Decomposing Finite Languages

The paper completely characterizes the primality of acyclic DFAs, where a DFA $\mathcal{A}$ is prime if there do not exist DFAs $\mathcal{A}_1,\dots,\mathcal{A}_t$ with $\mathcal{L}(\mathcal{A}) = \bigcap_{i=1}^{t} \mathcal{L}({\mathcal{A}_i})$ such that each $\mathcal{A}_i$ has strictly less states than the minimal DFA recognizing the same language as $\mathcal{A}$. A regular language is prime if its minimal DFA is prime. Thus, this result also characterizes the primality of finite languages. Further, the $\mathsf{NL}$-completeness of the corresponding decision problem $\mathsf{PrimeDFA}_{\text{fin}}$ is proven. The paper also characterizes the primality of acyclic DFAs under two different notions of compositionality, union and union-intersection compositionality. Additionally, the paper introduces the notion of S-primality, where a DFA $\mathcal{A}$ is S-prime if there do not exist DFAs $\mathcal{A}_1,\dots,\mathcal{A}_t$ with $\mathcal{L}(\mathcal{A}) = \bigcap_{i=1}^{t} \mathcal{L}(\mathcal{A}_i)$ such that each $\mathcal{A}_i$ has strictly less states than $\mathcal{A}$ itself. It is proven that the problem of deciding S-primality for a given DFA is $\mathsf{NL}$-hard. To do so, the $\mathsf{NL}$-completeness of $\mathsf{2MinimalDFA}$, the basic problem of deciding minimality for a DFA with at most two letters, is proven

Growth Mindset: Trend or Real Science?

The following literature review begins by answering the question, �growth mindset: trend or real science?� It answers this question with a brief history of how, in the 1970s, the idea of �attribution of failure behaviour� from researcher Carol Dweck (1975) evolved to the well-known concept of growth mindset today. The discovery that the brain is elastic and intelligence can be grown led researchers to wonder the ways in which mindset could be manipulated to improve outcomes in education. The research then follows a path of growth mindset interventions in primary schools and parent guided settings as well. Finally, the review addresses cost effectiveness of growth mindset interventions and potential challenges of the studies

The Demand For NFL Attendance: A Rational Addiction Model

This paper examines the demand for attendance at National Football League (NFL) games using a rational addiction model to test the hypothesis that professional football displays the properties of a habit-forming good.  Rational addiction theory suggests that past and future consumption play a part in determining the current period’s consumption for habit-forming goods.  Additionally, we postulate the behavioral implications of profit-maximizing ticket pricing behavior by NFL teams.  Previous studies have been unable to detect pricing power by NFL teams.  Our model of pricing power allows us to identify theoretically- anticipated pricing behavior.  A pooled data set is collected using statistics from each NFL team from the 1983 to the 2008 seasons.  Current attendance is modeled as a function of team specific variables, including past and future attendance, ticket price, and team performance.  The model is estimated using Two-Stage Least Squares (2SLS).  We also treat the censored nature of ticket demand as NFL teams frequently experience sell-outs.  It is found that past and future attendance, winning percentage, the age of the stadium in which a team plays, and own-price demand elasticity influence attendance.  The fact that coefficients for past and future attendance are positive and significant in this analysis lends support to the notion that NFL fans display characteristics of rational addiction in their consumption behavior.  Further, we find evidence to support profit-maximizing behavior in ticket sales

Empirical model of global electron temperature distribution between 300 and 700 km based on data from Aeros-A

An empirical model function of the global electron temperature distribution has been determined based on the measurements of the planar Retarding Potential Analyzer on-board the Aeros-A satellite. The model represents the mean temperature between 300 and 700 km altitude at 0300 LT and 1500 LT depending on latitude, longitude, and height. The model values are compared with all the measured data to show the accuracy achieved and the mean spread of the data for different latitudes. A clear correlation was not found between the electron temperature and geophysical indices such as Kp or sunspot number for the period of low solar activity between January and August, 1973. Seasonal and annual effects could not be detected. The mathematical background and method used to generate the model function is described in the appendix.           ARK: https://n2t.net/ark:/88439/y033123 Permalink: https://geophysicsjournal.com/article/286 &nbsp

Does Affirmative Action Lead to Mismatch? A New Test and Evidence

We argue that once we take into account the students' rational enrollment decisions, mismatch in the sense that the intended beneficiary of affirmative action admission policies are made worse off could occur only if selective universities possess private information about students' post-enrollment treatment effects. This necessary condition for mismatch provides the basis for a new test. We propose an empirical methodology to test for private information in such a setting. The test is implemented using data from Campus Life and Learning Project (CLL) at Duke. Evidence shows that Duke does possess private information that is a statistically significant predictor of the students' post-enrollment academic performance. We also propose strategies to evaluate more conclusively whether the evidence of Duke private information has generated mismatch.

Career success: the role of teenage career aspirations, ambition value and gender in predicting adult social status and earnings

Links between family social background, teenage career aspirations, educational performance and adult social status attainment are well documented. Using a contextual developmental framework, this article extends previous research by examining the role of gender and teenage ambition value in shaping social status attainment and earnings in adulthood. Drawing on data from an 18-year British follow up study we tested a path model linking family background factors (such as family social status and parental aspirations) and individual agency factors in adolescence (in particular, career aspirations and ambition value) to social status attainment and earnings in adulthood. The findings suggest that ambition value is linked to adult earnings. That is, young people for whom it is important to get on in their job earn more money in adulthood than their less ambitious peers. The findings also confirm that teenage career aspirations are linked to adult social status attainment, and suggest that family background factors, teenage career aspirations and ambition value interact to influence social status attainment and earnings in adulthood. Gender differences are discusse