Search results for: Brando Villalobos-Villalobos

Authors: Brando Vagenende, Marie-Anne Guerry

Abstract:

For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: Alan Ruiz-Padilla, Brando Villalobos-Villalobos, Yeniley Ruiz-Noa, Claudia Mendoza-Macías, Claudia Palafox-Sánchez, Miguel Marín-Rosales, Álvaro Cruz, Rubén Rangel-Salazar

Abstract:

Introduction: In patients with rheumatoid arthritis, resistance or poor response to disease modifying antirheumatic drugs (DMARD) may be a reflection of the increase in g-P. The expression of g-P may be important in mediating the effluence of DMARD from the cell. In addition, P-glycoprotein is involved in the transport of cytokines, IL-1, IL-2 and IL-4, from normal lymphocytes activated to the surrounding extracellular matrix, thus influencing the activity of RA. The involvement of P-glycoprotein in the transmembrane transport of cytokines can serve as a modulator of the efficacy of DMARD. It was shown that a number of lymphocytes with glycoprotein P activity is increased in patients with RA; therefore, P-glycoprotein expression could be related to the activity of RA and could be a predictor of poor response to therapy. Objective: To evaluate in RA patients, if the G2677T/A MDR1 polymorphisms is associated with differences in the rate of therapeutic response to disease-modifying antirheumatic agents in patients with rheumatoid arthritis. Material and Methods: A prospective cohort study was conducted. Fifty seven patients with RA were included. They had an active disease according to DAS-28 (score >3.2). We excluded patients receiving biological agents. All the patients were followed during 6 months in order to identify the rate of therapeutic response according to the American College of Rheumatology (ACR) criteria. At the baseline peripheral blood samples were taken in order to identify the G2677T/A MDR1 polymorphisms using PCR- Specific allele. The fragment was identified by electrophoresis in polyacrylamide gels stained with ethidium bromide. For statistical analysis, the genotypic and allelic frequencies of MDR1 gene polymorphism between responders and non-responders were determined. Chi-square tests as well as, relative risks with 95% confidence intervals (95%CI) were computed to identify differences in the risk for achieving therapeutic response. Results: RA patients had a mean age of 47.33 ± 12.52 years, 87.7% were women with a mean for DAS-28 score of 6.45 ± 1.12. At the 6 months, the rate of therapeutic response was 68.7 %. The observed genotype frequencies were: for G/G 40%, T/T 32%, A/A 19%, G/T 7% and for A/A genotype 2%. Patients with G allele developed at 6 months of treatment, higher rate for therapeutic response assessed by ACR20 compared to patients with others alleles (p=0.039). Conclusions: Patients with G allele of the - G2677T/A MDR1 polymorphisms had a higher rate of therapeutic response at 6 months with DMARD. These preliminary data support the requirement for a deep evaluation of these and other genotypes as factors that may influence the therapeutic response in RA.

Keywords: pharmacogenetics, MDR1, P-glycoprotein, therapeutic response, rheumatoid arthritis

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