Ultrametric spaces of branches on arborescent singularities

Let $S$ be a normal complex analytic surface singularity. We say that $S$ is arborescent if the dual graph of any resolution of it is a tree. Whenever $A,B$ are distinct branches on $S$, we denote by $A \cdot B$ their intersection number in the sense of Mumford. If $L$ is a fixed branch, we define $U_L(A,B)= (L \cdot A)(L \cdot B)(A \cdot B)^{-1}$ when $A \neq B$ and $U_L(A,A) =0$ otherwise. We generalize a theorem of P{\l}oski concerning smooth germs of surfaces, by proving that whenever $S$ is arborescent, then $U_L$ is an ultrametric on the set of branches of $S$ different from $L$. We compute the maximum of $U_L$, which gives an analog of a theorem of Teissier. We show that $U_L$ encodes topological information about the structure of the embedded resolutions of any finite set of branches. This generalizes a theorem of Favre and Jonsson concerning the case when both $S$ and $L$ are smooth. We generalize also from smooth germs to arbitrary arborescent ones their valuative interpretation of the dual trees of the resolutions of $S$. Our proofs are based in an essential way on a determinantal identity of Eisenbud and Neumann.Comment: 37 pages, 16 figures. Compared to the first version on Arxiv, il has a new section 4.3, accompanied by 2 new figures. Several passages were clarified and the typos discovered in the meantime were correcte

Which older people decline participation in a primary care trial of physical activity and why: insights from a mixed methods approach

This article is available through the Brunel Open Access Publishing Fund. Copyright 2014 Rogers et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.Background: Physical activity is of vital importance to older peoples’ health. Physical activity intervention studies with older people often have low recruitment, yet little is known about non-participants. Methods: Patients aged 60–74 years from three UK general practices were invited to participate in a nurse-supported pedometer-based walking intervention. Demographic characteristics of 298 participants and 690 non-participants were compared. Health status and physical activity of 298 participants and 183 non-participants who completed a survey were compared using age, sex adjusted odds ratios (OR) (95% confidence intervals). 15 non-participants were interviewed to explore perceived barriers to participation. Results: Recruitment was 30% (298/988). Participants were more likely than non-participants to be female (54% v 47%; p = 0.04) and to live in affluent postcodes (73% v 62% in top quintile; p < 0.001). Participants were more likely than non-participants who completed the survey to have an occupational pension OR 2.06 (1.35-3.13), a limiting longstanding illness OR 1.72 (1.05-2.79) and less likely to report being active OR 0.55 (0.33-0.93) or walking fast OR 0.56 (0.37-0.84). Interviewees supported general practice-based physical activity studies, particularly walking, but barriers to participation included: already sufficiently active, reluctance to walk alone or at night, physical symptoms, depression, time constraints, trial equipment and duration. Conclusion: Gender and deprivation differences suggest some selection bias. However, trial participants reported more health problems and lower activity than non-participants who completed the survey, suggesting appropriate trial selection in a general practice population. Non-participant interviewees indicated that shorter interventions, addressing physical symptoms and promoting confidence in pursuing physical activity, might increase trial recruitment and uptake of practice-based physical activity endeavours.The National Institute for Health Research (NIHR) under its Research for Patient Benefit Programme (Grant Reference Number PB-PG-0909-20055)

Natural coagulates for wastewater treatment; a review for application and mechanism

The increase of water demand and wastewater generation is among the global concerns in the world. The less effective management of water sources leads to serious consequences, the direct disposal of untreated wastewater is associated with the environmental pollution, elimination of aquatic life and the spread of deadly epidemics. The flocculation process is one of the most important stages in water and wastewater treatment plants, wherein this phase the plankton, colloidal particles, and pollutants are precipitated and removed. Two major types of coagulants are used in the flocculation process included the chemical and natural coagulants. Many studies have been performed to optimize the flocculation process while most of these studies have confirmed the hazardous effects of chemical coagulants utilization on the ecosystem. This chapter reviews a summary of the coagulation/flocculation processes using natural coagulants as well as reviews one of the most effective natural methods of water and wastewater treatment

Beam Energy and Centrality Dependence of Direct-Photon Emission from Ultrarelativistic Heavy-Ion Collisions.

The PHENIX collaboration presents first measurements of low-momentum (0.41  GeV/c) direct-photon yield dN_{γ}^{dir}/dη is a smooth function of dN_{ch}/dη and can be well described as proportional to (dN_{ch}/dη)^{α} with α≈1.25. This scaling behavior holds for a wide range of beam energies at the Relativistic Heavy Ion Collider and the Large Hadron Collider, for centrality selected samples, as well as for different A+A collision systems. At a given beam energy, the scaling also holds for high p_{T} (&gt;5  GeV/c), but when results from different collision energies are compared, an additional sqrt[s_{NN}]-dependent multiplicative factor is needed to describe the integrated-direct-photon yield

Modeling the Impact of Tuberculosis Control Strategies in Highly Endemic Overcrowded Prisons

