The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

ENIGMA and global neuroscience: A decade of large-scale studies of the brain in health and disease across more than 40 countries

This review summarizes the last decade of work by the ENIGMA (Enhancing NeuroImaging Genetics through Meta Analysis) Consortium, a global alliance of over 1400 scientists across 43 countries, studying the human brain in health and disease. Building on large-scale genetic studies that discovered the first robustly replicated genetic loci associated with brain metrics, ENIGMA has diversified into over 50 working groups (WGs), pooling worldwide data and expertise to answer fundamental questions in neuroscience, psychiatry, neurology, and genetics. Most ENIGMA WGs focus on specific psychiatric and neurological conditions, other WGs study normal variation due to sex and gender differences, or development and aging; still other WGs develop methodological pipelines and tools to facilitate harmonized analyses of "big data" (i.e., genetic and epigenetic data, multimodal MRI, and electroencephalography data). These international efforts have yielded the largest neuroimaging studies to date in schizophrenia, bipolar disorder, major depressive disorder, post-traumatic stress disorder, substance use disorders, obsessive-compulsive disorder, attention-deficit/hyperactivity disorder, autism spectrum disorders, epilepsy, and 22q11.2 deletion syndrome. More recent ENIGMA WGs have formed to study anxiety disorders, suicidal thoughts and behavior, sleep and insomnia, eating disorders, irritability, brain injury, antisocial personality and conduct disorder, and dissociative identity disorder. Here, we summarize the first decade of ENIGMA's activities and ongoing projects, and describe the successes and challenges encountered along the way. We highlight the advantages of collaborative large-scale coordinated data analyses for testing reproducibility and robustness of findings, offering the opportunity to identify brain systems involved in clinical syndromes across diverse samples and associated genetic, environmental, demographic, cognitive, and psychosocial factors

Fashion retailing – past, present and future

This issue of Textile Progress reviews the way that fashion retailing has developed as a result of the application of the World Wide Web and information and communications technology (ICT) by fashion-retail companies. The review therefore first considers how fashion retailing has evolved, analysing retail formats, global strategies, emerging and developing economies, and the factors that are threatening and driving growth in the fashion-retail market. The second part of the review considers the emergence of omni-channel retailing, analysing how retail has progressed and developed since the adoption of the Internet and how ICT initiatives such as mobile commerce (m-commerce), digital visualisation online, and in-store and self-service technologies have been proven to support the progression and expansion of fashion retailing. The paper concludes with recommendations on future research opportunities for gaining a better understanding of the impacts of ICT and omni-channel retailing, through which it may be possible to increase and develop knowledge and understanding of the way the sector is developing and provide fresh impetus to an already-innovative and competitive industr

The Cholecystectomy As A Day Case (CAAD) Score: A Validated Score of Preoperative Predictors of Successful Day-Case Cholecystectomy Using the CholeS Data Set

Background Day-case surgery is associated with significant patient and cost benefits. However, only 43% of cholecystectomy patients are discharged home the same day. One hypothesis is day-case cholecystectomy rates, defined as patients discharged the same day as their operation, may be improved by better assessment of patients using standard preoperative variables. Methods Data were extracted from a prospectively collected data set of cholecystectomy patients from 166 UK and Irish hospitals (CholeS). Cholecystectomies performed as elective procedures were divided into main (75%) and validation (25%) data sets. Preoperative predictors were identified, and a risk score of failed day case was devised using multivariate logistic regression. Receiver operating curve analysis was used to validate the score in the validation data set. Results Of the 7426 elective cholecystectomies performed, 49% of these were discharged home the same day. Same-day discharge following cholecystectomy was less likely with older patients (OR 0.18, 95% CI 0.15–0.23), higher ASA scores (OR 0.19, 95% CI 0.15–0.23), complicated cholelithiasis (OR 0.38, 95% CI 0.31 to 0.48), male gender (OR 0.66, 95% CI 0.58–0.74), previous acute gallstone-related admissions (OR 0.54, 95% CI 0.48–0.60) and preoperative endoscopic intervention (OR 0.40, 95% CI 0.34–0.47). The CAAD score was developed using these variables. When applied to the validation subgroup, a CAAD score of ≤5 was associated with 80.8% successful day-case cholecystectomy compared with 19.2% associated with a CAAD score >5 (p < 0.001). Conclusions The CAAD score which utilises data readily available from clinic letters and electronic sources can predict same-day discharges following cholecystectomy

Search for the Zγ decay mode of new high-mass resonances in pp collisions at √s = 13 TeV with the ATLAS detector

