83), African, 1.67 (1.37-2.02), and Hispanic, 2.10 (1.66-2.65). Finally, when binary definitions were compared, HR for CVD events was 2.34 (1.91-2.87) for MetS-PC versus 1.79 (1.46-2.20) for NCEP MetS. In the Health ABC cohort, in a fully adjusted model, MetS-PC per 1-SD (Health ABC) remained associated with CVD events (HR = 1.21, 95%CI 1.12-1.32) overall, and for each ethnicity, Caucasian (HR = 1.24, 95%CI 1.12-1.39) and African Americans (HR = 1.16, 95%CI 1.01-1.32). Finally, when using a binary definition of MetS-PC (cut point 0.505) designed to match the NCEP definition in terms of prevalence in the Health ABC cohort (35%), the fully adjusted HR for CVD events was 1.39, 95%CI 1.17-1.64 compared with 1.46, 95%CI 1.23-1.72 using the NCEP definition. Conclusion. MetS-PC is a continuous measure of metabolic syndrome and was a better predictor of CVD events overall and in individual ethnicities. Additionally, a binary MetS-PC definition was better than the NCEP MetS definition in predicting incident CVD events in the MESA cohort, but this superiority was not evident in the Health ABC cohort

Large-Scale Distributed Bayesian Matrix Factorization using Stochastic Gradient MCMC

Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of inference. In this paper, we propose a scalable distributed Bayesian matrix factorization algorithm using stochastic gradient MCMC. Our algorithm, based on Distributed Stochastic Gradient Langevin Dynamics, can not only match the prediction accuracy of standard MCMC methods like Gibbs sampling, but at the same time is as fast and simple as stochastic gradient descent. In our experiments, we show that our algorithm can achieve the same level of prediction accuracy as Gibbs sampling an order of magnitude faster. We also show that our method reduces the prediction error as fast as distributed stochastic gradient descent, achieving a 4.1% improvement in RMSE for the Netflix dataset and an 1.8% for the Yahoo music dataset