Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Friedmanniella spumicola sp nov and Friedmanniella capsulata sp nov from activated sludge foam: Gram-positive cocci that grow in aggregates of repeating groups of cocci

Two Gram-positive, non-motile, non-spore-forming, strictly aerobic, pigmented cocci, strains Ben 107(T) and Ben 108(T), growing in aggregates were isolated from activated sludge samples by micromanipulation. Both possessed the rare type A3 gamma' peptidoglycan. Major menaquinones of strain Ben 107(T) were MK-9(H-4) and MK-7(H-2), and the main cellular fatty acid was 12-methyltetradecanoic acid (ai-C-15:0). In strain Ben 108(T), MK-9(H-4), MK-9(H-2) and MK-7(H-4) were the menaquinones and again the main fatty acid was 12-methyltetradecanoic acid (ai-C-15:0). Polar lipids in both strains consisted of phosphatidyl inositol, phosphatidyl glycerol and diphosphatidyl glycerol with two other unidentified glycolipids and phospholipids also present in both. These data, together with the 16S rDNA sequence data, suggest that strain Ben 107(T) belongs to the genus Friedmanniella which presently includes a single recently described species, Friedmanniella antarctica. Although the taxonomic status of strain Ben 108(T) is far less certain, on the basis of its 16S rRNA sequence it is also adjudged to be best placed in the genus Friedmanniella, The chemotaxonomic characteristics and DNA-DNA hybridization data support the view that Ben 107(T) and Ben 108(T) are novel species of the genus Friedmanniella. Hence, it is proposed that strain Ben 107(T) (=ACM 5121(T)) is named as Friedmanniella spumicola sp. nov. and strain Ben 108(T) (=ACM 5120(T)) as Friedmanniella capsulata sp. nov.

Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Assessment of intracellular water by whole body bioelectrical impedance and total body potassium in HIV-positive patients

.:Abstract-Objective: Bioelectrical impedance analysis (BIA) is widely used as bedside assessment of body composition. Body cell mass (BCM) and intracellular water (ICW) are clinically important body compartments. Estimates of ICW obtained from BIA by different calculation approaches were compared to a reference method in male HIV-infected patients. Patients: Representative subsample of clinically stable HIV-infected outpatients, consisting of 42 men with a body mass index of 22.4 +/- 3.8 kg/m(2) (range, 13-31 kg/m(2)). Methods: Total body potassium was assessed in a whole body counter, and compared to 50 kHz mono-frequency BIA and multifrequency bioelectrical impedance spectroscopy. Six different prediction equations for ICW from BIA data were applied. Methods were compared by the Bland-Altman method. Results: BIA-derived ICW estimates explained 58% to 73% of the observed variance in ICW (TBK), but limits of confidence were wide (-16.6 to +18.2% for the best method). BIA overestimated low ICW (TBK) and underestimated high ICW (TBK) when normalized for weight or height. Mono- and multifrequency BIA were not different in precision but population-specific equations tended to narrower confidence limits. Conclusion: BIA is an unreliable method to estimate ICW in this population, in contrast to the better established estimation of total body water and extracellular water. Potassium depletion in severe malnutrition may contribute to this finding but a major part of the residual between methods remains unexplained. (C) 2000 Harcourt Publishers Ltd.

Mesoionic pyridopyrimidinylium and pyridooxazinylium olates and non-mesoionic pyridopyrimidinones. Structures in the solid state, solution, and matrices

