Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Current Population Reports Series P-26, Federal-State cooperative program for population estimates, July 1974

T his report presents population estimates for July 1, 1972 and provisional estimates for July 1, 1973, for counties and metropolitan areas prepared under the auspices of the Federal State Cooperative Program for Local Population Estimates. The objective of this program. is the development and publication of State - prepared estimates of the population of counties using uniform procedures largely standardized for data input and methodology. The methods used have been mutually agreed upon by the individual States and the Bureau of the Census on the basis of a test of methods against the 1970 census. For a more detailed description of the program.

Current Population Reports Series P-26, Federal-State cooperative program for population estimates, September 1975

This report presents population estimates for July 1, 1973 and provisional estimates for July 1, for counties and metropolitan areas prepared under the auspices of the Federal State Cooperative Program for Local Population Estimates. The objective of this program. is the development and publication of State - prepared estimates of the population of counties using uniform procedures largely standardized for data input and methodology. The methods used have been mutually agreed upon by the individual States and the Bureau of the Census on the basis of a test of methods against the 1970 census. For a more detailed description of the program.

Predictive analysis and mapping of indoor radon concentrations in a complex environment using kernel estimation: an application to Switzerland.

PURPOSE: The aim of this study was to develop models based on kernel regression and probability estimation in order to predict and map IRC in Switzerland by taking into account all of the following: architectural factors, spatial relationships between the measurements, as well as geological information. METHODS: We looked at about 240,000 IRC measurements carried out in about 150,000 houses. As predictor variables we included: building type, foundation type, year of construction, detector type, geographical coordinates, altitude, temperature and lithology into the kernel estimation models. We developed predictive maps as well as a map of the local probability to exceed 300 Bq/m(3). Additionally, we developed a map of a confidence index in order to estimate the reliability of the probability map. RESULTS: Our models were able to explain 28% of the variations of IRC data. All variables added information to the model. The model estimation revealed a bandwidth for each variable, making it possible to characterize the influence of each variable on the IRC estimation. Furthermore, we assessed the mapping characteristics of kernel estimation overall as well as by municipality. Overall, our model reproduces spatial IRC patterns which were already obtained earlier. On the municipal level, we could show that our model accounts well for IRC trends within municipal boundaries. Finally, we found that different building characteristics result in different IRC maps. Maps corresponding to detached houses with concrete foundations indicate systematically smaller IRC than maps corresponding to farms with earth foundation. CONCLUSIONS: IRC mapping based on kernel estimation is a powerful tool to predict and analyze IRC on a large-scale as well as on a local level. This approach enables to develop tailor-made maps for different architectural elements and measurement conditions and to account at the same time for geological information and spatial relations between IRC measurements.

Hierarchical modeling gave plausible estimates of associations between metabolic syndrome and components of antiretroviral therapy.

OBJECTIVE: Hierarchical modeling has been proposed as a solution to the multiple exposure problem. We estimate associations between metabolic syndrome and different components of antiretroviral therapy using both conventional and hierarchical models. STUDY DESIGN AND SETTING: We use discrete time survival analysis to estimate the association between metabolic syndrome and cumulative exposure to 16 antiretrovirals from four drug classes. We fit a hierarchical model where the drug class provides a prior model of the association between metabolic syndrome and exposure to each antiretroviral. RESULTS: One thousand two hundred and eighteen patients were followed for a median of 27 months, with 242 cases of metabolic syndrome (20%) at a rate of 7.5 cases per 100 patient years. Metabolic syndrome was more likely to develop in patients exposed to stavudine, but was less likely to develop in those exposed to atazanavir. The estimate for exposure to atazanavir increased from hazard ratio of 0.06 per 6 months' use in the conventional model to 0.37 in the hierarchical model (or from 0.57 to 0.81 when using spline-based covariate adjustment). CONCLUSION: These results are consistent with trials that show the disadvantage of stavudine and advantage of atazanavir relative to other drugs in their respective classes. The hierarchical model gave more plausible results than the equivalent conventional model.

