Scheduling MapReduce Jobs under Multi-Round Precedences

We consider non-preemptive scheduling of MapReduce jobs with multiple tasks in the practical scenario where each job requires several map-reduce rounds. We seek to minimize the average weighted completion time and consider scheduling on identical and unrelated parallel processors. For identical processors, we present LP-based O(1)-approximation algorithms. For unrelated processors, the approximation ratio naturally depends on the maximum number of rounds of any job. Since the number of rounds per job in typical MapReduce algorithms is a small constant, our scheduling algorithms achieve a small approximation ratio in practice. For the single-round case, we substantially improve on previously best known approximation guarantees for both identical and unrelated processors. Moreover, we conduct an experimental analysis and compare the performance of our algorithms against a fast heuristic and a lower bound on the optimal solution, thus demonstrating their promising practical performance

Fire and climate: contrasting pressures on tropical Andean timberline species

Department of Biological Sciences; Florida Institute of Technology; Melbourne FL USA Department of Biological Sciences; Florida Institute of Technology; Melbourne FL USA Department of Biological Sciences; Florida Institute of Technology; Melbourne FL USA Geography, College of Life & Environmental Sciences; University of Exeter; Exeter UK Department of Biological Sciences; Florida Institute of Technology; Melbourne FL USA CEPSAR; The Open University; Milton Keynes UK Instituto de Geología; Universidad Nacional Autónoma de México; Ciudad Universitaria; Mexico City Mexico Department of Forest and Soil Sciences; University of Natural Resources and Life Sciences Vienna; Vienna Austria Department of Biology and Center for Energy; Environment and Sustainability; Wake Forest University; Winston Salem NC USACopyright © 2015 John Wiley & Sons Ltd.Aim: The aim was to test competing hypotheses regarding migration of the Andean timberline within the last 2000 years. Location: The upper forest limit in Manu National Park, Peru. Methods: A randomized stratified design provided 21 soil profiles from forested sites just below the timberline, 15 from puna grassland sites just above the timberline and 15 from the transitional habitat at the puna–forest boundary. From each profile a surface sample (hereafter modern) and a sample from the base of the organic horizon (hereafter historical) were collected. Pollen and charcoal were analysed from the modern and historical layers of the 51 soil profiles. A chronological framework was provided by 24 14C dates. Data were ordinated as modern and historical groups and the temporal trends illustrated by Procrustes rotation. Results: The organic layer from the soil profiles represented the last 600–2000 years. Fire was much more abundant in all habitat types (puna, transitional and forested) in the modern compared with the historical groups. Samples that had historically been in puna just above the timberline showed encroachment by woody species. Samples that had been forested were still classified as forest but their composition had become more transitional. Sites that were transitional appeared to represent a new or expanded class of sites that was far less abundant historically. Main conclusions: Our results are consistent with ongoing warming causing an upslope migration of species, although not necessarily of the timberline. Weedy fire-tolerant species are spreading upslope, creating a transitional forest, softening the boundary between forest and puna. Simultaneously, fire introduced to improve grazing outside the park has increasingly penetrated the forest and is causing the upper timberline to shift towards more fire-tolerant and weedy species. Consequently, both the form of the ecotone between forest and grassland and the species composition of these forests is changing and is expected to continue to change, representing a shifting baseline for what is considered to be natural.Gordon and Betty Moore Foundation Andes-to-Amazon programmeBlue Moon FundNational Science Foundatio

The quark anti-quark potential and the cusp anomalous dimension from a TBA equation

We derive a set of integral equations of the TBA type for the generalized cusp anomalous dimension, or the quark antiquark potential on the three sphere, as a function of the angles. We do this by considering a family of local operators on a Wilson loop with charge L. In the large L limit the problem can be solved in terms of a certain boundary reflection matrix. We determine this reflection matrix by using the symmetries and the boundary crossing equation. The cusp is introduced through a relative rotation between the two boundaries. Then the TBA trick of exchanging space and time leads to an exact equation for all values of L. The L=0 case corresponds to the cusped Wilson loop with no operators inserted. We then derive a slightly simplified integral equation which describes the small angle limit. We solve this equation up to three loops in perturbation theory and match the results that were obtained with more direct approaches.Comment: 63 pages, 12 figures. v2: references added, typos correcte

Analytic Solution of Bremsstrahlung TBA

We consider the quark--anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the vacuum potential in the near BPS limit with $L$ units of R-charge. Equivalently, we study the anomalous dimension of a super-Wilson loop with L local fields inserted at a cusp. The system is described by a recently proposed infinite set of non-linear integral equations of the Thermodynamic Bethe Ansatz (TBA) type. That system of TBA equations is very similar to the one of the spectral problem but simplifies a bit in the near BPS limit. Using techniques based on the Y-system of functional equations we first reduced the infinite system of TBA equations to a Finite set of Nonlinear Integral Equations (FiNLIE). Then we solve the FiNLIE system analytically, obtaining a simple analytic result for the potential! Surprisingly, we find that the system has equivalent descriptions in terms of an effective Baxter equation and in terms of a matrix model. At L=0, our result matches the one obtained before using localization techniques. At all other L's, the result is new. Having a new parameter, L, allows us to take the large L classical limit. We use the matrix model description to solve the classical limit and match the result with a string theory computation. Moreover, we find that the classical string algebraic curve matches the algebraic curve arising from the matrix model.Comment: 50 pages, 5 figures. v2: references added, JHEP versio

