Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Estimating the risk of developing type 2 diabetes: a comparison of several risk scores: the Cohorte Lausannoise study.

To compare in the Swiss population the results of several scores estimating the risk of developing type 2 diabetes. This was a single-center, cross-sectional study conducted between 2003 and 2006 in Lausanne, Switzerland. Overall, 3,251 women and 2,937 men, aged 35-75 years, were assessed, of which 5,760 (93%) were free from diabetes and included in the current study. The risk of developing type 2 diabetes was assessed using seven different risk scores, including clinical data with or without biological data. Participants were considered to be eligible for primary prevention according to the thresholds provided for each score. The results were then extrapolated to the Swiss population of the same sex and age. The risk of developing type 2 diabetes increased with age in all scores. The prevalence of participants at high risk ranged between 1.6 and 24.9% in men and between 1.1 and 15.7% in women. Extrapolated to the Swiss population of similar age, the overall number of participants at risk, and thus susceptible to intervention, ranged between 46,708 and 636,841. In addition, scores that included the same clinical variables led to a significantly different prevalence of participants at risk (4.2% [95% CI 3.4-5.0] vs. 12.8% [11.5-14.1] in men and 2.9% [2.4-3.6] vs. 6.0% [5.2-6.9] in women). CONCLUSIONS; The prevalence of participants at risk for developing type 2 diabetes varies considerably according to the scoring system used. To adequately prevent type 2 diabetes, risk-scoring systems must be validated for each population considered.

A logistic regression approach to estimating customer profit loss due to lapses in insurance

This article focuses on business risk management in the insurance industry. A methodology for estimating the profit loss caused by each customer in the portfolio due to policy cancellation is proposed. Using data from a European insurance company, customer behaviour over time is analyzed in order to estimate the probability of policy cancelation and the resulting potential profit loss due to cancellation. Customers may have up to two different lines of business contracts: motor insurance and other diverse insurance (such as, home contents, life or accident insurance). Implications for understanding customer cancellation behaviour as the core of business risk management are outlined.

Estimating the Prevalence of Problem Opiate and Problem Cocaine Use in Northern Ireland (PDF 213 KB)

Apr-06

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

PHE-CRCE-010: Estimating Local Mortality Burdens associated with Particulate Air Pollution

The increase in mortality risk associated with long-term exposure to particulate air pollution is one of the most important, and best-characterised, effects of air pollution on health. This report presents estimates of the size of this effect on mortality in local authority areas in the UK, building upon the attributable fractions reported as an indicator in the public health outcomes framework for England. It discusses the concepts and assumptions underlying these calculations and gives information on how such estimates can be made. The estimates are expected to be useful to health and wellbeing boards when assessing local public health priorities, as well as to others working in the field of air quality and public health. The estimates of mortality burden are based on modelled annual average concentrations of fine particulate matter (PM2.5) in each local authority area originating from human activities. Local data on the adult population and adult mortality rates is also used. Central estimates of the fraction of mortality attributable to long-term exposure to current levels of anthropogenic (human-made) particulate air pollution range from around 2.5% in some local authorities in rural areas of Scotland and Northern Ireland and between 3 and 5% in Wales, to over 8% in some London boroughs. Because of uncertainty in the increase in mortality risk associated with ambient PM2.5, the actual burdens associated with these modelled concentrations could range from approximately one-sixth to about double these figures. Thus, current levels of particulate air pollution have a considerable impact on public health. Measures to reduce levels of particulate air pollution, or to reduce exposure of the population to such pollution, are regarded as an important public health initiative.

Review of methods for estimating life expectancy by social class using the ONS Longitudinal Study

Life expectancy by socio-economic status is an important measure of health inequality. This article presents proposed changes in the methods used to estimate life expectancy by social class using the ONS Longitudinal Study.

Estimating attributable mortality due to nosocomial infections acquired in intensive care units.

