We develop a method that allows us to construct families of orthogonal matrix polynomials of size N ×N satisfying second order difference equations with polynomial coefficients. The existence (and properties) of these orthogonal families strongly depends on the non commutativity of the matrix product, the existence of singular matrices and the matrix size N .

An analysis of IQ in relation to head size (and by inference, brain size) was performed on some 14,000 children and their full siblings, almost evenly divided by race (white and black) and sex, on whom data were obtained at ages 4 and 7 years in the National Collaborative Perinatal Project. Within each race X sex group, IQ is significantly correlated with head size, age and body size having bee...

In this paper, we propose a new class of regular fractional repetition (FR) codes constructed from perfect difference families and quasi-perfect difference families to store big data in distributed storage systems. The main advantage of the proposed construction method is that it supports a wide range of code parameter values compared to existing ones, which is an important feature to be adopte...

It is well known that the classical families of orthogonal polynomials are characterized as the polynomial eigenfunctions of a second order homogenous linear differential/difference hypergeometric operator with polynomial coefficients. In this paper we present a study of the classical orthogonal polynomials sequences, in short classical OPS, in a more general framework by using the differential...

Using a national sample of 1,461 child protective services (CPS) investigations in the United States, we examine differences between black and white families with regard to caseworker ratings of risk and harm to the child, as well as the probability that a case is substantiated for maltreatment. We employ difference-in-difference methods to identify whether gaps in outcomes for black and white ...

BACKGROUND Brain arteriovenous malformations (BAVMs) are thought to be sporadic developmental vascular lesions, but familial occurrence has been described. We compared the characteristics of patients with familial BAVMs with those of patients with sporadic BAVMs. METHODS We systematically reviewed the literature on patients with familial BAVMs. Three families that were found in our centre wer...

Reducing the prevalence of household food insecurity has been a long-standing objective of the federal government. Previous research has found many negative consequences of food insecurity for families and households but has not examined its relationship with housing instability. Using longitudinal data from the Fragile Families and Child Wellbeing Study, difference-in-difference models show th...

Background The first and most important step in characterizing familial nonmedullary thyroid carcinoma (NMTC) is to distinguish the true familial patients, which is the prerequisite for all accurate analyses. This study aimed to investigate whether patients from families with ≥3 first-degree relatives affected with NMTC have different characteristics than patients from families with only two af...