Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

Local-global splitting for spatiotemporal-adaptive multiscale methods

We present a novel spatiotemporal-adaptive Multiscale Finite Volume (MsFV) method, which is based on the natural idea that the global coarse-scale problem has longer characteristic time than the local fine-scale problems. As a consequence, the global problem can be solved with larger time steps than the local problems. In contrast to the pressure-transport splitting usually employed in the standard MsFV approach, we propose to start directly with a local-global splitting that allows to locally retain the original degree of coupling. This is crucial for highly non-linear systems or in the presence of physical instabilities. To obtain an accurate and efficient algorithm, we devise new adaptive criteria for global update that are based on changes of coarse-scale quantities rather than on fine-scale quantities, as it is routinely done before in the adaptive MsFV method. By means of a complexity analysis we show that the adaptive approach gives a noticeable speed-up with respect to the standard MsFV algorithm. In particular, it is efficient in case of large upscaling factors, which is important for multiphysics problems. Based on the observation that local time stepping acts as a smoother, we devise a self-correcting algorithm which incorporates the information from previous times to improve the quality of the multiscale approximation. We present results of multiphase flow simulations both for Darcy-scale and multiphysics (hybrid) problems, in which a local pore-scale description is combined with a global Darcy-like description. The novel spatiotemporal-adaptive multiscale method based on the local-global splitting is not limited to porous media flow problems, but it can be extended to any system described by a set of conservation equations.

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.

Preliminary Experience in Treatment of Papillary and Macular Retinoblastoma: Evaluation of Local Control and Local Complications After Treatment with Linear Accelerator-Based Stereotactic Radiotherapy with Micromultileaf Collimator as Second-Line or Salvage Treatment after chemotherapy.

PURPOSE: To determine the local control and complication rates for children with papillary and/or macular retinoblastoma progressing after chemotherapy and undergoing stereotactic radiotherapy (SRT) with a micromultileaf collimator. METHODS AND MATERIALS: Between 2004 and 2008, 11 children (15 eyes) with macular and/or papillary retinoblastoma were treated with SRT. The mean age was 19 months (range, 2-111). Of the 15 eyes, 7, 6, and 2 were classified as International Classification of Intraocular Retinoblastoma Group B, C, and E, respectively. The delivered dose of SRT was 50.4 Gy in 28 fractions using a dedicated micromultileaf collimator linear accelerator. RESULTS: The median follow-up was 20 months (range, 13-39). Local control was achieved in 13 eyes (87%). The actuarial 1- and 2-year local control rates were both 82%. SRT was well tolerated. Late adverse events were reported in 4 patients. Of the 4 patients, 2 had developed focal microangiopathy 20 months after SRT; 1 had developed a transient recurrence of retinal detachment; and 1 had developed bilateral cataracts. No optic neuropathy was observed. CONCLUSIONS: Linear accelerator-based SRT for papillary and/or macular retinoblastoma in children resulted in excellent tumor control rates with acceptable toxicity. Additional research regarding SRT and its intrinsic organ-at-risk sparing capability is justified in the framework of prospective trials.

Multiple-scale hydrological and geophysical data integration through non-linear Bayesian sequential simulation

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the scale of a field site represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed downscaling procedure based on a non-linear Bayesian sequential simulation approach. The main objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity logged at collocated wells and surface resistivity measurements, which are available throughout the studied site. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariatekernel density function. Then a stochastic integration of low-resolution, large-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities is applied. The overall viability of this downscaling approach is tested and validated by comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure allows obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Concomitant cisplatin and hyperfractionated radiotherapy in locally advanced head and neck cancer: 10-year follow-up of a randomized phase III trial (SAKK 10/94).

