Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation

We consider the polynomials $\phi_n(z)= \kappa_n (z^n+ b_{n-1} z^{n-1}+ >...)$ orthonormal with respect to the weight $\exp(\sqrt{\lambda} (z+ 1/z)) dz/2 \pi i z$ on the unit circle in the complex plane. The leading coefficient $\kappa_n$ is found to satisfy a difference-differential (spatially discrete) equation which is further proved to approach a third order differential equation by double scaling. The third order differential equation is equivalent to the Painlev\'e II equation. The leading coefficient and second leading coefficient of $\phi_n(z)$ can be expressed asymptotically in terms of the Painlev\'e II function.Comment: 16 page

Market Structure, Strike Activity, and Union Wage Settlements

We attempt a synthesis of the industrial relations market structure hypothesis with the modern asymmetric information theory of wage and strike outcomes The industrial relations literature contains a variety of arguments indicating that wage settlements should be positively related to the degree of product market sales concentration and the degree of product market coverage by the union. An asymmetric information bargaining model is specified that relates these same variables to strike probabilities as well as wage settlements. Our empirical analysis is conducted for :he periods from 1970-1380 (strikes) and 1976-1980 (wages). We find that the relation between trade-adjusted sales concentration and wage settlements is positive at low levels of concentration but negative at high levels of concentration. The relation is always negative for strike probabilities. We also find that the relation between the trade-adjusted percent of the product market covered by the same union and the percentage covered by other union are positively related to both wage settlements and strike probabilities. Our empirical analysis includes a rich set of controls including unrestricted time and industry effects, which do not affect the major conclusions.

Evaluating Midwifery Units (EMU): A prospective cohort study of freestanding midwifery units in New South Wales, Australia

© 2014, BMJ Publishing Group. All rights reserved. Objective: To compare maternal and neonatal birth outcomes and morbidities associated with the intention to give birth in two freestanding midwifery units and two tertiary-level maternity units in New South Wales, Australia. Design: Prospective cohort study. Participants: 494 women who intended to give birth at freestanding midwifery units and 3157 women who intended to give birth at tertiary-level maternity units. Participants had low risk, singleton pregnancies and were at less than 28+0 weeks gestation at the time of booking. Primary and secondary outcome measures: Primary outcomes were mode of birth, Apgar score of less than 7 at 5 min and admission to the neonatal intensive care unit or special care nursery. Secondary outcomes were onset of labour, analgesia, blood loss, management of third stage of labour, perineal trauma, transfer, neonatal resuscitation, breastfeeding, gestational age at birth, birth weight, severe morbidity and mortality. Results: Women who planned to give birth at a freestanding midwifery unit were significantly more likely to have a spontaneous vaginal birth (AOR 1.57; 95% CI 1.20 to 2.06) and significantly less likely to have a caesarean section (AOR 0.65; 95% CI 0.48 to 0.88). There was no significant difference in the AOR of 5 min Apgar scores, however, babies from the freestanding midwifery unit group were significantly less likely to be admitted to neonatal intensive care or special care nursery (AOR 0.60; 95% CI 0.39 to 0.91). Analysis of secondary outcomes indicated that planning to give birth in a freestanding midwifery unit was associated with similar or reduced odds of intrapartum interventions and similar or improved odds of indicators of neonatal well-being. Conclusions: The results of this study support the provision of care in freestanding midwifery units as an alternative to tertiary-level maternity units for women with low risk pregnancies at the time of booking

Gap Probabilities for Edge Intervals in Finite Gaussian and Jacobi Unitary Matrix Ensembles

The probabilities for gaps in the eigenvalue spectrum of the finite dimension $N \times N$ random matrix Hermite and Jacobi unitary ensembles on some single and disconnected double intervals are found. These are cases where a reflection symmetry exists and the probability factors into two other related probabilities, defined on single intervals. Our investigation uses the system of partial differential equations arising from the Fredholm determinant expression for the gap probability and the differential-recurrence equations satisfied by Hermite and Jacobi orthogonal polynomials. In our study we find second and third order nonlinear ordinary differential equations defining the probabilities in the general $N$ case. For N=1 and N=2 the probabilities and thus the solution of the equations are given explicitly. An asymptotic expansion for large gap size is obtained from the equation in the Hermite case, and also studied is the scaling at the edge of the Hermite spectrum as $N \to \infty$, and the Jacobi to Hermite limit; these last two studies make correspondence to other cases reported here or known previously. Moreover, the differential equation arising in the Hermite ensemble is solved in terms of an explicit rational function of a {Painlev\'e-V} transcendent and its derivative, and an analogous solution is provided in the two Jacobi cases but this time involving a {Painlev\'e-VI} transcendent.Comment: 32 pages, Latex2

Injecting New Workforce Leaders in Tourism, Hospitality and Environmental Science: A Community-Engaged Learning and Immersion Class

Tourism, especially nature-based tourism, is a major and growing industry in Maine. Therefore, it is important that colleges and universities graduate leaders into the Maine workforce with specific knowledge of the tourism and hospitality industry and with a connection to the environment in which it is flourishing. To graduate these potential leaders, schools must do a better job at retaining and graduating students from diverse socioeconomic backgrounds. Community-engaged learning, including immersion classes, are a key strategy to increase student persistence in some programs at the University of Southern Maine (USM). Two academic units at USM, the Program in Tourism and Hospitality and the Department of Environmental Science and Policy, collaborate in delivering a colocated intensive immersion class for all new majors. This engagement early in their college career fosters a sense of community among the students and with the industry in which they will work. We argue that this community engagement is a factor contributing to student retention and success in these programs and will help create the creative, resilient, locally active leaders needed to guide sustainable tourism development in Maine

{\bf τ\tau-Function Evaluation of Gap Probabilities in Orthogonal and Symplectic Matrix Ensembles}

It has recently been emphasized that all known exact evaluations of gap probabilities for classical unitary matrix ensembles are in fact $\tau$-functions for certain Painlev\'e systems. We show that all exact evaluations of gap probabilities for classical orthogonal matrix ensembles, either known or derivable from the existing literature, are likewise $\tau$-functions for certain Painlev\'e systems. In the case of symplectic matrix ensembles all exact evaluations, either known or derivable from the existing literature, are identified as the mean of two $\tau$-functions, both of which correspond to Hamiltonians satisfying the same differential equation, differing only in the boundary condition. Furthermore the product of these two $\tau$-functions gives the gap probability in the corresponding unitary symmetry case, while one of those $\tau$-functions is the gap probability in the corresponding orthogonal symmetry case.Comment: AMS-Late

The weight-inclusive vs. weight-normative approach to health: Evaluating the evidence for prioritizing well-being over weight

Using an ethical lens, this review evaluates two methods of working within patient care and public health: the weight-normative approach (emphasis on weight and weight loss when defining health and well-being) and the weight-inclusive approach (emphasis on viewing health and well-being as multifaceted while directing efforts toward improving health access and reducing weight stigma). Data reveal that the weight-normative approach is not effective for most people because of high rates of weight regain and cycling from weight loss interventions, which are linked to adverse health and well-being. Its predominant focus on weight may also foster stigma in health care and society, and data show that weight stigma is also linked to adverse health and well-being. In contrast, data support a weight-inclusive approach, which is included in models such as Health at Every Size for improving physical (e.g., blood pressure), behavioral (e.g., binge eating), and psychological (e.g., depression) indices, as well as acceptability of public health messages. Therefore, the weight-inclusive approach upholds nonmaleficience and beneficience, whereas the weight-normative approach does not. We offer a theoretical framework that organizes the research included in this review and discuss how it can guide research efforts and help health professionals intervene with their patients and community