The Lebesgue Universal Covering Problem

In 1914 Lebesgue defined a "universal covering" to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pal, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before. However, Hansen's last reduction was microsopic: he claimed to remove an area of $6 \cdot 10^{-18}$, but we show that he actually removed an area of just $8 \cdot 10^{-21}$. In the following, with the help of Greg Egan, we find a new, smaller universal covering with area less than $0.8441153$. This reduces the area of the previous best universal covering by a whopping $2.2 \cdot 10^{-5}$.Comment: 11 pages, 5 jpeg figures, numerical errors correcte

Using Current Legal Tools to Achieve Net Zero Greenhouse Gas Emissions from New and Existing Federal Oil and Gas Leases

Fossil fuel development on federal lands accounts for 24% of all U.S. carbon dioxide (CO2) emissions. These emissions can be reduced significantly by requiring federal oil and gas development activity to mitigate greenhouse gas (GHG) emissions. The Bureau of Land Management (BLM) has authority to define the terms and conditions of new oil and gas leases and to impose conditions of approval on existing leases at the drilling stage. Using this authority, the BLM could require net zero emissions on some existing and all new oil and gas leases without waiting for congressional action or regulatory changes. Applying existing legal tools would allow for continued energy production while a long-term climate strategy is developed, and still drive significant GHG emission reductions in the meantime. Additionally, green jobs would be created by incentivizing oil and gas operators to generate offset credits by plugging the more than 2 million orphaned or abandoned oil and gas wells that litter the landscape. Finally, the incentive to plug idle wells and retire leases early would reward operators for deciding to keep some fossil fuel resources in the ground

The BLM’s Duty to Incorporate Climate Science into Permitting Practices and a Proposal for Implementing a Net Zero Requirement into Oil and Gas Permitting

Almost one quarter of all U.S. carbon dioxide (CO2) emissions come from fossil fuels extracted from public lands, and these resources are managed by the Bureau of Land Management (BLM). This article argues that the BLM has a statutory duty to respond to climate change, which includes the duty to avoid exacerbating climate change. The article then moves the legal discussion from aspiration to action by proposing a legal strategy, using the existing legal framework, by which the BLM can achieve net zero emissions from all new mineral development activity. While the article focuses on oil and gas development, the same methodology could be applied to coal mining, tar sands, and other sources of GHG emissions

Solution phase, solid state, and theoretical investigations on the MacMillan imidazolidinone

A combination of soln. phase NMR, X-ray crystallog. studies, and DFT calcns. provide a consistent structural conformation for iminium ions derived from the MacMillan imidazolidinone

Taking Development Seriously: Critique of the 2008 \u3ci\u3eJME\u3c/i\u3e Special Issue on Moral Functioning

This essay comments on articles that composed a Journal of Moral Education Special Issue (September, 2008, 37[3]). The issue was intended to honor the 50th anniversary of Lawrence Kohlberg’s doctoral dissertation and his subsequent impact on the field of moral development and education. The articles were characterized by the issue editor (Don Collins Reed) as providing a “look forward” from Kohlberg’s work toward a more comprehensive or integrated model of moral functioning. Prominent were culturally pluralist and biologically based themes, such as cultural learning; expert skill; culturally shaped and neurobiologically based predispositions or intuitions; and moral self-relevance or centrality. Inadequately represented, however, was Kohlberg’s (and Piaget’s) key concept of development as the construction of a deeper or more adequate understanding not reducible to particular socialization practices or cultural contexts. Also neglected were related cognitive-developmental themes, along with supportive evidence. Robert Coles’s account of a sudden rescue is used as a heuristic to depict Piaget’s/Kohlberg’s approach to the development of moral functioning. We conclude that, insofar as the Special Issue does not take development seriously, it moves us not forward but, instead, back to the problems of moral relativism and moral paralysis that Kohlberg sought to redress from the start of his work more than 50 years ago

Radiotherapy for Soft Tissue Sarcoma of the Proximal Lower Extremity

Soft-tissue sarcoma (STS) is a histopathologically diverse group of tumors accounting for approximately 10,000 new malignancies in the US each year. The proximal lower extremity is the most common site for STS, accounting for approximately one-third of all cases. Coordinated multimodality management in the form of surgery and radiation is often critical to local control, limb preservation, and functional outcome. Based on a review of currently available Medline literature and professional experience, this paper provides an overview of the treatment of STS of the lower extremity with a particular focus on the modern role of radiotherapy

On Infrared Excesses Associated With Li-Rich K Giants

Infrared (IR) excesses around K-type red giants (RGs) have previously been discovered using IRAS data, and past studies have suggested a link between RGs with overabundant Li and IR excesses, implying the ejection of circumstellar shells or disks. We revisit the question of IR excesses around RGs using higher spatial resolution IR data, primarily from WISE. Our goal was to elucidate the link between three unusual RG properties: fast rotation, enriched Li, and IR excess. We have 316 targets thought to be K giants, about 40% of which we take to be Li-rich. In 24 cases with previous detections of IR excess at low spatial resolution, we believe that source confusion is playing a role, in that either (a) the source that is bright in the optical is not responsible for the IR flux, or (b) there is more than one source responsible for the IR flux as measured in IRAS. We looked for IR excesses in the remaining sources, identifying 28 that have significant IR excesses by ~20 um (with possible excesses for 2 additional sources). There appears to be an intriguing correlation in that the largest IR excesses are all in Li-rich K giants, though very few Li-rich K giants have IR excesses (large or small). These largest IR excesses also tend to be found in the fastest rotators. There is no correlation of IR excess with the carbon isotopic ratio, 12C/13C. IR excesses by 20 um, though relatively rare, are at least twice as common among our sample of Li-rich K giants. If dust shell production is a common by-product of Li enrichment mechanisms, these observations suggest that the IR excess stage is very short-lived, which is supported by theoretical calculations. Conversely, the Li-enrichment mechanism may only occasionally produce dust, and an additional parameter (e.g., rotation) may control whether or not a shell is ejected.Comment: 73 pages, 21 figures (some of which substantially degraded to meet arXiv file size requirements), accepted to AJ. Full table 1 (and full-res figures) available upon request to the autho

Data-Driven, Data-Informed, Data-Augmented: How Ubisoft’s Ghost Recon Wildlands Live Unit Uses Data for Continuous Product Innovation

To stay ahead of the competition, firms must continuously learn from their customers and swiftly adopt those lessons to improve their products. A unit at Ubisoft, a leading game publisher headquartered in Paris, has established a three-pronged approach to drive product innovation based on three practices: data-driven exploration, data-augmented ideation, and data-informed validation. By establishing processes and capabilities for these practices and blending them in a portfolio approach to product design, they maximize the value generation potential of the data at their disposal. Product development in a variety of industries can benefit from the lessons of these data-oriented innovation practices

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate-dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present new results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, waveback velocity exhibits pronounced rate-dependence and the wavefront velocity does not. Moreover, the discrepancy between waveback velocity RCs is most significant for small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wavefront and waveback velocities. Our calculations show that waveback velocity rate-dependence is due to APD restitution, not memory.Comment: 17 pages, 7 figure