Some Marginal Densities of the Wishart Distribution

Евелина Илиева Велева - Разпределението на Уишарт се среща в практиката като разпределението на извадъчната ковариационна матрица за наблюдения над многомерно нормално разпределение. Изведени са някои маргинални плътности, получени чрез интегриране на плътността на Уишарт разпределението. Доказани са необходими и достатъчни условия за положителна определеност на една матрица, които дават нужните граници за интегрирането.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.

Sequential and parallel synchronous alternating iterative methods

The so-called parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra and its Applications 103:175-192 (1988)] for solving a nonsingular linear system Ax = b using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when A is a monotone matrix using a weak nonnegative multisplitting of the second type and when A is a symmetric positive definite matrix using a P -regular multisplitting. Also, nonstationary alternating iterative methods are studied. Finally, combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. When matrix A is monotone and the multisplittings are weak nonnegative of the first or of the second type, both models lead to convergent schemes. Also, when matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.

Studies on the generalisation of Gaussian processes and Bayesian neural networks

The assessment of the reliability of systems which learn from data is a key issue to investigate thoroughly before the actual application of information processing techniques to real-world problems. Over the recent years Gaussian processes and Bayesian neural networks have come to the fore and in this thesis their generalisation capabilities are analysed from theoretical and empirical perspectives. Upper and lower bounds on the learning curve of Gaussian processes are investigated in order to estimate the amount of data required to guarantee a certain level of generalisation performance. In this thesis we analyse the effects on the bounds and the learning curve induced by the smoothness of stochastic processes described by four different covariance functions. We also explain the early, linearly-decreasing behaviour of the curves and we investigate the asymptotic behaviour of the upper bounds. The effect of the noise and the characteristic lengthscale of the stochastic process on the tightness of the bounds are also discussed. The analysis is supported by several numerical simulations. The generalisation error of a Gaussian process is affected by the dimension of the input vector and may be decreased by input-variable reduction techniques. In conventional approaches to Gaussian process regression, the positive definite matrix estimating the distance between input points is often taken diagonal. In this thesis we show that a general distance matrix is able to estimate the effective dimensionality of the regression problem as well as to discover the linear transformation from the manifest variables to the hidden-feature space, with a significant reduction of the input dimension. Numerical simulations confirm the significant superiority of the general distance matrix with respect to the diagonal one.In the thesis we also present an empirical investigation of the generalisation errors of neural networks trained by two Bayesian algorithms, the Markov Chain Monte Carlo method and the evidence framework; the neural networks have been trained on the task of labelling segmented outdoor images.

A solution of the trigonometric moment problem via Tagamlitzki's "Theorem of the Cones"

In 1952 Y. Tagamlitzki gave an elegant proof of the classical Bochner’s theorem on the positively definite functions. Unfortunately, he never published his proof. In this paper we consider a related but simpler problem, the trigonometric moment problem, by using Tagamlitzki’s approach.

Marginal Densities of the Wishart Distribution

2010 Mathematics Subject Classification: 62H10.

Expression of smooth muscle and extracellular matrix proteins in relation to airway function in asthma

Background: Smooth muscle content is increased within the airway wall in patients with asthma and is likely to play a role in airway hyperresponsiveness. However, smooth muscle cells express several contractile and structural proteins, and each of these proteins may influence airway function distinctly. Objective: We examined the expression of contractile and structural proteins of smooth muscle cells, as well as extracellular matrix proteins, in bronchial biopsies of patients with asthma, and related these to lung function, airway hyperresponsiveness, and responses to deep inspiration. Methods: Thirteen patients with asthma (mild persistent, atopic, nonsmoking) participated in this cross-sectional study. FEV1 % predicted, PC20 methacholine, and resistance of the respiratory system by the forced oscillation technique during tidal breathing and deep breath were measured. Within 1 week, a bronchoscopy was performed to obtain 6 bronchial biopsies that were immunuhistochemically stained for alpha-SM-actin, desmin, myosin light chain kinase (MLCK), myosin, calponin, vimentin, elastin, type III collagen, and fibronectin. The level of expression was determined by automated densitometry. Results: PC20 methacholine was inversely related to the expression of alpha-smooth muscle actin (r = -0.62), desmin (r = -0.56), and elastin (r = -0.78). In addition, FEV1% predicted was positively related and deep inspiration-induced bronchodilation inversely related to desmin (r = -0.60), MLCK (r = -0.60), and calponin (r = -0.54) expression. Conclusion: Airway hyperresponsiveness, FEV1% predicted, and airway responses to deep inspiration are associated with selective expression of airway smooth muscle proteins and components of the extracellular matrix.

