Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Rugged miniaturized mass sensors for use in plutonium conversion processes

Ionization is produced either through Plasma Desorption, in the case of a solid, using fission fragments from a Cf-252 source; or in the case of a gas, via an electron avalanche from the impact on a microsphere detector of {alpha} particles from a radioactive source. The gaseous compound analysis yielded multiple peaks on parent ion and molecular fragments. In the solid compound analysis, the results indicated that solid-state mass spectrometry will provide important information about the degradation of materials by measured changes in molecular weight

Transcript quantification with RNA-Seq data

Motivation Novel high-throughput sequencing technologies open exciting new approaches to transcriptome profiling. Sequencing transcript populations of interest, e.g. from different tissues or variable stress conditions, with RNA sequencing (RNA-Seq) [1] generates millions of short reads. Accurately aligned to a reference genome, they provide digital counts and thus facilitate transcript quantification. As the observed read counts only provide the summation of all expressed sequences at one locus, the inference of the underlying transcript abundances is crucial for further quantitative analyses. Methods To approach this problem, we have developed a new technique, called rQuant, based on quadratic programming. Given a gene annotation and position-wise exon/intron read coverage from read alignments, we determine the abundances for each annotated transcript by minimising a suitable loss function. It penalises the deviation of the observed from the expected read coverage given the transcript weights. The observed read coverage is typically non-uniformly distributed over the transcript due to several biases in the generation of the sequencing libraries and the sequencing. This leads to distortions of the transcript abundances, if not corrected properly. We therefore extended our approach to jointly optimise transcript profiles, modeling the coverage deviations depending on the position in the transcript. Our method can be applied without knowledge of the underlying transcript abundances and equally benefits from loci with and without alternative transcripts. Results To quantitatively evaluate the quality of our abundance predictions, we used a set of simulated reads from transcripts with known expression as a benchmark set. It was generated using the Flux Simulator [2] modeling biases in RNA-Seq as well as preparation experiments. Table 1 shows preliminary results with segment- and position-based loss as well as with and without the transcript profiles. Our results indicate that the position-based modeling together with transcript profiles allows us to accurately infer the underlying expression of single transcripts as well as of multiple isoforms of one gene locus

mGene.web: a web service for accurate computational gene finding

We describe mGene.web, a web service for the genome-wide prediction of protein coding genes from eukaryotic DNA sequences. It offers pre-trained models for the recognition of gene structures including untranslated regions in an increasing number of organisms. With mGene.web, users have the additional possibility to train the system with their own data for other organisms on the push of a button, a functionality that will greatly accelerate the annotation of newly sequenced genomes. The system is built in a highly modular way, such that individual components of the framework, like the promoter prediction tool or the splice site predictor, can be used autonomously. The underlying gene finding system mGene is based on discriminative machine learning techniques and its high accuracy has been demonstrated in an international competition on nematode genomes. mGene.web is available at http://www.mgene.org/web, it is free of charge and can be used for eukaryotic genomes of small to moderate size (several hundred Mbp)

mGene.web: a web service for accurate computational gene finding

We describe mGene.web, a web service for the genome-wide prediction of protein coding genes from eukaryotic DNA sequences. It offers pre-trained models for the recognition of gene structures including untranslated regions in an increasing number of organisms. With mGene.web, users have the additional possibility to train the system with their own data for other organisms on the push of a button, a functionality that will greatly accelerate the annotation of newly sequenced genomes. The system is built in a highly modular way, such that individual components of the framework, like the promoter prediction tool or the splice site predictor, can be used autonomously. The underlying gene finding system mGene is based on discriminative machine learning techniques and its high accuracy has been demonstrated in an international competition on nematode genomes. mGene.web is available at http://www.mgene.org/web, it is free of charge and can be used for eukaryotic genomes of small to moderate size (several hundred Mbp)

Assessing quality of life in a clinical study on heart rehabilitation patients: how well do value sets based on given or experienced health states reflect patients' valuations?

Background: Quality of life as an endpoint in a clinical study may be sensitive to the value set used to derive a single score. Focusing on patients' actual valuations in a clinical study, we compare different value sets for the EQ-5D-3L and assess how well they reproduce patients' reported results. Methods: A clinical study comparing inpatient (n = 98) and outpatient (n = 47) rehabilitation of patients after an acute coronary event is re-analyzed. Value sets include: 1. Given health states and time-trade-off valuation (GHS-TTO) rendering economic utilities;2. Experienced health states and valuation by visual analog scale (EHS-VAS). Valuations are compared with patient-reported VAS rating. Accuracy is assessed by mean absolute error (MAE) and by Pearson's correlation.. External validity is tested by correlation with established MacNew global scores. Drivers of differences between value sets and VAS are analyzed using repeated measures regression. Results: EHS-VAS had smaller MAEs and higher. in all patients and in the inpatient group, and correlated best with MacNew global score. Quality-adjusted survival was more accurately reflected by EHS-VAS. Younger, better educated patients reported lower VAS at admission than the EHS-based value set. EHS-based estimates were mostly able to reproduce patient-reported valuation. Economic utility measurement is conceptually different, produced results less strongly related to patients' reports, and resulted in about 20 % longer quality-adjusted survival. Conclusion: Decision makers should take into account the impact of choosing value sets on effectiveness results. For transferring the results of heart rehabilitation patients from another country or from another valuation method, the EHS-based value set offers a promising estimation option for those decision makers who prioritize patient-reported valuation. Yet, EHS-based estimates may not fully reflect patient-reported VAS in all situations

Rediscovering the genus Lyticum, multiflagellated symbionts of the order Rickettsiales

Among the bacterial symbionts harbored by the model organism Paramecium, many still lack a recent investigation that includes a molecular characterization. The genus Lyticum consists of two species of large-sized bacteria displaying numerous flagella, despite their inability to move inside their hosts’ cytoplasm. We present a multidisciplinary redescription of both species, using the deposited type strains as well as newly collected material. On the basis of 16S rRNA gene sequences, we assigned Lyticum to the order Rickettsiales, that is intensely studied because of its pathogenic representatives and its position as the extant group most closely related to the mitochondrial ancestor. We provide conclusive proofs that at least some Rickettsiales possess actual flagella, a feature that has been recently predicted from genomic data but never confirmed. We give support to the hypothesis that the mitochondrial ancestor could have been flagellated, and provide the basis for further studies on these ciliate endosymbionts

Smoking and health-related quality of life in English general population: Implications for economic evaluations

Copyright @ 2012 Vogl et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This article has been made available through the Brunel Open Access Publishing Fund.Background: Little is known as to how health-related quality of life (HRQoL) when measured by generic instruments such as EQ-5D differ across smokers, ex-smokers and never-smokers in the general population; whether the overall pattern of this difference remain consistent in each domain of HRQoL; and what implications this variation, if any, would have for economic evaluations of tobacco control interventions. Methods: Using the 2006 round of Health Survey for England data (n = 13,241), this paper aims to examine the impact of smoking status on health-related quality of life in English population. Depending upon the nature of the EQ-5D data (i.e. tariff or domains), linear or logistic regression models were fitted to control for biology, clinical conditions, socio-economic background and lifestyle factors that an individual may have regardless of their smoking status. Age- and gender-specific predicted values according to smoking status are offered as the potential 'utility' values to be used in future economic evaluation models. Results: The observed difference of 0.1100 in EQ-5D scores between never-smokers (0.8839) and heavy-smokers (0.7739) reduced to 0.0516 after adjusting for biological, clinical, lifestyle and socioeconomic conditions. Heavy-smokers, when compared with never-smokers, were significantly more likely to report some/severe problems in all five domains - mobility (67%), self-care (70%), usual activity (42%), pain/discomfort (46%) and anxiety/depression (86%) -. 'Utility' values by age and gender for each category of smoking are provided to be used in the future economic evaluations. Conclusion: Smoking is significantly and negatively associated with health-related quality of life in English general population and the magnitude of this association is determined by the number of cigarettes smoked. The varying degree of this association, captured through instruments such as EQ-5D, may need to be fed into the design of future economic evaluations where the intervention being evaluated affects (e.g. tobacco control) or is affected (e.g. treatment for lung cancer) by individual's (or patients') smoking status

Adiposity has differing associations with incident coronary heart disease and mortality in the Scottish population: cross-sectional surveys with follow-up

Objective: Investigation of the association of excess adiposity with three different outcomes: all-cause mortality, coronary heart disease (CHD) mortality and incident CHD. Design: Cross-sectional surveys linked to hospital admissions and death records. Subjects: 19 329 adults (aged 18–86 years) from a representative sample of the Scottish population. Measurements: Gender-stratified Cox proportional hazards models were used to estimate hazard ratios (HRs) for all-cause mortality, CHD mortality and incident CHD. Separate models incorporating the anthropometric measurements body mass index (BMI), waist circumference (WC) or waist–hip ratio (WHR) were created adjusted for age, year of survey, smoking status and alcohol consumption. Results: For both genders, BMI-defined obesity (greater than or equal to30 kg m−2) was not associated with either an increased risk of all-cause mortality or CHD mortality. However, there was an increased risk of incident CHD among the obese men (hazard ratio (HR)=1.78; 95% confidence interval=1.37–2.31) and obese women (HR=1.93; 95% confidence interval=1.44–2.59). There was a similar pattern for WC with regard to the three outcomes; for incident CHD, the HR=1.70 (1.35–2.14) for men and 1.71 (1.28–2.29) for women in the highest WC category (men greater than or equal to102 cm, women greater than or equal to88 cm), synonymous with abdominal obesity. For men, the highest category of WHR (greater than or equal to1.0) was associated with an increased risk of all-cause mortality (1.29; 1.04–1.60) and incident CHD (1.55; 1.19–2.01). Among women with a high WHR (greater than or equal to0.85) there was an increased risk of all outcomes: all-cause mortality (1.56; 1.26–1.94), CHD mortality (2.49; 1.36–4.56) and incident CHD (1.76; 1.31–2.38). Conclusions: In this study excess adiposity was associated with an increased risk of incident CHD but not necessarily death. One possibility is that modern medical intervention has contributed to improved survival of first CHD events. The future health burden of increased obesity levels may manifest as an increase in the prevalence of individuals living with CHD and its consequences