A "missing" family of classical orthogonal polynomials

We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi polynomials in the limit $q=-1$. We also show that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for $q=-1$.Comment: 20 page

Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we study the convergence of the Wall rational functions via the development of a rational analogue to the Szeg\H o theory, in the case where the interpolation points may accumulate on the unit circle. This leads us to generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields asymptotics of a novel type.Comment: a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\H o type asymptotics) is extende

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Chronic psychosocial and financial burden accelerates 5-year telomere shortening: findings from the Coronary Artery Risk Development in Young Adults Study.

Leukocyte telomere length, a marker of immune system function, is sensitive to exposures such as psychosocial stressors and health-maintaining behaviors. Past research has determined that stress experienced in adulthood is associated with shorter telomere length, but is limited to mostly cross-sectional reports. We test whether repeated reports of chronic psychosocial and financial burden is associated with telomere length change over a 5-year period (years 15 and 20) from 969 participants in the Coronary Artery Risk Development in Young Adults (CARDIA) Study, a longitudinal, population-based cohort, ages 18-30 at time of recruitment in 1985. We further examine whether multisystem resiliency, comprised of social connections, health-maintaining behaviors, and psychological resources, mitigates the effects of repeated burden on telomere attrition over 5 years. Our results indicate that adults with high chronic burden do not show decreased telomere length over the 5-year period. However, these effects do vary by level of resiliency, as regression results revealed a significant interaction between chronic burden and multisystem resiliency. For individuals with high repeated chronic burden and low multisystem resiliency (1 SD below the mean), there was a significant 5-year shortening in telomere length, whereas no significant relationships between chronic burden and attrition were evident for those at moderate and higher levels of resiliency. These effects apply similarly across the three components of resiliency. Results imply that interventions should focus on establishing strong social connections, psychological resources, and health-maintaining behaviors when attempting to ameliorate stress-related decline in telomere length among at-risk individuals

Is telomere length socially patterned? Evidence from the West of Scotland Twenty-07 study

Lower socioeconomic status (SES) is strongly associated with an increased risk of morbidity and premature mortality, but it is not known if the same is true for telomere length, a marker often used to assess biological ageing. The West of Scotland Twenty-07 Study was used to investigate this and consists of three cohorts aged approximately 35 (N = 775), 55 (N = 866) and 75 years (N = 544) at the time of telomere length measurement. Four sets of measurements of SES were investigated: those collected contemporaneously with telomere length assessment, educational markers, SES in childhood and SES over the preceding twenty years. We found mixed evidence for an association between SES and telomere length. In 35-year-olds, many of the education and childhood SES measures were associated with telomere length, i.e. those in poorer circumstances had shorter telomeres, as was intergenerational social mobility, but not accumulated disadvantage. A crude estimate showed that, at the same chronological age, social renters, for example, were nine years (biologically) older than home owners. No consistent associations were apparent in those aged 55 or 75. There is evidence of an association between SES and telomere length, but only in younger adults and most strongly using education and childhood SES measures. These results may reflect that childhood is a sensitive period for telomere attrition. The cohort differences are possibly the result of survival bias suppressing the SES-telomere association; cohort effects with regard different experiences of SES; or telomere possibly being a less effective marker of biological ageing at older ages

Geographic and Racial Variation in Premature Mortality in the U.S.: Analyzing the Disparities

Life expectancy at birth, estimated from United States period life tables, has been shown to vary systematically and widely by region and race. We use the same tables to estimate the probability of survival from birth to age 70 (S70), a measure of mortality more sensitive to disparities and more reliably calculated for small populations, to describe the variation and identify its sources in greater detail to assess the patterns of this variation. Examination of the unadjusted probability of S70 for each US county with a sufficient population of whites and blacks reveals large geographic differences for each race-sex group. For example, white males born in the ten percent healthiest counties have a 77 percent probability of survival to age 70, but only a 61 percent chance if born in the ten percent least healthy counties. Similar geographical disparities face white women and blacks of each sex. Moreover, within each county, large differences in S70 prevail between blacks and whites, on average 17 percentage points for men and 12 percentage points for women. In linear regressions for each race-sex group, nearly all of the geographic variation is accounted for by a common set of 22 socio-economic and environmental variables, selected for previously suspected impact on mortality; R2 ranges from 0.86 for white males to 0.72 for black females. Analysis of black-white survival chances within each county reveals that the same variables account for most of the race gap in S70 as well. When actual white male values for each explanatory variable are substituted for black in the black male prediction equation to assess the role explanatory variables play in the black-white survival difference, residual black-white differences at the county level shrink markedly to a mean of −2.4% (+/−2.4); for women the mean difference is −3.7% (+/−2.3)

Pathways of Early Fatherhood, Marriage, and Employment: A Latent Class Growth Analysis

http://dx.doi.org/10.1007/s13524-011-0022-

Maternal Risk of Breeding Failure Remained Low throughout the Demographic Transitions in Fertility and Age at First Reproduction in Finland

Radical declines in fertility and postponement of first reproduction during the recent human demographic transitions have posed a challenge to interpreting human behaviour in evolutionary terms. This challenge has stemmed from insufficient evolutionary insight into individual reproductive decision-making and the rarity of datasets recording individual long-term reproductive success throughout the transitions. We use such data from about 2,000 Finnish mothers (first births: 1880s to 1970s) to show that changes in the maternal risk of breeding failure (no offspring raised to adulthood) underlay shifts in both fertility and first reproduction. With steady improvements in offspring survival, the expected fertility required to satisfy a low risk of breeding failure became lower and observed maternal fertility subsequently declined through an earlier age at last reproduction. Postponement of the age at first reproduction began when this risk approximated zero–even for mothers starting reproduction late. Interestingly, despite vastly differing fertility rates at different stages of the transitions, the number of offspring successfully raised to breeding per mother remained relatively constant over the period. Our results stress the importance of assessing the long-term success of reproductive strategies by including measures of offspring quality and suggest that avoidance of breeding failure may explain several key features of recent life-history shifts in industrialized societies