Multifractal tubes

Tube formulas refer to the study of volumes of $r$ neighbourhoods of sets. For sets satisfying some (possible very weak) convexity conditions, this has a long history. However, within the past 20 years Lapidus has initiated and pioneered a systematic study of tube formulas for fractal sets. Following this, it is natural to ask to what extend it is possible to develop a theory of multifractal tube formulas for multifractal measures. In this paper we propose and develop a framework for such a theory. Firstly, we define multifractal tube formulas and, more generally, multifractal tube measures for general multifractal measures. Secondly, we introduce and develop two approaches for analysing these concepts for self-similar multifractal measures, namely: (1) Multifractal tubes of self-similar measures and renewal theory. Using techniques from renewal theory we give a complete description of the asymptotic behaviour of the multifractal tube formulas and tube measures of self-similar measures satisfying the Open Set Condition. (2) Multifractal tubes of self-similar measures and zeta-functions. Unfortunately, renewal theory techniques do not yield "explicit" expressions for the functions describing the asymptotic behaviour of the multifractal tube formulas and tube measures of self-similar measures. This is clearly undesirable. For this reason, we introduce and develop a second framework for studying multifractal tube formulas of self-similar measures. This approach is based on multifractal zeta-functions and allow us obtain "explicit" expressions for the multifractal tube formulas of self-similar measures, namely, using the Mellin transform and the residue theorem, we are able to express the multifractal tube formulas as sums involving the residues of the zeta-function.Comment: 122 page

Effect of growth temperature on the structural, optical and luminescence properties of cadmium telluride nanoparticles

Cadmium telluride (CdTe) has been successfully prepared by a simple wet chemical process at different reaction temperatures. Temperature is one parameter that thermodynamically plays an important role in controlling the growth rate, morphology, size and size distribution of the as-prepared nanoparticles (NPs). Effect of this parameter was investigated on the growth, structural and optical properties of CdTe NPs. It was observed that the Powder X-ray diffraction (XRD) pattern for samples prepared at 50 °C had many impurities from unreacted precursors while those prepared at > 100 °C displayed polycrystalline NPs. The XRD results revealed that the structure of the CdTe NPs was cubic with the planes (111), (220), (311) being the main observed peaks. The crystallite sizes obtained from Scherrer formula increased with the increase in growth temperature (2.86–3.62 nm grown at 50–200 °C respectively). The scanning electron microscopy micrographs showed that the morphology of the nanoparticles possessed spherical-shaped particles over the entire surface. This was further confirmed by high resolution transmission electron microscopy micrographs which also displayed increase in the particle size with an increase in the growth temperature. In the optic study, the photoluminescence (PL) spectra displayed a red shift (540–560 nm) in emission as growth temperature increased from 50 to 200 °C. The highest PL peak intensity was realized at a growth temperature of 150 °C. Absorption band maxima were observed to shift towards longer wavelength for higher growth temperatures. The optical band gap decreased with increase in the growth temperature from 2.67 to 2.08 eV for 50–200 °C respectively

Sins of Omission

Little is known about the relative incidence of serious errors of omission versus errors of commission. Objective : To identify the most common substantive medical errors identified by medical record review. Design : Retrospective cohort study. Setting : Twelve Veterans Affairs health care systems in 2 regions. Participants : Stratified random sample of 621 patients receiving care over a 2-year period. Main Outcome Measure : Classification of reported quality problems. Methods : Trained physicians reviewed the full inpatient and outpatient record and described quality problems, which were then classified as errors of omission versus commission. Results : Eighty-two percent of patients had at least 1 error reported over a 13-month period. The average number of errors reported per case was 4.7 (95% confidence intervals [CI]: 4.4, 5.0). Overall, 95.7% (95% CI: 94.9%, 96.4%) of errors were identified as being problems with underuse. Inadequate care for people with chronic illnesses was particularly common. Among errors of omission, obtaining insufficient information from histories and physicals (25.3%), inadequacies in diagnostic testing (33.9%), and patients not receiving needed medications (20.7%) were all common. Out of the 2,917 errors identified, only 27 were rated as being highly serious, and 26 (96%) of these were errors of omission. Conclusions : While preventing iatrogenic injury resulting from medical errors is a critically important part of quality improvement, we found that the overwhelming majority of substantive medical errors identifiable from the medical record were related to people getting too little medical care, especially for those with chronic medical conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74567/1/j.1525-1497.2005.0152.x.pd

