NNLO QCD + NLO EW with Matrix+OpenLoops: precise predictions for vector-boson pair production

We present the first combination of NNLO QCD and NLO EW corrections for vector-boson pair production at the LHC. We consider all final states with two, three and four charged leptons, including resonant and non-resonant diagrams, spin correlations and off-shell effects. Detailed predictions are discussed for three representative channels corresponding to W+W−, W±Z and Z Z production. Both QCD and EW corrections are very significant, and the details of their combination can play a crucial role to achieve the level of precision demanded by experimental analyses. In this context we point out nontrivial issues that arise at large transverse momenta, where the EW corrections are strongly enhanced by Sudakov logarithms and the QCD corrections can feature so-called giant K -factors. Our calculations have been carried out in the Matrix+OpenLoops framework and can be extended to the production of an arbitrary colour singlet in hadronic collisions, provided that the required two-loop QCD amplitudes are available. Combined NNLO QCD and NLO EW predictions for the full set of massive diboson processes will be made publicly available in the next release of Matrix and will be instrumental in advancing precision diboson studies and new-physics searches at the LHC and future hadron colliders

The Functional Form of Angular Forces around Transition Metal Ions in Biomolecules

A method for generating angular forces around $\sigma$-bonded transition metal ions is generalized to treat $\pi$-bonded configurations. The theoretical approach is based on an analysis of a ligand-field Hamiltonian based on the moments of the electron state distribution. The functional forms that are obtained involve a modification of the usual expression of the binding energy as a sum of ligand-ligand interactions, which however requires very little increased in CPU time. The angular interactions have simple forms involving sin and cos functions, whose relative weights depend on whether the ligands are $\sigma$- or $\pi$-bonded. They describe the ligand-field stabilization energy to an accuracy of about 10%. The resulting force field is used to model the structure of small clusters, including fragments of the copper blue protein structure. Large deviations from the typical square copper coordination are found when $\pi$-bonded ligands are present.Comment: Latex source, 9 postscript figure

Optimistic distributionally robust optimization for nonparametric likelihood approximation

The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of the likelihood that identifies a probability measure which lies in the neighborhood of the nominal measure and that maximizes the probability of observing the given sample point. We show that when the neighborhood is constructed by the Kullback-Leibler divergence, by moment conditions or by the Wasserstein distance, then our optimistic likelihood can be determined through the solution of a convex optimization problem, and it admits an analytical expression in particular cases. We also show that the posterior inference problem with our optimistic likelihood approximation enjoys strong theoretical performance guarantees, and it performs competitively in a probabilistic classification task

Planning with Information-Processing Constraints and Model Uncertainty in Markov Decision Processes

Information-theoretic principles for learning and acting have been proposed to solve particular classes of Markov Decision Problems. Mathematically, such approaches are governed by a variational free energy principle and allow solving MDP planning problems with information-processing constraints expressed in terms of a Kullback-Leibler divergence with respect to a reference distribution. Here we consider a generalization of such MDP planners by taking model uncertainty into account. As model uncertainty can also be formalized as an information-processing constraint, we can derive a unified solution from a single generalized variational principle. We provide a generalized value iteration scheme together with a convergence proof. As limit cases, this generalized scheme includes standard value iteration with a known model, Bayesian MDP planning, and robust planning. We demonstrate the benefits of this approach in a grid world simulation.Comment: 16 pages, 3 figure

Solving ill-posed bilevel programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solutions for the original optimistic problem by this process. Considering the intrinsic non-convexity of bilevel programs, computing local optimal solutions is the best one can hope to get in most cases. To achieve this goal, we start by establishing an equivalence between the original optimistic problem an a certain set-valued optimization problem. Next, we develop optimality conditions for the latter problem and show that they generalize all the results currently known in the literature on optimistic bilevel optimization. Our approach is then extended to multiobjective bilevel optimization, and completely new results are derived for problems with vector-valued upper- and lower-level objective functions. Numerical implementations of the results of this paper are provided on some examples, in order to demonstrate how the original optimistic problem can be solved in practice, by means of a special set-valued optimization problem

Jet-veto in bottom-quark induced Higgs production at next-to-next-to-leading order

We present results for associated Higgs+n-jet production in bottom quark annihilation, for n=0 and n>=1 at NNLO and NLO accuracy, respectively. We consider both the cases with and without b-tagging. Numerical results are presented for parameters relevant for experiments at the LHC.Comment: 27 pages, 13 figures, 8 table

A compact laboratory transmission X-ray microscope for the water window

In the water window (2.2-4.4 nm) the attenuation of radiation in water is significantly smaller than in organic material. Therefore, intact biological specimen (e.g. cells) can be investigated in their natural environment. In order to make this technique accessible to users in a laboratory environment a Full-Field Laboratory Transmission X-ray Microscope (L-TXM) has been developed. The L-TXM is operated with a nitrogen laser plasma source employing an InnoSlab high power laser system for plasma generation. For microscopy the Ly α emission of highly ionized nitrogen at 2.48 nm is used. A laser plasma brightness of 5 × 1011 photons/(s × sr × μm2 in line at 2.48 nm) at a laser power of 70 W is demonstrated. In combination with a state-of-the-art Cr/V multilayer condenser mirror the sample is illuminated with 106 photons/(μm2 × s). Using objective zone plates 35-40 nm lines can be resolved with exposure times < 60 s. The exposure time can be further reduced to 20 s by the use of new multilayer condenser optics and operating the laser at its full power of 130 W. These exposure times enable cryo tomography in a laboratory environment

Z-score mapping for standardized analysis and reporting of cardiovascular magnetic resonance modified Look-Locker inversion recovery (MOLLI) T1 data: normal behavior and validation in patients with amyloidosis

BACKGROUND: T1 mapping using modified Look-Locker inversion recovery (MOLLI) provides quantitative information on myocardial tissue composition. T1 results differ between sites due to variations in hardware and software equipment, limiting the comparability of results. The aim was to test if Z-scores can be used to compare the results of MOLLI T1 mapping from different cardiovascular magnetic resonance (CMR) platforms. METHODS: First, healthy subjects (n = 15) underwent 11 combinations of native short-axis T1 mapping (four CMR systems from two manufacturers at 1.5 T and 3 T, three MOLLI schemes). Mean and standard deviation (SD) of septal myocardial T1 were derived for each combination. T1 maps were transformed into Z-score maps based on mean and SD values using a prototype post-processing module. Second, Z-score mapping was applied to a validation sample of patients with cardiac amyloidosis at 1.5 T (n = 25) or 3 T (n = 13). RESULTS: In conventional T1 analysis, results were confounded by variations in field strength, MOLLI scheme, and manufacturer-specific system characteristics. Z-score-based analysis yielded consistent results without significant differences between any two of the combinations in part 1 of the study. In the validation sample, Z-score mapping differentiated between patients with cardiac amyloidosis and healthy subjects with the same diagnostic accuracy as standard T1 analysis regardless of field strength. CONCLUSIONS: T1 analysis based on Z-score mapping provides consistent results without significant differences due to field strengths, CMR systems, or MOLLI variants, and detects cardiac amyloidosis with the same diagnostic accuracy as conventional T1 analysis. Z-score mapping provides a means to compare native T1 results acquired with MOLLI across different CMR platforms