Endotrivial complexes

Let $G$ be a finite group, $p$ a prime, and $k$ a field of characteristic $p$. We introduce the notion of an endotrivial complex of $p$-permutation $kG$-modules, and study the corresponding group of endotrivial complexes, $\mathcal{E}_k(G)$. Such complexes are shown to induce splendid Rickard autoequivalences of $kG$. The elements of $\mathcal{E}_k(G)$ are determined uniquely by integral invariants arising from the Brauer construction and a degree 1 character $G \to k^\times$. Using ideas from Bouc's theory of biset functors, we provide a canonical decomposition of $\mathcal{E}_k(G)$, and as an application, determine complete descriptions of $\mathcal{E}_k(G)$ for abelian groups and $p$-groups of normal $p$-rank 1. We investigate the image of $\mathcal{E}_k(G)$ in the orthogonal unit group of the trivial source ring $O(T(kG))$ induced via the Lefschetz invariant map, and using recent results of Boltje and Carman, we determine a Frobenius stability condition an orthogonal unit must satisfy to lift to an endotrivial complex.Comment: Minor changes for version 2: fixed numerous typos and revised some proofs and statements for clarity and correctness. 36 pages, comments welcome

Optimal Leapfrogging, A Complete Guide

Suppose we have some checkers placed in the lower-left corner of a Go board, and wish to move them to the upper right corner in as few moves as possible, where the pieces move as they would in the game of Chinese Checkers. In 1993, Auslander, Benjamin, and Wilkerson generalized this game for integer lattices, defined a measure of speed for a starting configuration of pieces, and proved that a maximum speed exists, which only three configurations, called "speed-of-light" configurations can attain. It was conjectured that the maximum speed of a non-speed-of-light configuration has a smaller upper bound, which we prove.Comment: In progress for submissio

Time's Up: Homeless New Yorkers Demand Alternatives to Bloomberg's Failed Five-Year Plan

More people are living in homeless shelters now than when Mayor Bloomberg took office in 2002. On June 24th, 2004, Mayor Michael Bloomberg unveiled his Five Year Plan to reduce homelessness in New York City by two-thirds. The failure of Bloomberg's plan is evidence that what is needed are fundamental changes to housing policy in NYC, which is at the root of what is falsely portrayed as a homeless crisis.New York Magazine has said that his homeless policies are "the single biggest failure of the Bloomberg administration." The 2009 Mayor's Management Report found an across-the-board increase in the shelter census. As the five years of Bloomberg's plan comes to a close, this report focuses on the failures of one of its cornerstones, the Rental Subsidies Programs. Family and child homelessness have increased under these programs, even with thousands of households receiving vouchers, the rental subsidies have built-in obstacles to employment and self-sufficiency so crucial to making the transition out of the shelter system possible

Transmission and Transport of Energy in the Western U.S. and Canada: A Law and Policy Road Map

This collection of short essays arose from the inaugural meeting of the Idaho Symposium on Energy in the West, which was held in November, 2014. The topic for this first Symposium was Transmission and Transport of Energy in the Western U.S. and Canada: A Law and Policy Road Map. The essays in this collection provide a notable introduction to the major energy issues facing the West today. Topics include: building a resilient legal architecture for western energy production; natural gas flaring; transmission planning for wind energy; utilities and rooftop solar; special considerations for western states and the Clean Power Plan; the Clean Power Plan\u27s implications for the western grid; siting renewable energy on public lands; and implications of utility reform in New York and Hawaii for the Northwest

Active site loop engineering abolishes water capture in hydroxylating sesquiterpene synthases

Terpene synthases (TS) catalyze complex reactions to produce a diverse array of terpene skeletons from linear isoprenyl diphosphates. Patchoulol synthase (PTS) from Pogostemon cablin converts farnesyl diphosphate into patchoulol. Using simulation-guided engineering, we obtained PTS variants that eliminate water capture. Further, we demonstrate that modifying the structurally conserved Hα-1 loop also reduces hydroxylation in PTS, as well as in germacradiene-11-ol synthase (Gd11olS), leading to cyclic neutral intermediates as products, including α-bulnesene (PTS) and isolepidozene (Gd11olS). Hα-1 loop modification could be a general strategy for engineering sesquiterpene synthases to produce complex cyclic hydrocarbons without the need for structure determination or modeling

Compound specific trends of chemical defences in Ficus along an elevational gradient reflect a complex selective landscape

Elevational gradients affect the production of plant secondary metabolites through changes in both biotic and abiotic conditions. Previous studies have suggested both elevational increases and decreases in host-plant chemical defences. We analysed the correlation of alkaloids and polyphenols with elevation in a community of nine Ficus species along a continuously forested elevational gradient in Papua New Guinea. We sampled 204 insect species feeding on the leaves of these hosts and correlated their community structure to the focal compounds. Additionally, we explored species richness of folivorous mammals along the gradient. When we accounted for Ficus species identity, we found a general elevational increase in flavonoids and alkaloids. Elevational trends in non-flavonol polyphenols were less pronounced or showed non-linear correlations with elevation. Polyphenols responded more strongly to changes in temperature and humidity than alkaloids. The abundance of insect herbivores decreased with elevation, while the species richness of folivorous mammals showed an elevational increase. Insect community structure was affected mainly by alkaloid concentration and diversity. Although our results show an elevational increase in several groups of metabolites, the drivers behind these trends likely differ. Flavonoids may provide figs with protection against abiotic stressors. In contrast, alkaloids affect insect herbivores and may provide protection against mammalian herbivores and pathogens. Concurrent analysis of multiple compound groups alongside ecological data is an important approach for understanding the selective landscape that shapes plant defences

Compound Specific Trends of Chemical Defences in Ficus Along an Elevational Gradient Reflect a Complex Selective Landscape

