We present the most general covariant ghost-free gravitational action in a Minkowski vacuum. Apart from the much studied f(R) models, this includes a large class of nonlocal actions with improved UV behavior, which nevertheless recover Einstein's general relativity in the IR.

Various algorithms comparing 2D NMR spectra have been explored for their ability to dereplicate natural products as well as determine molecular structures. However, spectroscopic artefacts, solvent effects, and the interactive effect of functional group(s) on chemical shifts combine to hinder their effectiveness. Here, we leveraged Non-Uniform Sampling (NUS) 2D NMR techniques and deep Convolutional Neural Networks (CNNs) to create a tool, SMART, that can assist in natural products discovery efforts. First, an NUS heteronuclear single quantum coherence (HSQC) NMR pulse sequence was adapted to a state-of-the-art nuclear magnetic resonance (NMR) instrument, and data reconstruction methods were optimized, and second, a deep CNN with contrastive loss was trained on a database containing over 2,054 HSQC spectra as the training set. To demonstrate the utility of SMART, several newly isolated compounds were automatically located with their known analogues in the embedded clustering space, thereby streamlining the discovery pipeline for new natural products.

Jet counting and jet vetos are crucial analysis tools for many LHC searches. We can understand their properties from the distribution of the exclusive number of jets. LHC processes tend to show either a distinct staircase scaling or a Poisson scaling, depending on kinematic cuts. We illustrate our approach in a detailed study of jets in weak boson fusion Higgs production.

Jet emission at hadron colliders follows simple scaling patterns. Based on perturbative QCD we derive Poisson and staircase scaling for final state as well as initial state radiation. Parton density effects enhance staircase scaling at low multiplicities. We propose experimental tests of our theoretical findings in Z+jets and QCD gap jets production, based on minor additions to current LHC analyses.

We derive generating functions, valid to next-to-double logarithmic accuracy, for QCD jet rates according to the inclusive forms of the k t , Cambridge/Aachen and anti-k t algorithms, which are equivalent at this level of accuracy. We compare the analytical results with jet rates and average jet multiplicities from the SHERPA event generator, and study the transition between Poisson-like and staircase-like behaviour of jet ratios.