Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Quadratic Mean Radius of a Polynomial in C(Z)

* Dedicated to the memory of Prof. N. Obreshkoff

A Model for Bundled Conductors considering a Non-Homogeneous Distribution of the Current through Subconductors

This paper describes an alternative procedure to obtain an equivalent conductor from a bundled conductor, taking into account the distribution of the current in subcondutors of the bundle. Firstly, it is introduced a brief background about the concept of Geometric Mean Radius (GMR) and how this methodology is applied to define an equivalent conductor and its electric parameters. Emphasizing that the classical procedure, using GMR, is limited to premise which the current is equally distributed through subconductors. Afterwards, it is described the development of proposed method and applications for an equivalent conductor obtained from a conventional transmission line bundled conductor and from an equivalent conductor based on a bundle with compressed SF(6) insulation system, where the current is unequally distributed through subconductors.

Características dos parâmetros do condutor equivalente a um feixe de subcondutores de linhas de transmissão: análise inicial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um modelo para condutores múltiplos considerando a distribuição da corrente nos subcondutores

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

On the development of summer thunderstorms in the city of Sao Paulo: Mean meteorological characteristics and pollution effect

This study investigates how the summer thunderstorms developed over the city of Sao Paulo and if the pollution might affect its development or characteristics during the austral summer (December-January-February-March, DJFM months). A total of 605 days from December 1999 to March 2004 was separated as 241 thunderstorms days (TDs) and 364 non-thunderstorm days (NTDs). The analyses are performed by using hourly measurements of air temperature (T), web-bulb temperature (Tw), surface atmospheric pressure (P), wind velocity and direction, rainfall and thunder and lightning observations collected at the Meteorological Station of the University of Sao Paulo in conjunction with aerosol measurements obtained by AERONET (Aerosol Robotic Network), and the NCEP-DOE (National Centers for Environmental Prediction Department of Energy) reanalysis and radiosondes. The wind diurnal cycle shows that for TDs the morning flow is from the northwest rotating to the southeast after 16: 00 local time (LT) and it remains from the east until the night. For the NTDs, the wind is well characterized by the sea-breeze circulation that in the morning has the wind blowing from the northeast and in the afternoon from the southeast. The TDs show that the air temperature diurnal cycle presents higher amplitude and the maximum temperature of the day is 3.2 degrees C higher than in NTDs. Another important factor found is the difference between moisture that is higher during TDs. In terms of precipitation, the TDs represent 40% of total of days analyzed and those days are responsible for more than 60% of the total rain accumulation during the summer, for instance 50% of the TDs had more than 15.5mm day(-1) while the NTDs had 4 mm day(-1). Moreover, the rainfall distribution shows that TDs have higher rainfall rate intensities and an afternoon precipitation maximum; while in the NTDs there isn`t a defined precipitation diurnal cycle. The wind and temperature fields from NCEP reanalysis concur with the local weather station and radiosonde observations. The NCEP composites show that TDs are controlled by synoptic circulation characterized by a pre-frontal situation, with a baroclinic zone situated at southern part of Sao Paulo. In terms of pollution, this study employed the AERONET data to obtain the main aerosol characteristics in the atmospheric column for both TDs and NTDs. The particle size distribution and particle volume size distribution have similar concentrations for both TDs and NTDs and present a similar fine and coarse mode mean radius. In respect to the atmospheric loading, the aerosol optical depth (AOD) at different frequencies presented closed mean values for both TDs and NTDs that were statistically significant at 95% level. The spectral dependency of those values in conjunction with the Angstrom parameter reveal the higher concentration of the fine mode particles that are more likely to be hygroscopic and from urban areas. In summary, no significant aerosol effect could be found on the development of summer thunderstorms, suggesting the strong synoptic control by the baroclinic forcing for deep convective development. (C) 2010 Published by Elsevier B. V.

Propylthiouracil Quantification In Human Plasma By High-performance Liquid Chromatography Coupled With Electrospray Tandem Mass Spectrometry: Application In A Bioequivalence Study.