BACKGROUND: The strength of the association between intensive care unit (ICU)-acquired nosocomial infections (NIs) and mortality might differ according to the methodological approach taken. OBJECTIVE: To assess the association between ICU-acquired NIs and mortality using the concept of population-attributable fraction (PAF) for patient deaths caused by ICU-acquired NIs in a large cohort of critically ill patients. SETTING: Eleven ICUs of a French university hospital. DESIGN: We analyzed surveillance data on ICU-acquired NIs collected prospectively during the period from 1995 through 2003. The primary outcome was mortality from ICU-acquired NI stratified by site of infection. A matched-pair, case-control study was performed. Each patient who died before ICU discharge was defined as a case patient, and each patient who survived to ICU discharge was defined as a control patient. The PAF was calculated after adjustment for confounders by use of conditional logistic regression analysis. RESULTS: Among 8,068 ICU patients, a total of 1,725 deceased patients were successfully matched with 1,725 control patients. The adjusted PAF due to ICU-acquired NI for patients who died before ICU discharge was 14.6% (95% confidence interval [CI], 14.4%-14.8%). Stratified by the type of infection, the PAF was 6.1% (95% CI, 5.7%-6.5%) for pulmonary infection, 3.2% (95% CI, 2.8%-3.5%) for central venous catheter infection, 1.7% (95% CI, 0.9%-2.5%) for bloodstream infection, and 0.0% (95% CI, -0.4% to 0.4%) for urinary tract infection. CONCLUSIONS: ICU-acquired NI had an important effect on mortality. However, the statistical association between ICU-acquired NI and mortality tended to be less pronounced in findings based on the PAF than in study findings based on estimates of relative risk. Therefore, the choice of methods does matter when the burden of NI needs to be assessed.

Estimating the incidence of cancers in Switzerland: 1983-1987.

Estimates have recently been made of the incidence of cancers in the countries of the European Community. Similar estimates are given for Switzerland, based on data from the six Swiss cantonal cancer registries, all of which have been operating for at least 12 years. These registries cover Basel, Geneva, Neuchatel, St Gall and Appenzell, Vaud and Zurich, which account for about 50% of the Swiss population as a whole. Two different methods were used to extrapolate from the incidences observed in the regions covered by cancer registration to the entire country. The first method is based solely on the distribution of populations according to the country's main linguistic groups, whereas the second relies on mortality data. Estimates obtained by the second approach are presented and their reliability is discussed. Comparison of the age incidence curve with that of Denmark tends to confirm the validity of the estimations. Estimated standardised rates (world population) for all sites except nonmelanomatous skin cancer are 294.3 for males and 214.2 for females. Comparisons with other European countries show that in males, lung cancer is relatively less common in Switzerland, whereas in females, breast cancer is relatively more frequent.

Estimating the motion of an underwater robot from a monocular image sequence

When underwater vehicles perform navigation close to the ocean floor, computer vision techniques can be applied to obtain quite accurate motion estimates. The most crucial step in the vision-based estimation of the vehicle motion consists on detecting matchings between image pairs. Here we propose the extensive use of texture analysis as a tool to ameliorate the correspondence problem in underwater images. Once a robust set of correspondences has been found, the three-dimensional motion of the vehicle can be computed with respect to the bed of the sea. Finally, motion estimates allow the construction of a map that could aid to the navigation of the robot

Effect of CO2 and 1-octen-3-ol attractants for estimating species richness and the abundance of diurnal mosquitoes in the southeastern Atlantic forest, Brazil

