Two-Loop Maximal Unitarity with External Masses

We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique formulae for the coefficients of the master double-box integrals. These formulae can be used either analytically or numerically.Comment: 41 pages, 7 figures; small corrections, final journal versio

An Overview of Maximal Unitarity at Two Loops

We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals of total derivatives vanish on it. The resulting formulae, like their one-loop counterparts, can be applied either analytically or numerically.Comment: 7 pages, presented at Loops & Legs 2012, Wernigerode, German

Maximal Unitarity for the Four-Mass Double Box

We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero- through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals, and show how discrete symmetries of these varieties largely determine the constraints.Comment: 25 pages, 3 figures; final journal versio

Cross-Order Integral Relations from Maximal Cuts

We study the ABDK relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.Comment: 58 pages, 19 figures; v2 references adde

D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops

The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large N_c) maximally supersymmetric Yang-Mills theory in D = 5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L > 6 in the critical dimension D = 4 + 6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. The vacuum integrals are integrated via sector decomposition, using a modified version of the FIESTA program.Comment: 31 pages, revtex, 12 figure

Control and femtosecond time-resolved imaging of torsion in a chiral molecule

We study how the combination of long and short laser pulses, can be used to induce torsion in an axially chiral biphenyl derivative (3,5-difluoro-3',5'-dibromo-4'-cyanobiphenyl). A long, with respect to the molecular rotational periods, elliptically polarized laser pulse produces 3D alignment of the molecules, and a linearly polarized short pulse initiates torsion about the stereogenic axis. The torsional motion is monitored in real-time by measuring the dihedral angle using femtosecond time-resolved Coulomb explosion imaging. Within the first 4 picoseconds, torsion occurs with a period of 1.25 picoseconds and an amplitude of 3 degrees in excellent agreement with theoretical calculations. At larger times the quantum states of the molecules describing the torsional motion dephase and an almost isotropic distribution of the dihedral angle is measured. We demonstrate an original application of covariance analysis of two-dimensional ion images to reveal strong correlations between specific ejected ionic fragments from Coulomb explosion. This technique strengthens our interpretation of the experimental data.Comment: 11 pages, 9 figure

DEqMS : A Method for Accurate Variance Estimation in Differential Protein Expression Analysis

Quantitative proteomics by mass spectrometry is widely used in biomarker research and basic biology research for investigation of phenotype level cellular events. Despite the wide application, the methodology for statistical analysis of differentially expressed proteins has not been unified. Various methods such as t test, linear model and mixed effect models are used to define changes in proteomics experiments. However, none of these methods consider the specific structure of MS-data. Choices between methods, often originally developed for other types of data, are based on compromises between features such as statistical power, general applicability and user friendliness. Furthermore, whether to include proteins identified with one peptide in statistical analysis of differential protein expression varies between studies. Here we present DEqMS, a robust statistical method developed specifically for differential protein expression analysis in mass spectrometry data. In all data sets investigated there is a clear dependence of variance on the number of PSMs or peptides used for protein quantification. DEqMS takes this feature into account when assessing differential protein expression. This allows for a more accurate data-dependent estimation of protein variance and inclusion of single peptide identifications without increasing false discoveries. The method was tested in several data sets including E. coli proteome spike-in data, using both label-free and TMT-labeled quantification. Compared with previous statistical methods used in quantitative proteomics, DEqMS showed consistently better accuracy in detecting altered protein levels compared with other statistical methods in both label-free and labeled quantitative proteomics data. DEqMS is available as an R package in Bioconductor.Peer reviewe

Fee Arrangements and Fee Shifting: Lessons From the Experience in Ontario

About one-third of oestrogen receptor alpha-positive breast cancer patients treated with tamoxifen relapse. Here we identify the nuclear receptor retinoic acid receptor alpha as a marker of tamoxifen resistance. Using quantitative mass spectrometry-based proteomics, we show that retinoic acid receptor alpha protein networks and levels differ in a tamoxifen-sensitive (MCF7) and a tamoxifen-resistant (LCC2) cell line. High intratumoural retinoic acid receptor alpha protein levels also correlate with reduced relapse-free survival in oestrogen receptor alpha-positive breast cancer patients treated with adjuvant tamoxifen solely. A similar retinoic acid receptor alpha expression pattern is seen in a comparable independent patient cohort. An oestrogen receptor alpha and retinoic acid receptor alpha ligand screening reveals that tamoxifen-resistant LCC2 cells have increased sensitivity to retinoic acid receptor alpha ligands and are less sensitive to oestrogen receptor alpha ligands compared with MCF7 cells. Our data indicate that retinoic acid receptor alpha may be a novel therapeutic target and a predictive factor for oestrogen receptor alpha-positive breast cancer patients treated with adjuvant tamoxifen

Duhovne popijevke iz Hercegovine - Euharistijske popijevke iz Hercegovine

We propose a mathematical framework, inspired by the WirelessHART specification, for modeling and analysing multi-hop communication networks. The framework is designed for systems consisting of multiple control loops closed over a multi-hop communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system. The main technical contribution of the paper is an explicit translation of multi-hop control networks to switched systems. We describe a Mathematica notebook that automates the translation of multihop control networks to switched systems, and use this tool to show how techniques for analysis of switched systems can be used to address control and networking co-design challenges.QC 2012021