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.

Pioglitazone inhibits cell growth and reduces matrix production in human kidney fibroblasts

Peroxisome proliferator-activated receptor-gamma (PPAR-gamma) agonists are increasingly used in patients with diabetes, and small studies have suggested a beneficial effect on renal function, but their effects on. extracellular matrix (ECM) turnover are unknown. The aims of this study were to investigate the effects of the PPAR-gamma agonist pioglitazone on growth and matrix production in human cortical fibroblasts (CF). Cell growth and ECM production and turnover were measured in human CF in the presence and absence of 1 and 3 muM pioglitazone. Exposure of CF to pioglitazone caused an antiproliferative (P < 0.0001) and hypertrophic (P < 0.0001) effect; reduced type IV collagen secretion (P < 0.01), fibronectin secretion (P < 0.0001), and proline incorporation (P < 0.0001); decreased MMP-9 activity (P < 0.05); and reduced tissue inhibitor of metalloproteinase-1 (TIMP-1) and TIMP-2 secretion (P < 0.001 and P < 0.0001, respectively). These effects were independent of TGF-beta1. A reduction in ECM production was similarly observed when CF were exposed to a selective PPAR-gamma agonist (L-805645) in concentrations that caused no toxicity, confirming the antifibrotic effects of pioglitazone were mediated through a PPAR-gamma-dependent mechanism. Exposure of CF to high glucose conditions induced an increase in the expression of collagen IV (P < 0.05), which was reversed both in the presence of pioglitazone (1 and 3 muM) and by L-805645. In summary, exposure of human CIF to pioglitazone causes an antiproliferative effect and reduces ECM production through mechanisms that include reducing TIMP activity, independent of TGF-beta1. These studies suggest that the PPAR-gamma agonists may have a specific role in ameliorating the course of progressive tubulointerstitial fibrosis under both normoglycemic and hyperglycemic states.

Reduction of the in vitro pro-inflammatory response by macrophages to poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

This study evaluates the pro-inflammatory response to the thermoplastic biopolymer poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) through the analysis of cellular responses in vitro. The murine macrophage RAW264.7 cell line was cultured on solvent cast PHBV films, which was found to induce pro-inflammatory activity that required direct contact between the material and the macrophages. The identity of the pro-inflammatory stimulus was determined by culturing bone marrow-derived macrophages from bacterial lipopolysaccharide (LPS) hyporesponsive C3H/HeJ mice and CpG non-responsive TLR9-/- mice on PHBV. The lack of a pro-inflammatory response by the C3H/HeJ cells indicates that the pro-inflammatory agent present within PHBV is predominately LPS while the TLR9-/- macrophages confirmed that CpG-containing bacterial DNA is unlikely to contribute to the activity. A series of purification procedures was evaluated and one procedure was developed that utilized hydrogen peroxide treatment in solution. The optimized purification was found to substantially reduce the pro-inflammatory response to PHBV without adversely affecting either the molecular structure or molecular weight of the material thereby rendering it more amenable for use as a biomaterial in vivo. Crown Copyright (c) 2006 Published by Elsevier Ltd. All rights reserved.