Most metallic and ceramic materials are comprised of space-filling collections of crystalline grains separated by grain boundaries. While this grain structure has been studied for more than a century, there are few rigorous results regarding its global properties available in the literature. We present a rigorous result for three-dimensional grain structures that relates the integral of the Gaussian curvature over the grain boundaries to the numbers of grains and quadruple junctions. The result is numerically verified for a grain structure consisting of periodic truncated octahedra.

Significant advances in deep learning have led to more widely used and precise neural network-based generative models such as Generative Adversarial Networks (Gans). We introduce a post-hoc correction to deep generative models to further improve their fidelity, based on the Deep neural networks using the Classification for Tuning and Reweighting (Dctr) protocol. The correction takes the form of a reweighting function that can be applied to generated examples when making predictions from the simulation. We illustrate this approach using Gans trained on standard multimodal probability densities as well as calorimeter simulations from high energy physics. We show that the weighted Gan examples significantly improve the accuracy of the generated samples without a large loss in statistical power. This approach could be applied to any generative model and is a promising refinement method for high energy physics applications and beyond.

Abstract: Motivated by the high computational costs of classical simulations, machine-learned generative models can be extremely useful in particle physics and elsewhere. They become especially attractive when surrogate models can efficiently learn the underlying distribution, such that a generated sample outperforms a training sample of limited size. This kind of GANplification has been observed for simple Gaussian models. We show the same effect for a physics simulation, specifically photon showers in an electromagnetic calorimeter.

The cross section of top quark-antiquark pair production in proton-proton collisions at [Formula: see text] is measured by the CMS experiment at the LHC, using data corresponding to an integrated luminosity of 2.2[Formula: see text]. The measurement is performed by analyzing events in which the final state includes one electron, one muon, and two or more jets, at least one of which is identified as originating from hadronization of a b quark. The measured cross section is [Formula: see text], in agreement with the expectation from the standard model.