Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Effect of pair interactions on transition probabilities between inactive and active states: achieving collective behaviour via pair interactions in social insects

To understand the evolution of well-organized social behaviour, we must first understand the mechanism by which collective behaviour establishes. In this study, the mechanisms of collective behaviour in a colony of social insects were studied in terms of the transition probability between active and inactive states, which is linked to mutual interactions. The active and inactive states of the social insects were statistically extracted from the velocity profiles. From the duration distributions of the two states, we found that 1) the durations of active and inactive states follow an exponential law, and 2) pair interactions increase the transition probability from inactive to active states. The regulation of the transition probability by paired interactions suggests that such interactions control the populations of active and inactive workers in the colony.

Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

Root distributions of Australian herbaceous perennial legumes in response to phosphorus placement

Many Australian plant species have specific root adaptations for growth in phosphorus-impoverished soils, and are often sensitive to high external P concentrations. The growth responses of native Australian legumes in agricultural soils with elevated P availability in the surface horizons are unknown. The aim of these experiments was to test the hypothesis that increased P concentration in surface soil would reduce root proliferation at depth in native legumes. The effect of P placement on root distribution was assessed for two Australian legumes, Kennedia prorepens F. Muell. and Lotus australis Andrews, and the exotic Medicago sativa L. Three treatments were established in a low-P loam soil: amendment of 0.15 g mono-calcium phosphate in either (i) the top 50 mm (120 µg P g–1) or (ii) the top 500 mm (12 µg P g–1) of soil, and an unamended control. In the unamended soil M. sativa was shallow rooted, with 58% of the root length of in the top 50 mm. K. prorepens and L. australis had a more even distribution down the pot length, with only 4 and 22% of their roots in the 0–50 mm pot section, respectively. When exposed to amendment of P in the top 50 mm, root length in the top 50 mm increased 4-fold for K. prorepens and 10-fold for M. sativa, although the pattern of root distribution did not change for M. sativa. L. australis was relatively unresponsive to P additions and had an even distribution of roots down the pot. Shoot P concentrations differed according to species but not treatment (K. prorepens 2.1 mg g–1, L. australis 2.4 mg g–1, M. sativa 3.2 mg g–1). Total shoot P content was higher for K. prorepens than for the other species in all treatments. In a second experiment, mono-ester phosphatases were analysed from 1-mm slices of soil collected directly adjacent to the rhizosphere. All species exuded phosphatases into the rhizosphere, but addition of P to soil reduced phosphatase activity only for K. prorepens. Overall, high P concentration in the surface soil altered root distribution, but did not reduce root proliferation at depth. Furthermore, the Australian herbaceous perennial legumes had root distributions that enhanced P acquisition from low-P soils.

Testing projected wild bee distributions in agricultural habitats: predictive power depends on species traits and habitat type

Species distribution models (SDM) are increasingly used to understand the factors that regulate variation in biodiversity patterns and to help plan conservation strategies. However, these models are rarely validated with independently collected data and it is unclear whether SDM performance is maintained across distinct habitats and for species with different functional traits. Highly mobile species, such as bees, can be particularly challenging to model. Here, we use independent sets of occurrence data collected systematically in several agricultural habitats to test how the predictive performance of SDMs for wild bee species depends on species traits, habitat type, and sampling technique. We used a species distribution modeling approach parametrized for the Netherlands, with presence records from 1990 to 2010 for 193 Dutch wild bees. For each species, we built a Maxent model based on 13 climate and landscape variables. We tested the predictive performance of the SDMs with independent datasets collected from orchards and arable fields across the Netherlands from 2010 to 2013, using transect surveys or pan traps. Model predictive performance depended on species traits and habitat type. Occurrence of bee species specialized in habitat and diet was better predicted than generalist bees. Predictions of habitat suitability were also more precise for habitats that are temporally more stable (orchards) than for habitats that suffer regular alterations (arable), particularly for small, solitary bees. As a conservation tool, SDMs are best suited to modeling rarer, specialist species than more generalist and will work best in long-term stable habitats. The variability of complex, short-term habitats is difficult to capture in such models and historical land use generally has low thematic resolution. To improve SDMs’ usefulness, models require explanatory variables and collection data that include detailed landscape characteristics, for example, variability of crops and flower availability. Additionally, testing SDMs with field surveys should involve multiple collection techniques.

