Are NFL Athletes Receiving Over-Valued Contracts?

Many sport research studies have been conducted that examine the performance of professional athletes and their corresponding effect on franchise winning percentages, team revenues, economic repercussions, performance-based compensation, and much more. Research in the National Football League, however, has been found to be somewhat limited due to the numerous possible positions and resulting vastness of position-specific variables. The NFL lockout in 2011 caused many to question the specific relationship between professional athlete performance and salary distribution. This study’s purpose was to find a collection of variables with which all NFL athletes could be compared, and to identify relationships existing between a player’s performance and his value/salary. Data was collected from USAToday.com, Pro-football-reference.com, and AdvancedNFLStats.com. This data was then organized and manipulated into a format that allowed all players in the league during the 2009 season to be compared. Of the nine variables considered for this study, four were found to have a significant relationship with a player’s value/salary. These results were utilized to create a Player Valuation model and then analyze the overall salary distribution throughout the NFL. From this, it was observed while there are many athletes in the NFL that receive extravagant salaries well over their projected value, there is a much larger portion of the league that is undervalued and receive less than their projected value. It was then concluded that a super-star variable would be necessary to create a more accurate Player Valuation model, and the reason there is a larger proportion of NFL players receiving a lower salary than they deserve is due to franchise cap limits. These cap limits place pressure on franchises to push down the salaries of non-superstar athletes in order to compensate for the salaries required for the super-star athletes on their rosters

Quantum Loewner Evolution

What is the scaling limit of diffusion limited aggregation (DLA) in the plane? This is an old and famously difficult question. One can generalize the question in two ways: first, one may consider the {\em dielectric breakdown model} $\eta$-DBM, a generalization of DLA in which particle locations are sampled from the $\eta$-th power of harmonic measure, instead of harmonic measure itself. Second, instead of restricting attention to deterministic lattices, one may consider $\eta$-DBM on random graphs known or believed to converge in law to a Liouville quantum gravity (LQG) surface with parameter $\gamma \in [0,2]$. In this generality, we propose a scaling limit candidate called quantum Loewner evolution, QLE$(\gamma^2, \eta)$. QLE is defined in terms of the radial Loewner equation like radial SLE, except that it is driven by a measure valued diffusion $\nu_t$ derived from LQG rather than a multiple of a standard Brownian motion. We formalize the dynamics of $\nu_t$ using an SPDE. For each $\gamma \in (0,2]$, there are two or three special values of $\eta$ for which we establish the existence of a solution to these dynamics and explicitly describe the stationary law of $\nu_t$. We also explain discrete versions of our construction that relate DLA to loop-erased random walk and the Eden model to percolation. A certain "reshuffling" trick (in which concentric annular regions are rotated randomly, like slot machine reels) facilitates explicit calculation. We propose QLE$(2,1)$ as a scaling limit for DLA on a random spanning-tree-decorated planar map, and QLE$(8/3,0)$ as a scaling limit for the Eden model on a random triangulation. We propose using QLE$(8/3,0)$ to endow pure LQG with a distance function, by interpreting the region explored by a branching variant of QLE$(8/3,0)$, up to a fixed time, as a metric ball in a random metric space.Comment: 132 pages, approximately 100 figures and computer simulation

Climate Change Hysteria and the Supreme Court: The Economic Impact of Global Warming on the U.S. and the Misguided Regulation of Greenhouse Gas Emissions under the Clean Air Act