X-Ray crystal structures, C-13 NMR spectra and theoretical calculations (B3LYP/6-31G*) are reported for the mesoionic (zwitterionic) pyridopyrimidinylium- and pyridooxazinyliumolates 2a, 3a and 5a,b as well as the enol ether 11b and the enamine 11c. The 1-NH compounds like 1a, 2a and 3a exist in the mesoionic form in the crystal and in solution, but the OH tautomers such as 1b and 2b dominate in the gas phase as revealed by the Ar matrix IR spectra in conjunction with DFT calculations. All data indicate that the mesoionic compounds can be regarded as intramolecular pyridine-ketene zwitterions (cf. 16 --> 17) with a high degree of positive charge on the pyridinium nitrogen, a long pyridinium N-CO bond (ca. 1.44-1.49 Angstrom), and normal C=O double bonds (ca. 1.22 Angstrom). All mesoionic compounds exhibit a pronounced tilting of the olate C=O groups (the C=O groups formally derived from a ketene) towards the pyridinium nitrogen, giving NCO angles of 110-118 degrees. Calculations reveal a hydrogen bond with 6-CH, analogous to what is found in ketene-pyridine zwitterions and the C3O2-pyridine complex. The 2-OH tautomers of type 1b, 2b, and 11 also show a high degree of zwitterionic character as indicated by the canonical structures 11 12.

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying U-q(sl (2/1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.

Treatment implications of a positive sentinel lymph node biopsy for patients with early-stage breast carcinoma

BACKGROUND. Sentinel lymph node (SLN) mapping and biopsy is emerging as an alternative to axillary lymph node dissection (ALND) in determining the lymph node status of patients with early-stage breast carcinoma. The hypothesis of the technique is that the SLN is the first lymph node in the regional lymphatic basin that drains the primary tumor. Non-SLN (NSLN) metastasis in the axilla is unlikely if the axillary SLN shows no tumor involvement, and, thus, further axillary interference may be avoided. However, the optimal treatment of the axilla in which an SLN metastasis is found requires ongoing evaluation. The objectives of this study were to evaluate the predictors for NSLN metastasis in the presence of a tumor-involved axillary SLN and to examine the treatment implications for patients with early-stage breast carcinoma. METHODS. Between June 1998 and May 2000, 167 patients participated in the pilot study of SLN mapping and biopsy at Westmead Hospital. SLNs were identified successfully and biopsied in 140 axillae. All study patients also underwent ALND. The incidence of NSLN metastasis in the 51 patients with a SLN metastasis was correlated with clinical and pathologic characteristics. RESULTS. Of 51 patients with a positive SLN, 24 patients (47%) had NSLN metastases. The primary tumor size was the only significant predictor for NSLN involvement. NSLN metastasis occurred in 25% of patients (95% confidence interval [95%CI], 10-47%) with a primary tumor size less than or equal to 20 mm and in 67% of patients (95%CI, 46-83%) with a primary tumor size > 20 mm (P = 0.005). The size of the SLN metastasis was not associated significantly with NSLN involvement. Three of 7 patients (43%) with an SLN micrometastasis (< 1 mm) had NSLN involvement compared with 38 of 44 patients (48%) with an SLN macrometastasis (greater than or equal to 1 mm). CONCLUSIONS. The current study did not identify a subgroup of SLN positive patients in whom the incidence of NSLN involvement was low enough to warrant no further axillary interference. At present, a full axillary dissection should be performed in patients with a positive SLN. (C) 2001 American Cancer Society.

The interaction of metal ions and Marimastat with matrix metalloproteinase 9

The effect of a range of metal ions on the ability of Marimastat to inhibit matrix metalloproteinase 9 (MMP-9) was examined in a fluorescence based proteolytic assay. Whilst none of the metals examined significantly affected the inhibitory ability of Marimastat, several metal ions did have a significant effect on MMP-9 activity itself. In the absence of Marimastat, Zn(II) and Fe(II) significantly inhibited MMP-9 activity at metal ion concentrations of 10 and 100 muM, respectively. In both the absence and presence of Marimastat, Cd(II) significantly inhibited MMP-9 at 100 muM. In contrast, 1 mM Co(II) significantly upregulated MMP-9 proteolytic activity. (C) 2003 Elsevier Science Inc. All rights reserved.

