The three-loop cusp anomalous dimension in QCD

We present the full analytic result for the three-loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a closely related quantity in terms of an effective coupling defined by the light-like cusp anomalous dimension. We find evidence that this quantity is universal for any gauge theory, and use this observation to predict the non-planar $n_{f}$-dependent terms of the four-loop cusp anomalous dimension.Comment: 5 pages, 2 figure

The nfn_{f} terms of the three-loop cusp anomalous dimension in QCD

In this talk we present the result for the $n_f$ dependent piece of the three-loop cusp anomalous dimension in QCD. Remarkably, it is parametrized by the same simple functions appearing in analogous anomalous dimensions in ${\mathcal N}=4$ SYM at one and two loops. We also compute all required master integrals using a recently proposed refinement of the differential equation method. The analytic results are expressed in terms of harmonic polylogarithms of uniform weight.Comment: 8 pages, 2 figures; v2: typo in eq. (4.4) fixed, 'three-loop' added to titl

The two-loop five-particle amplitude in N=8\mathcal{N}=8 supergravity

We compute for the first time the two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity. Starting from the known integrand, we perform an integration-by-parts reduction and express the answer in terms of uniform weight master integrals. The latter are known to evaluate to non-planar pentagon functions, described by a 31-letter symbol alphabet. We express the final result for the amplitude in terms of uniform weight four symbols, multiplied by a small set of rational factors. The amplitude satisfies the expected factorization properties when one external graviton becomes soft, and when two external gravitons become collinear. We verify that the soft divergences of the amplitude exponentiate, and extract the finite remainder function. The latter depends on fewer rational factors, and is independent of one of the symbol letters. By analyzing identities involving rational factors and symbols we find a remarkably compact representation in terms of a single seed function, summed over all permutations of external particles. Finally, we work out the multi-Regge limit, and present explicitly the leading logarithmic terms in the limit. The full symbol of the IR-subtracted hard function is provided as an ancillary file.Comment: 22 pages, 1 figure, 8 ancillary file

Localization of adaptive variants in human genomes using averaged one-dependence estimation.

Statistical methods for identifying adaptive mutations from population genetic data face several obstacles: assessing the significance of genomic outliers, integrating correlated measures of selection into one analytic framework, and distinguishing adaptive variants from hitchhiking neutral variants. Here, we introduce SWIF(r), a probabilistic method that detects selective sweeps by learning the distributions of multiple selection statistics under different evolutionary scenarios and calculating the posterior probability of a sweep at each genomic site. SWIF(r) is trained using simulations from a user-specified demographic model and explicitly models the joint distributions of selection statistics, thereby increasing its power to both identify regions undergoing sweeps and localize adaptive mutations. Using array and exome data from 45 ‡Khomani San hunter-gatherers of southern Africa, we identify an enrichment of adaptive signals in genes associated with metabolism and obesity. SWIF(r) provides a transparent probabilistic framework for localizing beneficial mutations that is extensible to a variety of evolutionary scenarios

ATPase mechanism of the 5'-3' DNA helicase, RecD2: evidence for a pre-hydrolysis conformation change

The superfamily 1 helicase, RecD2, is a monomeric, bacterial enzyme with a role in DNA repair, but with 5'-3' activity unlike most enzymes from this superfamily. Rate constants were determined for steps within the ATPase cycle of RecD2 in the presence of ssDNA. The fluorescent ATP analog, mantATP (2'(3')-O-(N-methylanthraniloyl)ATP), was used throughout to provide a complete set of rate constants and determine the mechanism of the cycle for a single nucleotide species. Fluorescence stopped-flow measurements were used to determine rate constants for adenosine nucleotide binding and release, quenched-flow measurements were used for the hydrolytic cleavage step, and the fluorescent phosphate biosensor was used for phosphate release kinetics. Some rate constants could also be measured using the natural substrate, ATP, and these suggested a similar mechanism to that obtained with mantATP. The data show that a rearrangement linked to Mg(2+) coordination, which occurs before the hydrolysis step, is rate-limiting in the cycle and that this step is greatly accelerated by bound DNA. This is also shown here for the PcrA 3'-5' helicase and so may be a general mechanism governing superfamily 1 helicases. The mechanism accounts for the tight coupling between translocation and ATPase activity