High-precision measurements of the co-polar correlation coefficient: non-Gaussian errors and retrieval of the dispersion parameter µ in rainfall

The co-polar correlation coefficient (ρhv) has many applications, including hydrometeor classification, ground clutter and melting layer identification, interpretation of ice microphysics and the retrieval of rain drop size distributions (DSDs). However, we currently lack the quantitative error estimates that are necessary if these applications are to be fully exploited. Previous error estimates of ρhv rely on knowledge of the unknown "true" ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. We show that frequency distributions of ρhv estimates are in fact highly negatively skewed. A new variable: L = -log10(1 - ρhv) is defined, which does have Gaussian error statistics, and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, we demonstrate how the imperfect co-location of the horizontal and vertical polarisation sample volumes may be accounted for. The possibility of using L to estimate the dispersion parameter (µ) in the gamma drop size distribution is investigated. We find that including drop oscillations is essential for this application, otherwise there could be biases in retrieved µ of up to ~8. Preliminary results in rainfall are presented. In a convective rain case study, our estimates show µ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

The impact of smoke from forest fires on the spectral dispersion of cloud droplet size distributions in the Amazonian region

In this paper, the main microphysical characteristics of clouds developing in polluted and clean conditions in the biomass-burning season of the Amazon region are examined, with special attention to the spectral dispersion of the cloud droplet size distribution and its potential impact on climate modeling applications. The dispersion effect has been shown to alter the climate cooling predicted by the so-called Twomey effect. In biomass-burning polluted conditions, high concentrations of low dispersed cloud droplets are found. Clean conditions revealed an opposite situation. The liquid water content (0.43 +/- 0.19 g m(-3)) is shown to be uncorrelated with the cloud drop number concentration, while the effective radius is found to be very much correlated with the relative dispersion of the size distribution (R(2) = 0.81). The results suggest that an increase in cloud condensation nuclei concentration from biomass-burning aerosols may lead to an additional effect caused by a decrease in relative dispersion. Since the dry season in the Amazonian region is vapor limiting, the dispersion effect of cloud droplet size distributions could be substantially larger than in other polluted regions.

Dynamic picture of the inner asteroid belt: implications for the density, size and taxonomic distributions of real objects

In this paper, we construct a dynamic portrait of the inner asteroidal belt. We use information about the distribution of test particles, which were initially placed on a perfectly rectangular grid of initial conditions, after 4.2 Myr of gravitational interactions with the Sun and five planets, from Mars to Neptune. Using the spectral analysis method introduced by Michtchenko et al., the asteroidal behaviour is illustrated in detail on the dynamical, averaged and frequency maps. On the averaged and frequency maps, we superpose information on the proper elements and proper frequencies of real objects, extracted from the data base, AstDyS, constructed by Milani and Knezevic. A comparison of the maps with the distribution of real objects allows us to detect possible dynamical mechanisms acting in the domain under study; these mechanisms are related to mean-motion and secular resonances. We note that the two- and three-body mean-motion resonances and the secular resonances (strong linear and weaker non-linear) have an important role in the diffusive transportation of the objects. Their long-lasting action, overlaid with the Yarkovsky effect, may explain many observed features of the density, size and taxonomic distributions of the asteroids.

