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

Pattern formation and selection in quasi-static fracture

Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model produces cellular, hierarchical patterns of cracks, characterized by a mean fragment size linear in the layer thickness, in agreement with experiments. The selection of a stationary fragment size is explained by exploiting the correlations prior to cracking. A scaling behavior associated with the thickness and substrate coupling, derived and confirmed by simulations, suggests why patterns have similar morphology despite their disparity in scales.Comment: 4 pages, RevTeX, two-column, 5 PS figures include

Location of ser-4 near arg-2 on linkage group IV.

Location of ser-4 near arg-2 on linkage group IV

A weighted configuration model and inhomogeneous epidemics

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight. It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that $R_0$ can be substantially over- or underestimated if the correlation between degree and weight is not taken into account

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

Fast Gibbs sampling for high-dimensional Bayesian inversion

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and quantify its uncertainties. In applications where the inverse solution is subject to further analysis procedures, this can be a significant advantage. Alongside theoretical progress, various new computational techniques allow to sample very high dimensional posterior distributions: In [Lucka2012], a Markov chain Monte Carlo (MCMC) posterior sampler was developed for linear inverse problems with $\ell_1$-type priors. In this article, we extend this single component Gibbs-type sampler to a wide range of priors used in Bayesian inversion, such as general $\ell_p^q$ priors with additional hard constraints. Besides a fast computation of the conditional, single component densities in an explicit, parameterized form, a fast, robust and exact sampling from these one-dimensional densities is key to obtain an efficient algorithm. We demonstrate that a generalization of slice sampling can utilize their specific structure for this task and illustrate the performance of the resulting slice-within-Gibbs samplers by different computed examples. These new samplers allow us to perform sample-based Bayesian inference in high-dimensional scenarios with certain priors for the first time, including the inversion of computed tomography (CT) data with the popular isotropic total variation (TV) prior.Comment: submitted to "Inverse Problems

Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction

Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class. Here, we discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator-prey model variant where the predation process includes next-nearest-neighbor interactions. We find that the corresponding stochastic model reproduces the above scenario in dimensions 1< d \leq 4, in contrast with mean-field theory which predicts a first-order phase transition. However, the mean-field features are recovered upon allowing for nearest-neighbor particle exchange processes, provided these are sufficiently fast.Comment: 5 pages, 4 figures, 2-column revtex4 format. Emphasis on the lattice predator-prey model with next-nearest-neighbor interaction (Rapid Communication in PRE

Factors that control the stable carbon isotopic composition of methane produced in an anoxic marine sediment

The carbon isotopic composition of methane produced in anoxic marine sediment is controlled by four factors: (1) the pathway of methane formation, (2) the isotopic composition of the methanogenic precursors, (3) the isotope fractionation factors for methane production, and (4) the isotope fractionation associated with methane oxidation. The importance of each factor was evaluated by monitoring stable carbon isotope ratios in methane produced by a sediment microcosm. Methane did not accumulate during the initial 42-day period when sediment contained sulfate, indicating little methane production from 'noncompetitive' substrates. Following sulfate depletion, methane accumulation proceeded in three distinct phases. First, CO2 reduction was the dominant methanogenic pathway and the isotopic composition of the methane produced ranged from -80 to -94 per thousand. The acetate concentration increased during this phase, suggesting that acetoclastic methanogenic bacteria were unable to keep pace with acetate production. Second, acetate fermentation became the dominant methanogenic pathway as bacteria responded to elevated acetate concentrations. The methane produced during this phase was progressively enriched in C-13, reaching a maximum delta(C-13) value of -42 per thousand. Third, the acetate pool experienced a precipitous decline from greater than 5 mM to less than 20 micro-M and methane production was again dominated by CO2 reduction. The delta(C-13) of methane produced during this final phase ranged from -46 to -58 per thousand. Methane oxidation concurrent with methane production was detected throughout the period of methane accumulation, at rates equivalent to 1 to 8 percent of the gross methane production rate. Thus methane oxidation was too slow to have significantly modified the isotopic signature of methane. A comparison of microcosm and field data suggests that similar microbial interactions may control seasonal variability in the isotopic composition of methane emitted from undisturbed Cape Lookout Bight sediment

Monitoring the impacts of trade agreements on food environments

The liberalization of international trade and foreign direct investment through multilateral, regional and bilateral agreements has had profound implications for the structure and nature of food systems, and therefore, for the availability, nutritional quality, accessibility, price and promotion of foods in different locations. Public health attention has only relatively recently turned to the links between trade and investment agreements, diets and health, and there is currently no systematic monitoring of this area. This paper reviews the available evidence on the links between trade agreements, food environments and diets from an obesity and non-communicable disease (NCD) perspective. Based on the key issues identified through the review, the paper outlines an approach for monitoring the potential impact of trade agreements on food environments and obesity/NCD risks. The proposed monitoring approach encompasses a set of guiding principles, recommended procedures for data collection and analysis, and quantifiable ‘minimal’, ‘expanded’ and ‘optimal’ measurement indicators to be tailored to national priorities, capacity and resources. Formal risk assessment processes of existing and evolving trade and investment agreements, which focus on their impacts on food environments will help inform the development of healthy trade policy, strengthen domestic nutrition and health policy space and ultimately protect population nutrition.The following organizations provided funding support for the travel of participants to Italy for this meeting and the preparation of background research papers: The Rockefeller Foundation, International Obesity Taskforce (IOTF), University of Auckland, Deakin University, The George Institute, University of Sydney, Queensland University of Technology, University of Oxford, University of Pennsylvania Perelman School of Medicine, World Cancer Research Fund International, University of Toronto, and The Australian National University. The Faculty of Health at Deakin University kindly supported the costs for open access availability of this paper, and the Australian National Health and Medical Research Council Centre for Research Excellence in Obesity Policy and Food Systems (APP1041020) supported the coordination and finalizing of INFORMAS manuscripts