An exact formula for the radiation of a moving quark in N=4 super Yang Mills

We derive an exact formula for the cusp anomalous dimension at small angles. This is done by relating the latter to the computation of certain 1/8 BPS Wilson loops which was performed by supersymmetric localization. This function of the coupling also determines the power emitted by a moving quark in N=4 super Yang Mills, as well as the coefficient of the two point function of the displacement operator on the Wilson loop. By a similar method we compute the near BPS expansion of the generalized cusp anomalous dimension.Comment: 22 pages, 5 figures. v2: references added, typos correcte

Effects of dapagliflozin on major adverse kidney and cardiovascular events in patients with diabetic and non-diabetic chronic kidney disease: a prespecified analysis from the DAPA-CKD trial

Background: Dapagliflozin reduces the risk of kidney failure and heart failure in patients with chronic kidney disease. We aimed to investigate the effects of dapagliflozin on kidney, cardiovascular, and mortality outcomes according to presence or absence of type 2 diabetes and according to underlying cause of chronic kidney disease, reported as diabetic nephropathy, chronic glomerulonephritides, ischaemic or hypertensive chronic kidney disease, or chronic kidney disease of other or unknown cause. Methods: DAPA-CKD was a multicentre, double-blind, placebo-controlled, randomised trial done at 386 study sites in 21 countries, in which participants with a urinary albumin-to-creatinine ratio of 200–5000 mg/g and an estimated glomerular filtration rate (eGFR) of 25–75 mL/min per 1·73m2 were randomly assigned (1:1) to dapagliflozin 10 mg once daily or matching placebo, as an adjunct to standard care. The primary outcome was a composite of sustained decline in eGFR of at least 50%, end-stage kidney disease, or kidney-related or cardiovascular death. Secondary efficacy outcomes were a kidney-specific composite (the same as the primary outcome but excluding cardiovascular death), a composite of cardiovascular death or hospital admission for heart failure, and all-cause mortality. In this study, we conducted a prespecified subgroup analysis of the DAPA-CKD primary and secondary endpoints by presence or absence of type 2 diabetes and by aetiology of chronic kidney disease. DAPA-CKD is registered with ClinicalTrials.gov, NCT03036150. Findings: The study took place between Feb 2, 2017, and June 12, 2020. 4304 participants were randomly assigned (2152 to dapagliflozin and 2152 to placebo) and were followed up for a median of 2·4 years (IQR 2·0–2·7). Overall, 2906 (68%) participants had a diagnosis of type 2 diabetes, of whom 396 (14%) had chronic kidney disease ascribed to causes other than diabetic nephropathy. The relative risk reduction for the primary composite outcome with dapagliflozin was consistent in participants with type 2 diabetes (hazard ratio [HR] 0·64, 95% CI 0·52–0·79) and those without diabetes (0·50, 0·35–0·72; pinteraction=0·24). Similar findings were seen for the secondary outcomes: kidney-specific composite outcome (0·57 [0·45–0·73] vs 0·51 [0·34–0·75]; Pinteraction=0·57), cardiovascular death or hospital admission for heart failure (0·70 [0·53–0·92] vs 0·79 [0·40–1·55]; Pinteraction=0·78), and all-cause mortality (0·74 [0·56–0·98] vs 0·52 [0·29–0·93]; Pinteraction=0·25). The effect of dapagliflozin on the primary outcome was also consistent among patients with diabetic nephropathy (n=2510; HR 0·63, 95% CI 0·51–0·78), glomerulonephritides (n=695; 0·43, 0·26–0·71), ischaemic or hypertensive chronic kidney disease (n=687; 0·75, 0·44–1·26), and chronic kidney disease of other or unknown cause (n=412; 0·58, 0·29–1·19; Pinteraction=0·53), with similar consistency seen across the secondary outcomes. The proportions of participants in the dapagliflozin and placebo groups who had serious adverse events or discontinued study drug due to adverse events did not vary between those with and those without type 2 diabetes. Interpretation: Dapagliflozin reduces the risks of major adverse kidney and cardiovascular events and all-cause mortality in patients with diabetic and non-diabetic chronic kidney disease

The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories

We construct a generalized cusped Wilson loop operator in N = 6 super Chern-Simons-matter theories which is locally invariant under half of the supercharges. It depends on two parameters and interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines, representing a natural generalization of the quark-antiquark potential in ABJ(M) theories. For particular choices of the parameters we obtain 1/6 BPS configurations that, mapped on S^2 by a conformal transformation, realize a three-dimensional analogue of the wedge DGRT Wilson loop of N = 4. The cusp couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bifundamental representation of the U(N)xU(M) gauge group and its expectation value is expressed as the holonomy of a suitable superconnection. We discuss the definition of these observables in terms of traces and the role of the boundary conditions of fermions along the loop. We perform a complete two-loop analysis, obtaining an explicit result for the generalized cusp at the second non-trivial order, from which we read off the interaction potential between heavy 1/2 BPS particles in the ABJ(M) model. Our results open the possibility to explore in the three-dimensional case the connection between localization properties and integrability, recently advocated in D = 4.Comment: 53 pages, 10 figures, added references, this is the version appeared on JHE