Empirical errors of small area estimates from the multisource National Forest Inventory in Eastern Finland

Abstract

Robust parametric indirect estimates of the expected cost of a hospital stay with covariates and censored data.

We consider the problem of estimating the mean hospital cost of stays of a class of patients (e.g., a diagnosis-related group) as a function of patient characteristics. The statistical analysis is complicated by the asymmetry of the cost distribution, the possibility of censoring on the cost variable, and the occurrence of outliers. These problems have often been treated separately in the literature, and a method offering a joint solution to all of them is still missing. Indirect procedures have been proposed, combining an estimate of the duration distribution with an estimate of the conditional cost for a given duration. We propose a parametric version of this approach, allowing for asymmetry and censoring in the cost distribution and providing a mean cost estimator that is robust in the presence of extreme values. In addition, the new method takes covariate information into account.

Comparisons of Estimates of Annual Exceedance-Probability Discharges for Small Drainage Basins in Iowa, Based on Data through Water Year 2013, TR-678, 2015

Traditionally, the Iowa Department of Transportation has used the Iowa Runoff Chart and single-variable regional-regression equations (RREs) from a U.S. Geological Survey report (published in 1987) as the primary methods to estimate annual exceedance-probability discharge (AEPD) for small (20 square miles or less) drainage basins in Iowa. With the publication of new multi- and single-variable RREs by the U.S. Geological Survey (published in 2013), the Iowa Department of Transportation needs to determine which methods of AEPD estimation provide the best accuracy and the least bias for small drainage basins in Iowa. Twenty five streamgages with drainage areas less than 2 square miles (mi2) and 55 streamgages with drainage areas between 2 and 20 mi2 were selected for the comparisons that used two evaluation metrics. Estimates of AEPDs calculated for the streamgages using the expected moments algorithm/multiple Grubbs-Beck test analysis method were compared to estimates of AEPDs calculated from the 2013 multivariable RREs; the 2013 single-variable RREs; the 1987 single-variable RREs; the TR-55 rainfall-runoff model; and the Iowa Runoff Chart. For the 25 streamgages with drainage areas less than 2 mi2, results of the comparisons seem to indicate the best overall accuracy and the least bias may be achieved by using the TR-55 method for flood regions 1 and 3 (published in 2013) and by using the 1987 single-variable RREs for flood region 2 (published in 2013). For drainage basins with areas between 2 and 20 mi2, results of the comparisons seem to indicate the best overall accuracy and the least bias may be achieved by using the 1987 single-variable RREs for the Southern Iowa Drift Plain landform region and for flood region 3 (published in 2013), by using the 2013 multivariable RREs for the Iowan Surface landform region, and by using the 2013 or 1987 single-variable RREs for flood region 2 (published in 2013). For all other landform or flood regions in Iowa, use of the 2013 single-variable RREs may provide the best overall accuracy and the least bias. An examination was conducted to understand why the 1987 single-variable RREs seem to provide better accuracy and less bias than either of the 2013 multi- or single-variable RREs. A comparison of 1-percent annual exceedance-probability regression lines for hydrologic regions 1–4 from the 1987 single-variable RREs and for flood regions 1–3 from the 2013 single-variable RREs indicates that the 1987 single-variable regional-regression lines generally have steeper slopes and lower discharges when compared to 2013 single-variable regional-regression lines for corresponding areas of Iowa. The combination of the definition of hydrologic regions, the lower discharges, and the steeper slopes of regression lines associated with the 1987 single-variable RREs seem to provide better accuracy and less bias when compared to the 2013 multi- or single-variable RREs; better accuracy and less bias was determined particularly for drainage areas less than 2 mi2, and also for some drainage areas between 2 and 20 mi2. The 2013 multi- and single-variable RREs are considered to provide better accuracy and less bias for larger drainage areas. Results of this study indicate that additional research is needed to address the curvilinear relation between drainage area and AEPDs for areas of Iowa.

Reliable selfing rate estimates from imperfect population genetic data.