Purpose: To compare the long-term outcome of treatment with concomitant cisplatin and hyperfractionated radiotherapy versus treatment with hyperfractionated radiotherapy alone in patients with locally advanced head and neck cancer.Methods and Materials: From July 1994 to July 2000, a total of 224 patients with squamous cell carcinoma of the head and neck were randomized to receive either hyperfractionated radiotherapy alone (median total dose, 74.4 Gy; 1.2 Gy twice daily; 5 days per week) or the same radiotherapy combined with two cycles of cisplatin (20 mg/m(2) for 5 consecutive days during weeks 1 and 5). The primary endpoint was the time to any treatment failure; secondary endpoints were locoregional failure, metastatic failure, overall survival, and late toxicity assessed according to Radiation Therapy Oncology Group criteria.Results: Median follow-up was 9.5 years (range, 0.1-15.4 years). Median time to any treatment failure was not significantly different between treatment arms (hazard ratio [HR], 1.2 [95% confidence interval [CM 0.9-1.7; p = 0.17]). Rates of locoregional failure-free survival (HR, 1.5 [95% CI, 1.1-2.1;p = 0.021), distant metastasis-free survival (HR, 1.6 [95% CI, 1.1-2.5; p = 0.021), and cancer-specific survival (HR, 1.6 [95% CI, 1.0-2.5;p = 0.03]) were significantly improved in the combined-treatment arm, with no difference in major late toxicity between treatment arms. However, overall survival was not significantly different (HR, 1.3 [95% CI, 0.9-1.8; p = 0.11]).Conclusions: After long-term follow-up, combined-treatment with cisplatin and hyperfractionated radiotherapy maintained improved rates of locoregional control, distant metastasis-free survival, and cancer-specific survival compared to that of hyperfractionated radiotherapy alone, with no difference in major late toxicity. (C) 2012 Elsevier Inc.

Local Distance-Based Generalized Linear Models using the dbstats package for R

This paper introduces local distance-based generalized linear models. These models extend (weighted) distance-based linear models firstly with the generalized linear model concept, then by localizing. Distances between individuals are the only predictor information needed to fit these models. Therefore they are applicable to mixed (qualitative and quantitative) explanatory variables or when the regressor is of functional type. Models can be fitted and analysed with the R package dbstats, which implements several distancebased prediction methods.

Effect of Platinum-Based Chemoradiotherapy on Cellular Proliferation in Bone Marrow and Spleen, Estimated by 18F-FLT PET/CT in Patients with Locally Advanced Non-Small Cell Lung Cancer.

Historically, it has been difficult to monitor the acute impact of anticancer therapies on hematopoietic organs on a whole-body scale. Deeper understanding of the effect of treatments on bone marrow would be of great potential value in the rational design of intensive treatment regimens. 3'-deoxy-3'-(18)F-fluorothymidine ((18)F-FLT) is a functional radiotracer used to study cellular proliferation. It is trapped in cells in proportion to thymidine-kinase 1 enzyme expression, which is upregulated during DNA synthesis. This study investigates the potential of (18)F-FLT to monitor acute effects of chemotherapy on cellular proliferation and its recovery in bone marrow, spleen, and liver during treatment with 2 different chemotherapy regimens.

Binary classification of dyslipidemia from the waist-to-hip ratio and body mass index: a comparison of linear, logistic, and CART models.

BACKGROUND: We sought to improve upon previously published statistical modeling strategies for binary classification of dyslipidemia for general population screening purposes based on the waist-to-hip circumference ratio and body mass index anthropometric measurements. METHODS: Study subjects were participants in WHO-MONICA population-based surveys conducted in two Swiss regions. Outcome variables were based on the total serum cholesterol to high density lipoprotein cholesterol ratio. The other potential predictor variables were gender, age, current cigarette smoking, and hypertension. The models investigated were: (i) linear regression; (ii) logistic classification; (iii) regression trees; (iv) classification trees (iii and iv are collectively known as "CART"). Binary classification performance of the region-specific models was externally validated by classifying the subjects from the other region. RESULTS: Waist-to-hip circumference ratio and body mass index remained modest predictors of dyslipidemia. Correct classification rates for all models were 60-80%, with marked gender differences. Gender-specific models provided only small gains in classification. The external validations provided assurance about the stability of the models. CONCLUSIONS: There were no striking differences between either the algebraic (i, ii) vs. non-algebraic (iii, iv), or the regression (i, iii) vs. classification (ii, iv) modeling approaches. Anticipated advantages of the CART vs. simple additive linear and logistic models were less than expected in this particular application with a relatively small set of predictor variables. CART models may be more useful when considering main effects and interactions between larger sets of predictor variables.

Biological embedding of early life exposures and disease risk in humans: a role for DNA methylation.

BACKGROUND: Following wider acceptance of "the thrifty phenotype" hypothesis and the convincing evidence that early life exposures can influence adult health even decades after the exposure, much interest has been placed on the mechanisms through which early life exposures become biologically embedded. METHODS: In this review, we summarize the current literature regarding biological embedding of early life experiences. To this end we conducted a literature search to identify studies investigating early life exposures in relation to DNA methylation changes. In addition, we summarize the challenges faced in investigations of epigenetic effects, stemming from the peculiarities of this emergent and complex field. A proper systematic review and meta-analyses were not feasible given the nature of the evidence. RESULTS: We identified 7 studies on early life socioeconomic circumstances, 10 studies on childhood obesity, and 6 studies on early life nutrition all relating to DNA methylation changes that met the stipulated inclusion criteria. The pool of evidence gathered, albeit small, favours a role of epigenetics and DNA methylation in biological embedding, but replication of findings, multiple comparison corrections, publication bias, and causality are concerns remaining to be addressed in future investigations. CONCLUSIONS: Based on these results, we hypothesize that epigenetics, in particular DNA methylation, is a plausible mechanism through which early life exposures are biologically embedded. This review describes the current status of the field and acts as a stepping stone for future, better designed investigations on how early life exposures might become biologically embedded through epigenetic effects. This article is protected by copyright. All rights reserved.

