1,572 research outputs found

    On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

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    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 ξk+1\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 ξk+1ξ\xi_{k+1}\leq\xi with a constant ξ1\xi\geq 1. The method is guaranteed to converge linearly provided that ξk+1\xi_{k+1} is bounded by a small multiple of the reciprocal of the residual norm rk\|r_k\| of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require ξk+1<1\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 ξk+1\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

    Molecular profiles of BRCA1-mutated and matched sporadic breast tumours: relation with clinico-pathological features

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    About 5–10% of breast cancers are hereditary; a genetically and clinically heterogeneous disease in which several susceptibility genes, including BRCA1, have been identified. While distinct tumour features can be used to estimate the likelihood that a breast tumour is caused by a BRCA1 germline mutation it is not yet possible to categorize a BRCA1 mutated tumour. The aim of the present study is to molecularly classify BRCA1 mutated breast cancers by resolving gene expression patterns of BRCA1 and matched sporadic surgical breast tumour specimens. The expression profiles of 6 frozen breast tumour tissues with a proven BRCA1 gene mutation were weighed against those from 12 patients without a known family history but who had similar clinico-pathological characteristics. In addition two fibroblast cultures, the breast cancer cell-line HCC1937 and its corresponding B-lymphoblastoid cell line (heterozygous for mutation BRCA1 5382insC) and an epithelial ovarian cancer cell line (A2780) were studied. Using a high density membrane based array for screening of RNA isolated from these samples and standard algorithms and software, we were able to distinguish subgroups of sporadic cases and a group consisting mainly of BRCA1-mutated breast tumours. Furthermore this pilot analysis revealed a gene cluster that differentially expressed genes related to cell substrate formation, adhesion, migration and cell organization in BRCA1-mutated tumours compared to sporadic breast tumours. © 2001 Cancer Research Campaign http://www.bjcancer.co

    Motor Preparatory Activity in Posterior Parietal Cortex is Modulated by Subjective Absolute Value

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    For optimal response selection, the consequences associated with behavioral success or failure must be appraised. To determine how monetary consequences influence the neural representations of motor preparation, human brain activity was scanned with fMRI while subjects performed a complex spatial visuomotor task. At the beginning of each trial, reward context cues indicated the potential gain and loss imposed for correct or incorrect trial completion. FMRI-activity in canonical reward structures reflected the expected value related to the context. In contrast, motor preparatory activity in posterior parietal and premotor cortex peaked in high “absolute value” (high gain or loss) conditions: being highest for large gains in subjects who believed they performed well while being highest for large losses in those who believed they performed poorly. These results suggest that the neural activity preceding goal-directed actions incorporates the absolute value of that action, predicated upon subjective, rather than objective, estimates of one's performance

    Advances in multispectral and hyperspectral imaging for archaeology and art conservation

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    Multispectral imaging has been applied to the field of art conservation and art history since the early 1990s. It is attractive as a noninvasive imaging technique because it is fast and hence capable of imaging large areas of an object giving both spatial and spectral information. This paper gives an overview of the different instrumental designs, image processing techniques and various applications of multispectral and hyperspectral imaging to art conservation, art history and archaeology. Recent advances in the development of remote and versatile multispectral and hyperspectral imaging as well as techniques in pigment identification will be presented. Future prospects including combination of spectral imaging with other noninvasive imaging and analytical techniques will be discussed
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