Genotypic frequencies at codominant marker loci in population samples convey information on mating systems. A classical way to extract this information is to measure heterozygote deficiencies (FIS) and obtain the selfing rate s from FIS = s/(2 - s), assuming inbreeding equilibrium. A major drawback is that heterozygote deficiencies are often present without selfing, owing largely to technical artefacts such as null alleles or partial dominance. We show here that, in the absence of gametic disequilibrium, the multilocus structure can be used to derive estimates of s independent of FIS and free of technical biases. Their statistical power and precision are comparable to those of FIS, although they are sensitive to certain types of gametic disequilibria, a bias shared with progeny-array methods but not FIS. We analyse four real data sets spanning a range of mating systems. In two examples, we obtain s = 0 despite positive FIS, strongly suggesting that the latter are artefactual. In the remaining examples, all estimates are consistent. All the computations have been implemented in a open-access and user-friendly software called rmes (robust multilocus estimate of selfing) available at http://ftp.cefe.cnrs.fr, and can be used on any multilocus data. Being able to extract the reliable information from imperfect data, our method opens the way to make use of the ever-growing number of published population genetic studies, in addition to the more demanding progeny-array approaches, to investigate selfing rates.

Kernel-PCA data integration with enhanced interpretability

Background Nowadays, combining the different sources of information to improve the biological knowledge available is a challenge in bioinformatics. One of the most powerful methods for integrating heterogeneous data types are kernel-based methods. Kernel-based data integration approaches consist of two basic steps: firstly the right kernel is chosen for each data set; secondly the kernels from the different data sources are combined to give a complete representation of the available data for a given statistical task. Results We analyze the integration of data from several sources of information using kernel PCA, from the point of view of reducing dimensionality. Moreover, we improve the interpretability of kernel PCA by adding to the plot the representation of the input variables that belong to any dataset. In particular, for each input variable or linear combination of input variables, we can represent the direction of maximum growth locally, which allows us to identify those samples with higher/lower values of the variables analyzed. Conclusions The integration of different datasets and the simultaneous representation of samples and variables together give us a better understanding of biological knowledge.

Study of the impact of tissue density heterogeneities on 3-dimensional abdominal dosimetry: comparison between dose kernel convolution and direct monte carlo methods.

Dose kernel convolution (DK) methods have been proposed to speed up absorbed dose calculations in molecular radionuclide therapy. Our aim was to evaluate the impact of tissue density heterogeneities (TDH) on dosimetry when using a DK method and to propose a simple density-correction method. METHODS: This study has been conducted on 3 clinical cases: case 1, non-Hodgkin lymphoma treated with (131)I-tositumomab; case 2, a neuroendocrine tumor treatment simulated with (177)Lu-peptides; and case 3, hepatocellular carcinoma treated with (90)Y-microspheres. Absorbed dose calculations were performed using a direct Monte Carlo approach accounting for TDH (3D-RD), and a DK approach (VoxelDose, or VD). For each individual voxel, the VD absorbed dose, D(VD), calculated assuming uniform density, was corrected for density, giving D(VDd). The average 3D-RD absorbed dose values, D(3DRD), were compared with D(VD) and D(VDd), using the relative difference Δ(VD/3DRD). At the voxel level, density-binned Δ(VD/3DRD) and Δ(VDd/3DRD) were plotted against ρ and fitted with a linear regression. RESULTS: The D(VD) calculations showed a good agreement with D(3DRD). Δ(VD/3DRD) was less than 3.5%, except for the tumor of case 1 (5.9%) and the renal cortex of case 2 (5.6%). At the voxel level, the Δ(VD/3DRD) range was 0%-14% for cases 1 and 2, and -3% to 7% for case 3. All 3 cases showed a linear relationship between voxel bin-averaged Δ(VD/3DRD) and density, ρ: case 1 (Δ = -0.56ρ + 0.62, R(2) = 0.93), case 2 (Δ = -0.91ρ + 0.96, R(2) = 0.99), and case 3 (Δ = -0.69ρ + 0.72, R(2) = 0.91). The density correction improved the agreement of the DK method with the Monte Carlo approach (Δ(VDd/3DRD) < 1.1%), but with a lesser extent for the tumor of case 1 (3.1%). At the voxel level, the Δ(VDd/3DRD) range decreased for the 3 clinical cases (case 1, -1% to 4%; case 2, -0.5% to 1.5%, and -1.5% to 2%). No more linear regression existed for cases 2 and 3, contrary to case 1 (Δ = 0.41ρ - 0.38, R(2) = 0.88) although the slope in case 1 was less pronounced. CONCLUSION: This study shows a small influence of TDH in the abdominal region for 3 representative clinical cases. A simple density-correction method was proposed and improved the comparison in the absorbed dose calculations when using our voxel S value implementation.