The game to play: expanding the co-opetition proposal through the strategic games matrix

Purpose - Using Brandenburger and Nalebuff`s 1995 co-opetition model as a reference, the purpose of this paper is to seek to develop a tool that, based on the tenets of classical game theory, would enable scholars and managers to identify which games may be played in response to the different conflict of interest situations faced by companies in their business environments. Design/methodology/approach - The literature on game theory and business strategy are reviewed and a conceptual model, the strategic games matrix (SGM), is developed. Two novel games are described and modeled. Findings - The co-opetition model is not sufficient to realistically represent most of the conflict of interest situations faced by companies. It seeks to address this problem through development of the SGM, which expands upon Brandenburger and Nalebuff`s model by providing a broader perspective, through incorporation of an additional dimension (power ratio between players) and three novel, respectively, (rival, individualistic, and associative). Practical implications - This proposed model, based on the concepts of game theory, should be used to train decision- and policy-makers to better understand, interpret and formulate conflict management strategies. Originality/value - A practical and original tool to use game models in conflict of interest situations is generated. Basic classical games, such as Nash, Stackelberg, Pareto, and Minimax, are mapped on the SGM to suggest in which situations they Could be useful. Two innovative games are described to fit four different types of conflict situations that so far have no corresponding game in the literature. A test application of the SGM to a classic Intel Corporation strategic management case, in the complex personal computer industry, shows that the proposed method is able to describe, to interpret, to analyze, and to prescribe optimal competitive and/or cooperative strategies for each conflict of interest situation.

Positive end expiratory pressure during resuscitation of premature lambs rapidly improves blood gases without adversely affecting arterial pressure

Positive end expiratory pressure (PEEP) is important for neonatal ventilation but is not considered in guidelines for resuscitation. Our aim was to investigate the effects of PEEP on cardiorespiratory parameters during resuscitation of very premature lambs delivered by hysterotomy at similar to125 d gestation (term similar to147 d). Before delivery, they were intubated and lung fluid was drained. Immediately after delivery, they were ventilated with a Drager Babylog plus ventilator in volume guarantee mode with a tidal volume of 5 mL/kg. Lambs were randomized to receive 0, 4, 8, or 12 cm H2O of PEEP. They were ventilated for a 15-min resuscitation period followed by 2 h of stabilization at the same PEEP. Tidal volume, peak inspiratory pressure, PEEP, arterial pressure, oxygen saturation, and blood gases were measured regularly, and respiratory system compliance and alveolar/ arterial oxygen differences were calculated. Lambs that received 12 cm H2O of PEEP died from pneumothoraces; all others survived without pneumothoraces. Oxygenation was significantly improved by 8 and 12 cm H2O of PEEP compared with 0 and 4 cm H2O of PEEP. Lambs with 0 PEEP did not oxygenate adequately. The compliance of the respiratory system was significantly higher at 4 and 8 cm H2O of PEEP than at 0 PEEP. There were no significant differences in partial pressure of carbon dioxide in arterial blood between groups. Arterial pressure was highest with 8 cm H2O of PEEP, and there was no cardiorespiratory compromise at any level of PEEP. Applying PEEP during resuscitation of very premature infants might be advantageous and merits further investigation.

Surface modification of metals by calcium carbonate thin films on a layer-by-layer polyelectrolyte matrix

A multilayer organic film containing poly(acrylic acid) and chitosan was fabricated on a metallic support by means of the layer-by-layer technique. This film was used as a template for calcium carbonate crystallization and presents two possible binding sites where the nucleation may be initiated, either calcium ions acting as counterions of the polyelectrolyte or those trapped in the template gel network formed by the polyelectrolyte chains. Calcium carbonate formation was carried out by carbon dioxide diffusion, where CO, was generated from ammonium carbonate decomposition. The CaCO3 nanocrystals obtained, formed a dense, homogeneous, and continuous film. Vaterite and calcite CaCO3 crystalline forms were detected. (c) 2007 Elsevier B.V All rights reserved.