A rapid, sensitive and specific method for quantifying propylthiouracil in human plasma using methylthiouracil as the internal standard (IS) is described. The analyte and the IS were extracted from plasma by liquid-liquid extraction using an organic solvent (ethyl acetate). The extracts were analyzed by high performance liquid chromatography coupled with electrospray tandem mass spectrometry (HPLC-MS/MS) in negative mode (ES-). Chromatography was performed using a Phenomenex Gemini C18 5μm analytical column (4.6mm×150mm i.d.) and a mobile phase consisting of methanol/water/acetonitrile (40/40/20, v/v/v)+0.1% of formic acid. For propylthiouracil and I.S., the optimized parameters of the declustering potential, collision energy and collision exit potential were -60 (V), -26 (eV) and -5 (V), respectively. The method had a chromatographic run time of 2.5min and a linear calibration curve over the range 20-5000ng/mL. The limit of quantification was 20ng/mL. The stability tests indicated no significant degradation. This HPLC-MS/MS procedure was used to assess the bioequivalence of two propylthiouracil 100mg tablet formulations in healthy volunteers of both sexes in fasted and fed state. The geometric mean and 90% confidence interval CI of Test/Reference percent ratios were, without and with food, respectively: 109.28% (103.63-115.25%) and 115.60% (109.03-122.58%) for Cmax, 103.31% (100.74-105.96%) and 103.40% (101.03-105.84) for AUClast. This method offers advantages over those previously reported, in terms of both a simple liquid-liquid extraction without clean-up procedures, as well as a faster run time (2.5min). The LOQ of 20ng/mL is well suited for pharmacokinetic studies. The assay performance results indicate that the method is precise and accurate enough for the routine determination of the propylthiouracil in human plasma. The test formulation with and without food was bioequivalent to reference formulation. Food administration increased the Tmax and decreased the bioavailability (Cmax and AUC).

Observations on Haemagogus janthinomys Dyar (Diptera: Culicidae) and other mosquito populations within tree holes in a gallery forest in the northwestern region of Sao Paulo state, Brazil

In 2000, an outbreak of sylvatic yellow fever possibly occurred in gallery forests of the Grande river in the Paraná basin in the northwestern region of São Paulo state. The aim of this study was to obtain information on the bionomics of Haemagogus and other mosquitoes inside tree holes in that area. Eighteen open tree holes were sampled for immature specimens. Adults were collected twice a month in the forest in Santa Albertina county from July 2000 to June 2001. The seasonal frequency of fourth instars was obtained by the Williams geometric mean (Mw), while the adult frequency was estimated either by hourly arithmetic or the Williams' means. Cole's index was applied to evaluate larval inter-specific associations. Among the ten mosquito species identified, the most abundant was Aedes terrens Walker followed by Sabethes tridentatus Cerqueira and Haemagogus janthinomys Dyar. Larval and adult abundance of these species was higher in summer than in winter. Although larval abundance of Hg. janthinomys peaked in the rainy season, correlation with rainfall was not significant. Six groups of larval associations were distinguished, one of which the most positively stable. The Hg. janthinomys and Ae. terrens association was significant, and Limatus durhamii Theobald was the species with most negative associations.

Immunogenicity of a Whole-Cell Pertussis Vaccine with Low Lipopolysaccharide Content in Infants

The lack of a clear correlation between the levels of antibody to pertussis antigens and protection against disease lends credence to the possibility that cell-mediated immunity provides primary protection against disease. This phase I comparative trial had the aim of comparing the in vitro cellular immune response and anti-pertussis toxin (anti-PT) immunoglobulin G (IgG) titers induced by a cellular pertussis vaccine with low lipopolysaccharide (LPS) content (wP(low) vaccine) with those induced by the conventional whole-cell pertussis (wP) vaccine. A total of 234 infants were vaccinated at 2, 4, and 6 months with the conventional wP vaccine or the wP(low) vaccine. Proliferation of CD3(+) T cells was evaluated by flow cytometry after 6 days of peripheral blood mononuclear cell culture with stimulation with heat-killed Bordetella pertussis or phytohemagglutinin (PHA). CD3(+), CD4(+), CD8(+), and T-cell receptor gamma delta-positive (gamma delta(+)) cells were identified in the gate of blast lymphocytes. Gamma interferon, tumor necrosis factor alpha, interleukin-4 (IL-4), and IL-10 levels in super-natants and serum anti-PT IgG levels were determined using enzyme-linked immunosorbent assay (ELISA). The net percentage of CD3(+) blasts in cultures with B. pertussis in the group vaccinated with wP was higher than that in the group vaccinated with the wP(low) vaccine (medians of 6.2% for the wP vaccine and 3.9% for the wP(low) vaccine; P = 0.029). The frequencies of proliferating CD4(+), CD8(+), and gamma delta(+) cells, cytokine concentrations in supernatants, and the geometric mean titers of anti-PT IgG were similar for the two vaccination groups. There was a significant difference between the T-cell subpopulations for B. pertussis and PHA cultures, with a higher percentage of gamma delta(+) cells in the B. pertussis cultures (P < 0.001). The overall data did suggest that wP vaccination resulted in modestly better specific CD3(+) cell proliferation, and gamma delta(+) cell expansions were similar with the two vaccines.