Imbalanced circulating matrix metalloproteinases in polycystic ovary syndrome

Altered levels of matrix metalloproteinases (MMPs) may reflect relevant pathogenetic mechanisms of disease conditions. The objective of this study was to compare the plasma levels of MMPs and tissue inhibitors of MMPs (TIMPs) in polycystic ovary syndrome (PCOS) patients with those found in healthy ovulatory controls and to examine whether the levels of these biomarkers are associated with clinical and biochemical features of this syndrome. Sixty-five healthy ovulatory subjects (controls) and 80 patients with PCOS were include in this study. MMP-2, MMP-8, MMP-9, TIMP-1, TIMP-2 concentrations were measured in plasma samples by gelatin zymography or enzyme-linked immunoassays. MMP-2, MMP-8, MMP-9, and TIMP-1 levels were similar in PCOS patients and in healthy controls (P > 0.05). PCOS patients had lower plasma TIMP-2 levels than healthy controls (P < 0.05). We found higher MMP-2/TIMP-2 and MMP-9/TIMP-1 ratios in PCOS patients than in healthy controls (all P < 0.05). Testosterone levels correlated positively with the MMP-9/TIMP-1 ratio and negatively with TIMP-2 levels (r = 0.26, P < 0.01 and r = -0.21, P = 0.02, respectively). In addition, only testosterone was an independent predictor of TIMP-2 levels (estimate = -0.35, P = 0.04) and the MMP-9/TIMP-1 ratio (estimate = 0.01, P = 0.04). We found evidence indicating that the balance between MMPs and TIMPs in women with PCOS is altered, probably due to androgen excess found in these women.

Institutional and matrix support and its relationship with primary healthcare

OBJECTIVE To analyze whether the level of institutional and matrix support is associated with better certification of primary healthcare teams.METHODS In this cross-sectional study, we evaluated two kinds of primary healthcare support – 14,489 teams received institutional support and 14,306 teams received matrix support. Logistic regression models were applied. In the institutional support model, the independent variable was “level of support” (as calculated by the sum of supporting activities for both modalities). In the matrix support model, in turn, the independent variables were the supporting activities. The multivariate analysis has considered variables with p < 0.20. The model was adjusted by the Hosmer-Lemeshow test.RESULTS The teams had institutional and matrix supporting activities (84.0% and 85.0%), respectively, with 55.0% of them performing between six and eight activities. For the institutional support, we have observed 1.96 and 3.77 chances for teams who had medium and high levels of support to have very good or good certification, respectively. For the matrix support, the chances of their having very good or good certification were 1.79 and 3.29, respectively. Regarding to the association between institutional support activities and the certification, the very good or good certification was positively associated with self-assessment (OR = 1.95), permanent education (OR = 1.43), shared evaluation (OR = 1.40), and supervision and evaluation of indicators (OR = 1.37). In regards to the matrix support, the very good or good certification was positively associated with permanent education (OR = 1.50), interventions in the territory (OR = 1.30), and discussion in the work processes (OR = 1.23).CONCLUSIONS In Brazil, supporting activities are being incorporated in primary healthcare, and there is an association between the level of support, both matrix and institutional, and the certification result.

