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Linearized (Schwarz) domain decomposition approaches for nonlinear boundary value problems of the form u '' = f(x, u, u'), subject to Dirichlet boundary conditions, are proposed and analyzed. In the presence of subsolutions and su...
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Linearized (Schwarz) domain decomposition approaches for nonlinear boundary value problems of the form u '' = f(x, u, u'), subject to Dirichlet boundary conditions, are proposed and analyzed. In the presence of subsolutions and supersolutions, we construct a globally convergent, linear, monotone iteration suitable for implementation in a distributed computing environment. These iterations provide an alternative to the typical, locally convergent, approach of discretizing and solving the resulting non-linear algebraic equations using a Newton iteration. The work also extends previous results obtained in the case where f has no dependence on the derivative of the solution. The Schwarz iteration is first proposed and studied in detail on two subdomains. The result is then generalized to an arbitrary number of subdomains. Both alternating and parallel Schwarz iterations are analyzed. Numerical results are provided to demonstrate the theory and the utility of the proposed iterations. (C) 2018 Elsevier B.V. All rights reserved.
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We study the eigenvalues of the MOTS stability operator for the Kerr black hole with angular momentum per unit mass vertical bar a vertical bar << M. We prove that each eigenvalue depends analytically on a (in a neighbourhood of a = 0), and compute its first nonvanishing derivative. Recalling that a = 0 corresponds to the Schwarzschild solution, where each eigenvalue has multiplicity 2l + 1, we find that this degeneracy is completely broken for nonzero a. In particular, for 0 < vertical bar a vertical bar << M we obtain a cluster consisting of l distinct complex conjugate pairs and one real eigenvalue. As a special case of our results, we get a simple formula for the variation of the principal eigenvalue. For perturbations that preserve the total area or mass of the black hole, we find that the principal eigenvalue has a local maximum at a = 0. However, there are other perturbations for which the principal eigenvalue has a local minimum at a = 0....
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We study the eigenvalues of the MOTS stability operator for the Kerr black hole with angular momentum per unit mass vertical bar a vertical bar << M. We prove that each eigenvalue depends analytically on a (in a neighbourhood of a = 0), and compute its first nonvanishing derivative. Recalling that a = 0 corresponds to the Schwarzschild solution, where each eigenvalue has multiplicity 2l + 1, we find that this degeneracy is completely broken for nonzero a. In particular, for 0 < vertical bar a vertical bar << M we obtain a cluster consisting of l distinct complex conjugate pairs and one real eigenvalue. As a special case of our results, we get a simple formula for the variation of the principal eigenvalue. For perturbations that preserve the total area or mass of the black hole, we find that the principal eigenvalue has a local maximum at a = 0. However, there are other perturbations for which the principal eigenvalue has a local minimum at a = 0.
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While the mimetic finite-difference method shares many similarities with the finite-element and finite-volume methods, it has the advantage of naturally accommodating grids with arbitrary polyhedral elements. In this study, we use...
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While the mimetic finite-difference method shares many similarities with the finite-element and finite-volume methods, it has the advantage of naturally accommodating grids with arbitrary polyhedral elements. In this study, we use this attribute to develop an adaptive scheme for the solution of the geophysical electromagnetic modelling problem on unstructured grids. Starting with an initial tetrahedral grid, our mesh adaptivity implements an iterative h-refinement where a residual- and jump-based goal-oriented error estimator is used to mark a certain portion of the elements. The marked elements are decomposed into new tetrahedra by regular subdivision, creating an octree-like unstructured grid. Since arbitrary polyhedra are naturally permitted in the mimetic finite-difference method, the added nodes are not regarded as hanging nodes and hence any level of non-conformity can be implemented without a modification to the mimetic scheme. In this study, we consider 2-irregularity where two levels of non-conformity between the adjacent elements is permitted. We use a total field approach where the electric field is defined at the edges of the polyhedral elements and the electromagnetic source may have an arbitrary shape and location. The accuracy of the mimetic scheme and the effectiveness of the proposed mesh adaptivity are verified using benchmark and realistic examples that represent various magnetotelluric and controlled-source survey scenarios. The mesh adaptivity generates grids with refinement generally concentrated at the transmitter and receiver locations and the interfaces of materials with contrasting conductivities, and the mimetic finite-difference solutions have good agreement with the reference numerical and real data. We also demonstrate the practicality of our method using an example with an analytical solution and comparison with a standard mesh regeneration technique. The results show that our mesh adaptivity procedure can result in a higher accuracy, with similar numbers of elements, when compared with the mesh regeneration approach. Also, using a generic sparse direct solver, our method is found to be more efficient than the mesh regeneration approach in terms of computation time and memory usage. Moreover, a comparison between 1- and 2-irregularity shows the higher efficiency of the latter in terms of the number of elements required to reach a certain level of accuracy.
