Local chromatic number of quadrangulations of surfaces

The local chromatic number of a graph G, as introduced in [4], is the minimum integer k such that G admits a proper coloring (with an arbitrary number of colors) in which the neighborhood of each vertex uses less than k colors. In [17] a connection of the local chromatic number to topological properties of (a box complex of) the graph was established and in [18] it was shown that a topological condition implying the usual chromatic number being at least four has the stronger consequence that the local chromatic number is also at least four. As a consequence one obtains a generalization of the following theorem of Youngs [19]: If a quadrangulation of the projective plane is not bipartite it has chromatic number four. The generalization states that in this case the local chromatic number is also four. Both papers [1] and [13] generalize Youngs’ result to arbitrary non-orientable surfaces replacing the condition of the graph being not bipartite by a more technical condition of an odd quadrangulation. This paper investigates when these general results are true for the local chromatic number instead of the chromatic number. Surprisingly, we find out that (unlike in the case of the chromatic number) this depends on the genus of the surface. For the non-orientable surfaces of genus at most four, the local chromatic number of any odd quadrangulation is at least four, but this is not true for non-orientable surfaces of genus 5 or higher. We also prove that face subdivisions of odd quadrangulations and Fisk triangulations of arbitrary surfaces exhibit the same behavior for the local chromatic number as they do for the usual chromatic number

The importance of ST elevation in V2–4 ECG leads in athletes

Background Early repolarization in the anterior ECG leads (ERV2–4) is considered to be a sign of right ventricular (RV) remodeling, but its etiology and importance are unclear. Methods A total of 243 top-level endurance-trained athletes (ETA; 183 men and 60 women, weekly training hours: 15–20) and 120 leisure-time athletes (LTA; 71 men and 49 women, weekly training hours: 5–6) were investigated. The ERV2–4 sign was evaluated concerning type of sport, gender, transthoracic echocardiographic parameters, and ECG changes, which can indicate elevated RV systolic pressure [left atrium enlargement (LAE), right atrium enlargement (RAE), RV conduction defect (RVcd)]. Results Stroke volume and left ventricular mass were higher in ETAs vs. LTAs in both genders (p < 0.01). Prevalence of the ERV2–4 sign was significantly higher in men than in women [p = 0.000, odds ratio (OR) = 36.4] and in ETAs than in LTAs (p = 0.000). The highest ERV2–4 prevalence appeared in the most highly trained triathlonists and canoe and kayak paddlers (OR = 13.8 and 5.2, respectively). Within the ETA group, the post-exercise LAE, RAE, and RVcd changes developed more frequently in cases with than without ERV2–4 (LAE: men: p < 0.05, females: p < 0.005; RAE: men: p < 0.05, females: p < 0.005; RVcd: N.S.). These post-exercise appearing LAE, RAE, and RVcd are associated with the ERV2–4 sign (OR = 4.0, 3.7, and 3.8, respectively). Conclusions According to these results, ERV2–4 develops mainly in male ETAs due to long-lasting and repeated endurance training. The ERV2–4 sign indicates RV’s adaptation to maintain higher compensatory pulmonary pressure and flow during exercise but its danger regarding malignant arrhythmias is unclear

Quantification of complementarity in multi-qubit systems

Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation between classically incompatible properties, such as visibility of interference fringes and "which-way" information, but also between purely quantum mechanical properties, such as measures of entanglement. We discuss different complementarity relations for systems of 2-, 3-, or \textit{n} qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.Comment: 12 pages, 10 figures (A display error about the figures in the previous version

Invalidation of the Kelvin Force in Ferrofluids

Direct and unambiguous experimental evidence for the magnetic force density being of the form $M\nabla B$ in a certain geometry - rather than being the Kelvin force $M\nabla H$ - is provided for the first time. (M is the magnetization, H the field, and B the flux density.)Comment: 4 pages, 4 figure

Aerodynamic Evaluation of Two Compact Radial-Inflow Turbine Rotors

The aerodynamic evaluation of two highly loaded compact radial turbine rotors was conducted at the NASA Lewis Research Center Small Engine Component Test Facility (SECTF). The experimental results were used for proof-of-concept, for modeling radial inflow turbine rotors, and for providing data for code verification. Two rotors were designed to have a shorter axial length, up to a 10-percent reduced diameter, a lighter weight, and equal or higher efficiencies with those of conventional radial inflow turbine rotors. Three configurations were tested: rotor 1, having a 40-percent shorter axial length, with the design stator (stator 1); rotor 1 with the design stator vanes closed down (stator 2); and rotor 2, slightly shorter axially and having higher loading, with stator 2. The stator had 36 vanes and the rotors each had 14 solid blades. Although presently uncooled, the rotor blades were designed for thicknesses which would allow cooling passages to be added. The overall stage performance measurements and the rotor and stator exit flow field surveys were obtained. Measurements of steady state temperatures, pressures, mass flow rates, flow angles, and output power were made at various operating conditions. Data were obtained at corrected speeds of 80, 90, 100, 110, and 120 percent of design over a range of equivalent inlet-to-exit pressure ratios of 3.5, 4.0, 4.5, and 5.0, the maximum pressure ratio achieved. The test showed that the configuration of rotor 1 with stator 1 running at the design pressure ratio produced a flow rate which was 5.6 percent higher than expected. This result indicated the need to close down the stator flow area to reduce the flow. The flow area reduction was accomplished by restaggering the vanes. Rotor 1 was retested with the closed-down stator vanes and achieved the correct mass flow. Rotor 2 was tested only with the restaggered vanes. The test results of the three turbine configurations were nearly identical. Although the measured efficiencies of the compact designs fell 2 to 3 points below the predicted efficiency of 91 percent, they did meet and exceed by up to 2.5 percentage points the efficiences of state-of-the-art turbines found in the literature

Constraints and entropy in a model of network evolution

Barab´asi-Albert’s ‘Scale Free’ model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however, indicates that the model is in some cases, only a rough approximation to the dynamical evolution of real networks. In particular, the exponent γ of the power law distribution of degree is predicted by the model to be exactly 3, whereas in a number of real world networks it has values between 1.2 and 2.9. In addition, the degree distributions of real networks exhibit cut offs at high node degree, which indicates the existence of maximal node degrees for these networks. In this paper we propose a simple extension to the ‘Scale Free’ model, which offers better agreement with the experimental data. This improvement is satisfying, but the model still does not explain why the attachment probabilities should favor high degree nodes, or indeed how constraints arrive in non-physical networks. Using recent advances in the analysis of the entropy of graphs at the node level we propose a first principles derivation for the ‘Scale Free’ and ‘constraints’ model from thermodynamic principles, and demonstrate that both preferential attachment and constraints could arise as a natural consequence of the second law of thermodynamics

Varespladib and cardiovascular events in patients with an acute coronary syndrome: the VISTA-16 randomized clinical trial

IMPORTANCE: Secretory phospholipase A2(sPLA2) generates bioactive phospholipid products implicated in atherosclerosis. The sPLA2inhibitor varespladib has favorable effects on lipid and inflammatory markers; however, its effect on cardiovascular outcomes is unknown. OBJECTIVE: To determine the effects of sPLA2inhibition with varespladib on cardiovascular outcomes. DESIGN, SETTING, AND PARTICIPANTS: A double-blind, randomized, multicenter trial at 362 academic and community hospitals in Europe, Australia, New Zealand, India, and North America of 5145 patients randomized within 96 hours of presentation of an acute coronary syndrome (ACS) to either varespladib (n = 2572) or placebo (n = 2573) with enrollment between June 1, 2010, and March 7, 2012 (study termination on March 9, 2012). INTERVENTIONS: Participants were randomized to receive varespladib (500 mg) or placebo daily for 16 weeks, in addition to atorvastatin and other established therapies. MAIN OUTCOMES AND MEASURES: The primary efficacy measurewas a composite of cardiovascular mortality, nonfatal myocardial infarction (MI), nonfatal stroke, or unstable angina with evidence of ischemia requiring hospitalization at 16 weeks. Six-month survival status was also evaluated. RESULTS: At a prespecified interim analysis, including 212 primary end point events, the independent data and safety monitoring board recommended termination of the trial for futility and possible harm. The primary end point occurred in 136 patients (6.1%) treated with varespladib compared with 109 patients (5.1%) treated with placebo (hazard ratio [HR], 1.25; 95%CI, 0.97-1.61; log-rank P = .08). Varespladib was associated with a greater risk of MI (78 [3.4%] vs 47 [2.2%]; HR, 1.66; 95%CI, 1.16-2.39; log-rank P = .005). The composite secondary end point of cardiovascular mortality, MI, and stroke was observed in 107 patients (4.6%) in the varespladib group and 79 patients (3.8%) in the placebo group (HR, 1.36; 95% CI, 1.02-1.82; P = .04). CONCLUSIONS AND RELEVANCE: In patients with recent ACS, varespladib did not reduce the risk of recurrent cardiovascular events and significantly increased the risk of MI. The sPLA2inhibition with varespladib may be harmful and is not a useful strategy to reduce adverse cardiovascular outcomes after ACS. TRIAL REGISTRATION: clinicaltrials.gov Identifier: NCT01130246. Copyright 2014 American Medical Association. All rights reserved