Distributed Symmetry Breaking in Hypergraphs

Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and $\Delta +1$-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, comparatively much less is known on the complexity of distributed symmetry breaking in {\em hypergraphs}. In particular, a key question is whether a fast (randomized) algorithm for MIS exists for hypergraphs. In this paper, we study the distributed complexity of symmetry breaking in hypergraphs by presenting distributed randomized algorithms for a variety of fundamental problems under a natural distributed computing model for hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can be solved in $O(\log^2 n)$ rounds ($n$ is the number of nodes of the hypergraph) in the LOCAL model. We then present a key result of this paper --- an $O(\Delta^{\epsilon}\text{polylog}(n))$-round hypergraph MIS algorithm in the CONGEST model where $\Delta$ is the maximum node degree of the hypergraph and $\epsilon > 0$ is any arbitrarily small constant. To demonstrate the usefulness of hypergraph MIS, we present applications of our hypergraph algorithm to solving problems in (standard) graphs. In particular, the hypergraph MIS yields fast distributed algorithms for the {\em balanced minimal dominating set} problem (left open in Harris et al. [ICALP 2013]) and the {\em minimal connected dominating set problem}. We also present distributed algorithms for coloring, maximal matching, and maximal clique in hypergraphs.Comment: Changes from the previous version: More references adde

Aharonov-Bohm Physics with Spin II: Spin-Flip Effects in Two-dimensional Ballistic Systems

We study spin effects in the magneto-conductance of ballistic mesoscopic systems subject to inhomogeneous magnetic fields. We present a numerical approach to the spin-dependent Landauer conductance which generalizes recursive Green function techniques to the case with spin. Based on this method we address spin-flip effects in quantum transport of spin-polarized and -unpolarized electrons through quantum wires and various two-dimensional Aharonov-Bohm geometries. In particular, we investigate the range of validity of a spin switch mechanism recently found which allows for controlling spins indirectly via Aharonov-Bohm fluxes. Our numerical results are compared to a transfer-matrix model for one-dimensional ring structures presented in the first paper (Hentschel et al., submitted to Phys. Rev. B) of this series.Comment: 29 pages, 15 figures. Second part of a series of two article

Evolution of the electronic structure with size in II-VI semiconductor nanocrystals

In order to provide a quantitatively accurate description of the band gap variation with sizes in various II-VI semiconductor nanocrystals, we make use of the recently reported tight-binding parametrization of the corresponding bulk systems. Using the same tight-binding scheme and parameters, we calculate the electronic structure of II-VI nanocrystals in real space with sizes ranging between 5 and 80 {\AA} in diameter. A comparison with available experimental results from the literature shows an excellent agreement over the entire range of sizes.Comment: 17 pages, 4 figures, accepted in Phys. Rev.

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

Superconducting properties of natural and artificial grain boundaries in bulk melt-textured YBCO

A range of experimental techniques have been used to characterize melt-processed YBa2Cu3O7-d samples containing single-grain boundaries. Both natural high-angle boundaries, which sometimes appear during the grain growth process, and artificial low-angle boundaries, obtained by joining two single domains, have been investigated. Electrical resistivity, current-voltage characteristics, magnetic moment measurements and Hall probe mapping techniques have been employed to investigate the boundaries. Results are compared with the properties of single domain material (i.e., containing no grain boundary) for which T-c approximate to 89 K and J(c)parallel to ab (77 K, 1 T) > 10^4 A/cm(2). Resistance measurements across all the grain boundaries show a stronger dependence on current and magnetic field than that measured within the grains and exhibit a pronounced resistive 'tail'. The I-V curves obtained for the high-angle natural grain boundary are sharp and differ from the rounded I-V curves which are characteristic of single-grains. Field mapping measurements used to evaluate the critical current anisotropy are in agreement with magnetisation measurements. The limitations of this technique for investigating boundaries are discussed. It was found that current anisotropy can conceal a weak link between two grains, leading to a false indication of single-grain behaviour. Artificially engineered boundaries are shown to have significant potential for applications in high fields at 77 K. (C) 1998 Elsevier Science B.V. All rights reserved