Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem

We provide a pure Nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of Reny (1999). In comparison with Reny's argument, our proof is brief. Our result subsumes a prior existence result of Reny (1999) that is not covered by his theorem. We use the main result to prove the existence of pure Nash equilibrium in a class of finite games in which agents' pure strategies are subsets of a given set, and in turn use this to prove the existence of stable configurations for games, similar to those used by Schelling (1971, 1972) to study residential segregation, in which agents choose locations.     

Fitting In: The Roles of Social Acceptance and Discrimination in Shaping the Academic Motivations of Latino Youth in the U.S. Southeast

Using data on 459 Latino ninth graders from the LA-SIAA and the NC-SIAA studies, we evaluate the specific educational values and beliefs that motivate the academic achievement of Latino youth and contrast the school experiences of Latino youth in an emerging Latino community, North Carolina, with the school experiences of youth living in a traditional settlement community, Los Angeles. Despite their greater fears of discrimination, we find that Latino youth in North Carolina are more academically motivated than their peers in Los Angeles. This is partially because they are more likely to be immigrants. Being an immigrant, having a stronger sense of ethnic identification, and having a stronger sense of family obligation were each linked to a more positive view of school environments. Therefore, these factors each partially explained the immigrant advantage in academic motivation and helped to counter the harmful effects of discrimination on academic motivation.     

Sacred Rites and Civil Rights: Religion's Effect on Attitudes Toward Same‐Sex Unions and the Perceived Cause of Homosexuality*

Objective. Past research reveals how religion and opinions about the cause of homosexuality influence attitudes concerning same‐sex unions. No study to date contains a comprehensive collection of religion measures while also accounting for views of the cause of homosexuality. Therefore, this study investigates the extent to which religion predicts certain attribution beliefs as well as attitudes toward same‐sex unions while controlling for attribution beliefs. Method. The Baylor Religion Survey (2007 ) is used to estimate binary logistic models predicting the effects of religion and attribution beliefs on attitudes toward same‐sex unions. Findings. First, religion is strongly associated with the belief that homosexuals choose their sexual orientation. Second, religion maintains a significant association with attitudes toward same‐sex unions despite inclusion of an attribution variable. Conclusion. Even if a biological explanation for homosexuality is ultimately proven, unfavorable attitudes toward same‐sex unions will most likely endure due to religion's persistent effect.     

Job satisfaction and ‘welfare‐to‐work‘: is any job a good job for Australian single mothers?

This exploratory study sought to assess the job satisfaction of employed Australian single mothers who had mandatory employment participation requirements. In particular, we sought to identify the characteristics of the job and the individual that were closely associated with participant's job satisfaction. Self‐report data on job satisfaction, employment characteristics and parenting stress were collected from 155 employed single mothers. Participant job satisfaction was compared to female Australian population norms and linear regression analyses determined the job‐related and individual predictors of single mothers' job satisfaction. Findings from this exploratory study revealed that single mothers involved in a mandatory welfare‐to‐work program experienced significantly lower job satisfaction than the Australian female population. The individual variable, parental distress, negatively predicted each of the six job satisfaction domains while being employed on a casual basis was inversely associated with three domains (job security, work hours and overall job satisfaction). The Australian government purported that making the transition from welfare to work would improve wellbeing for program participants, under the assumption that ‘any job's a good job‘. However, the relatively low levels of job satisfaction experienced by single mothers in the current study provide little support for this assumption.     

Parallelizing computation of expected values in recombinant binomial trees

Recombinant binomial trees are binary trees where each non-leaf node has two child nodes, but adjacent parents share a common child node. Such trees arise in option pricing in finance. For example, an option can be valued by evaluating the expected payoffs with respect to random paths in the tree. The cost to exactly compute expected values over random paths grows exponentially in the depth of the tree, rendering a serial computation of one branch at a time impractical. We propose a parallelization method that transforms the calculation of the expected value into an embarrassingly parallel problem by mapping the branches of the binomial tree to the processes in a multiprocessor computing environment. We also discuss a parallel Monte Carlo method and verify the convergence and the variance reduction behavior by simulation study. Performance results from R and Julia implementations are compared on a distributed computing cluster.     

A Leadership Training Group for at Risk Fifth & Seventh Graders: Results from A Brief Strength-Based Group Program

ABSTRACT

An increasing number of youth are exhibiting social, emotional, and behavioral problems that hinder their ability to function at grade level. Subsequently, school mental health services have not been able to address the need for services particularly among students who are minority and poor. A mixed methodology study was conducted to determine the treatment outcomes from a brief strength-based leadership training group for primarily students who are African American and poor. Pre–post scores on three scales and focus group data revealed significant positive changes in regard to internal areas of functioning and social skills, anger management skills, and school attitude. Gender and age significantly impacted outcomes.     

A comment on the orthogonalization of B-spline basis functions and their derivatives

Through the use of a matrix representation for B-splines presented by Qin (Vis. Comput. 16:177–186, 2000) we are able to reexamine calculus operations on B-spline basis functions. In this matrix framework the problem associated with generating orthogonal splines is reexamined, and we show that this approach can simplify the operations involved to linear matrix operations. We apply these results to a recent paper (Zhou et al. in Biometrika 95:601–619, 2008) on hierarchical functional data analysis using a principal components approach, where a numerical integration scheme was used to orthogonalize a set of B-spline basis functions. These orthogonalized basis functions, along with their estimated derivatives, are then used to construct estimates of mean functions and functional principal components. By applying the methods presented here such algorithms can benefit from increased speed and precision. An R package is available to do the computations.