Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A single statistic for monitoring the covariance matrix of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Increased Levels of NOTCH1, NF-kappa B, and Other Interconnected Transcription Factors Characterize Primitive Sets of Hematopoietic Stem Cells

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

Preliminary core sets of measures for disease activity and damage assessment in juvenile systemic lupus erythematosus and juvenile dermatomyositis

Objective. To identify preliminary core sets of outcome variables for disease activity and damage assessment in juvenile systemic lupus erythematosus (JSLE) and juvenile dermatomyositis (JDM). Methods. Two questionnaire surveys were mailed to 267 physicians from 46 different countries asking each member to select and rank the response variables used when assessing clinical response in patients with JSLE or JDM. Next, 40 paediatric rheumatologists from 34 countries met and, using the nominal group technique, selected the domains to be included in the disease activity and damage core sets for JSLE and JDM. Results. A total of 41 response variables for JSLE and 37 response variables for JDM were selected and ranked through the questionnaire surveys. In the consensus conference, domains selected for both JSLE and JDM activity or damage core sets included the physician and parent/patient subjective assessments and a global score tool. Domains specific for JSLE activity were the immunological tests and the kidney function parameters. Concerning JDM, functional ability and muscle strength assessments were indicated for both activity and damage core sets, whereas serum muscle enzymes were included only in the activity core set. A specific paediatric domain called 'growth and development' was introduced in the disease damage core set for both diseases and the evaluation of health-related quality of life was advised in order to capture the influence of the disease on the patient lifestyle. Conclusions. We developed preliminary core sets of measures for disease activity and damage assessment in JSLE and JDM. The prospective validation of the core sets is in progress.

Description and genetic analysis of three sets of monozygotic twins resulting from transfers of single embryos to recipient mares

Case Description-3 sets of monozygotic twins resulting from transfers of single embryos to recipient mares were examined. Clinical Findings-In all 3 recipient mares with twin pregnancies, only 1 embryonic vesicle was detected before day 25 of gestation. In 1 recipient mare, 2 apparent adjacent vesicles, each containing an embryo with a heartbeat, were visualized on ultrasonographic examination on day 37 of gestation. The other 2 recipient mares underwent ultrasonographic examination on day 30 of gestation, at which time only 1 vesicle and embryo was identified. In these latter 2 recipient mares, however, a thorough ultrasonographic examination for a second conceptus on day 30 had not been performed, as only 1 embryo had been transferred and visualized on early ultrasonographic examination. Treatment and Outcome-All twin pregnancies resulted in death of both fetuses. Genetic analysis confirmed that each set of monozygotic twins originated from the transferred embryo. Clinical Relevance-Monozygotic twin pregnancy may occur after embryo transfer; thus recipient mares should be examined thoroughly for multiple conceptuses, especially between 25 and 30 days of gestation. At this time, the allantoides of monozygotic twins should be visible ultrasonographically and effective management may still be possible.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Energy expenditure during multiple sets of leg press and bench press

The purpose of this study was to quantify energy expenditure (EE) during multiple sets of leg press (LP) and bench press (BP) exercises in 10 males with at least 1 yr of resistance training (RT). The subjects underwent two sessions to determine 1 repetition maximum (1RM) on the BP and LP and one protocol consisting of a warm up and 4 sets for 10 repetitions at 70% 1RM with a 3-min rest period between sets for each exercise. Energy expenditure was calculated as the sum of oxygen uptake (aerobic component), EPOC, and lactate production (anaerobic component). There were no significant differences in EE between exercises for sets 1 to 4 and the total energy expended. However, statistical analysis revealed a significant difference (P<0.05) between exercises in RT economy (BP, 0.0206 ± 0.0044 kcal·kg-1 vs. LP, 0.0051 ± 0.0015 kcal·kg-1). Within exercise comparison showed set 4 was significantly different from sets 1 and 3 for BP, and for LP a significant difference was found between set 4 and sets 1, 2 and 3. Our results point to an increase in EE during multiple sets at 70% 1RM and show that in spite of the difference in muscle mass involved and total work done during each type of exercise, EE was not different due to greater economy during the LP.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures

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

Description of the attainable sets of one-dimensional differential inclusions

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.

Attribute charts for monitoring the mean vector of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

‘Gene shaving’ as a method for identifying distinct sets of genes with similar expression patterns

Background: Large gene expression studies, such as those conducted using DNA arrays, often provide millions of different pieces of data. To address the problem of analyzing such data, we describe a statistical method, which we have called ‘gene shaving’. The method identifies subsets of genes with coherent expression patterns and large variation across conditions. Gene shaving differs from hierarchical clustering and other widely used methods for analyzing gene expression studies in that genes may belong to more than one cluster, and the clustering may be supervised by an outcome measure. The technique can be ‘unsupervised’, that is, the genes and samples are treated as unlabeled, or partially or fully supervised by using known properties of the genes or samples to assist in finding meaningful groupings. Results: We illustrate the use of the gene shaving method to analyze gene expression measurements made on samples from patients with diffuse large B-cell lymphoma. The method identifies a small cluster of genes whose expression is highly predictive of survival. Conclusions: The gene shaving method is a potentially useful tool for exploration of gene expression data and identification of interesting clusters of genes worth further investigation.

Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.