Uniqueness of Conformal Ricci Flow using Energy Methods

We analyze an energy functional associated to Conformal Ricci Flow along closed manifolds with constant negative scalar curvature. Given initial conditions we use this functional to demonstrate the uniqueness of both the metric and the pressure function along Conformal Ricci Flow

NNLL Resummation for Jet Broadening

The resummation for the event-shape variable jet broadening is extended to next-to-next-to-leading logarithmic accuracy by computing the relevant jet and soft functions at one-loop order and the collinear anomaly to two-loop accuracy. The anomaly coefficient is extracted from the soft function and expressed in terms of polylogarithmic as well as elliptic functions. With our results, the uncertainty on jet-broadening distributions is reduced significantly, which should allow for a precise determination of the strong coupling constant from the existing experimental data and provide a consistency check on the extraction of alpha_s from higher-log resummations of thrust.Comment: 44 pages, 9 figure

Ethnic differences in adiposity and diabetes risk – insights from genetic studies

Type 2 diabetes is more common in non-Europeans and starts at a younger age and at lower BMI cut-offs. This review discusses the insights from genetic studies about pathophysiological mechanisms which determine risk of disease with a focus on the role of adiposity and body fat distribution in ethnic disparity in risk of type 2 diabetes. During the past decade, genome-wide association studies (GWAS) have identified more than 400 genetic variants associated with the risk of type 2 diabetes. The Eurocentric nature of these genetic studies have made them less effective in identifying mechanisms that make non-Europeans more susceptible to higher risk of disease. One possible mechanism suggested by epidemiological studies is the role of ethnic difference in body fat distribution. Using genetic variants associated with an ability to store extra fat in a safe place, which is subcutaneous adipose tissue, we discuss how different ethnic groups could be genetically less susceptible to type 2 diabetes by developing a more favourable fat distribution

Transverse-momentum spectra of electroweak bosons near threshold at NNLO

We obtain the next-to-next-to-leading order corrections to transverse-momentum spectra of W, Z and Higgs bosons near the partonic threshold. In the threshold limit, the electroweak boson recoils against a low-mass jet and all radiation is either soft, or collinear to the jet or the beam directions. We extract the virtual corrections from known results for the relevant two-loop four-point amplitudes and combine them with the soft and collinear two-loop functions as defined in Soft-Collinear Effective Theory. We have implemented these results in a public code PeTeR and present numerical results for the threshold resummed cross section of W and Z bosons at next-to-next-to-next-to-leading logarithmic accuracy, matched to next-to-leading fixed-order perturbation theory. The two-loop corrections lead to a moderate increase in the cross section and reduce the scale uncertainty by about a factor of two. The corrections are significantly larger for Higgs production.Comment: 33 pages, 3 figures; v2: journal version, correction in (73); v3: corrected qg-channel in (73

The transverse-momentum spectrum of Higgs bosons near threshold at NNLO

We give next-to-next-to-leading order (NNLO) predictions for the Higgs production cross section at large transverse momentum in the threshold limit. Near the partonic threshold, all radiation is either soft or collinear to the final state jet which recoils against the Higgs boson. We find that the real emission corrections are of moderate size, but that the virtual corrections are large. We discuss the origin of these corrections and give numerical predictions for the transverse-momentum spectrum. The threshold result is matched to the known NLO result and implemented in the public code PeTeR.Comment: 17 pages, 9 Figures; v2: journal version, correction in the qg channe

The Dynamical Mordell-Lang problem

Let X be a Noetherian space, let f be a continuous self-map on X, let Y be a closed subset of X, and let x be a point on X. We show that the set S consisting of all nonnegative integers n such that f^n(x) is in Y is a union of at most finitely many arithmetic progressions along with a set of Banach density zero. In particular, we obtain that given any quasi-projective variety X, any rational self-map map f on X, any subvariety Y of X, and any point x in X whose orbit under f is in the domain of definition for f, the set S is a finite union of arithmetic progressions together with a set of Banach density zero. We prove a similar result for the backward orbit of a point