In the spring of 2007, the U.S. Supreme Court ruled in Massachusetts v. EPA that the U.S. Environmental Protection Agency (EPA) must promulgate automobile tailpipe C02 emission standards under Section 202 of the Clean Air Act (CAA). American environmentalists hailed the Supreme Court's decision as an important victory in the battle to curb global warming. This article argues to the contrary that: 1) a large body of economic work demonstrates that the likely pattern of costs and benefits from climate change in the United States bears no resemblance to the pollution problems that Congress intended to deal with in the Clean Air Act, with moderate climate change predominantly benefiting, rather than harming, the U.S. -- so that that the Clean Air Act cannot reasonably be interpreted to cover greenhouse gas emissions; 2) By effectively forcing the EPA to regulate ghg emissions under a statute that was never intended to cover the very different problem of climate change, the Court has changed the policy status quo in a way that makes socially desirable federal climate change legislation less likely; and 3) given the global nature of the greenhouse gas emission problem, unilateral emission limits in the U.S. are likely to be worse than ineffective, in that they will likely have the perverse effect of lessening the incentive for latecomers to climate change regulation (such as China) to themselves take costly action to reduce such emissions. The article concludes by arguing that a sensible formulation of U.S. climate change policy would involve measures to respond both to the long-term threat to the U.S. and the short-term threat to developing countries. There are policy instruments appropriate to these goals: large increases in subsidies for research and development into clean coal and alternative fuels to respond to the long term threat to the U.S.; redirecting foreign aid to fund climate change adaptation in developing countries to respond to the short term threat to developing countries.

An online narrative archive of service user experiences to support the education of undergraduate physiotherapy and social work students in North East England: An evaluation study.

Background: Patient narratives are a viable process for patients to contribute to the education of future health professionals and social workers. Narratives can facilitate a deeper understanding of the self and others through self-reflection and encourage transformative learning among students. Increasingly, accounts of health and care are available online but their use in health and social work education requires evaluation. This study explored the experiences of stakeholders who contributed to, developed and used an online narrative archive, which was developed in collaboration with five universities and healthcare providers in the North East of England (CETL4HealthNE). Methods: Realistic evaluation principles were used to underpin data collection, which consisted of semi-structured interviews, a focus group and observations of educators using narrative resources in teaching sessions with different professional groups in two universities. Participants included educators, storytellers, narrative interviewers, students and a transcriber. Data were analysed thematically by two researchers and verified by a third researcher. Findings: Stakeholders reported that listening to patient narratives was challenging. The process of contributing the story was a positive cathartic experience for patients, and the powerful storyteller voice often evoked empathy. Students commented on the ability of the online audio-visual narratives to enable them to see the patient holistically, and educators reported that narratives provided a means to introduce sensitive topics. Conclusions: The use of a locally generated online narrative archive is beneficial for storytellers, students and educators, providing an opportunity to influence healthcare professional training. Care needs to be taken when exposing individuals to potentially sensitive narratives

Achieving better than 1 minute accuracy in the Heliocentric and Barycentric Julian Dates

As the quality and quantity of astrophysical data continue to improve, the precision with which certain astrophysical events can be timed becomes limited not by the data themselves, but by the manner, standard, and uniformity with which time itself is referenced. While some areas of astronomy (most notably pulsar studies) have required absolute time stamps with precisions of considerably better than 1 minute for many decades, recently new areas have crossed into this regime. In particular, in the exoplanet community, we have found that the (typically unspecified) time standards adopted by various groups can differ by as much as a minute. Left uncorrected, this ambiguity may be mistaken for transit timing variations and bias eccentricity measurements. We argue that, since the commonly-used Julian Date, as well as its heliocentric and barycentric counterparts, can be specified in several time standards, it is imperative that their time standards always be reported when accuracies of 1 minute are required. We summarize the rationale behind our recommendation to quote the site arrival time, in addition to using BJD_TDB, the Barycentric Julian Date in the Barycentric Dynamical Time standard for any astrophysical event. The BJD_TDB is the most practical absolute time stamp for extra-terrestrial phenomena, and is ultimately limited by the properties of the target system. We compile a general summary of factors that must be considered in order to achieve timing precisions ranging from 15 minutes to 1 microsecond. Finally, we provide software tools that, in principal, allow one to calculate BJD_TDB to a precision of 1 microsecond for any target from anywhere on Earth or from any spacecraft.Comment: Online BJD_TDB calculator at http://astroutils.astronomy.ohio-state.edu/time/utc2bjd.html. PASP accepted, 11 pages, 6 figures, updated to match published versio