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Binary dynamic fixed and mixed logit models are extensively studied in the literature. These models are developed to examine the effects of certain fixed covariates through a parametric regression function as a part of the models....
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Binary dynamic fixed and mixed logit models are extensively studied in the literature. These models are developed to examine the effects of certain fixed covariates through a parametric regression function as a part of the models. However, there are situations where one may like to consider more covariates in the model but their direct effect is not of interest. In this paper we propose a generalization of the existing binary dynamic logit (BDL) models to the semi-parametric longitudinal setup to address this issue of additional covariates. The regression function involved in such a semi-parametric BDL model contains (i) a parametric linear regression function in some primary covariates, and (ii) a non-parametric function in certain secondary covariates. We use a simple semi-parametric conditional quasi-likelihood approach for consistent estimation of the non-parametric function, and a semi-parametric likelihood approach for the joint estimation of the main regression and dynamic dependence parameters of the model. The finite sample performance of the estimation approaches is examined through a simulation study. The asymptotic properties of the estimators are also discussed. The proposed model and the estimation approaches are illustrated by reanalysing a longitudinal infectious disease data.
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Ranked set sampling (RSS) design as a cost-effective sampling is a powerful tool in situations where measuring the variable of interest is costly and time-consuming; however, ranking information about sampling units can be obtaine...
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Ranked set sampling (RSS) design as a cost-effective sampling is a powerful tool in situations where measuring the variable of interest is costly and time-consuming; however, ranking information about sampling units can be obtained easily through inexpensive and easy to measure characteristics at little or no cost. In this paper, we study RSS data for analysis of an ordinal population. First, we compare the problem of non-representative extreme samples under RSS and commonly-used simple random sampling. Using RSS data with tie information, we propose non-parametric and maximum likelihood estimators for population parameters. Through extensive numerical studies, we investigate the effect of various factors including ranking ability, tie generating mechanisms, the number of categories and population setting on the performance of the estimators. Finally, we apply the proposed methods to the bone disorder data to estimate the proportions of patients with osteopenia and osteoporosis status.
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Here, we demonstrate that the upregulation of catalase is required to compensate for the loss of nicotinamide nucleotide transhydrogenase (NNT) to maintain hydrogen peroxide (H2O2) steady-state levels in C57BL/6J liver mitochondri...
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Here, we demonstrate that the upregulation of catalase is required to compensate for the loss of nicotinamide nucleotide transhydrogenase (NNT) to maintain hydrogen peroxide (H2O2) steady-state levels in C57BL/6J liver mitochondria. Our investigations using the closely related mouse strains C57BL/6NJ (6NJ; +NNT) and C57BL/6J (6J; -NNT) revealed that NNT is required for the provision of NADPH and that the upregulation of isocitrate dehydrogenase-2 (IDH2) activity is not enough to compensate for the absence of NNT, which is consistent with previous observations. Intriguingly, despite the absence of NNT, 6J mitochondria had rates of H2O2 production (58.56 +/- 3.79 pmol mg(-1) min(-1)) that were similar to samples collected from 6NJ mice (72.75 +/- 14.26 pmol mg(-1) min(-1)) when pyruvate served as the substrate. However, 6NJ mitochondria energized with succinate produced significantly less H2O2 (59.95 +/- 2.13 pmol mg(-1) min(-1)) when compared to samples from 6J mice (116.39 +/- 20.74 pmol mg(-1) min(-1)), an effect that was attributed to the presence of NNT. Further investigations into the H2O2 eliminating capacities of these mitochondria led to the novel observation that 6J mitochondria compensate for the loss of NNT by upregulating catalase. Indeed, 6NJ and 6J mitochondria energized with pyruvate or succinate displayed similar rates for H2O2 elimination, quenching similar to 84% and similar to 86% of the H2O2, respectively, in the surrounding medium within 30 s. However, inclusion of palmitoyl-CoA, an NNT inhibitor, significantly limited H2O2 degradation by 6NJ mitochondria only (similar to 55% of H2O2 eliminated in 30 s). Liver mitochondria from 6J mice treated with palmitoyl-CoA still cleared similar to 80% of the H2O2 from the surrounding environment. Inhibition of catalase with triazole compromised the capacity of 6J mitochondria to maintain H2O2 steady-state levels. By contrast, disabling NADPH-dependent antioxidant systems had a limited effect on the H2O2 clearing capacity of 6J mitochondria. Liver mitochondria collected from 6NJ mice, on the other hand, were more reliant on the GSH and TRX systems to clear exogenously added H2O2. However, catalase still played an integral in eliminating H2O2 in 6NJ liver mitochondria. Immunoblot analyses demonstrated that catalase protein levels were similar to 7.7-fold higher in 6J mitochondria. Collectively, our findings demonstrate for the first time that 6J liver mitochondria compensate for the loss of NNT by increasing catalase levels for the maintenance of H2O2 steady-state levels. In general, our observations reveal that catalase is an integral arm of the antioxidant response in liver mitochondria.
