Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.Comment: 35 pages, 2 figures, to appear in Notices of the American Mathematical Society 61 (2014), no.

All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets

The lightlike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. The solutions fall into two classes, depending on whether the Killing spinor is constant or not. In both cases, we give explicit examples of supersymmetric backgrounds. Among these BPS solutions, which preserve one quarter of the supersymmetry, there are gravitational waves propagating on domain walls or on bubbles of nothing that asymptote to AdS_4. Furthermore, we obtain the additional constraints obeyed by half-supersymmetric vacua. These are divided into four categories, that include bubbles of nothing which are asymptotically AdS_4, pp-waves on domain walls, AdS_3 x R, and spacetimes conformal to AdS_3 times an interval.Comment: 55 pages, uses JHEP3.cls. v2: Minor errors corrected, small changes in introductio

Assessment of Ischemic Index in Retinal Vascular Diseases Using Ultra-Wide-Field Fluorescein Angiography:Single Versus Summarized Image

Background and Objective: To compare a single image with a computer-generated summarized image from the ultra-wide-field fluorescein angiogram (UWFFA) sequence for evaluation of ischemic index (ISI).Materials and Methods: UWFFA sequences from patients with diabetic retinopathy (DR) (n=5), branch retinal vein occlusion (BRVO) (n=5), and central retinal vein occlusion (CRVO) (n=5) were evaluated by six graders. A single image best illustrating retinal non-perfusion was compared to a summarized image generated by computerized superimposition of angiograms. Non-perfused and ungradable retinal areas were outlined and the ISI between the single and summarized images was compared.Results: The mean ISI in the single versus (vs) summarized images was 17% vs 15% in BRVO (p=0.12), 48% vs 48% in CRVO (p=0.67), and 25% vs 23% in DR (p=0.005). Inter-grader agreement of ISI in single versus summarized images was 0.43 vs 0.40 in BRVO, 0.69 vs 0.71 in CRVO, and 0.53 vs 0.34 in DR.Conclusion: Computer-generated summarized images were similar to single images for grading ISI in BRVO and CRVO, but underestimated it in DR.</p

Universal nonequilibrium properties of dissipative Rydberg gases

We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and properties of the phase diagram and identify the universality class of the transition, both for the statics and the dynamics. We show that the proper dynamical order parameter is in fact not the excitation density and find evidence that the dynamical transition is in the “model A” universality class; i.e., it features a nontrivial Z2 symmetry and a dynamics with nonconserved order parameter. This sheds light on some relevant and observable aspects of dynamical transitions in Rydberg gases. In particular it permits a quantitative understanding of a recent experiment [C. Carr, Phys. Rev. Lett. 111, 113901 (2013)] which observed bistable behavior as well as power-law scaling of the relaxation time. The latter emerges not due to critical slowing down in the vicinity of a second order transition, but from the nonequilibrium dynamics near a so-called spinodal line

Measurement of Atmospheric Neutrino Oscillations with the ANTARES Neutrino Telescope

The data taken with the ANTARES neutrino telescope from 2007 to 2010, a total live time of 863 days, are used to measure the oscillation parameters of atmospheric neutrinos. Muon tracks are reconstructed with energies as low as 20 GeV. Neutrino oscillations will cause a suppression of vertical upgoing muon neutrinos of such energies crossing the Earth. The parameters determining the oscillation of atmospheric neutrinos are extracted by fitting the event rate as a function of the ratio of the estimated neutrino energy and reconstructed flight path through the Earth. Measurement contours of the oscillation parameters in a two-flavour approximation are derived. Assuming maximum mixing, a mass difference of $\Delta m_{32}^2=(3.1\pm 0.9)\cdot 10^{-3}$ eV$^2$ is obtained, in good agreement with the world average value.Comment: 9 pages, 5 figure

Status and Recent Results of the Acoustic Neutrino Detection Test System AMADEUS

The AMADEUS system is an integral part of the ANTARES neutrino telescope in the Mediterranean Sea. The project aims at the investigation of techniques for acoustic neutrino detection in the deep sea. Installed at a depth of more than 2000m, the acoustic sensors of AMADEUS are based on piezo-ceramics elements for the broad-band recording of signals with frequencies ranging up to 125kHz. AMADEUS was completed in May 2008 and comprises six "acoustic clusters", each one holding six acoustic sensors that are arranged at distances of roughly 1m from each other. The clusters are installed with inter-spacings ranging from 15m to 340m. Acoustic data are continuously acquired and processed at a computer cluster where online filter algorithms are applied to select a high-purity sample of neutrino-like signals. 1.6 TB of data were recorded in 2008 and 3.2 TB in 2009. In order to assess the background of neutrino-like signals in the deep sea, the characteristics of ambient noise and transient signals have been investigated. In this article, the AMADEUS system will be described and recent results will be presented.Comment: 7 pages, 8 figures. Proceedings of ARENA 2010, the 4th International Workshop on Acoustic and Radio EeV Neutrino Detection Activitie

Colorectal Cancers from Distinct Ancestral Populations Show Variations in BRAF Mutation Frequency

It has been demonstrated for some cancers that the frequency of somatic oncogenic mutations may vary in ancestral populations. To determine whether key driver alterations might occur at different frequencies in colorectal cancer, we applied a high-throughput genotyping platform (OncoMap) to query 385 mutations across 33 known cancer genes in colorectal cancer DNA from 83 Asian, 149 Black and 195 White patients. We found that Asian patients had fewer canonical oncogenic mutations in the genes tested (60% vs Black 79% (P = 0.011) and White 77% (P = 0.015)), and that BRAF mutations occurred at a higher frequency in White patients (17% vs Asian 4% (P = 0.004) and Black 7% (P = 0.014)). These results suggest that the use of genomic approaches to elucidate the different ancestral determinants harbored by patient populations may help to more precisely and effectively treat colorectal cancer