Quantitave and qualitative interferences of pentoxifillyne on hepatic Schistosoma mansoni granulomas: effects on extracellular matrix and eosinophil population

Mast cells and eosinophils actively participate in tissue repair and are prominent components of Schistosoma mansoni granulomas. Since pentoxifillyne (PTX) is an immunomodulatory and antifibrotic substance, we aimed to characterize, by morphological techniques, the effect of this drug on fibrosis developed inside murine hepatic schistosomal granulomatous reaction, beyond the quantification of eosinophil and mast cell populations. The drug (1 mg/100 g animal weight) was administrated from 35 to 90 days post-infection, when the animals were killed. The intragranulomatous interstitial collagen network was analyzed by confocal laser scanning microscopy, the number of eosinophils and mast cells was quantified and the results were validated by t-student test. Treatment did not interfere on the granuloma evolution but caused a significant decrease in the total and involutive number of hepatic granulomas (p = 0.01 and 0.001, respectivelly), and in the intragranulomatous accumulation of eosinophils (p = 0.0001). Otherwise, the number of mast cells was not significantly altered (p = 0.9); however, it was positively correlated with the number of granulomatous structures (r = 0.955). In conclusion, PTX does not affect development and collagen deposition in S. mansoni murine granuloma, but decreases the intragranulomatous eosinophil accumulation possibly due to its immunomodulatory capability, interfering in cellular recruitment and/or differentiation.

1D.03: Inactive matrix GLA protein is associated with renal resistive index in a population-based study

OBJECTIVE: Renal resistive index (RRI) varies directly with renal vascular stiffness and pulse pressure. RRI correlates positively with arteriolosclerosis in damaged kidneys and predicts progressive renal dysfunction. Matrix Gla-protein (MGP) is a vascular calcification inhibitor that needs vitamin K to be activated. Inactive MGP, known as desphospho-uncarboxylated MGP (dp-ucMGP), can be measured in plasma and has been associated with various cardiovascular (CV) markers, CV outcomes and mortality. In this study we hypothesize that increased RRI is associated with high levels of dp-ucMGP. DESIGN AND METHOD: We recruited participants via a multi-center family-based cross-sectional study in Switzerland exploring the role of genes and kidney hemodynamics in blood pressure regulation. Dp-ucMGP was quantified in plasma samples by sandwich ELISA. Renal doppler sonography was performed using a standardized protocol to measure RRIs on 3 segmental arteries in each kidney. The mean of the 6 measures was reported. Multiple regression analysis was performed to estimate associations between RRI and dp-ucMGP adjusting for sex, age, pulse pressure, mean pressure, renal function and other CV risk factors. RESULTS: We included 1035 participants in our analyses. Mean values were 0.64 ± 0.06 for RRI and 0.44 ± 0.21 (nmol/L) for dp-ucMGP. RRI was positively associated with dp-ucMGP both before and after adjustment for sex, age, body mass index, pulse pressure, mean pressure, heart rate, renal function, low and high density lipoprotein, smoking status, diabetes, blood pressure and cholesterol lowering drugs, and history of CV disease (P < 0.001). CONCLUSIONS: RRI is independently and positively associated with high levels of dp-ucMGP after adjustment for pulse pressure and common CV risk factors. Further studies are needed to determine if vitamin K supplementation can have a positive effect on renal vascular stiffness and kidney function.

Inactive Matrix Gla-Protein is associated with arterial stiffness in an adult population-based study

Increased pulse wave velocity (PWV) is a marker of aortic stiffness and an independent predictor of mortality. Matrix Gla-protein (MGP) is a vascular calcification inhibitor that needs vitamin K to be activated. Inactive MGP, known as desphospho-uncarboxylated MGP (dp-ucMGP), can be measured in plasma and has been associated with various cardiovascular markers, cardiovascular outcomes, and mortality. In this study, we hypothesized that high levels of dp-ucMGP are associated with increased PWV. We recruited participants via a multicenter family-based cross-sectional study in Switzerland. Dp-ucMGP was quantified in plasma by sandwich ELISA. Aortic PWV was determined by applanation tonometry using carotid and femoral pulse waveforms. Multiple regression analysis was performed to estimate associations between PWV and dp-ucMGP adjusting for age, renal function, and other cardiovascular risk factors. We included 1001 participants in our analyses (475 men and 526 women). Mean values were 7.87±2.10 m/s for PWV and 0.43±0.20 nmol/L for dp-ucMGP. PWV was positively associated with dp-ucMGP both before and after adjustment for sex, age, body mass index, height, systolic and diastolic blood pressure (BP), heart rate, renal function, low- and high-density lipoprotein, glucose, smoking status, diabetes mellitus, BP and cholesterol lowering drugs, and history of cardiovascular disease (P≤0.01). In conclusion, high levels of dp-ucMGP are independently and positively associated with arterial stiffness after adjustment for common cardiovascular risk factors, renal function, and age. Experimental studies are needed to determine whether vitamin K supplementation slows arterial stiffening by increasing MGP carboxylation.

