Low-rank approximation in the Frobenius norm by column and row subset selection

A CUR approximation of a matrix A is a particular type of low-rank approximation A approx CUR, where C and R consist of columns and rows of A, respectively. One way to obtain such an approximation is to apply column subset selection to A and AT . In this work, we describe a numerically robust and much faster variant of the column subset selection algorithm proposed by Deshpande and Rademacher, which guarantees an error close to the best approximation error in the Frobenius norm. For cross approximation, in which U is required to be the inverse of a submatrix of A described by the intersection of C and R, we obtain a new algorithm with an error bound that stays within a factor k + 1 of the best rank-k approximation error in the Frobenius norm. To the best of our knowledge, this is the first deterministic polynomial-time algorithm for which this factor is bounded by a polynomial in k. Our derivation and analysis of the algorithm is based on derandomizing a recent existence result by Zamarashkin and Osinsky. To illustrate the versatility of our new column subset selection algorithm, an extension to low multilinear rank approximations of tensors is provided as well. © 2020 Society for Industrial and Applied Mathematics

On randomized trace estimates for indefinite matrices with an application to determinants

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of xTBx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number of applications give rise to indefinite B. Most notably, this is the case for log-determinant estimation, a task that features prominently in statistical learning, for instance in maximum likelihood estimation for Gaussian process regression. The analysis of randomized trace estimates, including tail bounds, has mostly focused on the SPD case. In this work, we derive new tail bounds for randomized trace estimates applied to indefinite B with Rademacher or Gaussian random vectors. These bounds significantly improve existing results for indefinite B, reducing the number of required samples by a factor n or even more, where n is the size of B. Even for an SPD matrix, our work improves an existing result by Roosta-Khorasani and Ascher (Found Comput Math, 15(5):1187–1212, 2015) for Rademacher vectors. This work also analyzes the combination of randomized trace estimates with the Lanczos method for approximating the trace of f(B). Particular attention is paid to the matrix logarithm, which is needed for log-determinant estimation. We improve and extend an existing result, to not only cover Rademacher but also Gaussian random vectors

Model Predictive Anti-Surge Control of Centrifugal Compressors with Variable-Speed Drives

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Low-rank updates of matrix functions II: Rational Krylov methods

This work develops novel rational Krylov methods for updating a large-scale matrix function ƒ(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified convergence analysis. For the rational case, our convergence analysis is based on an exactness result that is connected to work by Bernstein and Van Loan on rank-one updates of rational matrix functions. We demonstrate the usefulness of the derived error bounds for guiding the choice of poles in the rational Krylov method for the exponential function and Markov functions. Low-rank updates of the matrix sign function require additional attention; we develop and analyze a combination of our methods with a squaring trick for this purpose. A curious connection between such updates and existing rational Krylov subspace methods for Sylvester matrix equations is pointed out

Reproducibility of the WHO histological criteria for the diagnosis of Philadelphia chromosome-negative myeloproliferative neoplasms.

This study, performed on behalf of the Italian Registry of Thrombocythaemias (Registro Italiano Trombocitemie), aimed to test the inter-observer reproducibility of the histological parameters proposed by the WHO classification for the diagnosis of the Philadelphia chromosome-negative myeloproliferative neoplasms. A series of 103 bone marrow biopsy samples of Philadelphia chromosome-negative myeloproliferative neoplasms consecutively collected in 2004 were classified according to the WHO criteria as follows: essential thrombocythaemia (n=34), primary myelofibrosis (n=44) and polycythaemia vera (n=25). Two independent groups of pathologists reviewed the bone marrow biopsies. The first group was asked to reach a collegial 'consensus' diagnosis. The second group reviewed individually all the cases to recognize the main morphological parameters indicated by the WHO classification and report their results in a database. They were subsequently instructed to individually build a 'personal' diagnosis of myeloproliferative neoplasms subtype just assembling the parameters collected in the database. Our results indicate that high levels of agreement ( 6570%) have been reached for about all of the morphological features. Moreover, among the 18 evaluated histological features, 11 resulted statistically more useful for the differential diagnosis among the different Philadelphia chromosome-negative myeloproliferative neoplasms. Finally, we found a high percentage of agreement (76%) between the 'personal' and 'consensus' diagnosis (Cohen's kappa statistic >0.40). In conclusion, our results support the use of the histological criteria proposed by the WHO classification for the Philadelphia chromosome-negative myeloproliferative neoplasms to ensure a more precise and early diagnosis for these patients

1472pimmunotherapy in elderly patients 75 yrs with advanced non small cell lung cancer nsclc a multicenter italian experience

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Pemetrexed plus carboplatin in elderly patients with malignant pleural mesothelioma: combined analysis of two phase II trials

The incidence of malignant pleural mesothelioma (MPM) in elderly patients is increasing. In this study, pooled data from two phase II trials of pemetrexed and carboplatin (PC) as first-line therapy were retrospectively analysed for comparisons between age groups. Patients received pemetrexed 500 mg m−2 and carboplatin AUC 5 mg ml−1 min−1 intravenously every 21 days with standard vitamin supplementation. Elderly patients were defined as those ⩾70 years old. A total of 178 patients with an ECOG performance status of ⩽2 were included. Median age was 65 years (range 38–79), with 48 patients ⩾70 years (27%). Grade 3–4 haematological toxicity was slightly worse in ⩾70 vs <70-year-old patients, with neutropenia observed in 25.0 vs 13.8% (P=0.11), anaemia in 20.8 vs 6.9% (P=0.01) and thrombocytopenia in 14.6 vs 8.5% (P=0.26). Non-haematological toxicity was mild and similar in the two groups. No significant difference was observed in terms of overall disease control (60.4 vs 66.9%, P=0.47), time to progression (7.2 vs 7.5 months, P=0.42) and survival (10.7 vs 13.9 months, P=0.12). Apart from slightly worse haematological toxicity, there was no significant difference in outcome or toxicity between age groups. The PC regimen is effective and well tolerated in selected elderly patients with MPM

Verbal task and motor responses (VTMR) in an adult hearing screening programme

The aim of this study was to test the efficacy of Verbal Tasks and Motor Responses (VTMR) speech audiometry in providing a rapid and true-to-life assessment of hearing-related problems as a single test in adult hearing screening programmes. The VTMR consists in manual execution of 5 verbal commands received by patients at different signal intensity levels and fixed masking noise; it provides a score of speech comprehension in noise. This was a prospective observational study in 916 individuals out of 1,300 volunteers (605 males, 695 females, aged 56 \ub1 17 years) who completed adult hearing screening. VTMR speech audiometry was performed at signal to noise (S/N) ratios of 0 dB and \u201310 dB. The difference between normal and hearing impaired subjects in terms of all the considered variables was statistically significant for pure-tone audiometry and VTMR testing. VTMR testing at a S/N ratio of \u201310 dB with a cut-off of four correctly executed tasks and was a rapid, feasible and efficient means of differentiating between normal and hearing impaired subjects. When used to screen hearing impaired subjects with participation restrictions, the sensitivity and specificity of the VTMR test rose to 90% and 62%, respectively. The VTMR test in noise could be used as a stand-alone tool when screening for impairment and self-perceived participation restriction together