Alcohol consumption and body composition in a population-based sample of elderly Australian men

Background: Alcohol is calorie dense, and impacts&nbsp;activity, appetite and lipid processing. The aim of this&nbsp;study was to therefore investigate the association between&nbsp;alcohol consumption and components of body composition&nbsp;including bone, fat and lean tissue.Methods: Participants were recruited from a randomly&nbsp;selected, population-based sample of 534 men aged&nbsp;65 years and older enrolled in the Geelong Osteoporosis&nbsp;Study. Alcohol intake was ascertained using a food&nbsp;frequency questionnaire and the sample categorised as nondrinkers or alcohol users who consumed B2, 3&ndash;4 or C5&nbsp;standard drinks on a usual drinking day. Bone mineral&nbsp;density (BMD), lean body mass and body fat mass were&nbsp;measured using dual energy X-ray absorptiometry; overall&nbsp;adiposity (%body fat), central adiposity (%truncal fat) and&nbsp;body mass index (BMI) were calculated. Bone quality was&nbsp;determined by quantitative heel ultrasound (QUS).Results: There were 90 current non-drinkers (16.9 %),&nbsp;266 (49.8 %) consumed 1&ndash;2 drinks/day, 104 (19.5 %) 3&ndash;4&nbsp;drinks/day and 74 (13.8 %) C5 drinks/day. Those consuming C5 drinks/day had greater BMI (?4.8 %), fat mass&nbsp;index (?20.1 %), waist circumference (?5.0 %), %body&nbsp;fat (?15.2 %) and proportion of trunk fat (?5.3 %) and&nbsp;lower lean mass (-5.0 %) than non-drinkers after adjustment for demographic and lifestyle factors. Furthermore,&nbsp;they were more likely to be obese than non-drinkers&nbsp;according to criteria based on BMI (OR = 2.83, 95 %CI&nbsp;1.10&ndash;7.29) or waist circumference (OR = 3.36, 95 %CI&nbsp;1.32&ndash;8.54). There was an inverse relationship between&nbsp;alcohol consumption and QUS parameters and BMD at the&nbsp;mid forearm site; no differences were detected for BMD at&nbsp;other skeletal sites.Conclusion:&nbsp;Higher alcohol intake was associated with&nbsp;greater total and central adiposity and reduced bone&nbsp;quality.<br /

Geographical distribution and prevalence of podoconiosis in Rwanda: a cross-sectional country-wide survey

Background Podoconiosis is a type of tropical lymphoedema that causes massive swelling of the lower limbs. The disease is associated with both economic insecurity, due to long-term morbidity-related loss of productivity, and intense social stigma. Reliable and detailed data on the prevalence and distribution of podoconiosis are scarce. We aimed to fill this data gap by doing a nationwide community-based study to estimate the number of cases throughout Rwanda. Methods We did a population-based cross-sectional survey to determine the national prevalence of podoconiosis. A podoconiosis case was defined as a person with bilateral, asymmetrical lymphoedema of the lower limb present for more than 1 year, who tested negative for Wuchereria bancrofti antigen (determined by Filariasis Test Strip) and specific IgG4 (determined by Wb123 test), and had a history of any of the associated clinical signs and symptoms. All adults (aged ≥15 years) who resided in any of the 30 districts of Rwanda for 10 or more years were invited at the household level to participate. Participants were interviewed and given a physical examination before Filariasis Test Strip and Wb123 testing. We fitted a binomial mixed model combining the site-level podoconiosis prevalence with continuous environmental covariates to estimate prevalence at unsampled locations. We report estimates of cases by district combining our mean predicted prevalence and a contemporary gridded map of estimated population density. Findings Between June 12, and July 28, 2017, 1 360 612 individuals—719730 (53%) women and 640 882 (47%) men— were screened from 80 clusters in 30 districts across Rwanda. 1143 individuals with lymphoedema were identified, of whom 914 (80%) had confirmed podoconiosis, based on the standardised diagnostic algorithm. The overall prevalence of podoconiosis was 68·5 per 100000 people (95% CI 41·0–109·7). Podoconiosis was found to be widespread in Rwanda. District-level prevalence ranged from 28·3 per 100 000 people (16·8–45·5, Nyarugenge, Kigali province) to 119·2 per 100 000 people (59·9–216·2, Nyamasheke, West province). Prevalence was highest in districts in the North and West provinces: Nyamasheke, Rusizi, Musanze, Nyabihu, Nyaruguru, Burera, and Rubavu. We estimate that 6429 (95% CI 3938–10088) people live with podoconiosis across Rwanda. Interpretation Despite relatively low prevalence, podoconiosis is widely distributed geographically throughout Rwanda. Many patients are likely to be undiagnosed and morbidity management is scarce. Targeted interventions through a well coordinated health system response are needed to manage those affected. Our findings should inform national level planning, monitoring, and implementation of interventions

Search for Charginos with a Small Mass Difference with the Lightest Supersymmetric Particle at \sqrt{s} = 189 GeV

A search for charginos nearly mass-degenerate with the lightest supersymmetric particle is performed using the 176 pb^-1 of data collected at 189 GeV in 1998 with the L3 detector. Mass differences between the chargino and the lightest supersymmetric particle below 4 GeV are considered. The presence of a high transverse momentum photon is required to single out the signal from the photon-photon interaction background. No evidence for charginos is found and upper limits on the cross section for chargino pair production are set. For the first time, in the case of heavy scalar leptons, chargino mass limits are obtained for any \tilde{\chi}^{+-}_1 - \tilde{\chi}^0_1 mass difference