We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.

with among the highest numbers of patients with COVID-19 in the country. We selected HCWs, including physicians, nurses, laboratory medical technologists, radiological technologists, and pharmacists, who worked in departments in which they had contact with patients with COVID-19, including emergency departments, general internal medicine departments, respiratory medicine departments, infectious disease departments, general wards, and intensive care units. An explanation of the sample size calculation appears in the eAppendix in the Supplement. This study was approved by the institutional review board of St Luke's International Hospital in Tokyo, Japan. A letter of informed consent was distributed to the participants via email, and completion of the questionnaire implied their consent. This study followed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) reporting guideline.The web-based survey was generated using SurveyMonkey, a cloud-based survey development application. The survey solicited responses regarding participants' demographic characteristics (age and gender), professional history (job category and years of experience), working environment characteristics (mean weekly working hours, days off per month, and hours of sleep per day), types of anxiety perceived, changes compared with before the pandemic, and types of support needed.The primary outcome was the prevalence of burnout among frontline HCWs in departments with direct contact with patients with COVID-19, using the validated Japanese version of the Maslach Burnout Inventory-General Survey, 3 which is currently considered the criterion standard for measuring burnout. This 16-item questionnaire contains 3 subscales that evaluate what are considered the 3 major domains of burnout, ie, emotional exhaustion, cynicism (ie, depersonalization), and professional efficacy (ie, personal accomplishment). High levels of exhaustion (>3.5) plus either high cynicism (>3.5) or low professional efficacy (<2.5) were selected as the primary criteria for burnout.We first compared the baseline characteristics of those who did and did not have burnout by using the χ 2 difference test for categorical variables and the Mann-Whitney U test for continuous variables. Given the limited information available on confounding by potential risk factors for burnout, we used logistic regression analyses to evaluate whether any factors, such as types of anxiety perceived, changes compared with the prepandemic period, and types of support needed, were significant by integrating data on the participants' backgrounds into the model. All analyses

Background and Purpose-About one half of those who develop adult-onset moyamoya disease experience intracranial hemorrhage. Despite the extremely high frequency of rebleeding attacks and poor prognosis, measures to prevent rebleeding have not been established. The purpose of this study is to determine whether extracranial-intracranial bypass can reduce incidence of rebleeding and improve patient prognosis. Methods-This study was a multicentered, prospective, randomized, controlled trial conducted by 22 institutes in Japan.Adult patients with moyamoya disease who had experienced intracranial hemorrhage within the preceding year were given either conservative care or bilateral extracranial-intracranial direct bypass and were observed for 5 years. Primary and secondary end points were defined as all adverse events and rebleeding attacks, respectively. Results-Eighty patients were enrolled (surgical, 42; nonsurgical, 38). Adverse events causing significant morbidity were observed in 6 patients in the surgical group (14.3%) and 13 patients in the nonsurgical group (34.2%). Kaplan-Meier survival analysis revealed significant differences between the 2 groups (3.2%/y versus 8.2%/y; P=0.048). The hazard ratio of the surgical group calculated by Cox regression analysis was 0.391 (95% confidence interval, 0.148-1.029).Rebleeding attacks were observed in 5 patients in the surgical group (11.9%) and 12 in the nonsurgical group (31.6%), significantly different in the Kaplan-Meier survival analysis (2.7%/y versus 7.6%/y; P=0.042). The hazard ratio of the surgical group was 0.355 (95% confidence interval, 0.125-1.009). Conclusions-Although statistically marginal, Kaplan-Meier analysis revealed the significant difference between surgical and nonsurgical group, suggesting the preventive effect of direct bypass against rebleeding. Clinical Trial Registration

