Sums of hermitian squares and the BMV conjecture

Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.Comment: 21 pages; minor changes; a companion Mathematica notebook is now available in the source fil

Approximate tight-binding sum rule for the superconductivity related change of c-axis kinetic energy in multilayer cuprate superconductors

We present an extension of the c-axis tight-binding sum rule discussed by Chakravarty, Kee, and Abrahams [Phys. Rev. Lett. 82, 2366 (1999)] that applies to multilayer high-Tc cuprate superconductors (HTCS) and use it to estimate--from available infrared data--the change below Tc of the c-axis kinetic energy, Hc, in YBa2Cu3O(7-delta) (delta=0.45,0.25,0.07), Bi2Sr2CaCu2O8, and Bi2Sr2Ca2Cu3O10. In all these compounds Hc decreases below Tc and except for Bi2Sr2CaCu2O8 the change of Hc is of the same order of magnitude as the condensation energy. This observation supports the hypothesis that in multilayer HTCS superconductivity is considerably amplified by the interlayer tunnelling mechanism.Comment: 6 pages, 2 figure

Current but not past smoking increases the risk of cardiac events: insights from coronary computed tomographic angiography

Aims We evaluated coronary artery disease (CAD) extent, severity, and major adverse cardiac events (MACEs) in never, past, and current smokers undergoing coronary CT angiography (CCTA). Methods and results We evaluated 9456 patients (57.1 ± 12.3 years, 55.5% male) without known CAD (1588 current smokers; 2183 past smokers who quit ≥3 months before CCTA; and 5685 never smokers). By risk-adjusted Cox proportional-hazards models, we related smoking status to MACE (all-cause death or non-fatal myocardial infarction). We further performed 1:1:1 propensity matching for 1000 in each group evaluate event risk among individuals with similar age, gender, CAD risk factors, and symptom presentation. During a mean follow-up of 2.8 ± 1.9 years, 297 MACE occurred. Compared with never smokers, current and past smokers had greater atherosclerotic burden including extent of plaque defined as segments with any plaque (2.1 ± 2.8 vs. 2.6 ± 3.2 vs. 3.1 ± 3.3, P < 0.0001) and prevalence of obstructive CAD [1-vessel disease (VD): 10.6% vs. 14.9% vs. 15.2%, P < 0.001; 2-VD: 4.4% vs. 6.1% vs. 6.2%, P = 0.001; 3-VD: 3.1% vs. 5.2% vs. 4.3%, P < 0.001]. Compared with never smokers, current smokers experienced higher MACE risk [hazard ratio (HR) 1.9, 95% confidence interval (CI) 1.4-2.6, P < 0.001], while past smokers did not (HR 1.2, 95% CI 0.8-1.6, P = 0.35). Among matched individuals, current smokers had higher MACE risk (HR 2.6, 95% CI 1.6-4.2, P < 0.001), while past smokers did not (HR 1.3, 95% CI 0.7-2.4, P = 0.39). Similar findings were observed for risk of all-cause death. Conclusion Among patients without known CAD undergoing CCTA, current and past smokers had increased burden of atherosclerosis compared with never smokers; however, risk of MACE was heightened only in current smoker

Evidence for the strangeness-changing weak decay Ξb−→Λb0π−\Xi_b^-\to\Lambda_b^0\pi^-

Using a $pp$ collision data sample corresponding to an integrated luminosity of 3.0~fb$^{-1}$, collected by the LHCb detector, we present the first search for the strangeness-changing weak decay $\Xi_b^-\to\Lambda_b^0\pi^-$. No $b$ hadron decay of this type has been seen before. A signal for this decay, corresponding to a significance of 3.2 standard deviations, is reported. The relative rate is measured to be ${{f_{\Xi_b^-}}\over{f_{\Lambda_b^0}}}{\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-) = (5.7\pm1.8^{+0.8}_{-0.9})\times10^{-4}$, where $f_{\Xi_b^-}$ and $f_{\Lambda_b^0}$ are the $b\to\Xi_b^-$ and $b\to\Lambda_b^0$ fragmentation fractions, and ${\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-)$ is the branching fraction. Assuming $f_{\Xi_b^-}/f_{\Lambda_b^0}$ is bounded between 0.1 and 0.3, the branching fraction ${\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-)$ would lie in the range from $(0.57\pm0.21)\%$ to $(0.19\pm0.07)\%$.Comment: 7 pages, 2 figures, All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-047.htm

Gender differences in the prevalence, severity, and composition of coronary artery disease in the young: a study of 1635 individuals undergoing coronary CT angiography from the prospective, multinational confirm registry

