QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Ribozyme-mediated reduction of wild-type and mutant cartilage oligomeric matrix protein (COMP) mRNA and protein.

Dominant-negative mutations in the homopentameric extracellular matrix glycoprotein cartilage oligomeric matrix protein (COMP) result in inappropriate intracellular retention of misfolded COMP in the rough endoplasmic reticulum of chondrocytes, causing chondrocyte cell death, which leads to two skeletal dysplasias: pseudoachondroplasia (PSACH) and multiple epiphyseal dysplasia (EDM1). COMP null mice show no adverse effects on normal bone development and growth, suggesting a possible therapy involving removal of COMP mRNA. The goal of this study was to assess the ability of a hammerhead ribozyme (Ribo56, designed against the D469del mutation) to reduce COMP mRNA expression. In COS7 cells transfected with plasmids that overexpress wild-type or mutant COMP mRNA and Ribo56, the ribozyme reduced overexpressed normal COMP mRNA by 46% and mutant COMP mRNA by 56% in a dose-dependent manner. Surprisingly, the use of recombinant adenoviruses to deliver wild-type or mutant COMP mRNA and Ribo56 simultaneously into COS7 cells proved problematic for the activity of the ribozyme to reduce COMP expression. However, in normal human costochondral cells (hCCCs) infected only with adenoviruses expressing Ribo56, expression of endogenous wild-type COMP mRNA was reduced in a dose-dependent manner by 50%. In chondrocytes that contain heterozygous COMP mutations (D469del, G427E and D511Y) that cause PSACH, Ribo56 was more effective at reducing COMP mRNA (up to 70%). These results indicate that Ribo56 is effective at reducing mutant and wild-type COMP levels in cells and suggests a possible mode of therapy to reduce the mutant protein load.

Evaluation of in vitro human gingival fibroblast seeding on acellular dermal matrix

The acellular dermal matrix (ADM) was introduced in periodontology as a substitute for the autogenous grafts, which became restricted because of the limited source of donor's tissue. The aim of this study was to investigate, in vitro, the distribution, proliferation and viability of human gingival fibroblasts seeded onto ADM. ADM was seeded with human gingival fibroblasts for up to 21 days. The following parameters were evaluated: cell distribution, proliferation and viability. Results revealed that, at day 7, fibroblasts were adherent and spread on ADM surface, and were unevenly distributed, forming a discontinuous single cell layer; at day 14, a confluent fibroblastic monolayer lining ADM surface was noticed. At day 21, the cell monolayer exhibited a reduction in cell density. At 7 days, about to 90% of adherent cells on ADM surface were cycling while at 14 and 21 days this proportion was significantly reduced. A high proportion of viable cell was detected on AMD surface both on 14 and 21 days. The results suggest that fibroblast seeding onto ADM for 14 days can allow good conditions for cell adhesion and spreading on the matrix; however, migration inside the matrix was limited.

Modulation of extracellular matrix by nutritional hepatotrophic factors in thioacetamide-induced liver cirrhosis in the rat

Nutritional substances associated to some hormones enhance liver regeneration when injected intraperitoneally, being denominated hepatotrophic factors (HF). Here we verified if a solution of HF (glucose, vitamins, salts, amino acids, glucagon, insulin, and triiodothyronine) can revert liver cirrhosis and how some extracellular matrices are affected. Cirrhosis was induced for 14 weeks in 45 female Wistar rats (200 mg) by intraperitoneal injections of thioacetamide (200 mg/kg). Twenty-five rats received intraperitoneal HF twice a day for 10 days (40 mL·kg-1·day-1) and 20 rats received physiological saline. Fifteen rats were used as control. The HF applied to cirrhotic rats significantly: a) reduced the relative mRNA expression of the genes: Col-α1 (-53%), TIMP-1 (-31.7%), TGF-β1 (-57.7%), and MMP-2 (-41.6%), whereas Plau mRNA remained unchanged; b) reduced GGT (-43.1%), ALT (-17.6%), and AST (-12.2%) serum levels; c) increased liver weight (11.3%), and reduced liver collagen (-37.1%), regenerative nodules size (-22.1%), and fibrous septum thickness. Progranulin protein (immunohistochemistry) and mRNA (in situ hybridization) were found in fibrous septa and areas of bile duct proliferation in cirrhotic livers. Concluding, HF improved the histology and serum biochemistry of liver cirrhosis, with an important reduction of interstitial collagen and increased extracelullar matrix degradation by reducing profibrotic gene expression.

Capacity of the extracellular matrix of the bone marrow to induce proliferation of myeloid cells in vitro in model of protein malnutrition in mice

The aim of this study was to verify the capacity of the extracellular matrix (ECM) obtained from bone marrow of malnourished mice to sustain survival and to induce the proliferation of myeloid cells. We also verified the capacity of the tests to interact with in vitro hematopoietic cytokines. Male ""Swiss"" mice were submitted to protein malnutrition with a diet contents of 4% casein until they lost 20% of the original weight, while the group-control was kept with a diet content of 14% of casein. The bone marrow was extracted with 1.0 mg of aprotinin/mL in PBS. The proliferation tests were carried out with myeloid cell line FDCP-1, by the colorimetric method of reduction of the MTT. The obtained ECM from nourished and undernourished mice induced cellular proliferation in vitro. Tests performed with Il-3 and GM-CSF cytokines in a concentration of 10 and 500 rho g/mL displayed synergic and regulatory effects respectively. The ECM obtained from the malnourished group submitted to the binding to GM-CSF demonstrated higher cellular proliferation than the ECM obtained from the control group (p<0.05). The results suggest that the alterations in the composition of ECM of bone marrow caused by malnutrition might lead to modification of the GM-CSF activity modulation.

Lercanidipine reduces matrix metalloproteinase-2 activity and reverses vascular dysfunction in renovascular hypertensive rats

Increased expression/activity of matrix metalloproteinases (MMPs), especially MMP-2, plays a role in the vascular alterations induced by hypertension, and increased oxidative stress is a major factor activating MMPs. Here, we hypothesized that lercanidipine, a calcium channel blocker, could attenuate the increases in oxidative stress and MMP-2 expression/activity in the two-kidney, one-clip (2K-1C) hypertensive rats. Sham-operated or 2K-1C hypertension rats were treated with lercanidipine 2.5 mg/kg/day (or vehicle) starting three weeks after hypertension was induced. Systolic blood pressure was monitored weekly. After five weeks of treatment, aortic rings were isolated to assess endothelium-dependent and independent relaxations. Quantitative morphometry of structural changes in the aortic wall were studied in hematoxylin/eosin sections. Aortic MMP-2 levels were determined by gelatin zymography. Aortic MMP-2/tissue inhibitor of metalloproteinases (TIMP)-2 mRNA levels were determined by quantitative real-time RT-PCR. Plasma thiobarbituric acid reactive substances concentrations were determined using a fluorometric method. Lercanidipine attenuated 2K-1C hypertension (224 12 versus 183 11 mm Hg in 2K-1C rats and 2K-1C + Lercandipine rats, respectively; P < 0.01) and prevented the reduction in endothelium-dependent vasorelaxation found in 2K-1C rats. Increased MMP-2 and Pro-MMP-2 levels were found in the aortas of 2K-1C rats (all P < 0.05). Lercandipine attenuated 2K-1C-induced increases in MMP-2 by more than 60% and blunted 2K-1C-induced increases in oxidative stress (both P < 0.001). While hypertension-induced significant aortic wall hypertrophy and approximately 9-fold increases in the ratio of MMP-2MMP-2 mRNA expression (both P < 0.05), lercandipine did not affect these changes. These results suggest that lercanidipine produces antihypertensive effects and reverses the endothelial dysfunction associated with 2K-1C hypertension, probably through mechanisms involving antioxidant effects leading to lower MMP-2 activation. (C) 2008 Elsevier B.V. All rights reserved.

Antioxidant treatment reduces matrix metalloproteinase-2-induced vascular changes in renovascular hypertension

Mounting evidence indicates that structural and functional vascular changes associated with two-kidney, one-clip (2K-1C) hypertension result, at least in part, from altered activity of matrix metalloproteinases (MMPs). Because MMPs are upregulated by increased formation of reactive oxygen species (ROS), we hypothesized that antioxidant approaches could attenuate the increases in MMP-2 expression/activity and the vascular dysfunction and remodeling associated with 2K-1C hypertension. Sham-operated or 2K-1C hypertensive rats were treated with tempol 18 mg/kg/day or apocyanin 25 mg/kg/day (or vehicle). Systolic blood pressure was monitored weekly. After 8 weeks of treatment, aortic rings were isolated to assess endothelium-dependent and -independent relaxation. Quantitative morphometry of structural changes in the aortic wall was studied in hematoxylin/eosin sections. Aortic and systemic ROS levels were measured using dihydroethidine and thiobarbituric acid-reactive substances, respectively. Aortic MMP-2 levels and activity were determined by gelatin and in situ zymography, fluorimetry, and immunohistochemistry. Tempol and apocyanin attenuated 2K-1C hypertension (181 +/- 20.8 and 192 +/- 17.6 mm Hg, respectively, versus 213 +/- 18 mm Hg in hypertensive controls; both p<0.05) and prevented the reduction in endothelium-dependent vasorelaxation found in 2K-1C rats. Tempol, but not apocyanin (p>0.05), prevented the vascular remodeling found in 2K-1C rats (all p<0.01). Tempol was more effective than apocyanin in attenuating hypertension-induced increases in oxidative stress (both p<0.05), MMP-2 levels, and MMP-2 activity in hypertensive rats (all p<0.05). Our results suggest that antioxidant approaches decrease MMP-2 upregulation and attenuate the vascular dysfunction and remodeling during 2K-1C hypertension. (C) 2009 Elsevier Inc. All rights reserved.

Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

Development of novel bioanodes for ethanol biofuel cell using PAMAM dendrimers as matrix for enzyme immobilization

This paper describes the preparation and application of a novel bioanode for use in ethanol/O(2) biofuel cells based upon immobilization of alcohol dehydrogenase (ADH) and polyamidoamine (PAMAM) dendrimers onto carbon cloth platforms. The power density measurements indicated a direct relationship between the amount of anchored ADH and the anode power values, which increased upon enzyme loading. The power density values ranged from 0.04 to 0.28 mW cm(-2), and the highest power density was achieved with the bioanode prepared with 28 U of ADH, which provided a power density of 0.28 mW cm(-2) at 0.3 V. The latter power output values were the maximum observed, even for higher enzyme concentrations. Stability of the bioanodes was quite satisfactory, since there was no appreciable reduction of enzymatic activity during the measurements. The method of bioanode preparation described here has proven to be very effective. The PAMAM dendrimer represents a friendly environment for the immobilization of enzymes, and it is stable and capable of generating high power density compared to other immobilization methods. (C) 2010 Elsevier B.V. All rights reserved.

A practical approach to assess depression risk and to guide risk reduction strategies in later life

Background: Many factors have been associated with the onset and maintenance of depressive symptoms in later life, although this knowledge is yet to be translated into significant health gains for the population. This study gathered information about common modifiable and non-modifiable risk factors for depression with the aim of developing a practical probabilistic model of depression that can be used to guide risk reduction strategies. \Methods: A cross-sectional study was undertaken of 20,677 community-dwelling Australians aged 60 years or over in contact with their general practitioner during the preceding 12 months. Prevalent depression (minor or major) according to the Patient Health Questionnaire (PHQ-9) assessment was the main outcome of interest. Other measured exposures included self-reported age, gender, education, loss of mother or father before age 15 years, physical or sexual abuse before age 15 years, marital status, financial stress, social support, smoking and alcohol use, physical activity, obesity, diabetes, hypertension, and prevalent cardiovascular diseases, chronic respiratory diseases and cancer. Results: The mean age of participants was 71.7 +/- 7.6 years and 57.9% were women. Depression was present in 1665 (8.0%) of our subjects. Multivariate logistic regression showed depression was independently associated with age older than 75 years, childhood adverse experiences, adverse lifestyle practices (smoking, risk alcohol use, physical inactivity), intermediate health hazards (obesity, diabetes and hypertension), comorbid medical conditions (clinical history of coronary heart disease, stroke, asthma, chronic obstructive pulmonary disease, emphysema or cancers), and social or financial strain. We stratified the exposures to build a matrix that showed that the probability of depression increased progressively with the accumulation of risk factors, from less than 3% for those with no adverse factors to more than 80% for people reporting the maximum number of risk factors. Conclusions: Our probabilistic matrix can be used to estimate depression risk and to guide the introduction of risk reduction strategies. Future studies should now aim to clarify whether interventions designed to mitigate the impact of risk factors can change the prevalence and incidence of depression in later life.

Treatment of infrabony defects with or without enamel matrix proteins: A 24-month follow-up randomized pilot study

Objective: To evaluate a comparison of open-flap debridement (OFD) with or without the use of enamel matrix proteins (EMP) for the treatment of infrabony defects. Method and Materials: Ten volunteers (38 infrabony defects) were randomized to receive OFD + EMP (test site) and OFD (control site). Clinical outcomes included mean changes in Plaque Index, Gingival Index, probing pocket depth (PPD), relative attachment level (RAL), gingival recession, width of keratinized tissue, and dental mobility at baseline and at 24 months. Results: A significant reduction of 4.21 +/- 0.97 mm was observed in PPD for the OFD + EMP group (from 6.30 +/- 0.99 mm to 2.09 +/- 0.97 mm) and of 3.28 +/- 1.23 mm for the OFD group (from 6.13 +/- 0.88 mm to 2.85 +/- 1.42 mm) (P < .001). The reduction in PPD was statistically significantly greater for OFD + EMP compared to OFD (P = .03). The mean RAL decreased from 13.26 +/- 1.88 mm to 7.57 +/- 2.05 mm for the OFD + EMP group (a gain of 5.69 +/- 1.96 mm) and from 13.37 +/- 1.71 mm to 8.13 +/- 1.34 min (P < .001) for the OFD group (a gain of 5.24 +/- 1.55 mm). Gingival recession was higher it) the OFD + EMP group than in the OFD group. The mean keratinized tissue significantly decreased from 4.41 +/- 1.39 mm to 3.63 +/- 1.54 mm for OFD flap group (P < .01). Conclusion: Both treatment modalities were efficient in improving RAL and PPD. Within groups, there was a significant reduction in keratinized tissue for OFD and a significant postoperative recession for the OFD + EMP group. Infrabony defects treated with OFD + EMP showed significantly more PPD reduction when compared to OFD. (Quintessence Int 2010;41:125-134)