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We classify gradings by arbitrary abelian groups on the classical simple Lie and Jordan superalgebras Q(n), n >= 2, over an algebraically closed field of characteristic different from 2 (and not dividing n+1 in the Lie case): Fine...
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We classify gradings by arbitrary abelian groups on the classical simple Lie and Jordan superalgebras Q(n), n >= 2, over an algebraically closed field of characteristic different from 2 (and not dividing n+1 in the Lie case): Fine gradings up to equivalence and G-gradings, for a fixed group G, up to isomorphism.
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In traditional edge searching one tries to clean all of the edges in a graph employing the least number of searchers. It is assumed that each edge of the graph initially has a weight equal to one. In this paper we modify the probl...
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In traditional edge searching one tries to clean all of the edges in a graph employing the least number of searchers. It is assumed that each edge of the graph initially has a weight equal to one. In this paper we modify the problem and introduce the Weighted Edge Searching Problem by considering graphs with arbitrary positive integer weights assigned to its edges. We give bounds on the weighted search number in terms of related graph parameters including pathwidth. We characterize the graphs for which two searchers are sufficient to clear all edges. We show that for every weighted graph the minimum number of searchers needed for a not-necessarily-monotonic weighted edge search strategy is enough for a monotonic weighted edge search strategy, where each edge is cleaned only once. This result proves the NP-completeness of the problem. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.
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Purpose To examine local practice for non-malignant polyps and to calculate morbidity and mortality associated with bowel resection for this indication. Methods This retrospective cohort study was conducted by reviewing our local ...
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Purpose To examine local practice for non-malignant polyps and to calculate morbidity and mortality associated with bowel resection for this indication. Methods This retrospective cohort study was conducted by reviewing our local gastrointestinal pathology database over a five-year period to identify colonic resections performed for benign polyps. Using search terms "polyp" and "adenoma," 272 cases were identified. Exclusion criteria included: cancer diagnosis, emergency surgeries, multiple resections, and subtotal colectomies for polyposis. 106 patients were included in the study. Primary outcome was perioperative mortality. Secondary outcomes included patient morbidity, characteristics of polyps requiring surgery, and the number of patients referred for a second endoscopic opinion prior to proceeding with surgery. Results 64 male and 42 female patients with a mean age of 65.3 years (+/- 8.6 years) underwent colon resection for benign polyps. The mean polyp size was 32.7 mm (+/- 19.5 mm). 30 patients (28.6%) had polyps equal to or less than 2 cm. Most of the polyps described were sessile (n = 55, 51.9%) and located in the right colon (n = 84, 79.3%). Endoscopic resection was attempted in 31 patients (29.2%), and five cases (4.7%) were referred for a second endoscopic opinion prior to proceeding with surgery. Endoscopists incorrectly felt that polyps were malignant in 62 cases (58.5%). Using Clavien-Dindo classification, most patients had no complications n = 36 (34.0%) or minor complications n = 41 (38.7%). Twelve patients (11.3%) had complications that required antibiotics, blood transfusions, or total parental nutrition. Nine patients (8.5%) required surgical or endoscopic management. Six patients (5.7%) required ICU admission. Mortality rate was 1.9% (n = 2). Conclusion Surgery for benign colonic polyps is associated with significant morbidity and mortality. These findings reveal a gap in endoscopic management of benign colonic polyps.
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Probabilistic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The domain is split into non-overlapping sub-domains and the solution on t...
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Probabilistic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The domain is split into non-overlapping sub-domains and the solution on the sub-domain boundaries is obtained by evaluating the stochastic form of the exact solution of Maxwell's equations by a Monte-Carlo approach. These sub-domains can be naturally chosen by splitting the sub-surface domain into regions of constant (or at least continuous) conductivity. The solution over each sub-domain is obtained by solving Maxwell's equations in the strong form. The sub-domain solver used for this purpose is a meshless method resting on radial basis function-based finite differences. The method is demonstrated by solving a number of classical magnetotelluric problems, including the quarter-space problem, the block-in-half-space problem and the triangle-in-half-space problem.
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