This letter presents a search for narrow, high-mass resonances in the Zγ final state with the Z boson decaying into a pair of electrons or muons. The √s = 13 TeV pp collision data were recorded by the ATLAS detector at the CERN Large Hadron Collider and have an integrated luminosity of 140 fb−1. The data are found to be in agreement with the Standard Model background expectation. Upper limits are set on the resonance production cross section times the decay branching ratio into Zγ. For spin-0 resonances produced via gluon–gluon fusion, the observed limits at 95% confidence level vary between 65.5 fb and 0.6 fb, while for spin-2 resonances produced via gluon–gluon fusion (or quark–antiquark initial states) limits vary between 77.4 (76.1) fb and 0.6 (0.5) fb, for the mass range from 220 GeV to 3400 GeV

Search for heavy Higgs bosons with flavour-violating couplings in multi-lepton plus b-jets final states in pp collisions at 13 TeV with the ATLAS detector

A search for new heavy scalars with flavour-violating decays in final states with multiple leptons and b-tagged jets is presented. The results are interpreted in terms of a general two-Higgs-doublet model involving an additional scalar with couplings to the top-quark and the three up-type quarks (ρtt, ρtc, and ρtu). The targeted signals lead to final states with either a same-sign top-quark pair, three top-quarks, or four top-quarks. The search is based on a data sample of proton-proton collisions at √s = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb−1. Events are categorised depending on the multiplicity of light charged leptons (electrons or muons), total lepton charge, and a deep-neural-network output to enhance the purity of each of the signals. Masses of an additional scalar boson mH between 200 − 630 GeV with couplings ρtt = 0.4, ρtc = 0.2, and ρtu = 0.2 are excluded at 95% confidence level. Additional interpretations are provided in models of R-parity violating supersymmetry, motivated by the recent flavour and (g − 2)μ anomalies

Search for a new heavy scalar particle decaying into a Higgs boson and a new scalar singlet in final states with one or two light leptons and a pair of τ-leptons with the ATLAS detector

A search for a new heavy scalar particle X decaying into a Standard Model (SM) Higgs boson and a new singlet scalar particle S is presented. The search uses a proton-proton (pp) collision data sample with an integrated luminosity of 140 fb−1 recorded at a centre-of-mass energy of s√ = 13 TeV with the ATLAS detector at the Large Hadron Collider. The most sensitive mass parameter space is explored in X mass ranging from 500 to 1500 GeV, with the corresponding S mass in the range 200–500 GeV. The search selects events with two hadronically decaying τ-lepton candidates from H → τ+τ− decays and one or two light leptons (ℓ = e, μ) from S → VV (V = W, Z) decays while the remaining V boson decays hadronically or to neutrinos. A multivariate discriminant based on event kinematics is used to separate the signal from the background. No excess is observed beyond the expected SM background and 95% confidence level upper limits between 72 fb and 542 fb are derived on the cross-section σ(pp → X → SH) assuming the same SM-Higgs boson-like decay branching ratios for the S → VV decay. Upper limits on the visible cross-sections σ(pp → X → SH → WWττ) and σ(pp → X → SH → ZZττ) are also set in the ranges 3–26 fb and 6–33 fb, respectively

Measurement of the cross-sections of the electroweak and total production of a Zγ pair in association with two jets in pp collisions at √s = 13 TeV with the ATLAS detector

This Letter presents the measurement of the fiducial and differential cross-sections of the electroweak production of a Zγ pair in association with two jets. The analysis uses 140 fb−1 of LHC proton–proton collision data taken at √s = 13 TeV recorded by the ATLAS detector during the years 2015–2018. Events with a Z boson candidate decaying into either an e+e− or μ+μ− pair, a photon and two jets are selected. The electroweak component is extracted by requiring a large dijet invariant mass and by using the information about the centrality of the system and is measured with an observed and expected significance well above five standard deviations. The fiducial pp → Zγ jj cross-section for the electroweak production is measured to be 3.6 ± 0.5 fb. The total fiducial cross-section that also includes contributions where the jets arise from strong interactions is measured to be 16.8+2.0 −1.8 fb. The results are consistent with the Standard Model predictions. Differential cross-sections are also measured using the same events and are compared with parton-shower Monte Carlo simulations. Good agreement is observed between data and predictions

The ATLAS trigger system for LHC Run 3 and trigger performance in 2022

The ATLAS trigger system is a crucial component of the ATLAS experiment at the LHC. It is responsible for selecting events in line with the ATLAS physics programme. This paper presents an overview of the changes to the trigger and data acquisition system during the second long shutdown of the LHC, and shows the performance of the trigger system and its components in the proton-proton collisions during the 2022 commissioning period as well as its expected performance in proton-proton and heavy-ion collisions for the remainder of the third LHC data-taking period (2022–2025)