Radiation induced apoptosis and initial DNA damage are inversely related in locally advanced breast cancer patients.

Background. DNA-damage assays, quantifying the initial number of DNA double-strand breaks induced by radiation, have been proposed as a predictive test for radiation-induced toxicity. Determination of radiation-induced apoptosis in peripheral blood lymphocytes by flow cytometry analysis has also been proposed as an approach for predicting normal tissue responses following radiotherapy. The aim of the present study was to explore the association between initial DNA damage, estimated by the number of double-strand breaks induced by a given radiation dose, and the radio-induced apoptosis rates observed. Methods. Peripheral blood lymphocytes were taken from 26 consecutive patients with locally advanced breast carcinoma. Radiosensitivity of lymphocytes was quantified as the initial number of DNA double-strand breaks induced per Gy and per DNA unit (200 Mbp). Radio-induced apoptosis at 1, 2 and 8 Gy was measured by flow cytometry using annexin V/propidium iodide. Results. Radiation-induced apoptosis increased in order to radiation dose and data fitted to a semi logarithmic mathematical model. A positive correlation was found among radio-induced apoptosis values at different radiation doses: 1, 2 and 8 Gy (p < 0.0001 in all cases). Mean DSB/Gy/DNA unit obtained was 1.70 ± 0.83 (range 0.63-4.08; median, 1.46). A statistically significant inverse correlation was found between initial damage to DNA and radio-induced apoptosis at 1 Gy (p = 0.034). A trend toward 2 Gy (p = 0.057) and 8 Gy (p = 0.067) was observed after 24 hours of incubation. Conclusions. An inverse association was observed for the first time between these variables, both considered as predictive factors to radiation toxicity.

The value of metabolic imaging to predict tumour response after chemoradiation in locally advanced rectal cancer

Background: We aim to investigate the possibility of using 18F-positron emission tomography/computer tomography (PET-CT) to predict the histopathologic response in locally advanced rectal cancer (LARC) treated with preoperative chemoradiation (CRT). Methods: The study included 50 patients with LARC treated with preoperative CRT. All patients were evaluated by PET-CT before and after CRT, and results were compared to histopathologic response quantified by tumour regression grade (patients with TRG 1-2 being defined as responders and patients with grade 3-5 as non-responders). Furthermore, the predictive value of metabolic imaging for pathologic complete response (ypCR) was investigated. Results: Responders and non-responders showed statistically significant differences according to Mandard's criteria for maximum standardized uptake value (SUVmax) before and after CRT with a specificity of 76,6% and a positive predictive value of 66,7%. Furthermore, SUVmax values after CRT were able to differentiate patients with ypCR with a sensitivity of 63% and a specificity of 74,4% (positive predictive value 41,2% and negative predictive value 87,9%); This rather low sensitivity and specificity determined that PET-CT was only able to distinguish 7 cases of ypCR from a total of 11 patients. Conclusions: We conclude that 18-F PET-CT performed five to seven weeks after the end of CRT can visualise functional tumour response in LARC. In contrast, metabolic imaging with 18-F PET-CT is not able to predict patients with ypCR accurately

Convex linear combination processes for compositions

Aitchison and Bacon-Shone (1999) considered convex linear combinations ofcompositions. In other words, they investigated compositions of compositions, wherethe mixing composition follows a logistic Normal distribution (or a perturbationprocess) and the compositions being mixed follow a logistic Normal distribution. Inthis paper, I investigate the extension to situations where the mixing compositionvaries with a number of dimensions. Examples would be where the mixingproportions vary with time or distance or a combination of the two. Practicalsituations include a river where the mixing proportions vary along the river, or acrossa lake and possibly with a time trend. This is illustrated with a dataset similar to thatused in the Aitchison and Bacon-Shone paper, which looked at how pollution in aloch depended on the pollution in the three rivers that feed the loch. Here, I explicitlymodel the variation in the linear combination across the loch, assuming that the meanof the logistic Normal distribution depends on the river flows and relative distancefrom the source origins