Elevational gradients affect the production of plant secondary metabolites through changes in both biotic and abiotic conditions. Previous studies have suggested both elevational increases and decreases in host-plant chemical defences. We analysed the correlation of alkaloids and polyphenols with elevation in a community of nine Ficus species along a continuously forested elevational gradient in Papua New Guinea. We sampled 204 insect species feeding on the leaves of these hosts and correlated their community structure to the focal compounds. Additionally, we explored species richness of folivorous mammals along the gradient. When we accounted for Ficus species identity, we found a general elevational increase in flavonoids and alkaloids. Elevational trends in non-flavonol polyphenols were less pronounced or showed non-linear correlations with elevation. Polyphenols responded more strongly to changes in temperature and humidity than alkaloids. The abundance of insect herbivores decreased with elevation, while the species richness of folivorous mammals showed an elevational increase. Insect community structure was affected mainly by alkaloid concentration and diversity. Although our results show an elevational increase in several groups of metabolites, the drivers behind these trends likely differ. Flavonoids may provide figs with protection against abiotic stressors. In contrast, alkaloids affect insect herbivores and may provide protection against mammalian herbivores and pathogens. Concurrent analysis of multiple compound groups alongside ecological data is an important approach for understanding the selective landscape that shapes plant defences

Sustained Sexual Behavior Change after Acute HIV Diagnosis in Malawi

Background Identification of acute HIV infection (AHI) allows for important opportunities for HIV prevention through behavior change and biomedical intervention. Here, we evaluate changes in sexual risk behaviors among persons with AHI enrolled in a combined behavioral and biomedical intervention designed to reduce onward transmission of HIV. Methods Participants were randomized to standard HIV counseling, a multisession behavioral intervention, or a multisession behavioral intervention plus antiretrovirals. Sexual behaviors were assessed periodically over 1 year. Results Four weeks after diagnosis, the predicted probability of reporting multiple sexual partners decreased from 24% to 9%, and the probability of reporting unprotected sex decreased from 71% to 27%. These declines in sexual risk behaviors were sustained over follow-up irrespective of study arm. Conclusions Diagnosis of AHI alone may be sufficient to achieve immediate and sustained behavior change during this highly infectious period

Human Immunodeficiency Virus (HIV)-1 Transmission among Persons with Acute HIV-1 Infection in Malawi: Demographic, Behavioral, and Phylogenetic Relationships

Background: Understanding sexual networks involving acute human immunodeficiency virus (HIV)-1 infections (AHI) may lead to prevention opportunities to mitigate high rates of onward transmission. We evaluated HIV-1 phylogenetic and behavioral characteristics among persons with AHI and their referred partners. Methods: Between 2012 and 2014, 46 persons with AHI in Malawi participated in a combined behavioral and biomedical intervention. Participants referred sexual partners by passive referral. Demographics and sexual behaviors were collected through interviews and HIV-1 genetic relationships were assessed with phylogenetics. Results: Among 45 AHI participants with HIV-1 sequences, none was phylogenetically-linked with another AHI index. There were 19 (42%) AHI participants who referred a single partner that returned for testing. Most partners (n = 17) were HIV-infected, with 15 (88%) presenting with an established infection. There were 14 index-partner pairs that had sequences available; 13 (93%) pairs were phylogenetically-linked dyads. The AHI index was female in 7/13 (54%) dyads. Age-disparate relationships among dyads were common (≥5-year age difference in 67% of dyads), including 3/6 dyads involving a male index and a younger woman. Index participants with a referred partner were more likely to report no casual partners and to be living with their current partner than participants not in dyads. Conclusions: Passive-partner referral successfully identified partners with genetically-similar HIV infections - the likely source of infection - but only 40% of index cases referred partners who presented for HIV-1 testing. Future work evaluating assisted partner notification may help reach susceptible partners or more people with untreated HIV-1 infections connected to acute transmission. Clinical Trials Registration: NCT01450189

Randomized Controlled Pilot Study of Antiretrovirals and a Behavioral Intervention for Persons with Acute HIV Infection: Opportunity for Interrupting Transmission

Background. Persons with acute HIV infection (AHI) have heightened transmission risk. We evaluated potential transmission reduction using behavioral and biomedical interventions in a randomized controlled pilot study in Malawi. Methods. Persons were randomized 1:2:2 to standard counseling (SC), 5-session behavioral intervention (BI), or behavioral intervention plus 12 weeks of antiretrovirals (ARVs; BIA). All were followed for 26-52 weeks and, regardless of arm, referred for treatment according to Malawi-ARV guidelines. Participants were asked to refer partners for testing. Results. Among 46 persons (9 SC, 18 BI, 19 BIA), the average age was 28; 61% were male. The median viral load (VL) was 5.9 log copies/mL at enrollment. 67% (10/15) of BIA participants were suppressed (<1000 copies/mL) at week 12 vs 25% BI and 50% SC (P = .07). Although the mean number of reported condomless sexual acts in the past week decreased from baseline across all arms (1.5 vs 0.3 acts), 36% experienced incident sexually transmitted infection by 52 weeks (12% SC, 28% BI, 18% BIA). Forty-one percent (19/46) of participants referred partners (44% SC, 44% BI, 37% BIA); 15 of the partners were HIV-infected. Conclusions. Diagnosis of AHI facilitates behavioral and biomedical risk reduction strategies during a high-transmission period that begins years before people are typically identified and started on ARVs. Sexually transmitted infection incidence in this cohort suggests ongoing risk behaviors, reinforcing the importance of early intervention with ARVs to reduce transmission. Early diagnosis coupled with standard AHI counseling and early ARV referral quickly suppresses viremia, may effectively change behavior, and could have tremendous public health benefit in reducing onward transmission