Optimally dense packings of hyperbolic space

In previous work a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an appropriate definition of optimal dense packings. Examples are given to illustrate various aspects of the density problem, in particular the shift in emphasis from the analysis of individual packings to spaces of packings.Comment: 27 pages, 11 figure

Measuring Impact: The Art, Science and Mystery of Nonprofit News

This report seeks to answer the two-pronged question, "What is 'impact,' and how can it be measured consistently across nonprofit newsrooms?" A review of recent, relevant literature and our informal conversations with experts in the field reveal growing ambitions toward the goal of developing a common framework for assessing journalism's impact, yet few definitive conclusions about how exactly to reach that framework. This is especially the case when journalism's "impact" is defined by its ultimate social outcomes -- not merely the familiar metrics of audience reach and website traffic. As with all journalism, the frame defines the story, and audience is all-important. Defining "impact" as a social outcome proves a complicated proposition that generally evolves according to the constituency attempting to define it. Because various stakeholders have their own reasons for wanting to measure the impact of news, understanding those interests is an essential step in crafting measurement tools and interpreting the metrics they produce. Limitations of impact assessment arise from several sources: the assumptions invariably made about the product and its outcome; the divergent and overlapping categories into which nonprofit journalism falls in the digital age; and the intractable problem of attempting to quantify "quality." These formidable challenges, though, don't seem to deter people from posing and attempting to find answers to the impact question. Various models for assessing impact are continually being tinkered with, and lessons from similar efforts in other fields offer useful insight for this journalistic endeavor. And past research has pointed to specific needs and suggestions for ways to advance the effort. From all of this collective wisdom, several principles emerge as the cornerstones upon which to build a common framework for impact assessment

On the job rotation problem

The job rotation problem (JRP) is the following: Given an $n \times n$ matrix $A$ over \Re \cup \{\ -\infty\ \}\ and $k \leq n$, find a $k \times k$ principal submatrix of $A$ whose optimal assignment problem value is maximum. No polynomial algorithm is known for solving this problem if $k$ is an input variable. We analyse JRP and present polynomial solution methods for a number of special cases

A Solidification Phenomenon in Random Packings

We prove that uniformly random packings of copies of a certain simply-connected figure in the plane exhibit global connectedness at all sufficiently high densities, but not at low densities

630-mV open circuit voltage, 12% efficient n-Si liquid junction

We report the first experimental observation of a semiconductor/liquid junction whose open circuit voltage Voc is controlled by bulk diffusion/recombination processes. Variation in temperature, minority-carrier diffusion length, and/or in majority-carrier concentration produces changes in the Voc of the n-Si/CH3OH interface in accord with bulk recombination/diffusion theory. Under AM2 irradiation conditions, the extrapolated intercept at 0 K of Voc vs T plots yields activation energies for the dominant recombination process of 1.1–1.2 eV, in accord with the 1.12-eV band gap of Si. A crucial factor in achieving optimum performance of the n-Si/CH3OH interface is assigned to photoelectrochemical oxide formation, which passivates surface recombination sites at the n-Si/CH3OH interface and minimizes deleterious effects of pinning of the Fermi level at the Si/CH3OH junction. Controlled Si oxide growth, combined with optimization of bulk crystal parameters in accord with diffusion theory, is found to yield improved photoelectrode output parameters, with 12.0±1.5% AM2 efficiencies and AM1 Voc values of 632–640 mV for 0.2-Ω cm Si materials

Public Sector Personnel Economics: Wages, Promotions, and the Competence-Control Trade-off

We model personnel policies in public agencies, examining how wages and promotion standards can partially offset a fundamental contracting problem: the inability of public sector workers to contract on performance, and the inability of political masters to contract on forbearance from meddling. Despite the dual contracting problem, properly constructed personnel policies can encourage intrinsically motivated public sector employees to invest in expertise, seek promotion, remain in the public sector, and develop policy projects. However, doing so requires internal personnel policies that sort slackers from zealots. Personnel policies that accomplish this task are quite different in agencies where acquired expertise has little value in the private sector, and agencies where acquired expertise commands a premium in the private sector. Finally, even with well-designed personnel policies, there remains an inescapable trade-off between political control and expertise acquisition