Objective Prior studies examining coronary atherosclerosis in the young have been limited by retrospective analyses in small cohorts. We examined the relationship between cardiovascular risk factors (RFs) and prevalence and severity of coronary atherosclerosis in a large, prospective, multinational registry of consecutive young individuals undergoing coronary computerized tomographic angiography (CCTA). Method and results Of 27 125 patients undergoing CCTA, 1635 young (<45 years) individuals without known coronary artery disease (CAD) or coronary anomalies were identified. Coronary plaque was assessed for any CAD, obstructive CAD (≥50% stenosis), and presence of calcified plaque (CP) and non-calcified plaque (NCP). Among 1635 subjects (70% men, age 38 ± 6 years), any CAD, obstructive CAD, CP, and NCP were observed in 19, 4, 5, and 8%, respectively. Compared with women, men demonstrated higher rates of any CAD (21 vs. 12%, P < 0.001), CP (6 vs. 3%, P = 0.01), and NCP (9 vs. 5%, P = 0.008), although no difference was observed for rates of obstructive CAD (5 vs. 4%, P = 0.46). Any CAD, obstructive CAD, and NCP were higher for young individuals with diabetes, hypertension, dyslipidaemia, current smoking, or family history of CAD; while only diabetes and dyslipidaemia were associated with CP. Increasing cardiovascular RFs was associated with a greater prevalence and extent and severity of CAD, with individuals with 0, 1, 2, ≥3 RFs manifesting a dose-response increase in any CAD (P < 0.001, for trend), obstructive CAD (P < 0.001, for trend), NCP (P < 0.001, for trend), and CP (P < 0.001, for trend). In multivariable analysis adjusting for sex and cardiovascular RFs, male sex was the strongest predictor for any CAD (odds ratio [OR] = 1.95, 95% confidence interval [CI] = 1.43-2.66, P < 0.001), CP (OR = 1.46, 95% CI = 1.08-1.98, P = 0.01), and NCP (OR = 1.33, 95% CI = 1.06-1.67, P = 0.01); family history of CAD was the strongest predictor for obstructive CAD (OR = 2.71, 95% CI = 1.65-4.45, P < 0.001). Conclusion Any and obstructive CAD is present in 1 in 5 and 1 in 20 young individuals, respectively, with family history associated with the greatest risk of obstructive CA

Limited rigor in studies of raptor mortality and mitigation at wind power facilities

Wind power is an expanding source of renewable energy. However, there are ecological challenges related to wind energy generation, including collisions of wildlife with turbines. Lack of rigor, and variation in study design, together limit efforts to understand the broad-scale effects of wind power infrastructure on wildlife populations. It is not clear, however, whether these types of limitations apply to groups of birds such as raptors that are particularly vulnerable to negative effects of wind energy. We reviewed 672 peer-reviewed publications, unpublished reports, and citations from 321 wind facilities in 12 countries to evaluate methods used to monitor and mitigate for wind facility impacts on raptors. Most reports that included raptor monitoring (86 %, n = 461) only conducted post-construction monitoring for raptor fatalities, while few (12 %; n = 65) estimated preconstruction raptor use. Only 27 % of facilities (n = 62) provided estimates of fatalities or raptor use across multiple construction phases, and the percentage of facilities with data available from multiple construction periods has not changed over time. A formal experimental study design was incorporated into surveys at only 29 % of facilities. Finally, mitigation practices to reduce impacts on raptors were only reported at 23 % of facilities. Our results suggest that rigorous data collection on wind energy impacts to raptors is rare, and that mitigation of detrimental effects is seldom reported. Expanding the use of rigorous research approaches and increasing data availability would improve understanding of the regional and global effects of wind energy on raptor populations

All-cause mortality benefit of coronary revascularization vs. medical therapy in patients without known coronary artery disease undergoing coronary computed tomographic angiography: results from CONFIRM (COronary CT Angiography EvaluatioN For Clinical Outcomes: An InteRnational Multicenter Registry)

Aims To date, the therapeutic benefit of revascularization vs. medical therapy for stable individuals undergoing invasive coronary angiography (ICA) based upon coronary computed tomographic angiography (CCTA) findings has not been examined. Methods and results We examined 15 223 patients without known coronary artery disease (CAD) undergoing CCTA from eight sites and six countries who were followed for median 2.1 years (interquartile range 1.4-3.3 years) for an endpoint of all-cause mortality. Obstructive CAD by CCTA was defined as a ≥50% luminal diameter stenosis in a major coronary artery. Patients were categorized as having high-risk CAD vs. non-high-risk CAD, with the former including patients with at least obstructive two-vessel CAD with proximal left anterior descending artery involvement, three-vessel CAD, and left main CAD. Death occurred in 185 (1.2%) patients. Patients were categorized into two treatment groups: revascularization (n = 1103; 2.2% mortality) and medical therapy (n = 14 120, 1.1% mortality). To account for non-randomized referral to revascularization, we created a propensity score developed by logistic regression to identify variables that influenced the decision to refer to revascularization. Within this model (C index 0.92, χ2 = 1248, P < 0.0001), obstructive CAD was the most influential factor for referral, followed by an interaction of obstructive CAD with pre-test likelihood of CAD (P = 0.0344). Within CCTA CAD groups, rates of revascularization increased from 3.8% for non-high-risk CAD to 51.2% high-risk CAD. In multivariable models, when compared with medical therapy, revascularization was associated with a survival advantage for patients with high-risk CAD [hazards ratio (HR) 0.38, 95% confidence interval 0.18-0.83], with no difference in survival for patients with non-high-risk CAD (HR 3.24, 95% CI 0.76-13.89) (P-value for interaction = 0.03). Conclusion In an intermediate-term follow-up, coronary revascularization is associated with a survival benefit in patients with high-risk CAD by CCTA, with no apparent benefit of revascularization in patients with lesser forms of CA

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR