A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.

Expression of matrix metalloproteinases, type IV collagen, and interleukin-10 in rabbits treated with morphine after lamellar keratectomy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chemical Composition of Lipids Present in Cat and Dog Oocyte by Matrix-Assisted Desorption Ionization Mass Spectrometry (MALDI- MS)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Proteoliposomes Harboring Alkaline Phosphatase and Nucleotide Pyrophosphatase as Matrix Vesicle Biomimetics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Kinetic Analysis of Substrate Utilization by Native and TNAP-, NPP1-, or PHOSPHO1-Deficient Matrix Vesicles

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Contribution of matrix vesicles and alkaline phosphatase to ectopic bone formation

Endochondral calcification involves the participation of matrix vesicles (MVs), but it remains unclear whether calcification ectopically induced by implants of demineralized bone matrix also proceeds via MVs. Ectopic bone formation was induced by implanting rat demineralized diaphyseal bone matrix into the dorsal subcutaneous tissue of Wistar rats and was examined histologically and biochemically. Budding of MVs from chondrocytes was observed to serve as nucleation sites for mineralization during induced ectopic osteogenesis, presenting a diameter with Gaussian distribution with a median of 306 ± 103 nm. While the role of tissue-nonspecific alkaline phosphatase (TNAP) during mineralization involves hydrolysis of inorganic pyrophosphate (PPi), it is unclear how the microenvironment of MV may affect the ability of TNAP to hydrolyze the variety of substrates present at sites of mineralization. We show that the implants contain high levels of TNAP capable of hydrolyzing p-nitrophenylphosphate (pNPP), ATP and PPi. The catalytic properties of glycosyl phosphatidylinositol-anchored, polidocanol-solubilized and phosphatidylinositol-specific phospholipase C-released TNAP were compared using pNPP, ATP and PPi as substrates. While the enzymatic efficiency (k cat/Km) remained comparable between polidocanol-solubilized and membrane-bound TNAP for all three substrates, the k cat/Km for the phosphatidylinositol-specific phospholipase C-solubilized enzyme increased approximately 108-, 56-, and 556-fold for pNPP, ATP and PPi, respectively, compared to the membrane-bound enzyme. Our data are consistent with the involvement of MVs during ectopic calcification and also suggest that the location of TNAP on the membrane of MVs may play a role in determining substrate selectivity in this micro-compartment.

Evaluation of an average numerator relationship matrix model and a Bayesian hierarchical model for growth traits in Nellore cattle with uncertain paternity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nitric oxide release using natural rubber latex as matrix

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A low-cost 3D reconstruction system using a single-shot projection of a pattern matrix

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Binding of extracellular matrix proteins to Paracoccidioides brasiliensis

Adhesion to extracellular matrix (ECM) proteins plays a crucial role in invasive fungal diseases. ECM proteins bind to the surface of Paracoccidioides brasiliensis yeast cells in distinct qualitative patterns. Extracts from Pb18 strain, before (18a) and after animal inoculation (18b), exhibited differential adhesion to ECM components. Pb18b extract had a higher capacity for binding to ECM components than Pb18a. Laminin was the most adherent component for both samples, followed by type I collagen, fibronectin, and type IV collagen for Pb18b. A remarkable difference was seen in the interaction of the two extracts with fibronectin and their fragments. Pb18b extract interacted significantly with the 120-kDa fragment. Ligand affinity binding assays showed that type I collagen recognized two components (47 and 80 kDa) and gp43 bound both fibronectin and laminin. The peptide 1 (NLGRDAKRHL) from gp43, with several positively charged amino acids, contributed most to the adhesion of P. brasiliensis to Vero cells. Synthetic peptides derived from peptide YIGRS of laminin or from RGD of both laminin and fibronectin showed the greatest inhibition of adhesion of gp43 to Vero cells. In conclusion, this work provided new molecular details on the interaction between P. brasiliensis and ECNI components. (c) 2006 Elsevier SAS. All rights reserved.

Metronidazole release using natural rubber latex as matrix

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)