Adolescents’ beverage choice at school and the impact on sugar intake

Background/Objectives: To examine students’ beverage choice in school, with reference to its contribution to students’ intake of non-milk extrinsic (NME) sugars. Subjects/Methods: Beverage and food selection data for students aged 11–18 years (n=2461) were collected from two large secondary schools in England, for a continuous period of 145 (school A) and 125 (school B) school days. Descriptive analysis followed by cluster analysis of the beverage data were performed separately for each school. Results: More than a third of all items selected by students were beverages, and juice-based beverages were students’ most popular choice (school A, 38.6%; school B, 35.2%). Mean NME sugars derived from beverages alone was high (school A, 16.7 g/student-day; school B, 12.9 g/student-day). Based on beverage purchases, six clusters of students were identified at each school (school A: ‘juice-based’, ‘assorted’, ‘water’, ‘cartoned flavoured milk’, ‘bottled flavoured milk’, ‘high volume juice-based’; school B: ‘assorted’, ‘water with juice-based’, ‘sparkling juice/juice-based’, ‘water’, ‘high volume water’, ‘high volume juice-based’). Both schools included ‘high volume juice-based’ clusters with the highest NME sugar means from beverages (school A, 28.6 g/student-day; school B, 24.4 g/student-day), and ‘water’ clusters with the lowest. A hierarchy in NME sugars was found according to cluster; students in the ‘high volume juice-based’ cluster returned significantly higher levels of NME sugars than students in other clusters. Conclusions: This study reveals the contribution that school beverages combined with students’ beverage choice behaviour is making to students’ NME sugar intake. These findings inform school food initiatives, and more generally public health policy around adolescents’ dietary intake

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

Search for supersymmetry in events with four or more leptons in √s =13 TeV pp collisions with ATLAS

Results from a search for supersymmetry in events with four or more charged leptons (electrons, muons and taus) are presented. The analysis uses a data sample corresponding to 36.1 fb −1 of proton-proton collisions delivered by the Large Hadron Collider at s √ =13 TeV and recorded by the ATLAS detector. Four-lepton signal regions with up to two hadronically decaying taus are designed to target a range of supersymmetric scenarios that can be either enriched in or depleted of events involving the production and decay of a Z boson. Data yields are consistent with Standard Model expectations and results are used to set upper limits on the event yields from processes beyond the Standard Model. Exclusion limits are set at the 95% confidence level in simplified models of General Gauge Mediated supersymmetry, where higgsino masses are excluded up to 295 GeV. In R -parity-violating simplified models with decays of the lightest supersymmetric particle to charged leptons, lower limits of 1.46 TeV, 1.06 TeV, and 2.25 TeV are placed on wino, slepton and gluino masses, respectively

Measurement of the t¯tZ and t¯tW cross sections in proton-proton collisions at √s=13 TeV with the ATLAS detector

A measurement of the associated production of a top-quark pair (t¯t) with a vector boson (W, Z) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented, using 36.1  fb−1 of integrated luminosity collected by the ATLAS detector at the Large Hadron Collider. Events are selected in channels with two same- or opposite-sign leptons (electrons or muons), three leptons or four leptons, and each channel is further divided into multiple regions to maximize the sensitivity of the measurement. The t¯tZ and t¯tW production cross sections are simultaneously measured using a combined fit to all regions. The best-fit values of the production cross sections are σt¯tZ=0.95±0.08stat±0.10syst pb and σt¯tW=0.87±0.13stat±0.14syst pb in agreement with the Standard Model predictions. The measurement of the t¯tZ cross section is used to set constraints on effective field theory operators which modify the t¯tZ vertex

Measurement of the tt¯tt¯ production cross section in pp collisions at √s=13 TeV with the ATLAS detector

A measurement of four-top-quark production using proton-proton collision data at a centre-of-mass energy of 13 TeV collected by the ATLAS detector at the Large Hadron Collider corresponding to an integrated luminosity of 139 fb−1 is presented. Events are selected if they contain a single lepton (electron or muon) or an opposite-sign lepton pair, in association with multiple jets. The events are categorised according to the number of jets and how likely these are to contain b-hadrons. A multivariate technique is then used to discriminate between signal and background events. The measured four-top-quark production cross section is found to be 26+17−15 fb, with a corresponding observed (expected) significance of 1.9 (1.0) standard deviations over the background-only hypothesis. The result is combined with the previous measurement performed by the ATLAS Collaboration in the multilepton final state. The combined four-top-quark production cross section is measured to be 24+7−6 fb, with a corresponding observed (expected) signal significance of 4.7 (2.6) standard deviations over the background-only predictions. It is consistent within 2.0 standard deviations with the Standard Model expectation of 12.0 ± 2.4 fb

Measurements of W+W−+ ≥ 1 jet production cross-sections in pp collisions at s \sqrt{s} = 13 TeV with the ATLAS detector

Fiducial and differential cross-section measurements of W+W− production in association with at least one hadronic jet are presented. These measurements are sensitive to the properties of electroweak-boson self-interactions and provide a test of perturbative quantum chromodynamics and the electroweak theory. The analysis is performed using proton-proton collision data collected at p s = 13TeV with the ATLAS experiment, corresponding to an integrated luminosity of 139 fb−1. Events are selected with exactly one oppositely charged electron-muon pair and at least one hadronic jet with a transverse momentum of pT > 30 GeV and a pseudorapidity of |�| < 4.5. After subtracting the background contributions and correcting for detector effects, the jet-inclusive W+W−+ � 1 jet fiducial cross-section and W+W−+ jets differential cross-sections with respect to several kinematic variables are measured. These measurements include leptonic quantities, such as the lepton transverse momenta and the transverse mass of the W+W− system, as well as jet-related observables such as the leading jet transverse momentum and the jet multiplicity. Limits on anomalous triple-gauge-boson couplings are obtained in a phase space where interference between the Standard Model amplitude and the anomalous amplitude is enhanced