Distributed Minimum Cut Approximation

We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST model). We present a distributed algorithm that, for any weighted graph and any $\epsilon \in (0, 1)$, with high probability finds a cut of size at most $O(\epsilon^{-1}\lambda)$ in $O(D) + \tilde{O}(n^{1/2 + \epsilon})$ rounds, where $\lambda$ is the size of the minimum cut. This algorithm is based on a simple approach for analyzing random edge sampling, which we call the random layering technique. In addition, we also present another distributed algorithm, which is based on a centralized algorithm due to Matula [SODA '93], that with high probability computes a cut of size at most $(2+\epsilon)\lambda$ in $\tilde{O}((D+\sqrt{n})/\epsilon^5)$ rounds for any $\epsilon>0$. The time complexities of both of these algorithms almost match the $\tilde{\Omega}(D + \sqrt{n})$ lower bound of Das Sarma et al. [STOC '11], thus leading to an answer to an open question raised by Elkin [SIGACT-News '04] and Das Sarma et al. [STOC '11]. Furthermore, we also strengthen the lower bound of Das Sarma et al. by extending it to unweighted graphs. We show that the same lower bound also holds for unweighted multigraphs (or equivalently for weighted graphs in which $O(w\log n)$ bits can be transmitted in each round over an edge of weight $w$), even if the diameter is $D=O(\log n)$. For unweighted simple graphs, we show that even for networks of diameter $\tilde{O}(\frac{1}{\lambda}\cdot \sqrt{\frac{n}{\alpha\lambda}})$, finding an $\alpha$-approximate minimum cut in networks of edge connectivity $\lambda$ or computing an $\alpha$-approximation of the edge connectivity requires $\tilde{\Omega}(D + \sqrt{\frac{n}{\alpha\lambda}})$ rounds

A renormalization group invariant scalar glueball operator in the (Refined) Gribov-Zwanziger framework

This paper presents a complete algebraic analysis of the renormalizability of the $d=4$ operator $F^2_{\mu\nu}$ in the Gribov-Zwanziger (GZ) formalism as well as in the Refined Gribov-Zwanziger (RGZ) version. The GZ formalism offers a way to deal with gauge copies in the Landau gauge. We explicitly show that $F^2_{\mu\nu}$ mixes with other $d=4$ gauge variant operators, and we determine the mixing matrix $Z$ to all orders, thereby only using algebraic arguments. The mixing matrix allows us to uncover a renormalization group invariant including the operator $F^2_{\mu\nu}$. With this renormalization group invariant, we have paved the way for the study of the lightest scalar glueball in the GZ formalism. We discuss how the soft breaking of the BRST symmetry of the GZ action can influence the glueball correlation function. We expect non-trivial mass scales, inherent to the GZ approach, to enter the pole structure of this correlation function.Comment: 27 page

Obesity, oxidative DNA damage and vitamin D as predictors of genomic instability in children and adolescents

Background/objectives Epidemiological evidence indicates obesity in childhood and adolescence to be an independent risk factor for cancer and premature mortality in adulthood. Pathological implications from excess adiposity may begin early in life. Obesity is concurrent with a state of chronic inflammation, a well-known aetiological factor for DNA damage. In addition, obesity has been associated with micro-nutritional deficiencies. Vitamin D has attracted attention for its anti-inflammatory properties and role in genomic integrity and stability. The aim of this study was to determine a novel approach for predicting genomic instability via the combined assessment of adiposity, DNA damage, systemic inflammation, and vitamin D status. Subjects/methods We carried out a cross-sectional study with 132 participants, aged 10–18, recruited from schools and paediatric obesity clinics in London. Anthropometric assessments included BMI Z-score, waist and hip circumference, and body fat percentage via bioelectrical impedance. Inflammation and vitamin D levels in saliva were assessed by enzyme-linked immunosorbent assay. Oxidative DNA damage was determined via quantification of 8-hydroxy-2′-deoxyguanosine in urine. Exfoliated cells from the oral cavity were scored for genomic instability via the buccal cytome assay. Results As expected, comparisons between participants with obesity and normal range BMI showed significant differences in anthropometric measures (p < 0.001). Significant differences were also observed in some measures of genomic instability (p < 0.001). When examining relationships between variables for all participants, markers of adiposity positively correlated with acquired oxidative DNA damage (p < 0.01) and genomic instability (p < 0.001), and negatively correlated with vitamin D (p < 0.01). Multiple regression analyses identified obesity (p < 0.001), vitamin D (p < 0.001), and oxidative DNA damage (p < 0.05) as the three significant predictors of genomic instability. Conclusions Obesity, oxidative DNA damage, and vitamin D deficiency are significant predictors of genomic instability. Non-invasive biomonitoring and predictive modelling of genomic instability in young patients with obesity may contribute to the prioritisation and severity of clinical intervention measures

A cosmological concordance model with dynamical vacuum term

We demonstrate that creation of dark-matter particles at a constant rate implies the existence of a cosmological term that decays linearly with the Hubble rate. We discuss the cosmological model that arises in this context and test it against observations of the first acoustic peak in the cosmic microwave background (CMB) anisotropy spectrum, the Hubble diagram for supernovas of type Ia (SNIa), the distance scale of baryonic acoustic oscillations (BAO) and the distribution of large scale structures (LSS). We show that a good concordance is obtained, albeit with a higher value of the present matter abundance than in the \Lambda CDM model. We also comment on general features of the CMB anisotropy spectrum and on the cosmic coincidence problem.Comment: Revised version. Accepted for publication in Physics Letters

Dark energy and dark matter from an inhomogeneous dilaton

A cosmological scenario is proposed where the dark matter (DM) and dark energy (DE) of the universe are two simultaneous manifestations of an inhomogenous dilaton. The equation of state of the field is scale-dependent and pressureless at galactic and larger scales and it has negative pressure as a DE at very large scales. The dilaton drives an inflationary phase followed by a kinetic energy-dominated one, as in the "quintessential inflation" model introduced by Peebles & Vilenkin, and soon after the end of inflation particle production seeds the first inhomogeneities that lead to galaxy formation. The dilaton is trapped near the minimum of the potential where it oscillates like a massive field, and the excess of kinetic energy is dissipated via the mechanism of "gravitational cooling" first introduced by Seidel & Suen. The inhomogeneities therefore behave like solitonic oscillations around the minimum of the potential, known as "oscillatons", that we propose account for most DM in galaxies. Those regions where the dilaton does not transform enough kinetic energy into reheating or carry an excess of it from regions that have cooled, evolve to the tail of the potential as DE, driving the acceleration of the universe.Comment: 9 pages, 8 figures, uses revtex, submitted PR

B-blockers, calcium antagonists, and mortality in stable coronary artery disease: An international cohort study

Aims: The effect of first-line antianginal agents, β-blockers, and calcium antagonists on clinical outcomes in stable coronary artery disease (CAD) remains uncertain. Methods and results We analysed the use of β-blockers or calcium antagonists (baseline and annually) and outcomes in 22 006 stable CAD patients (enrolled 2009–2010) followed annually to 5 years, in the CLARIFY registry (45 countries). Primary outcome was all-cause death. Secondary outcomes were cardiovascular death and the composite of cardiovascular death/non-fatal myocardial infarction (MI). After multivariable adjustment, baseline β-blocker use was not associated with lower all-cause death [1345 (7.8%) in users vs. 407 (8.4%) in non-users; hazard ratio (HR) 0.94, 95% confidence interval (CI) 0.84–1.06; P = 0.30]; cardiovascular death [861 (5.0%) vs. 262 (5.4%); HR 0.91, 95% CI 0.79–1.05; P = 0.20]; or cardiovascular death/non-fatal MI [1272 (7.4%) vs. 340 (7.0%); HR 1.03, 95% CI 0.91–1.16; P = 0.66]. Sensitivity analyses according to β-blocker use over time and to prescribed dose produced similar results. Among prior MI patients, for those enrolled in the year following MI, baseline β-blocker use was associated with lower all-cause death [205 (7.0%) vs. 59 (10.3%); HR 0.68, 95% CI 0.50–0.91; P = 0.01]; cardiovascular death [132 (4.5%) vs. 49 (8.5%); HR 0.52, 95% CI 0.37–0.73; P = 0.0001]; and cardiovascular death/non-fatal MI [212 (7.2%) vs. 59 (10.3%); HR 0.69, 95% CI 0.52–0.93; P = 0.01]. Calcium antagonists were not associated with any difference in mortality. Conclusion In this contemporary cohort of stable CAD, β-blocker use was associated with lower 5-year mortality only in patients enrolled in the year following MI. Use of calcium antagonists was not associated with superior mortality, regardless of history of MI

Monopole characteristics in various Abelian gauges

Renormalization group (RG) smoothing is employed on the lattice to investigate and to compare the monopole structure of the SU(2) vacuum as seen in different gauges (maximally Abelian (MAG), Polyakov loop (PG) and Laplacian gauge (LG)). Physically relevant types of monopoles (LG and MAG) are distinguished by their behavior near the deconfining phase transition. For the LG, Abelian projection reproduces well the gauge independent monopole structure encoded in an auxiliary Higgs field. Density and localization properties of monopoles, their non-Abelian action and topological charge are studied. Results are presented confirming the Abelian dominance with respect to the non-perturbative static potential for all gauges considered.Comment: 36 pages, 12 figure

Chronic kidney disease has a graded association with death and cardiovascular outcomes in stable coronary artery disease : An analysis of 21,911 patients from the CLARIFY registry

Chronic kidney disease (CKD) is associated with an increased cardiovascular risk in a broad spectrum of populations. However, the risk associated with a reduced estimated glomerular filtration rate (eGFR) in patients with stable coronary artery disease receiving standard care in the modern era, independently of baseline cardiovascular disease, risk factors, and comorbidities, remains unclear. We analyzed data from 21,911 patients with stable coronary artery disease, enrolled in 45 countries between November 2009 and July 2010 in the CLARIFY registry. Patients with abnormal renal function were older, with more comorbidities, and received slightly lower-although overall high-rates of evidence-based secondary prevention therapies than patients with normal renal function. The event rate of patients with CKD stage 3b or more (eGFR <45 mL/min/1.73 m) was much higher than that associated with any comorbid condition. In a multivariable adjusted Cox proportional hazards model, lower eGFR was independently associated with a graded increased risk of cardiovascular mortality, with adjusted HRs (95% CI) of 0.98 (0.81-1.18), 1.31 (1.05-1.63), 1.77 (1.38-2.27), and 3.12 (2.25-4.33) for eGFR 60-89, 45-59, 30-44, and <30 mL/min/1.73 m, compared with eGFR ≥90 mL/min/1.73 m. A strong graded independent relationship exists between the degree of CKD and cardiovascular mortality in this large cohort of patients with chronic coronary artery disease, despite high rates of secondary prevention therapies. Among clinical risk factors and comorbid conditions, CKD stage 3b or more is associated with the highest cardiovascular mortality