Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Insights into redox cycling of sulfur and iron in peatlands using high-resolution diffusive equilibrium thin film (DET) gel probe sampling

High spatial resolution vertical profiles of pore-water chemistry have been obtained for a peatland using diffusive equilibrium in thin films (DET) gel probes. Comparison of DET pore-water data with more traditional depth-specific sampling shows good agreement and the DET profiling method is less invasive and less likely to induce mixing of pore-waters. Chloride mass balances as water tables fell in the early summer indicate that evaporative concentration dominates and there is negligible lateral flow in the peat. Lack of lateral flow allows element budgets for the same site at different times to be compared. The high spatial resolution of sampling also enables gradients to be observed that permit calculations of vertical fluxes. Sulfate concentrations fall at two sites with net rates of 1.5 and 5.0nmol cm− 3 day− 1, likely due to a dominance of bacterial sulfate reduction, while a third site showed a net gain in sulfate due to oxidation of sulfur over the study period at an average rate of 3.4nmol cm− 3 day− 1. Behaviour of iron is closely coupled to that of sulfur; there is net removal of iron at the two sites where sulfate reduction dominates and addition of iron where oxidation dominates. The profiles demonstrate that, in addition to strong vertical redox related chemical changes, there is significant spatial heterogeneity. Whilst overall there is evidence for net reduction of sulfate within the peatland pore-waters, this can be reversed, at least temporarily, during periods of drought when sulfide oxidation with resulting acid production predominates.

An update of observed stratospheric temperature trends

An updated analysis of observed stratospheric temperature variability and trends is presented on the basis of satellite, radiosonde, and lidar observations. Satellite data include measurements from the series of NOAA operational instruments, including the Microwave Sounding Unit covering 1979–2007 and the Stratospheric Sounding Unit (SSU) covering 1979–2005. Radiosonde results are compared for six different data sets, incorporating a variety of homogeneity adjustments to account for changes in instrumentation and observational practices. Temperature changes in the lower stratosphere show cooling of 0.5 K/decade over much of the globe for 1979–2007, with some differences in detail among the different radiosonde and satellite data sets. Substantially larger cooling trends are observed in the Antarctic lower stratosphere during spring and summer, in association with development of the Antarctic ozone hole. Trends in the lower stratosphere derived from radiosonde data are also analyzed for a longer record (back to 1958); trends for the presatellite era (1958–1978) have a large range among the different homogenized data sets, implying large trend uncertainties. Trends in the middle and upper stratosphere have been derived from updated SSU data, taking into account changes in the SSU weighting functions due to observed atmospheric CO2 increases. The results show mean cooling of 0.5–1.5 K/decade during 1979–2005, with the greatest cooling in the upper stratosphere near 40–50 km. Temperature anomalies throughout the stratosphere were relatively constant during the decade 1995–2005. Long records of lidar temperature measurements at a few locations show reasonable agreement with SSU trends, although sampling uncertainties are large in the localized lidar measurements. Updated estimates of the solar cycle influence on stratospheric temperatures show a statistically significant signal in the tropics (30N–S), with an amplitude (solar maximum minus solar minimum) of 0.5 K (lower stratosphere) to 1.0 K (upper stratosphere).

Análise de dados coletados por respondent-driven sampling(RDS): um estudo da prevalência de HIV e fatores associados entre mulheres trabalhadoras do sexo em 10 cidades brasileiras

O grupo das mulheres trabalhadoras do sexo (MTS) é reconhecido como uma populaçãode maior risco à infecção pelo HIV, tanto pela prevalência elevada, como por suavulnerabilidade social como pelos fatores relacionados à própria atividade profissional. Porém, arealização de estudos nos subgrupos de maior risco ao HIV mediante estratégias convencionaisde amostragem é, em geral, problemática por essas populações possuírem pequena magnitudeem termos populacionais e por estarem vinculados a comportamentos estigmatizados ouatividades ilegais. Em 1997, foi proposto um método de amostragem probabilística parapopulações de difícil acesso denominado Respondent-Driven Sampling (RDS). O método éconsiderado como uma variante da amostragem em cadeia e possibilita a estimação estatísticados parâmetros de interesse. Na literatura internacional, para análise de dados coletados porRDS, muitos autores têm utilizado técnicas estatísticas multivariadas tradicionais, sem levar emconta a estrutura de dependência das observações, presente nos dados coletados por RDS.A presente tese tem por objetivo contribuir para suprir informações sobre as práticas derisco relacionadas ao HIV entre as mulheres trabalhadoras do sexo (MTS) com odesenvolvimento de método estatístico para análise de dados coletados com o método deamostragem RDS. Com tal finalidade, foram utilizadas as informações coletadas na PesquisaCorrente da Saúde realizada em dez cidades brasileiras, com 2.523 MTS recrutadas por RDS,entre os anos de 2008 e 2009. O questionário foi autopreenchido e incluiu módulos sobrecaracterísticas da atividade profissional, práticas sexuais, uso de drogas, testes periódicos deHIV, e acesso aos serviços de saúde.Primeiramente, foram descritos alguns pressupostos do RDS e todas as etapas deimplantação da pesquisa. Em seguida, foram propostos métodos de análise multivariada, considerando o RDS como um desenho complexo de amostragem.

