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

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

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

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

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Elevated blood lead levels are associated with reduced risk of malaria in Beninese infants

Introduction Elevated blood lead levels (BLL) and malaria carry an important burden of disease in West Africa. Both diseases might cause anemia and they might entail long-term consequences for the development and the health status of the child. Albeit the significant impact of malaria on lead levels described in Nigeria, no evaluation of the effect of elevated BLL on malaria risk has been investigated so far. Materials and Methods Between 2010 and 2012, blood lead levels of 203 Beninese infants from Allada, a semi-rural area 50km North from Cotonou, were assessed at 12 months of age. To assess lead levels, blood samples were analyzed by mass spectrometry. In parallel, clinical, microbiological and hematological data were collected. More precisely, hemoglobin, serum ferritin, CRP, vitamin B12, folate levels, and Plasmodium falciparum parasitemia were assessed and stool samples were also analyzed. Results At 12 months, the mean BLL of infants was 7.41 μg/dL (CI: 65.2; 83), and 128 infants (63%) had elevated blood lead levels, defined by the CDC as BLL>5 μg/dL. Lead poisoning, defined as BLL>10 μg/dL, was found in 39 infants (19%). Twenty-five infants (12.5%) had a positive blood smear at 12 months and 144 infants were anemic (71%, hemoglobin<110 g/L). Elevated blood lead levels were significantly associated with reduced risk of a positive blood smear (AOR = 0.38, P-value = 0.048) and P. falciparum parasite density (beta-estimate = -1.42, P-value = 0.03) in logistic and negative binomial regression multivariate models, respectively, adjusted on clinical and environmental indicators. Conclusion Our study shows for the first time that BLL are negatively associated with malarial risk considering other risk factors. Malaria is one of the main causes of morbidity and mortality in infants under 5 years worldwide, and lead poisoning is the 6th most important contributor to the global burden of diseases measured in disability adjusted life years (DALYs) according to the Institute of Health Metrics. In conclusion, due to the high prevalence of elevated BLL, health interventions should look forward to minimize the exposure to lead to better protect the population in West Africa

Cetuximab plus platinum-based chemotherapy in head and neck Squamous Cell Carcinoma: a retrospective study in a single Comprehensive European Cancer Institution

Background: The use of cetuximab in combination with platinum (P) plus 5-fluorouracil (F) has previously been demonstrated to be effective in the treatment of metastatic squamous cell cancer of head and neck (SCCHN). We investigated the efficacy and outcome of this protocol as a first-line treatment for patients with recurrent or metastatic disease. We evaluated overall-survival (OS), progression-free-survival (PFS), overall response rate (ORR) and the treatment toxicity profile in a retrospective cohort. Patients and Methods: This study enrolled 121 patients with untreated recurrent or metastatic SCCHN. The patients received PF+ cetuximab every 3 weeks for a maximum of 6 cycles. Patients with stable disease who received PF+ cetuximab continued to receive cetuximab until disease progressed or unacceptable toxic effects were experienced, whichever occurred first. Results: The median patient age was 53 (37-78) years. The patient cohort was 86.8% male. The addition of cetuximab to PF in the recurrent or metastatic setting provided an OS of 11 months (Confidential Interval, CI, 95%, 8.684-13.316) and PFS of 8 months (CI 95%, 6.051-9.949). The disease control rate was 48.9%, and the ORR was 23.91%. The most common grade 3 or 4 adverse events in the PF+ cetuximab regimen were febrile neutropenia (5.7%), skin rash (3.8%) and mucosistis (3.8%). Conclusions: The results of this study suggest that cetuximab plus platinum-fluorouracil chemotherapy is a good option for systemic treatment in advanced SSCHN patients. This regimen has a well-tolerated toxicity profile.info:eu-repo/semantics/publishedVersio