International audienceBACKGROUND: Tuberculosis (TB) in prisons is a major health problem in countries of high and intermediate TB endemicity such as Brazil. For operational reasons, TB control strategies in prisons cannot be compared through population based intervention studies. METHODOLOGY/PRINCIPAL FINDINGS: A mathematical model is proposed to simulate the TB dynamics in prison and evaluate the potential impact on active TB prevalence of several intervention strategies. The TB dynamics with the ongoing program was simulated over a 10 year period in a Rio de Janeiro prison (TB prevalence 4.6 %). Then, a simulation of the DOTS strategy reaching the objective of 70 % of bacteriologically-positive cases detected and 85 % of detected cases cured was performed; this strategy reduced only to 2.8% the average predicted TB prevalence after 5 years. Adding TB detection at entry point to DOTS strategy had no major effect on the predicted active TB prevalence. But, adding further a yearly X-ray mass screening of inmates reduced the predicted active TB prevalence below 1%. Furthermore, according to this model, after applying this strategy during 2 years (three annual screenings), the TB burden would be reduced and the active TB prevalence could be kept at a low level by associating X-ray screening at entry point and DOTS. CONCLUSIONS/SIGNIFICANCE: We have shown that X-ray mass screenings should be considered to control TB in highly endemic prison. Prisons with different levels of TB prevalence could be examined thanks to this model which provides a rational tool for public health deciders

Leisure-time physical activity, cardiorespiratory fitness and feelings of hopelessness in men

<p>Abstract</p> <p>Background</p> <p>Leisure-time physical activity (LTPA) and cardiorespiratory fitness contribute to mental health. Hopelessness has been linked to impaired mental health, cardiovascular events and mortality. Previous studies have focused on physical exercise and depression. We examined the associations of LTPA and cardiorespiratory fitness with feelings of hopelessness.</p> <p>Methods</p> <p>In this cross-sectional study leisure-time physical activity, maximal oxygen uptake (VO_2max), hopelessness and cardiovascular risk factors were assessed in a population-based cohort of 2428 men aged 42 – 60 years old at baseline.</p> <p>Results</p> <p>Men feeling more hopeless about their future and reaching goals were less physically active, less fit and had a higher prevalence of many cardiovascular risk factors than men with lower levels of hopelessness. In a logistic regression model adjusted for age, smoking, alcohol consumption, cardiovascular disease and socioeconomic status, men engaging in less than 60 min/week of moderate-to-vigorous LTPA were 37% (95% CI 11 – 67%) more likely to feel hopeless than those engaging in at least 2.5 h/wk of LTPA. After further adjusting for elevated depressive symptoms the association of LTPA and hopelessness remained significant. VO_2maxwas also associated with hopelessness, but not after adjustment for depressive symptoms.</p> <p>Conclusion</p> <p>Moderate and vigorous LTPA and cardiorespiratory fitness were inversely associated with hopelessness in these middle-aged men. These findings suggest that physical inactivity and poor cardiorespiratory fitness is an important associate of hopelessness, a distinct element of low subjective well-being.</p

Observation of associated near-side and away-side long-range correlations in √sNN=5.02 TeV proton-lead collisions with the ATLAS detector

Two-particle correlations in relative azimuthal angle (Δϕ) and pseudorapidity (Δη) are measured in √sNN=5.02  TeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1  μb-1 of data as a function of transverse momentum (pT) and the transverse energy (ΣETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Δη|<5) “near-side” (Δϕ∼0) correlation that grows rapidly with increasing ΣETPb. A long-range “away-side” (Δϕ∼π) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ΣETPb, is found to match the near-side correlation in magnitude, shape (in Δη and Δϕ) and ΣETPb dependence. The resultant Δϕ correlation is approximately symmetric about π/2, and is consistent with a dominant cos⁡2Δϕ modulation for all ΣETPb ranges and particle pT

The association between weekly hours of physical activity and mental health: A three-year follow-up study of 15–16-year-old students in the city of Oslo, Norway

<p>Abstract</p> <p>Background</p> <p>Mental health problems are a worldwide public health burden. The literature concerning the mental health benefits from physical activity among adults has grown. Adolescents are less studied, and especially longitudinal studies are lacking. This paper investigates the associations between weekly hours of physical activity at age 15–16 and mental health three years later.</p> <p>Methods</p> <p>Longitudinal self-reported health survey. The baseline study consisted of participants from the youth section of the Oslo Health Study, carried out in schools in 2000–2001 (<it>n </it>= 3811). The follow-up in 2003–2004 was conducted partly at school and partly through mail. A total of 2489 (1112 boys and 1377 girls) participated in the follow-up. Mental health was measured by the Strengths and Difficulties Questionnaire with an impact supplement. Physical activity was measured by a question on weekly hours of physical activity outside of school, defined as exertion 'to an extent that made you sweat and/or out of breath'. Adjustments were made for well-documented confounders and mental health at baseline.</p> <p>Results</p> <p>In boys, the number of hours spent on physical activity per week at age 15–16 was negatively associated with emotional symptoms [B (95%CI) = -0.09 (-0.15, -0.03)] and peer problems [B (95%CI) = -0.08 (-0.14, -0.03)] at age 18–19 after adjustments. In girls, there were no significant differences in SDQ subscales at age 18–19 according to weekly hours of physical activity at age 15–16 after adjustments. Boys and girls with five to seven hours of physical activity per week at age 15–16 had the lowest mean scores for total difficulties and the lowest percentage with high impact score at age 18–19, but the differences were not statistically significant after adjustments.</p> <p>Conclusion</p> <p>Weekly hours of physical activity at age 15–16 years was weakly associated with mental health at three-year follow-up in boys. Results encourage a search for further knowledge about physical activity as a possible protective factor in relation to mental health problems in adolescence.</p