CMV matrices in random matrix theory and integrable systems: a survey

We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.Comment: Based on a talk given at the Short Program on Random Matrices, Random Processes and Integrable Systems, CRM, Universite de Montreal, 200

Associations between breast cancer subtype and neighborhood socioeconomic and racial composition among Black and White women

PURPOSE: Studies of Black-White differences in breast cancer subtype often emphasize potential ancestry-associated genetic or lifestyle risk factors without fully considering how the social or economic implications of race in the U.S. may influence risk. We assess whether neighborhood racial composition and/or socioeconomic status are associated with odds of triple-negative breast cancer (TNBC) diagnosis relative to the less-aggressive hormone receptor-positive/HER2-negative subtype (HR+ /HER-), and whether the observed relationships vary across women\u27s race and age groups. METHODS: We use multilevel generalized estimating equation models to evaluate odds of TNBC vs. HR+ /HER2- subtypes in a population-based cohort of 7291 Black and 74,208 White women diagnosed with breast cancer from 2006 to 2014. Final models include both neighborhood-level variables, adjusting for individual demographics and tumor characteristics. RESULTS: Relative to the HR+ /HER- subtype, we found modestly lower odds of TNBC subtype among White women with higher neighborhood median household income (statistically significant within the 45-64 age group, OR = 0.981 per $10,000 increase). Among Black women, both higher neighborhood income and higher percentages of Black neighborhood residents were associated with lower odds of TNBC relative to HR+ /HER2-. The largest reduction was observed among Black women diagnosed at age ≥ 65 (OR = 0.938 per$10,000 increase; OR = 0.942 per 10% increase in Black residents). CONCLUSION: The relationships between neighborhood composition, neighborhood socioeconomic status, and odds of TNBC differ by race and age. Racially patterned social factors warrant further exploration in breast cancer subtype disparities research

Childbearing postponement and child well-being: a complex and varied relationship?

Over the past several decades, U.S. fertility has followed a trend toward the postponement of motherhood. The socioeconomic causes and consequences of this trend have been the focus of attention in the demographic literature. Given the socioeconomic advantages of those who postpone having children, some authors have argued that the disadvantage experienced by certain groups would be reduced if they postponed their births. The weathering hypothesis literature, by integrating a biosocial perspective, complicates this argument and posits that the costs and benefits of postponement may vary systematically across population subgroups. In particular, the literature on the weathering hypothesis argues that as a consequence of their unique experiences of racism and disadvantage, African American women may experience a more rapid deterioration of their health, which could offset or eventually reverse any socioeconomic benefit of postponement. But because very few African American women postpone motherhood, efforts to find compelling evidence to support the arguments of this perspective rely on a strategy of comparison that is problematic because a potentially selected group of older black mothers are used to represent the costs of postponement. This might explain why the weathering hypothesis has played a rather limited role in the way demographers conceptualize postponement and its consequences for well-being. In order to explore the potential utility of this perspective, we turn our attention to the UK context. Because first-birth fertility schedules are similar for black and white women, we can observe (rather than assume) whether the meaning and consequences of postponement vary across these population subgroups. The results, obtained using linked UK census and birth record data, reveal evidence consistent with the weathering hypothesis in the United Kingdom and lend support to the arguments that the demographic literature would benefit from integrating insights from this biosocial perspective

Are benefits conferred with greater socioeconomic position undermined by racial discrimination among African American men?

http://dx.doi.org/10.1016/j.jomh.2012.03.00

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

Jedi public health: Co-creating an identity-safe culture to promote health equity

© 2016 The Authors. The extent to which socially-assigned and culturally mediated social identity affects health depends on contingencies of social identity that vary across and within populations in day-to-day life. These contingencies are structurally rooted and health damaging inasmuch as they activate physiological stress responses. They also have adverse effects on cognition and emotion, undermining self-confidence and diminishing academic performance. This impact reduces opportunities for social mobility, while ensuring those who "beat the odds" pay a physical price for their positive efforts. Recent applications of social identity theory toward closing racial, ethnic, and gender academic achievement gaps through changing features of educational settings, rather than individual students, have proved fruitful. We sought to integrate this evidence with growing social epidemiological evidence that structurally-rooted biopsychosocial processes have population health effects. We explicate an emergent framework, Jedi Public Health (JPH). JPH focuses on changing features of settings in everyday life, rather than individuals, to promote population health equity, a high priority, yet, elusive national public health objective. We call for an expansion and, in some ways, a re-orienting of efforts to eliminate population health inequity. Policies and interventions to remove and replace discrediting cues in everyday settings hold promise for disrupting the repeated physiological stress process activation that fuels population health inequities with potentially wide application.National Institute on Aging (Grant # R01 AG032632)National Institute on Aging (Grant # T32 AG00221

Jordan algebras and orthogonal polynomials

We illustrate how Jordan algebras can provide a framework for the interpretation of certain classes of orthogonal polynomials. The big -1 Jacobi polynomials are eigenfunctions of a first order operator of Dunkl type. We consider an algebra that has this operator (up to constants) as one of its three generators and whose defining relations are given in terms of anticommutators. It is a special case of the Askey-Wilson algebra AW(3). We show how the structure and recurrence relations of the big -1 Jacobi polynomials are obtained from the representations of this algebra. We also present ladder operators for these polynomials and point out that the big -1 Jacobi polynomials satisfy the Hahn property with respect to a generalized Dunkl operator.Comment: 11 pages, 30 reference