Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure

This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure for x in [0,?), ? > ?1, a free parameter N and a shift c<0. We analyze the asymptotic behavior (both strong and relative to classical Laguerre polynomials) of these orthogonal polynomials as n tends to infinity

Zeros of Orthogonal Polynomials Generated by the Geronimus Perturbation of Measures

Proceedings of: 14th International Conference Computational Science and Its Applications (ICCSA 2014). Guimarães, Portugal, June 30 – July 3, 2014This paper deals with monic orthogonal polynomial sequences (MOPS in short) generated by a Geronimus canonical spectral transformation of a positive Borel measure μ, i.e., (x−c) −1dμ(x)+Nδ(x−c), for some free parameter N ∈ IR+ and shift c. We analyze the behavior of the corresponding MOPS. In particular, we obtain such a behavior when the mass N tends to infinity as well as we characterize the precise values of N such the smallest (respectively, the largest) zero of these MOPS is located outside the support of the original measure μ. When μ is semi-classical, we obtain the ladder operators and the second order linear differential equation satisfied by the Geronimus perturbed MOPS, and we also give an electrostatic interpretation of the zero distribution in terms of a logarithmic potential interaction under the action of an external field. We analyze such an equilibrium problem when the mass point of the perturbation c is located outside the support of μ

A new algorithm for computing the Geronimus transformations for large shifts

A monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. The basic Geronimus transformation with shift ? transforms the monic Jacobi matrix associated with a measure d? into the monic Jacobi matrix associated with d?/(x????)?+?C?(x????), for some constant C. In this paper we examine the algorithms available to compute this transformation and we propose a more accurate algorithm, estimate its forward errors, and prove that it is forward stable. In particular, we show that for C?=?0 the problem is very ill-conditioned, and we present a new algorithm that uses extended precision

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

Neighborhood risk and protective factors for teenage childbearing and fathering

Background and Purpose: Informed by ecological systems theory, social disorganization theory and social capital theory, this study investigates the neighborhood contexts associated with teenage childbearing and fathering for Latino and Black adolescents who resided in Denver public housing for a substantial period of time during their childhood. Specifically, I examine the extent to which teenage childbearing/fathering (between the ages of 15 and 19) are statistically related to various conditions in the neighborhoods in which these youth were raised. The purpose of this study is to examine how neighborhood effects may vary according to the timing and duration of neighborhood exposure. Methods: Methods This study utilized a secondary data source, the Denver Child Study, a large-scale, mixed-methods study of current and former residents of the Denver (CO) Housing Authority (DHA). Quasi-random assignment to neighborhoods offers a natural experiment for overcoming selection bias in the measurement of neighborhood effects. Data include (1) survey data from parent/caregivers; and (2) administrative data from the U.S.Census Bureau and the Piton 192 Foundation. Data gathered from parent/caregivers were geocoded for each year of their child(ren)\u27s life thereby providing a rare opportunity to comprehensively examine neighborhood exposure. The study sample (N=781) is approximately half Latino and half Black, and nearly one fifth of the sample birthed or fathered a child between the ages 15 and 19. Results: Using a two-level random effects logit model to account for clustering at the family level, I found that neighbborhoods with higher fractions of foreign born residents protected Black and Latino youth from teenage childbearing andfathering. This was true for contemporaneous, lagged, and cumulative models. In the cumulative model of neighborhood exposure, percentage of foreing born in the neighborhood evinced a larger effect on teenage childbearing/fathering than in separate developmental stages suggesting that neighborhood conditions across the lifecourse were magnified. Conclusions and Implications: Study findings are discussed in terms of their contributions to the literature regarding the magnitude of cumulative neighborhood effects and the existence of lagged and/or developmental stage specific effects of immigrant concentration on teenage childbearing/fathering for low-income Latino and Black youth. Study findings also are discussed in the context of expanding current policy and intervention efforts for teenage childbearing/fathering from focusing only on changing individual behavior to focusing on changeable social aspects of neighborhood. Finally recommendations for future research are made

Quantum walks: Schur functions meet symmetry protected topological phases

This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting of quantum walks, i.e. quantum analogs of classical random walks. We prove that topological indices classifying symmetry protected topological phases of quantum walks are encoded by matrix Schur functions built out of the walk. This main result of the paper reduces the calculation of these topological indices to a linear algebra problem: calculating symmetry indices of finite-dimensional unitaries obtained by evaluating such matrix Schur functions at the symmetry protected points $\pm1$. The Schur representation fully covers the complete set of symmetry indices for 1D quantum walks with a group of symmetries realizing any of the symmetry types of the tenfold way. The main advantage of the Schur approach is its validity in the absence of translation invariance, which allows us to go beyond standard Fourier methods, leading to the complete classification of non-translation invariant phases for typical examples.Comment: 33 pages, 1 figur

Essays on Health and Family Economics

This dissertation consists of three essays on health economics and family economics. Chapter 1 studies the impact of school on childhood obesity in Australia. Consistent with the global obesity epidemic, Australia's rate of childhood obesity has shown an alarming upward trend. While a trend of this magnitude can only be explained by the environment, the exact mechanism remains unclear. I compare early school entrants to late entrants, and finds large differences. This chapter reveals that the school environment is responsible for the phenomenon, and that the environment contributes mostly by exposing children to sugar sweetened beverages, rather than by causing a lack of physical exercise. Chapter 2 investigates the impact of gender-neutral and marriage-neutral custody laws on domestic violence and homicide in the United States. Using the difference in timing of custody law changes across different states, I find that a custody regime which is neutral in both gender and marriage leads to significant decline in domestic violence for women, and homicide for both men and women. Chapter 3 studies teen childbearing and establishes its quantitative relationship with maturation of adolescents. Teen childbearing is a particular social concern because unlike most other risky behaviors like smoking and binge drinking, it is a lifelong responsibility that cannot be reversed. Nevertheless, this irreversibility also makes it difficult to identify whether the involved individuals regret their childbearing decision or not. The answer to this question matters to adolescent policies since only if teen childbearing leads to maturation and regret, the society is in a position to intervene the autonomy of adolescents. This chapter applies the methodology devised in Mak (2015) to measure maturation using the simultaneous changes in many reversible risky behaviors. We find that teen childbearing is associated with 18% more probability of being mature conditional on being immature in the previous period for females; the corresponding figure for males are much smaller in magnitude. Together with some other supporting evidence, this result indicates that teen childbearing is a very negative shock to the involved females, yet the involved males tend to leave the burden to their partners