Cropland area estimates using Modis NDVI time series in the state of Mato Grosso, Brazil

The objective of this work was to evaluate a simple, semi‑automated methodology for mapping cropland areas in the state of Mato Grosso, Brazil. A Fourier transform was applied over a time series of vegetation index products from the moderate resolution imaging spectroradiometer (Modis) sensor. This procedure allows for the evaluation of the amplitude of the periodic changes in vegetation response through time and the identification of areas with strong seasonal variation related to crop production. Annual cropland masks from 2006 to 2009 were generated and municipal cropland areas were estimated through remote sensing. We observed good agreement with official statistics on planted area, especially for municipalities with more than 10% of cropland cover (R² = 0.89), but poor agreement in municipalities with less than 5% crop cover (R² = 0.41). The assessed methodology can be used for annual cropland mapping over large production areas in Brazil.

Population receptive field estimates of human auditory cortex.

Here we describe a method for measuring tonotopic maps and estimating bandwidth for voxels in human primary auditory cortex (PAC) using a modification of the population Receptive Field (pRF) model, developed for retinotopic mapping in visual cortex by Dumoulin and Wandell (2008). The pRF method reliably estimates tonotopic maps in the presence of acoustic scanner noise, and has two advantages over phase-encoding techniques. First, the stimulus design is flexible and need not be a frequency progression, thereby reducing biases due to habituation, expectation, and estimation artifacts, as well as reducing the effects of spatio-temporal BOLD nonlinearities. Second, the pRF method can provide estimates of bandwidth as a function of frequency. We find that bandwidth estimates are narrower for voxels within the PAC than in surrounding auditory responsive regions (non-PAC).

Wheat alleles introgress into selfing wild relatives: empirical estimates from approximate Bayesian computation in Aegilops triuncialis.

Extensive gene flow between wheat (Triticum sp.) and several wild relatives of the genus Aegilops has recently been detected despite notoriously high levels of selfing in these species. Here, we assess and model the spread of wheat alleles into natural populations of the barbed goatgrass (Aegilops triuncialis), a wild wheat relative prevailing in the Mediterranean flora. Our sampling, based on an extensive survey of 31 Ae. triuncialis populations collected along a 60 km × 20 km area in southern Spain (Grazalema Mountain chain, Andalousia, totalling 458 specimens), is completed with 33 wheat cultivars representative of the European domesticated pool. All specimens were genotyped with amplified fragment length polymorphism with the aim of estimating wheat admixture levels in Ae. triuncialis populations. This survey first confirmed extensive hybridization and backcrossing of wheat into the wild species. We then used explicit modelling of populations and approximate Bayesian computation to estimate the selfing rate of Ae. triuncialis along with the magnitude, the tempo and the geographical distance over which wheat alleles introgress into Ae. triuncialis populations. These simulations confirmed that extensive introgression of wheat alleles (2.7 × 10(-4) wheat immigrants for each Ae. triuncialis resident, at each generation) into Ae. triuncialis occurs despite a high selfing rate (Fis ≈ 1 and selfing rate = 97%). These results are discussed in the light of risks associated with the release of genetically modified wheat cultivars in Mediterranean agrosystems.