Velocity Estimation in Mixtures using Tomography

In oil production a lot of water is usually pumped up together with the oil. For many reasons the reduction of the water production is a very important issue. The method presented in this paper is meant to provide a necessary tool for this. Most drilling wells consist of a network of bore holes. Some of them may produce water, others oil or a mixture. At the moment the net flow of all bore holes together is brought to the surface. It is desirable to be able to detect how much water a specific bore hole contributes. If this amount surpasses a critical value one could then consider to close that bore hole. This leads to the question how the composition of the flow in a pipe can be determined in situ. In this paper we analyze how tomography techniques, well-known from medical applications, can be applied in the case of a bore hole. These techniques allow to measure instantaneously the mass distribution over a cross section of the pipe. For velocity estimation, the idea is to detect the mass distributions at two neighbouring cross sections at successive times. Correlating the obtained time series, one might be able to estimate the local velocity profile. The basic idea was already mentioned in literature before, but it was believed that the number of correlations to be evaluated is so huge, that the approach would fail in practice. In this paper we describe the mathematical details of the method and conclude that the number of time consuming calculations is not necessarily a limiting factor. In addition, suggestions are made to facilitate the use of tomography for velocity estimation

Multidirectional Subspace Expansion for One-Parameter and Multiparameter Tikhonov Regularization

Tikhonov regularization is a popular method to approximate solutions of linear discrete ill-posed problems when the observed or measured data is contaminated by noise. Multiparameter Tikhonov regularization may improve the quality of the computed approximate solutions. We propose a new iterative method for large-scale multiparameter Tikhonov regularization with general regularization operators based on a multidirectional subspace expansion. The multidirectional subspace expansion may be combined with subspace truncation to avoid excessive growth of the search space. Furthermore, we introduce a simple and effective parameter selection strategy based on the discrepancy principle and related to perturbation results

A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc

In the context of large-scale eigenvalue problems, methods of Davidson type such as Jacobi-Davidson can be competitive with respect to other types of algorithms, especially in some particularly difficult situations such as computing interior eigenvalues or when matrix factorization is prohibitive or highly inefficient. However, these types of methods are not generally available in the form of high-quality parallel implementations, especially for the case of non-Hermitian eigenproblems. We present our implementation of various Davidson-type methods in SLEPc, the Scalable Library for Eigenvalue Problem Computations. The solvers incorporate many algorithmic variants for subspace expansion and extraction, and cover a wide range of eigenproblems including standard and generalized, Hermitian and non-Hermitian, with either real or complex arithmetic. We provide performance results on a large battery of test problems.This work was supported by the Spanish Ministerio de Ciencia e Innovacion under project TIN2009-07519. Author's addresses: E. Romero, Institut I3M, Universitat Politecnica de Valencia, Cami de Vera s/n, 46022 Valencia, Spain), and J. E. Roman, Departament de Sistemes Informatics i Computacio, Universitat Politecnica de Valencia, Cami de Vera s/n, 46022 Valencia, Spain; email: [email protected] Alcalde, E.; Román Moltó, JE. (2014). A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc. ACM Transactions on Mathematical Software. 40(2):13:01-13:29. https://doi.org/10.1145/2543696S13:0113:29402P. Arbenz, M. Becka, R. Geus, U. Hetmaniuk, and T. Mengotti. 2006. On a parallel multilevel preconditioned Maxwell eigensolver. Parallel Comput. 32, 2, 157--165.Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Eds. 2000. 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On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Chromothripsis in healthy individuals affects multiple protein-coding genes and can result in severe congenital abnormalities in offspring

Chromothripsis represents an extreme class of complex chromosome rearrangements (CCRs) with major effects on chromosomal architecture. Although recent studies have associated chromothripsis with congenital abnormalities, the incidence and pathogenic effects of this phenomenon require further investigation. Here, we analyzed the genomes of three families in which chromothripsis rearrangements were transmitted from a mother to her child. The chromothripsis in the mothers resulted in completely balanced rearrangements involving 8-23 breakpoint junctions across three to five chromosomes. Two mothers did not show any phenotypic abnormalities, although 3-13 protein-coding genes were affected by breakpoints. Unbalanced but stable transmission of a subset of the derivative chromosomes caused apparently de novo complex copy-number changes in two children. This resulted in gene-dosage changes, which are probably responsible for the severe congenital phenotypes of these two children. In contrast, the third child, who has a severe congenital disease, harbored all three chromothripsis chromosomes from his healthy mother, but one of the chromosomes acquired de novo rearrangements leading to copy-number changes. These results show that the human genome can tolerate extreme reshuffling of chromosomal architecture, including breakage of multiple protein-coding genes, without noticeable phenotypic effects. The presence of chromothripsis in healthy individuals affects reproduction and is expected to substantially increase the risk of miscarriages, abortions, and severe congenital disease. © 2015 The American Society of Human Genetics

Measuring well-being in aphasia: The GHQ-28 versus the NHP

This study aimed to get the opinions of people with aphasia on two subjective well-being measures: the General Health Questionnaire 28-item version (GHQ-28) (Goldberg & Hillier, 1979) and the Nottingham Health Profile (NHP) (Hunt, McKenna, McEwen, Williams, & Papp, 1981). Twelve persons with moderate to mild aphasia of at least 2-years duration completed the GHQ-28 and the NHP. In a semistructured intenriew, they gave their feedback on the two questionnaires. All participants were able to complete both instruments. Nine out of 12 participants showed high psychological distress (> 5/28) in the GHQ-28. The NHP (part 1 less the physical abilities section) had a correlation of 0.78 (p < .01) with the GHQ-28. The social dysfunction subscale of the NHP identified more problems in the participants with aphasia than the social isolation subscale of the GHQ-28. The majority of the participants (10 out of 12) preferred the NHP, as they found it easier to understand and respond to. This small-scale study indicated that both the GHQ-28 and the NHP can be administered to people with moderate to mild aphasia and provide useful information on their well-being. Participants reported that the NHP was easier to do, and it asked questions more relevant to their situation