Inspired by a recent discovery of a peculiar integer quantum Hall effect ͑QHE͒ in graphene, we study QHE on a honeycomb lattice in terms of the topological quantum number, with two interests. First, how the zero-mass Dirac QHE around the center of the tight-binding band crosses over to the ordinary finite-mass fermion QHE around the band edges. Second, how the bulk QHE is related with the edge QHE for the entire spectrum including Dirac and ordinary behaviors. We find the following. ͑i͒ The zero-mass Dirac QHE ͓with xy = ϯ ͑2N +1͒e 2 / h , N: integer͔ persists, surprisingly, up to the van Hove singularities, at which the ordinary fermion behavior abruptly takes over. Here a technique developed in the lattice gauge theory enabled us to calculate the behavior of the topological number over the entire spectrum. This result indicates a robustness of the topological quantum number, and should be observable if the chemical potential can be varied over a wide range in graphene. ͑ii͒ To see if the honeycomb lattice is singular in producing the anomalous QHE, we have systematically surveyed over square ↔ honeycomb ↔-flux lattices, which is scanned by introducing a diagonal transfer tЈ. We find that the massless Dirac QHE ͓ϰ͑2N +1͔͒ forms a critical line, that is, the presence of Dirac cones in the Brillouin zone is preserved by the inclusion of tЈ and the Dirac region sits side by side with ordinary one persists all through the transformation. ͑iii͒ We have compared the bulk QHE number obtained by an adiabatic continuity of the Chern number across the square ↔ honeycomb ↔-flux transformation and numerically obtained edge QHE number calculated from the whole energy spectra for sample with edges, which shows that the bulk QHE number coincides, as in ordinary lattices, with the edge QHE number throughout the lattice transformation.

Background The effects of pharmacological blood pressure lowering at normal or high-normal blood pressure ranges in people with or without pre-existing cardiovascular disease remains uncertain. We analysed individual participant data from randomised trials to investigate the effects of blood pressure lowering treatment on the risk of major cardiovascular events by baseline levels of systolic blood pressure. MethodsWe did a meta-analysis of individual participant-level data from 48 randomised trials of pharmacological blood pressure lowering medications versus placebo or other classes of blood pressure-lowering medications, or between more versus less intensive treatment regimens, which had at least 1000 persons-years of follow-up in each group. Trials exclusively done with participants with heart failure or short-term interventions in participants with acute myocardial infarction or other acute settings were excluded. Data from 51 studies published between 1972 and 2013 were obtained by the Blood Pressure Lowering Treatment Trialists' Collaboration (Oxford University, Oxford, UK). We pooled the data to investigate the stratified effects of blood pressure-lowering treatment in participants with and without prevalent cardiovascular disease (ie, any reports of stroke, myocardial infarction, or ischaemic heart disease before randomisation), overall and across seven systolic blood pressure categories (ranging from <120 to ≥170 mm Hg). The primary outcome was a major cardiovascular event (defined as a composite of fatal and non-fatal stroke, fatal or non-fatal myocardial infarction or ischaemic heart disease, or heart failure causing death or requiring admission to hospital), analysed as per intention to treat.Findings Data for 344 716 participants from 48 randomised clinical trials were available for this analysis. Pre-randomisation mean systolic/diastolic blood pressures were 146/84 mm Hg in participants with previous cardiovascular disease (n=157 728) and 157/89 mm Hg in participants without previous cardiovascular disease (n=186 988). There was substantial spread in participants' blood pressure at baseline, with 31 239 (19•8%) of participants with previous cardiovascular disease and 14 928 (8•0%) of individuals without previous cardiovascular disease having a systolic blood pressure of less than 130 mm Hg. The relative effects of blood pressure-lowering treatment were proportional to the intensity of systolic blood pressure reduction. After a median 4•15 years' follow-up (Q1-Q3 2•97-4•96), 42 324 participants (12•3%) had at least one major cardiovascular event. In participants without previous cardiovascular disease at baseline, the incidence rate for developing a major cardiovascular event per 1000 person-years was 31•9 (95% CI 31•3-32•5) in the comparator group and 25•9 (25•4-26•4) in the intervention group. In participants with previous cardiovascular disease at baseline, the corresponding rates were 39•7 (95% CI 39•0-40•5) and 36•0 (95% CI 35•3-36•7), in the comparator and intervention groups, respectively. Haz...