Perioperative epidural analgesia and outcome after major abdominal surgery in high-risk patients

In a primary analysis of a large recently completed randomized trial in 915 high-risk patients undergoing major abdominal surgery, we found no difference in outcome between patients receiving perioperative epidural analgesia and those receiving IV opioids, apart from the incidence of respiratory failure. Therefore, we performed a selected number of predetermined subgroup analyses to identify specific types of patients who may have derived benefit from epidural analgesia. We found no difference in outcome between epidural and control groups in subgroups at increased risk of respiratory or cardiac complications or undergoing aortic surgery, nor in a subgroup with failed epidural block (all P > 0.05). There was a small reduction in the duration of postoperative ventilation (geometric mean [SD]: control group, 0.3 [6.5] h, versus epidural group, 0.2 [4.8] h, P = 0.048). No differences were found in length of stay in intensive care or in the hospital. There was no relationship between frequency of use of epidural analgesia in routine practice outside the trial and benefit from epidural analgesia in the trial. We found no evidence that perioperative epidural analgesia significantly influences major morbidity or mortality after major abdominal surgery.

Immunogenicity and safety of the 2009 non-adjuvanted influenza A/H1N1 vaccine in a large cohort of autoimmune rheumatic diseases

Background Despite the WHO recommendation that the 2010-2011 trivalent seasonal flu vaccine must contain A/California/7/2009/H1N1-like virus there is no consistent data regarding its immunogenicity and safety in a large autoimmune rheumatic disease (ARD) population. Methods 1668 ARD patients (systemic lupus erythematosus (SLE), rheumatoid arthritis (RA), ankylosing spondylitis (AS), systemic sclerosis, psoriatic arthritis (PsA), Behcet`s disease (BD), mixed connective tissue disease, primary antiphospholipid syndrome (PAPS), dermatomyositis (DM), primary Sjogren`s syndrome, Takayasu`s arteritis, polymyositis and Granulomatosis with polyangiitis (Wegener`s) (GPA)) and 234 healthy controls were vaccinated with a non-adjuvanted influenza A/California/7/2009(H1N1) virus-like strain flu. Subjects were evaluated before vaccination and 21 days post-vaccination. The percentage of seroprotection, seroconversion and the factor increase in geometric mean titre (GMT) were calculated. Results After immunisation, seroprotection rates (68.5% vs 82.9% p < 0.0001), seroconversion rates (63.4% vs 76.9%, p < 0.001) and the factor increase in GMT (8.9 vs 13.2 p < 0.0001) were significantly lower in ARD than controls. Analysis of specific diseases revealed that seroprotection significantly reduced in SLE (p < 0.0001), RA (p < 0.0001), PsA (p=0.0006), AS (p=0.04), BD (p=0.04) and DM (p=0.04) patients than controls. The seroconversion rates in SLE (p < 0.0001), RA (p < 0.0001) and PsA (p=0.0006) patients and the increase in GMTs in SLE (p < 0.0001), RA (p < 0.0001) and PsA (p < 0.0001) patients were also reduced compared with controls. Moderate and severe side effects were not reported. Conclusions The novel recognition of a diverse vaccine immunogenicity profile in distinct ARDs supports the notion that a booster dose may be recommended for diseases with suboptimal immune responses. This large study also settles the issue of vaccine safety. (ClinicalTrials.gov #NCT01151644)