Tossing the Red Flag: Official (Judicial) Review and Shareholder-Fan Activism in the Context of Publicly Traded Sports Teams

For some, it comes after their team squanders away a fourth quarter lead in the playoffs, engages in a hasty trade, or makes an ill-advised substitution. For others, an indefensible draft choice, announcement of team relocation, or decision not to re-sign a star player triggers the thought. Whether at a sports bar or on their own living room couch, at one time or another, every sports fan has transported him or herself to the owner’s box and imagined, “If I ran that team, things would be different.” In the face of numerous professional sports team bankruptcies and league lockouts in the last fifteen years, as well as the current economic client, all professional franchises should be reevaluating their ownership structures and investigating new sources of revenue. Although the notion of a publicly owned and traded sports team is not a new business revelation, current economic conditions have reactivated largely dormant discussions of the opportunity. While the decisions posed throughout this analysis are ultimately left to current sports team ownership, this Note is meant to serve as a thought experiment to provoke questions and to spark discussion regarding the viability of a public model of sports team ownership

Cluster Algebras and Polylogarithm Relations

We seek to illuminate the connection between multiple polylogarithm relations and cluster algebras in two ways. First, we give a uniform description of the cluster modular group of affine and doubly extended cluster algebras. This will be critical for the future work of extracting polylogarithm relations from infinite type cluster algebras. Second, we introduce a differential one form, ωn, associated to each multiple polylogarithm, which can be used to compute multiple polylogarithm relations. This form satisfies a clean recurrence relation, mirroring the inductive definition of multiple polylogarithms. We are able to use this recurrence to find several families of “small” polylogarithm relations that hold in any weight. Finally for small values of n, we extract polylogarithm relations from type An and Dn cluster algebras

Restrictions on Anosov subgroups of Sp(2n,R)

Let $n\in\mathbb{N}$ and let $\Theta \subset \{1,\dots,n\}$ be a non-empty subset. We prove that if $\Theta$ contains an odd integer, then any $P_\Theta$-Anosov subgroup of ${\rm Sp}(2n,\mathbb{R})$ is virtually isomorphic to a free group or a surface group. In particular, any Borel Anosov subgroup of ${\rm Sp}(2n,\mathbb{R})$ is virtually isomorphic to a free or surface group. On the other hand, if $\Theta$ does not contain any odd integers, then there exists a $P_\Theta$-Anosov subgroup of ${\rm Sp}(2n,\mathbb{R})$ which is not virtually isomorphic to a free or surface group. We also exhibit new examples of maximally antipodal subsets of certain flag manifolds; these arise as limit sets of rank $1$ subgroups.Comment: 18 pages, 1 figur

The Lie coalgebra of multiple polylogarithms

We use Goncharov's coproduct of multiple polylogarithms to define a Lie coalgebra over an arbitrary field. It is generated by symbols subject to inductively defined relations, which we think of as functional relations for multiple polylogarithms. In particular, we have inversion relations and shuffle relations. We relate our definition to Goncharov's Bloch groups, and to the concrete model in weight less than 5 by Goncharov and Rudenko.Comment: 14 page

Tuning Nanocrystal Surface Depletion by Controlling Dopant Distribution as a Route Toward Enhanced Film Conductivity

Electron conduction through bare metal oxide nanocrystal (NC) films is hindered by surface depletion regions resulting from the presence of surface states. We control the radial dopant distribution in tin-doped indium oxide (ITO) NCs as a means to manipulate the NC depletion width. We find in films of ITO NCs of equal overall dopant concentration that those with dopant-enriched surfaces show decreased depletion width and increased conductivity. Variable temperature conductivity data shows electron localization length increases and associated depletion width decreases monotonically with increased density of dopants near the NC surface. We calculate band profiles for NCs of differing radial dopant distributions and, in agreement with variable temperature conductivity fits, find NCs with dopant-enriched surfaces have narrower depletion widths and longer localization lengths than those with dopant-enriched cores. Following amelioration of NC surface depletion by atomic layer deposition of alumina, all films of equal overall dopant concentration have similar conductivity. Variable temperature conductivity measurements on alumina-capped films indicate all films behave as granular metals. Herein, we conclude that dopant-enriched surfaces decrease the near-surface depletion region, which directly increases the electron localization length and conductivity of NC films

Development of a health care systems curriculum.

Background: There is currently no gold standard for delivery of systems-based practice in medical education, and it is challenging to incorporate into medical education. Health systems competence requires physicians to understand patient care within the broader health care system and is vital to improving the quality of care clinicians provide. We describe a health systems curriculum that utilizes problem-based learning across 4 years of systems-based practice medical education at a single institution. Methods: This case study describes the application of a problem-based learning approach to system-based practice medical education. A series of behavioral statements, called entrustable professional activities, was created to assess student health system competence. Student evaluation of course curriculum design, delivery, and assessment was provided through web-based surveys. Results: To meet competency standards for system-based practice, a health systems curriculum was developed and delivered across 4 years of medical school training. Each of the health system lectures and problem-based learning activities are described herein. The majority of first and second year medical students stated they gained working knowledge of health systems by engaging in these sessions. The majority of the 2016 graduating students (88.24%) felt that the course content, overall, prepared them for their career. Conclusion: A health systems curriculum in undergraduate medical education using a problem-based learning approach is feasible. The majority of students learning health systems curriculum through this format reported being prepared to improve individual patient care and optimize the health system\u27s value (better care and health for lower cost)