We present a study of the Drude weight D(T ) of the spin-1/2 XXZ chain in the gapless regime. The thermodynamic Bethe ansatz (TBA) is applied in two different ways. In the first application we employ the particle basis of magnons and their bound states. In this case we rederive and considerably extend earlier work in the literature. However, in the course of our investigation we find arguments that cast doubt on the applicability of the TBA in this case. In a second application by use of the spinon and anti-spinon particle basis we obtain completely different results. Only for anisotropy parameter ∆ close to 0 we find that D(T ) is a monotonously decaying function of temperature. For ∆ close to 1 the behaviour is entirely different showing a finite temperature maximum. Also for the isotropic antiferromagnetic chain (∆ = 1) the results for D(T ) are finite for T = 0 as well as for T > 0 with an infinite positive slope at T = 0.

We derive an efficient formula for Z 2 topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model. Quantum spin Hall (QSH) effect [1][2][3][4][5] has been attracting much current interest as a new device of spintronics. [6][7][8][9] It is a topological insulator [10][11][12] analogous to the quantum Hall (QH) effect, but it is realized in time-reversal (T ) invariant systems. While QH states are specified by Chern numbers, 13,14) QSH states are characterized by Z 2 topological numbers, 2) which suggests that Z 2 invariants would have deep relationship with the Z 2 anomaly of the Majorana fermions. 15,16) Graphene has been expected to be in the QSH phase. 1,2)However, recent calculations have suggested that the spinorbit coupling in graphene is too small to reveal the QSH effect experimentally. 17,18) Recently, it has been pointed out that Bi thin film is another plausible material for QSH effect.19) Also by the idea of adiabatic deformation of the diamond lattice, it has been conjectured that Bi in three dimensions (3D) is in a topological phase. 20)While systems in two dimensions (2D) are characterized by a single Z 2 topological invariant, four independent Z 2 invariants are needed in 3D. [20][21][22][23] This makes it difficult to investigate realistic models, in which complicated many-band structure is involved. Therefore, for the direct study of Bi in 3D as well as for the search for other materials, to establish a simple and efficient computational method of Z 2 invariants in 3D is an urgent issue to be resolved.In this paper, we present a method of computing Z 2 invariants based on the formula derived by Fu and Kane 24) together with the recent development of computing Chern numbers in a lattice Brillouin zone. [25][26][27] This method is based on recent developments in lattice gauge theories [30][31][32][33][34][35] but simple enough to compute Z 2 invariants even for realistic 3D systems. Based on this, we study a tight-binding model for Bi and Sb.First, we derive a lattice version of the Fu-Kane formula.24) To this end, we restrict our discussions, for simplicity, to systems in 2D, where a single Z 2 invariant is relevant. Let T be the time-reversal transformation T ¼ i 2 K, and assume that the Hamiltonian in the momentum space HðkÞ transforms under T as T HðkÞT À1 ¼ HðÀkÞ. Let ðkÞ ¼ ðj1ðkÞi; . . . ; j2MðkÞiÞ denote the 2M dimensional ground state multiplet of the Hamiltonian: HðkÞjnðkÞi ¼ E n ðkÞjnðkÞi. 11,12) Assuming that the many-body energy gap is finite, we focus on topological invariants under the Uð2MÞ transformation ðkÞ ! ðkÞUðkÞ; UðkÞ 2 Uð2MÞ:As discussed, 2,27) the pfaffian defined by pðkÞ ¼ pf É y ðT ÉÞ characterizes the topological phases of T invariant systems. To be precise, the systems belong to topological insu...

The quinone of 2,4,5-trihydroxyphenylalanine (topa), recently identified as the covalently bound redox cofactor in copper amine oxidases, is encoded by a specific tyrosine codon. To elucidate the mechanism of its formation, the recombinant phenylethylamine oxidase of Arthrobacter globiformis has been overproduced in Escherichia cord and purified in a Cu2+-deficient form. The inactive precursor enzyme thus obtained was dramatically activated upon incubation with Cu 2÷, concomitantly with the formation of the topa quinone at the position corresponding to Tyr 382, occurring in the tetrapeptide sequence highly conserved in this class of enzymes. The topa quinone was produced only under aerobic conditions, but its formation required no external enzymatic systems. These findings demonstrate the Cu2+-dependent autooxidation of a specific tyrosyl residue to generate the topa quinone cofactor.