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

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

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

A written self-help intervention for depressed adults comparing behavioural activation combined with physical activity promotion with a self-help intervention based upon behavioural activation alone: study protocol for a parallel group pilot randomised controlled trial (BAcPAc)

notes: PMCID: PMC4061537types: Journal Article© 2014 Farrand et al.; licensee BioMed Central Ltd.Challenges remain to find ways to support patients with depression who have low levels of physical activity (PA) to overcome perceived barriers and enhance the perceived value of PA for preventing future relapse. There is an evidence-base for behavioural activation (BA) for depression, which focuses on supporting patients to restore activities that have been avoided, but practitioners have no specific training in promoting PA. We aimed to design and evaluate an integrated BA and PA (BAcPAc) practitioner-led, written, self-help intervention to enhance both physical and mental health.NPRI-

Is it pleasure or health from leisure that we benefit from most?:An analysis of well-being alternatives and implications for policy

International policy now constantly advocates a need for populations to engage in more physical activity to promote health and to reduce society’s health care costs. Such policy has developed guidelines on recommended levels and intensity of physical activity and implicitly equates health with well-being. It is assumed that individual, and hence social welfare will be enhanced if the activity guidelines are met. This paper challenges that claim and raises questions for public policy priorities. Using an instrumental variable analysis to value the well-being from active leisure, it is shown that the well-being experienced from active leisure that is not of a recommended intensity to generate health benefits, perhaps due to its social, recreational or fun purpose, has a higher value of well-being than active leisure that does meet the guidelines. This suggests rethinking the motivation and foundation of existing policy and perhaps a realignment of priorities towards activity that has a greater contribution to social welfare through its intrinsic fun and possibly social interaction

Alignment of the ALICE Inner Tracking System with cosmic-ray tracks

37 pages, 15 figures, revised version, accepted by JINSTALICE (A Large Ion Collider Experiment) is the LHC (Large Hadron Collider) experiment devoted to investigating the strongly interacting matter created in nucleus-nucleus collisions at the LHC energies. The ALICE ITS, Inner Tracking System, consists of six cylindrical layers of silicon detectors with three different technologies; in the outward direction: two layers of pixel detectors, two layers each of drift, and strip detectors. The number of parameters to be determined in the spatial alignment of the 2198 sensor modules of the ITS is about 13,000. The target alignment precision is well below 10 micron in some cases (pixels). The sources of alignment information include survey measurements, and the reconstructed tracks from cosmic rays and from proton-proton collisions. The main track-based alignment method uses the Millepede global approach. An iterative local method was developed and used as well. We present the results obtained for the ITS alignment using about 10^5 charged tracks from cosmic rays that have been collected during summer 2008, with the ALICE solenoidal magnet switched off.Peer reviewe

Search for additional heavy neutral Higgs and gauge bosons in the ditau final state produced in 36 fb−1 of pp collisions at √s=13 TeV with the ATLAS detector

A search for heavy neutral Higgs bosons and Z′ bosons is performed using a data sample corresponding to an integrated luminosity of 36.1 fb −1 from proton-proton collisions at s=13 TeV recorded by the ATLAS detector at the LHC during 2015 and 2016. The heavy resonance is assumed to decay to τ + τ − with at least one tau lepton decaying to final states with hadrons and a neutrino. The search is performed in the mass range of 0.2-2.25 TeV for Higgs bosons and 0.2-4.0 TeV for Z′ bosons. The data are in good agreement with the background predicted by the Standard Model. The results are interpreted in benchmark scenarios. In the context of the hMSSM scenario, the data exclude tan β > 1.0 for m A = 0.25 TeV and tan β > 42 for m A = 1.5 TeV at the 95% confidence level. For the Sequential Standard Model, Z SSM ′ with m Z′ < 2.42 TeV is excluded at 95% confidence level, while Z NU ′ with m Z ′ < 2.25 TeV is excluded for the non-universal G(221) model that exhibits enhanced couplings to third-generation fermions

Operation and performance of the ATLAS Tile Calorimeter in Run 1

The Tile Calorimeter is the hadron calorimeter covering the central region of the ATLAS experiment at the Large Hadron Collider. Approximately 10,000 photomultipliers collect light from scintillating tiles acting as the active material sandwiched between slabs of steel absorber. This paper gives an overview of the calorimeter’s performance during the years 2008–2012 using cosmic-ray muon events and proton–proton collision data at centre-of-mass energies of 7 and 8TeV with a total integrated luminosity of nearly 30 fb−1. The signal reconstruction methods, calibration systems as well as the detector operation status are presented. The energy and time calibration methods performed excellently, resulting in good stability of the calorimeter response under varying conditions during the LHC Run 1. Finally, the Tile Calorimeter response to isolated muons and hadrons as well as to jets from proton–proton collisions is presented. The results demonstrate excellent performance in accord with specifications mentioned in the Technical Design Report