Equidistribution of small points, rational dynamics, and potential theory

If phi(z) is a rational function on P^1 of degree at least 2 with coefficients in a number field k, we compute the homogeneous transfinite diameter of the v-adic filled Julia sets of phi for all places v of k by introducing a new quantity called the homogeneous sectional capacity. In particular, we show that the product over all places of these homogeneous transfinite diameters is 1. We apply this product formula and some new potential-theoretic results concerning Green's functions on Riemann surfaces and Berkovich spaces to prove an adelic equidistribution theorem for dynamical systems on the projective line. This theorem, which generalizes the results of Baker-Hsia, says that for each place v of k, there is a canonical probability measure on the Berkovich space P^1_{Berk,v} over C_v such that if z_n is a sequence of algebraic points in P^1 whose canonical heights with respect to phi tend to zero, then the z_n's and their Galois conjugates are equidistributed with respect to mu_{phi,v} for all places v of k. For archimedean v, P^1_{Berk,v} is just the Riemann sphere, mu_{phi,v} is Lyubich's invariant measure, and our result is closely related to a theorem of Lyubich and Freire-Lopes-Mane.Comment: 50 pages; v2 contains additional references, exposition has been modified, and Sections 7 and 8 from v1 have been removed to shorten the paper's lengt

Negotiating Among Opportunity and Constraint: The Participation of Young People in Out-of-School-Time Activities

Out-of-school opportunities -- such as arts and music programs, sports teams, community service and youth entrepreneurship opportunities -- are increasingly seen as potentially powerful tools to promote positive youth development and to prevent problematic behaviors. Based on in-depth, semi-structured interviews conducted with 99 students in 10th grade in four Chicago Public Schools, this Chapin Hall report explores young people's perspectives on their use of out-of-school time and the influences, barriers, contexts, and processes that contribute to their choices and experiences. The report investigates how young people learn about and choose to get involved in different kinds of out-of-school opportunities and the influence that family members, peers, and non-family adults have on their thinking and decision making. It also explores the relationship between young people's participation in out-of-school programs and their interests, aspirations, and assessments of the kinds of opportunities and barriers found within their families, schools and neighborhoods. Finally, it offers conclusions and recommendations about how to improve opportunities for young people based on the insights provided by them, including specific suggestions about approaches to outreach, access, ongoing engagement and program provision

Evaluation of reliability modeling tools for advanced fault tolerant systems

The Computer Aided Reliability Estimation (CARE III) and Automated Reliability Interactice Estimation System (ARIES 82) reliability tools for application to advanced fault tolerance aerospace systems were evaluated. To determine reliability modeling requirements, the evaluation focused on the Draper Laboratories' Advanced Information Processing System (AIPS) architecture as an example architecture for fault tolerance aerospace systems. Advantages and limitations were identified for each reliability evaluation tool. The CARE III program was designed primarily for analyzing ultrareliable flight control systems. The ARIES 82 program's primary use was to support university research and teaching. Both CARE III and ARIES 82 were not suited for determining the reliability of complex nodal networks of the type used to interconnect processing sites in the AIPS architecture. It was concluded that ARIES was not suitable for modeling advanced fault tolerant systems. It was further concluded that subject to some limitations (the difficulty in modeling systems with unpowered spare modules, systems where equipment maintenance must be considered, systems where failure depends on the sequence in which faults occurred, and systems where multiple faults greater than a double near coincident faults must be considered), CARE III is best suited for evaluating the reliability of advanced tolerant systems for air transport

Humans to Mars in 1999

A set of vehicle designs and a mission architecture that was developed to send humans to Mars in the 1990's are discussed. Launching, landing, a 500 day stay on Mars, and a return to Earth are discussed. The plan is not merely a one shot expedition, but puts into place immediately an economical method of Earth-Mars transportation, real surface exploratory mobility, and significant base capabilities that can rapidly evolve into a mostly self-sufficient Mars colony. Since the plans call for the use of a combination of off the shelf technology and new technology that can be easily developed, the authors argue that there is no reason to postpone the exploration of Mars until several decades after a lunar base build-up

Of Junk Food and Junk Science

The popular press has triumphantly announced that the cause of the obesity epidemic is “junk food.†After a moment’s reflection, however, it seems likely that the true causal structure of the obesity epidemic can be neither single-equation nor univariate. Therefore, while the hypothesis that “junk food†is the cause of obesity has little a priori plausibility, these articles in the popular press present a testable hypothesis that, in spite of some measurement impossibilities, is tested here. While one can always argue about p values etc., it is safe to say that the results show no evidence to indicate support for a causal link. The second section of the paper explains this result and suggests a rudimentary structural model of obesity that begins to address the issues of specification error, simultaneity, etc., that plague much of the obesity research. This model shows that because of the dynamic nature of weight status, there is no necessary reason to expect to find a statistical relation between a person’s observed weight and the amount he or she is currently eating or exercising. Therefore, studies which regress weight, obesity, or the probability of obesity on eating and exercise patterns have serious specification error. Further development of structural econometric models of obesity may lead to consistent estimates of the partial effects of exogenous variables on obesity levels. We conclude with a discussion of the implications for policy development and industry.obesity, junk food, Granger-causality, Research Methods/ Statistical Methods, Teaching/Communication/Extension/Profession, Q10, Q16,

Securities Transaction Taxes for U.S. Financial Markets

This paper examines the viability of security transaction excise taxes (STETs) as one policy tool for promoting a more stable financial environment, specifically with respect to the U.S. economy. Contrary to a large recent critical literature, we show that a STET can be designed without creating large distortions between segments of the financial market. We also show that a modest STET for the U.S.—beginning with a 0.5 percent tax on equity trades and scaled appropriately for other financial instruments—would generate substantial new government revenues, on the order of $100 billion per year.Financial Market; Securities