On the Bohr inequality

The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\sum_{n=0}^\infty |a_n|r^n \leq 1$ holds whenever $|\sum_{n=0}^\infty a_nz^n|\leq 1$ in the unit disk $\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\mathbb{D},$ as well as for analytic functions from $\mathbb{D}$ into particular domains. These domains include the punctured unit disk, the exterior of the closed unit disk, and concave wedge-domains. The analogous Bohr radius is also studied for harmonic and starlike logharmonic mappings in $\mathbb{D}.$ The Bohr phenomenon which is described in terms of the Euclidean distance is further investigated using the spherical chordal metric and the hyperbolic metric. The exposition concludes with a discussion on the $n$-dimensional Bohr radius

Dyspraxia and autistic traits in adults with and without autism spectrum conditions

BACKGROUND: Autism spectrum conditions (ASC) are frequently associated with motor coordination difficulties. However, no studies have explored the prevalence of dyspraxia in a large sample of individuals with and without ASC or associations between dyspraxia and autistic traits in these individuals. METHODS: Two thousand eight hundred seventy-one adults (with ASC) and 10,706 controls (without ASC) self-reported whether they have been diagnosed with dyspraxia. A subsample of participants then completed the Autism Spectrum Quotient (AQ; 1237 ASC and 6765 controls) and the Empathy Quotient (EQ; 1147 ASC and 6129 controls) online through the Autism Research Centre website. The prevalence of dyspraxia was compared between those with and without ASC. AQ and EQ scores were compared across the four groups: (1) adults with ASC with dyspraxia, (2) adults with ASC without dyspraxia, (3) controls with dyspraxia, and (4) controls without dyspraxia. RESULTS: Adults with ASC were significantly more likely to report a diagnosis of dyspraxia (6.9%) than those without ASC (0.8%). In the ASC group, those with co-morbid diagnosis of dyspraxia did not have significantly different AQ or EQ scores than those without co-morbid dyspraxia. However, in the control group (without ASC), those with dyspraxia had significantly higher AQ and lower EQ scores than those without dyspraxia. CONCLUSIONS: Dyspraxia is significantly more prevalent in adults with ASC compared to controls, confirming reports that motor coordination difficulties are significantly more common in this group. Interestingly, in the general population, dyspraxia was associated with significantly higher autistic traits and lower empathy. These results suggest that motor coordination skills are important for effective social skills and empathy

Utility of CD4 cell counts for early prediction of virological failure during antiretroviral therapy in a resource-limited setting

BACKGROUND: Viral load monitoring is not available for the vast majority of patients receiving antiretroviral therapy in resource-limited settings. However, the practical utility of CD4 cell count measurements as an alternative monitoring strategy has not been rigorously assessed. METHODS: In this study, we used a novel modelling approach that accounted for all CD4 cell count and VL values measured during follow-up from the first date that VL suppression was achieved. We determined the associations between CD4 counts (absolute values and changes during ART), VL measurements and risk of virological failure (VL > 1,000 copies/ml) following initial VL suppression in 330 patients in South Africa. CD4 count changes were modelled both as the difference from baseline (DeltaCD4 count) and the difference between consecutive values (CD4 count slope) using all 3-monthly CD4 count measurements during follow-up. RESULTS: During 7093.2 patient-months of observation 3756 paired CD4 count and VL measurements were made. In patients who developed virological failure (n = 179), VL correlated significantly with absolute CD4 counts (r = - 0.08, P = 0.003), DeltaCD4 counts (r = - 0.11, P < 0.01), and most strongly with CD4 count slopes (r = - 0.30, P < 0.001). However, the distributions of the absolute CD4 counts, DeltaCD4 counts and CD4 count slopes at the time of virological failure did not differ significantly from the corresponding distributions in those without virological failure (P = 0.99, P = 0.92 and P = 0.75, respectively). Moreover, in a receiver operating characteristic (ROC) curve, the association between a negative CD4 count slope and virological failure was poor (area under the curve = 0.59; sensitivity = 53.0%; specificity = 63.6%; positive predictive value = 10.9%). CONCLUSION: CD4 count changes correlated significantly with VL at group level but had very limited utility in identifying virological failure in individual patients. CD4 count is an inadequate alternative to VL measurement for early detection of virological failure

New Detection Systems of Bacteria Using Highly Selective Media Designed by SMART: Selective Medium-Design Algorithm Restricted by Two Constraints

Culturing is an indispensable technique in microbiological research, and culturing with selective media has played a crucial role in the detection of pathogenic microorganisms and the isolation of commercially useful microorganisms from environmental samples. Although numerous selective media have been developed in empirical studies, unintended microorganisms often grow on such media probably due to the enormous numbers of microorganisms in the environment. Here, we present a novel strategy for designing highly selective media based on two selective agents, a carbon source and antimicrobials. We named our strategy SMART for highly Selective Medium-design Algorithm Restricted by Two constraints. To test whether the SMART method is applicable to a wide range of microorganisms, we developed selective media for Burkholderia glumae, Acidovorax avenae, Pectobacterium carotovorum, Ralstonia solanacearum, and Xanthomonas campestris. The series of media developed by SMART specifically allowed growth of the targeted bacteria. Because these selective media exhibited high specificity for growth of the target bacteria compared to established selective media, we applied three notable detection technologies: paper-based, flow cytometry-based, and color change-based detection systems for target bacteria species. SMART facilitates not only the development of novel techniques for detecting specific bacteria, but also our understanding of the ecology and epidemiology of the targeted bacteria

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in pp collisions at √s = 7 TeV with the ATLAS detector

This paper presents a measurement of the cross-section for high transverse momentum W and Z bosons produced in pp collisions and decaying to all-hadronic final states. The data used in the analysis were recorded by the ATLAS detector at the CERN Large Hadron Collider at a centre-of-mass energy of √s = 7 TeV;{\rm Te}{\rm V}$and correspond to an integrated luminosity of$4.6\;{\rm f}{{{\rm b}}^{-1}}$. The measurement is performed by reconstructing the boosted W or Z bosons in single jets. The reconstructed jet mass is used to identify the W and Z bosons, and a jet substructure method based on energy cluster information in the jet centre-of-mass frame is used to suppress the large multi-jet background. The cross-section for events with a hadronically decaying W or Z boson, with transverse momentum${{p}_{{\rm T}}}\gt 320\;{\rm Ge}{\rm V}$and pseudorapidity$|\eta |\lt 1.9$, is measured to be${{\sigma }_{W+Z}}=8.5\pm 1.7$ pb and is compared to next-to-leading-order calculations. The selected events are further used to study jet grooming techniques