Measurements and modelling of airflows in houses using passive sampling and HAM software

Passive samplers have been predominantly used to monitor environmental conditions in single volumes. However, measurements using a calibrated passive sampler- Solid Phase Microextraction (SPME) fibre, in three houses with cold pitched roof, successfully demonstrated the potential of the SPME fibre as a device for monitoring air movement in two volumes. The roofs monitored were pitched at 15° - 30° with insulation thickness varying between 200-300 mm on the ceiling. For effective analysis, two constant sources of volatile organic compounds were diffused steadily in the house. Emission rates and air movement from the house to the roof was predicted using developed algorithms. The airflow rates which were calibrated against conventional tracer gas techniques were introduced into a HAM software package to predict the effects of air movement on other varying parameters. On average it was shown from the in situ measurements that about 20-30% of air entering the three houses left through gaps and cracks in the ceiling into the roof. Although these field measurements focus on the airflows, it is associated with energy benefits such that; if these flows are reduced then significantly energy losses would also be reduced (as modelled) consequently improving the energy efficiency of the house. Other results illustrated that condensation formation risks were dependent on the airtightness of the building envelopes including configurations of their roof constructions.

Assessing bee species richness in two Mediterranean communities: importance of habitat type and sampling techniques

The decline of bees has raised concerns regarding their conservation and the maintenance of ecosystem services they provide to bee-pollinated wild flowers and crops. Although the Mediterranean region is a hotspot for bee species richness, their status remains poorly studied. There is an urgent need for cost-effective, reliable, and unbiased sampling methods that give good bee species richness estimates. This study aims: (a) to assess bee species richness in two common Mediterranean habitat types: semi-natural scrub (phrygana) and managed olive groves; (b) to compare species richness in those systems to that of other biogeographic regions, and (c) to assess whether six different sampling methods (pan traps, variable and standardized transect walks, observation plots and trap nests), previously tested in other European biogeographic regions, are suitable in Mediterranean communities. Eight study sites, four per habitat type, were selected on the island of Lesvos, Greece. The species richness observed was high compared to other habitat types worldwide for which comparable data exist. Pan traps collected the highest proportion of the total bee species richness across all methods at the scale of a study site. Variable and standardized transect walks detected the highest total richness over all eight study sites. Trap nests and observation plots detected only a limited fraction of the bee species richness. To assess the total bee species richness in bee diversity hotspots, such as the studied habitats, we suggest a combination of transect walks conducted by trained bee collectors and pan trap sampling

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Sampling series for determination of probability density of CDMA multiple access interference

Consideration is given to a standard CDMA system and determination of the density function of the interference with and without Gaussian noise using sampling theory concepts. The formula derived provides fast and accurate results and is a simple, useful alternative to other methods

A study on orthogonality sampling.

The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of scattered waves in electromagnetics or acoustics. Orthogonality sampling can be seen as a special beam forming algorithm with some links to the point source method and to the linear sampling method. The basic idea of orthogonality sampling is to sample the space under consideration by calculating scalar products of the measured far field pattern , with a test function for all y in a subset Q of the space , m = 2, 3. The way in which this is carried out is important to extract the information which the scattered fields contain. The theoretical foundation of orthogonality sampling is only partly resolved, and the goal of this work is to initiate further research by numerical demonstration of the high potential of the approach. We implement the method for a two-dimensional setting for the Helmholtz equation, which represents electromagnetic scattering when the setup is independent of the third coordinate. We show reconstructions of the location and shape of objects from measurements of the scattered field for one or several directions of incidence and one or many frequencies or wave numbers, respectively. In particular, we visualize the indicator function both with the Dirichlet and Neumann boundary condition and for complicated inhomogeneous media.

A refined sampling strategy for intra-tooth stable isotope analysis of mammalian enamel

Serial sampling and stable isotope analysis performed along the growth axis of vertebrate tooth enamel records differences attributed to seasonal variation in diet, climate or animal movement. Because several months are required to obtain mature enamel in large mammals, modifications in the isotopic composition of environmental parameters are not instantaneously recorded, and stable isotope analysis of tooth enamel returns a time-averaged signal attenuated in its amplitude relative to the input signal. For convenience, stable isotope profiles are usually determined on the side of the tooth where enamel is thickest. Here we investigate the possibility of improving the time resolution by targeting the side of the tooth where enamel is thinnest. Observation of developing third molars (M3) in sheep shows that the tooth growth rate is not constant but decreases exponentially, while the angle between the first layer of enamel deposited and the enamel–dentine junction increases as a tooth approaches its maximal length. We also noted differences in thickness and geometry of enamel growth between the mesial side (i.e., the side facing the M2) and the buccal side (i.e., the side facing the cheek) of the M3. Carbon and oxygen isotope variations were measured along the M3 teeth from eight sheep raised under controlled conditions. Intra-tooth variability was systematically larger along the mesial side and the difference in amplitude between the two sides was proportional to the time of exposure to the input signal. Although attenuated, the mesial side records variations in the environmental signal more faithfully than the buccal side. This approach can be adapted to other mammals whose teeth show lateral variation in enamel thickness and could potentially be used as an internal check for diagenesis.

Ken Thompson's 6-man Statistical Graphs

This note reviews Ken Thompson's statistics on 6-man White wins with Black to move and explains the way in which the statistics have been graphed logarithmically.

PDFOS: PDF estimation based over-sampling for imbalanced two-class problems

This contribution proposes a novel probability density function (PDF) estimation based over-sampling (PDFOS) approach for two-class imbalanced classification problems. The classical Parzen-window kernel function is adopted to estimate the PDF of the positive class. Then according to the estimated PDF, synthetic instances are generated as the additional training data. The essential concept is to re-balance the class distribution of the original imbalanced data set under the principle that synthetic data sample follows the same statistical properties. Based on the over-sampled training data, the radial basis function (RBF) classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier’s structure and the parameters of RBF kernels are determined using a particle swarm optimisation algorithm based on the criterion of minimising the leave-one-out misclassification rate. The effectiveness of the proposed PDFOS approach is demonstrated by the empirical study on several imbalanced data sets.