REMOVABLE SETS FOR LIPSCHITZ HARMONIC FUNCTIONS ON CARNOT GROUPS

Abstract. Let G be a Carnot group with homogeneous dimension Q ≥ 3 and let L be a sub-Laplacian on G. We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is (Q − 1). Moreover we construct self-similar sets with positive and finite H Q−1 measure which are removable. 1

The Formation and Evolution of the First Massive Black Holes

The first massive astrophysical black holes likely formed at high redshifts (z>10) at the centers of low mass (~10^6 Msun) dark matter concentrations. These black holes grow by mergers and gas accretion, evolve into the population of bright quasars observed at lower redshifts, and eventually leave the supermassive black hole remnants that are ubiquitous at the centers of galaxies in the nearby universe. The astrophysical processes responsible for the formation of the earliest seed black holes are poorly understood. The purpose of this review is threefold: (1) to describe theoretical expectations for the formation and growth of the earliest black holes within the general paradigm of hierarchical cold dark matter cosmologies, (2) to summarize several relevant recent observations that have implications for the formation of the earliest black holes, and (3) to look into the future and assess the power of forthcoming observations to probe the physics of the first active galactic nuclei.Comment: 39 pages, review for "Supermassive Black Holes in the Distant Universe", Ed. A. J. Barger, Kluwer Academic Publisher

Long-term management of GERD in the elderly with pantoprazole

The prevalence of gastroesophageal reflux disease (GERD) increases with age and elderly are more likely to develop severe disease. Older patients often complain of less severe or frequent heartburn than younger patients and they may present with atypical symptoms such as dysphagia, weight loss, or extraesophageal symptoms. Proton pump inhibitors (PPIs) are central in the management of GERD and are unchallenged with regards to their efficacy. They are considered safe and more effective than histamine receptor antagonists for healing esophagitis and for preventing its recurrence using a long term maintenance treatment. PPI have minimal side effects and few slight drug interactions and are considered safe for long term treatment. Pantoprazole is significantly effective both for acute and long-term treatment with excellent control of relapse and symptoms. It is well tolerated even for long-term therapy and its tolerability is optimal. Pantoprazole shows to have minimal interactions with other drugs because of a lower affinity for cytocrome P450 than older PPIs. Although the majority of elderly has concomitant illnesses and receive other drugs, this does not adversely effect the efficacy of pantoprazole because of its pharmacokinetics, which are independent of patient age. Clinical practice suggests that a low dose maintenance of PPIs should be used in older patients with GERD

From little things, big things grow: trends and fads in 110 years of Australian ornithology

Publishing histories can reveal changes in ornithological effort, focus or direction through time. This study presents a bibliometric content analysis of Emu (1901–2011) which revealed 115 trends (long-term changes in publication over time) and 18 fads (temporary increases in publication activity) from the classification of 9,039 articles using 128 codes organised into eight categories (author gender, author affiliation, article type, subject, main focus, main method, geographical scale and geographical location). Across 110 years, private authorship declined, while publications involving universities and multiple institutions increased; from 1960, female authorship increased. Over time, question-driven studies and incidental observations increased and decreased in frequency, respectively. Single species and ‘taxonomic group’ subjects increased while studies of birds at specific places decreased. The focus of articles shifted from species distribution and activities of the host organisation to breeding, foraging and other biological/ecological topics. Site- and Australian-continental-scales slightly decreased over time; non-Australian studies increased from the 1970s. A wide variety of fads occurred (e.g. articles on bird distribution, 1942–1951, and using museum specimens, 1906–1913) though the occurrence of fads decreased over time. Changes over time are correlated with technological, theoretical, social and institutional changes, and suggest ornithological priorities, like those of other scientific disciplines, are temporally labil

Multi-scale Inference of Interaction Rules in Animal Groups Using Bayesian Model Selection

Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis). We show that these exhibit a stereotypical ‘phase transition’, whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have ‘memory’ of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects

HIV Disclosure, Condom Use, and Awareness of HIV Infection Among HIV-Positive, Heterosexual Drug Injectors in St. Petersburg, Russian Federation

We examined the prevalence of HIV disclosure to sexual partners by HIV-positive drug injectors (IDUs) in St. Petersburg, Russia and compared the magnitude and direction of associations of condom use with awareness of one’s HIV infection and disclosure to partners. Among 157 HIV-infected participants, awareness of infection at time of last intercourse was associated with condom use with partners perceived to be HIV-negative (aOR 6.68, 95% CI 1.60–27.88). Among the 70 participants aware of their infection prior to enrolment, disclosure to potentially uninfected sexual partners was independently and negatively associated with condom use (aOR 0.13, 95% CI 0.02–0.66). Disclosure was independently associated with having injected ≥9 years (aOR 6.04, 95% CI 1.53–23.77) and partnership with another IDU (aOR 3.61, 95% CI 1.44–9.06) or HIV-seropositive (aOR 45.12, 95% CI 2.79–730.46). Scaling up HIV testing services and interventions that increase the likelihood of individuals receiving their test results is recommended