Long-term stability of dentin matrix following treatment with various natural collagen cross-linkers

Objectives: Collagen disorganization is one of the main degradation patterns found in unsuccessful adhesive restorations. The hypothesis of this study was that pretreatment using natural collagen cross-linking agents rich in proanthocyanidin (PA) would improve mechanical properties and stability over time of the dentin collagen and, thus, confer a more resistant and lasting substrate for adhesive restorations. Methods: PA-based extracts, from grape seed (GSE), cocoa seed (CSE), cranberry (CRE), cinnamon (CNE) and acai berry (ACE) were applied over the demineralized dentin. The apparent elastic modulus (E) of the treated dentin collagen was analyzed over a 12 month period. Specimens were immersed in the respective solution and E values were obtained by a micro-flexural test at baseline, 10, 30, 60, 120 and 240 min. Samples were stored in artificial saliva and re-tested after 3, 6 and 12 months. Data was analyzed using ANOVA and Tukey test. Results: GSE and CSE extracts showed a time-dependent effect and were able to improve [240 min (MPa): GSE = 108.96 +/- 56.08: CSE = 59.21 +/- 24.87] and stabilize the E of the organic matrix [12 months (MPa): GSE = 40.91 +/- 19.69; CSE = 42.11 +/- 13.46]. CRE and CNE extracts were able to maintain the E of collagen matrices constant over 12 months [CRE = 11.17 +/- 7.22; CNE = 9.96 +/- 6.11; MPa]. ACE (2.64 +/- 1.22 MPa) and control groups immersed in neat distilled water (1.37 +/- 0.69 MPa) and ethanol-water (0.95 +/- 0.33 MPa) showed no effect over dentin organic matrix and enable their degradation and reduction of mechanical properties. Significance: Some PA-based extracts were capable of improving and stabilizing collagen matrices through exogenous cross-links induction. (C) 2011 Elsevier Ltd. All rights reserved.

Abnormal extracellular matrix protein transport associated with increased apoptosis of vascular smooth muscle cells in Marfan syndrome and bicuspid aortic valve thoracic aortic aneurysm

Background - Marfan syndrome (MS) is a genetic disorder caused by a mutation in the fibrillin gene FBN1. Bicuspid aortic valve (BAV) is a congenital heart malformation of unknown cause. Both conditions are associated with ascending aortic aneurysm and premature death. This study examined the relationship among the secretion of extracellular matrix proteins fibrillin, fibronectin, tenascin, and vascular smooth muscle cell (VSMC) apoptosis. The role of matrix metalloproteinase (MMP)- 2 in VSMC apoptosis was studied in MS aneurysm. Methods and Results - Aneurysm tissue was obtained from patients undergoing surgery ( MS: 4 M, 1 F, age 27 - 45 years; BAV: 3 M, 2 F, age 28 - 65 years). Normal aorta from subjects with nonaneurysm disease was also collected ( 4 M, 1 F, age 23 - 93 years). MS and BAV aneurysm histology showed areas of cystic medial necrosis (CMN) without inflammatory infiltrate. Immunohistochemical study of cultured MS and BAV VSMC showed intracellular accumulation and reduction of extracellular distribution of fibrillin, fibronectin, and tenascin. Western blot showed no increase in expression of fibrillin, fibronectin, or tenascin in MS or BAV VSMC and increased expression of MMP-2 in MS VSMCs. There was 4-fold increase in loss of cultured VSMC incubated in serum-free medium for 24 hours in both MS ( 27 +/- 8%) and BAV ( 32 +/- 14%) compared with control ( 7 +/- 5%). Conclusions - In MS and BAV there is alteration in both the amount and quality of secreted proteins and an increased degree of VSMC apoptosis. Up-regulation of MMP-2 might play a role in VSMC apoptosis in MS VSMC. The findings suggest the presence of a fundamental cellular abnormality in BAV thoracic aorta, possibly of genetic origin.