Caesium, potassium and ammonium distributions in different organs of tropical plants

In the present work the distribution of ions in aboveground plant parts was studied in order to establish the suitability of using radiocaesium as a tracer for the plant absorption of nutrients, such as potassium (K(+)) and ammonium (NH(4)(+)). We present the results for the distributions of (137)Cs, (40)K and NH(4)(+) from four tropical plant species: lemon (Citrus aurantifolia), orange (Citrus sinensis), guava (Psidium guajava) and chili pepper (Capsicum frutescens). Activity concentrations of (137)Cs and (40)K were measured by gamma spectrometry and concentrations of free NH(4)(+) ions by a colorimetric method. Similarly to potassium and ammonium, caesium showed a high mobility within the plants, exhibiting the highest values of concentration in the growing parts of the tree (fruits, new leaves, twigs, and barks). A significant correlation between activity concentrations of (137)Cs and (40)K was observed in these tropical plants. The K/Cs discrimination ratios were approximately equal to unity in different compartments of each individual plant, suggesting that caesium could be a good tracer for (40)K in tropical woody fruit species. Despite the similarity observed for the behaviour of caesium and ammonium in the newly grown plant compartments, (137)Cs was not well correlated with NH(4)(+). Significant temporal changes in the NH(4)(+) concentrations were observed during the development of fruits, while the (137)Cs activity concentration alterations were not of great importance, indicating, therefore, that Cs(+) and free NH(4)(+) ions could have distinct concentration ratios for each particular plant organ. (C) 2008 Elsevier B.V. All rights reserved.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

A unified view on lifetime distributions arising from selection mechanisms

In this paper, we formulate a flexible density function from the selection mechanism viewpoint (see, for example, Bayarri and DeGroot (1992) and Arellano-Valle et al. (2006)) which possesses nice biological and physical interpretations. The new density function contains as special cases many models that have been proposed recently in the literature. In constructing this model, we assume that the number of competing causes of the event of interest has a general discrete distribution characterized by its probability generating function. This function has an important role in the selection procedure as well as in computing the conditional personal cure rate. Finally, we illustrate how various models can be deduced as special cases of the proposed model. (C) 2011 Elsevier B.V. All rights reserved.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics

The purpose of this paper is to develop a Bayesian analysis for nonlinear regression models under scale mixtures of skew-normal distributions. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the error distributions cover both skewness and heavy-tailed distributions such as the skew-t, skew-slash and the skew-contaminated normal distributions. The main advantage of these class of distributions is that they have a nice hierarchical representation that allows the implementation of Markov chain Monte Carlo (MCMC) methods to simulate samples from the joint posterior distribution. In order to examine the robust aspects of this flexible class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. Further, some discussions on the model selection criteria are given. The newly developed procedures are illustrated considering two simulations study, and a real data previously analyzed under normal and skew-normal nonlinear regression models. (C) 2010 Elsevier B.V. All rights reserved.

Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective

Linear mixed models were developed to handle clustered data and have been a topic of increasing interest in statistics for the past 50 years. Generally. the normality (or symmetry) of the random effects is a common assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize skew-normal/independent distributions as a tool for robust modeling of linear mixed models under a Bayesian paradigm. The skew-normal/independent distributions is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal distribution, skew-t, skew-slash and the skew-contaminated normal distributions as special cases, providing an appealing robust alternative to the routine use of symmetric distributions in this type of models. The methods developed are illustrated using a real data set from Framingham cholesterol study. (C) 2009 Elsevier B.V. All rights reserved.

Statistical analysis of proficiency testing results under elliptical distributions

The use of inter-laboratory test comparisons to determine the performance of individual laboratories for specific tests (or for calibration) [ISO/IEC Guide 43-1, 1997. Proficiency testing by interlaboratory comparisons - Part 1: Development and operation of proficiency testing schemes] is called Proficiency Testing (PT). In this paper we propose the use of the generalized likelihood ratio test to compare the performance of the group of laboratories for specific tests relative to the assigned value and illustrate the procedure considering an actual data from the PT program in the area of volume. The proposed test extends the test criteria in use allowing to test for the consistency of the group of laboratories. Moreover, the class of elliptical distributions are considered for the obtained measurements. (C) 2008 Elsevier B.V. All rights reserved.