Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic

In analogy with the Riemann zeta function at positive integers, for each finite field F_p^r with fixed characteristic p we consider Carlitz zeta values zeta_r(n) at positive integers n. Our theorem asserts that among the zeta values in {zeta_r(1), zeta_r(2), zeta_r(3), ... | r = 1, 2, 3, ...}, all the algebraic relations are those algebraic relations within each individual family {zeta_r(1), zeta_r(2), zeta_r(3), ...}. These are the algebraic relations coming from the Euler-Carlitz relations and the Frobenius relations. To prove this, a motivic method for extracting algebraic independence results from systems of Frobenius difference equations is developed.Comment: 14 page

In its focus on genetics and race, global newspaper coverage of athletics is far from “post-racial”

With the years of racially segregated sports now long behind us, many would consider that sports coverage is color-blind and post-racial. In new research which examines newspaper coverage of race, sport and genetics from 2003 to 2014, Matthew W. Hughey and Devon R. Goss find that this is not the case. They write that the media persistently reinforces the notions that African American’s athletic success is based on biology, while whites’ comes from hard work and intelligence. They also debunk the ideas often seen in the media that race has a biological reality which can be defined by genes, and that the historic process of slavery somehow eliminated ‘weaker genes’ from the African American population, making them a more athletic race

Do Courts Change Politics? Heller and the Limits of Policy Feedback Effects

District of Columbia v. Heller was a landmark ruling in which the Supreme Court established that citizens have a constitutional right to possess firearms in their homes for self-protection. The 5-4 decision—along with the Court’s subsequent ruling in McDonald v. Chicago—upended the prevailing wisdom that the Second Amendment protected the right of the states to assemble militias for collective security. In this Article, we examine the effects of these rulings on gun regulation in the United States and, more to the point, on gun politics. We situate our analysis within several related theoretical frameworks, most notably those focused on policy feedback and on the role of courts in producing social change. We argue that the effects of Heller (together with the parallel decision in McDonald) have been rather limited. We examine the rulings’ first-order effects on pre-existing gun control laws, as well as second-order effects on a number of related outcomes. We find that Heller and its progeny have had generally small or non-existent impacts on gun policy, on the organizational capacities and political strategies of pro-gun and pro-regulation groups, and on public attitudes toward gun regulation. Our findings support a constrained view of the Court’s ability to drive social and political change. We conclude, however, by noting that recent developments—particularly hints that some Supreme Court Justices are eager to develop Second Amendment jurisprudence—have the potential to alter these conclusions

A single Streptomyces symbiont makes multiple antifungals to support the fungus farming ant Acromyrmex octospinosus

Attine ants are dependent on a cultivated fungus for food and use antibiotics produced by symbiotic Actinobacteria as weedkillers in their fungus gardens. Actinobacterial species belonging to the genera Pseudonocardia, Streptomyces and Amycolatopsis have been isolated from attine ant nests and shown to confer protection against a range of microfungal weeds. In previous work on the higher attine Acromyrmex octospinosus we isolated a Streptomyces strain that produces candicidin, consistent with another report that attine ants use Streptomyces-produced candicidin in their fungiculture. Here we report the genome analysis of this Streptomyces strain and identify multiple antibiotic biosynthetic pathways. We demonstrate, using gene disruptions and mass spectrometry, that this single strain has the capacity to make candicidin and multiple antimycin compounds. Although antimycins have been known for > 60 years we report the sequence of the biosynthetic gene cluster for the first time. Crucially, disrupting the candicidin and antimycin gene clusters in the same strain had no effect on bioactivity against a co-evolved nest pathogen called Escovopsis that has been identified in similar to 30% of attine ant nests. Since the Streptomyces strain has strong bioactivity against Escovopsis we conclude that it must make additional antifungal(s) to inhibit Escovopsis. However, candicidin and antimycins likely offer protection against other microfungal weeds that infect the attine fungal gardens. Thus, we propose that the selection of this biosynthetically prolific strain from the natural environment provides A. octospinosus with broad spectrum activity against Escovopsis and other microfungal weeds.Publisher PDFPeer reviewe

A Weil-Barsotti formula for Drinfeld modules

We study the group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t-module. Our main result is a Drinfeld module analogue of the Weil-Barsotti formula for abelian varieties. Extensions of general t-modules are also considered, in particular extensions of tensor powers of the Carlitz module. We motivate these results from various directions and compare to the situation of elliptic curves.Comment: 20 pages, latex file. To appear in Journal of Number Theor

Mountain Research Initiative: 20 Years of Making Connections for Our Changing Mountains

In 2021, the Mountain Research Initiative (MRI) Coordination Office celebrated its 20th anniversary. By the standards of the ancient mountains that inspire and connect the work of the thousands of individuals who make up the MRI network, this two-decade milestone may seem insignificant. During this time, however, the MRI has achieved a great deal; a testament to the efforts of the mountain researchers worldwide who have come together across borders and disciplines to advance our understanding of global change in mountain social-ecological systems

Mountain Research Initiative: 20 Years of Making Connections for Our Changing Mountains

In 2021, the Mountain Research Initiative (MRI) Coordination Office celebrated its 20th anniversary. By the standards of the ancient mountains that inspire and connect the work of the thousands of individuals who make up the MRI network, this two-decade milestone may seem insignificant. During this time, however, the MRI has achieved a great deal; a testament to the efforts of the mountain researchers worldwide who have come together across borders and disciplines to advance our understanding of global change in mountain social-ecological systems

Low cost current measurement of three phase cables

© 2018 IEEE. Recent growth in embedded generation alongside the anticipated consumer uptake of electric vehicles (EVs) and heat pumps present new challenges for distribution networks. This includes greater fluctuation in electricity demand. Data from existing maximum demand indicators in distribution substations is inadequate to understand the spread of demand over time. Retro-fit datalogging solutions are available for substation monitoring, but cost typically >£1200, which would be difficult to justify for all distribution substations. This paper looks at the development of a novel low cost alternative designed for measuring load on three phase cables