Studies have shown that both carbon dioxide (CO2) and octenol (1-octen-3-ol) are effective attractants for mosquitoes. The objective of the present study was to evaluate the attractiveness of 1-octen-3-ol and CO2 for diurnal mosquitoes in the southeastern Atlantic forest. A Latin square experimental design was employed with four treatments: CDC-light trap (CDC-LT), CDC-LT and 1-octen-3-ol, CDC-LT and CO2 and CDC-LT with 1-octen-3-ol and CO2. Results demonstrated that both CDC-CO2 and CDC-CO2-1-octen-3-ol captured a greater number of mosquito species and specimens compared to CDC-1-octen-3-ol; CDC-LT was used as the control. Interestingly, Anopheles (Kerteszia) sp. was generally attracted to 1-octen-3-ol, whereas Aedes serratus was the most abundant species in all Latin square collections. This species was recently shown to be competent to transmit the yellow fever virus and may therefore play a role as a disease vector in rural areas of Brazil.

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Lifelong dynamics of human CD4+CD25+ regulatory T cells: insights from in vivo data and mathematical modeling.

Despite their limited proliferation capacity, regulatory T cells (T(regs)) constitute a population maintained over the entire lifetime of a human organism. The means by which T(regs) sustain a stable pool in vivo are controversial. Using a mathematical model, we address this issue by evaluating several biological scenarios of the origins and the proliferation capacity of two subsets of T(regs): precursor CD4(+)CD25(+)CD45RO(-) and mature CD4(+)CD25(+)CD45RO(+) cells. The lifelong dynamics of T(regs) are described by a set of ordinary differential equations, driven by a stochastic process representing the major immune reactions involving these cells. The model dynamics are validated using data from human donors of different ages. Analysis of the data led to the identification of two properties of the dynamics: (1) the equilibrium in the CD4(+)CD25(+)FoxP3(+)T(regs) population is maintained over both precursor and mature T(regs) pools together, and (2) the ratio between precursor and mature T(regs) is inverted in the early years of adulthood. Then, using the model, we identified three biologically relevant scenarios that have the above properties: (1) the unique source of mature T(regs) is the antigen-driven differentiation of precursors that acquire the mature profile in the periphery and the proliferation of T(regs) is essential for the development and the maintenance of the pool; there exist other sources of mature T(regs), such as (2) a homeostatic density-dependent regulation or (3) thymus- or effector-derived T(regs), and in both cases, antigen-induced proliferation is not necessary for the development of a stable pool of T(regs). This is the first time that a mathematical model built to describe the in vivo dynamics of regulatory T cells is validated using human data. The application of this model provides an invaluable tool in estimating the amount of regulatory T cells as a function of time in the blood of patients that received a solid organ transplant or are suffering from an autoimmune disease.

Estimating Gross Value Added (GVA) across multiple scales: theoretical approach and empirical validation

This paper presents an application of the Multi-Scale Integrated Analysis of Societal and Ecosystem Metabolism (MuSIASEM) approach to the estimation of quantities of Gross Value Added (GVA) referring to economic entities defined at different scales of study. The method first estimates benchmark values of the pace of GVA generation per hour of labour across economic sectors. These values are estimated as intensive variables –e.g. €/hour– by dividing the various sectorial GVA of the country (expressed in € per year) by the hours of paid work in that same sector per year. This assessment is obtained using data referring to national statistics (top down information referring to the national level). Then, the approach uses bottom-up information (the number of hours of paid work in the various economic sectors of an economic entity –e.g. a city or a province– operating within the country) to estimate the amount of GVA produced by that entity. This estimate is obtained by multiplying the number of hours of work in each sector in the economic entity by the benchmark value of GVA generation per hour of work of that particular sector (national average). This method is applied and tested on two different socio-economic systems: (i) Catalonia (considered level n) and Barcelona (considered level n-1); and (ii) the region of Lima (considered level n) and Lima Metropolitan Area (considered level n-1). In both cases, the GVA per year of the local economic entity –Barcelona and Lima Metropolitan Area – is estimated and the resulting value is compared with GVA data provided by statistical offices. The empirical analysis seems to validate the approach, even though the case of Lima Metropolitan Area indicates a need for additional care when dealing with the estimate of GVA in primary sectors (agriculture and mining).