Prevalence of vascular-endothelial growth factor, matrix metalloproteinases and tissue inhibitors of metalloproteinases in primary breast cancer

Our objective was to determine the presence of vascular endothelial growth factor (VEGF), matrix metalloproteinase-2 (MMP-2) and MMP-9 and specific tissue inhibitors of matrix metalloproteinase (TIMP-1 and TIMP-2) in tumor samples obtained from patients with primary breast cancer. We attempted to correlate these findings with the status of the sentinel lymph node (SLN) and clinical-pathological characteristics such as age, tumor size, histological type, histological grade, and vascular invasion. Tumor samples from 88 patients with primary breast cancer were analyzed. The immunoreactivity of VEGF, MMP-2, MMP-9, TIMP-1, and TIMP-2 in tumors was correlated with clinical and pathological features, as well as SLN status. Nonparametric, Mann-Whittney, Kruskal-Wallis, and Spearmann tests were used. Categorical variables were analyzed by the Pearson test. No statistically significant correlation was found between the amount of VEGF, MMP-2, MMP-9, TIMP-1, and TIMP-2 and the presence of tumor cells in the SLN. However, larger tumor diameter (P < 0.01) and the presence of vascular invasion (P < 0.01) were correlated positively with a positive SLN. A significant correlation of higher VEGF levels (P = 0.04) and lower TIMP-1 levels (P = 0.04) with ductal histology was also observed. Furthermore, lower TIMP-2 levels showed a statistically significant correlation with younger age (<50 years) and larger tumor diameter (2.0-5.0 cm). A positive SLN correlated significantly with a larger tumor diameter and the presence of vascular invasion. Higher VEGF and lower TIMP-1 levels were observed in patients with ductal tumors, while higher TIMP-1 levels were observed in lobular tumors.

Regulation of cell migration in cancer: investigation into the regulation of cancer cell blebbing in the extracellular matrix

Cell migration is a highly coordinated process and any aberration in the regulatory mechanisms could result in pathological conditions such as cancer. The ability of cancer cells to disseminate to distant sites within the body has made it difficult to treat. Cancer cells also exhibit plasticity that makes them able to interconvert from an elongated, mesenchymal morphology to an amoeboid blebbing form under different physiological conditions. Blebs are spherical membrane protrusions formed by actomyosin-mediated contractility of cortical actin resulting in increased hydrostatic pressure and subsequent detachment of the membrane from the cortex. Tumour cells use blebbing as an alternative mode of migration by squeezing through preexisting gaps in the ECM, and bleb formation is believed to be mediated by the Rho-ROCK signaling pathway. However, the involvement of transmembrane water and ion channels in cell blebbing has not been examined. In the present study, the role of the transmembrane water channels, aquaporins, transmembrane ion transporters and lipid signaling enzymes in the regulation of blebbing was investigated. Using 3D matrigel matrix as an in vitro model to mimic normal extracellular matrix, and a combination of confocal and time-lapse microscopy, it was found that AQP1 knockdown by siRNA ablated blebbing of HT1080 and ACHN cells, and overexpression of AQP1-GFP not only significantly increased bleb size with a corresponding decrease in bleb numbers, but also induced bleb formation in non-blebbing cell lines. Importantly, AQP1 overexpression reduces bleb lifespan due to faster bleb retraction. This novel finding of AQP1-facilitated bleb retraction requires the activity of the Na+/H+ pump as inhibition of the ion transporter, which was found localized to intracellular vesicles, blocked bleb retraction in both cell lines. This study also demonstrated that a differential regulation of cell blebbing by AQP isoforms exists as knockdown of AQP5 had no effect on bleb formation. Data from this study also demonstrates that the lipid signaling PLD2 signals through PA in the LPA-LPAR-Rho-ROCK axis to positively regulate bleb formation in both cell lines. Taken together, this work provides a novel role of AQP1 and Na+/H+ pump in regulation of cell blebbing, and this could be exploited in the development of new therapy to treat cancer.

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.