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Gaussian processes are widely employed as versatile modelling and predictive tools in spa- tial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over Euclidean spaces, where they are specified using covariance functions or covariograms for modelling complex dependencies. There is a growing literature on Gaussian processes over Riemannian manifolds in order to develop richer and more flexible inferential frameworks for non-Euclidean data. While numerical approximations through graph representations have been well studied for the Mat´ern covariogram and heat kernel, the behaviour of asymptotic inference on the param- eters of the covariogram has received relatively scant attention. We focus on asymptotic behaviour for Gaussian processes constructed over compact Riemannian manifolds. Build- ing upon a recently introduced Mat´ern covariogram on a compact Riemannian manifold, we employ formal notions and conditions for the equivalence of two Mat´ern Gaussian random measures on compact manifolds to derive the parameter that is identifiable, also known as the microergodic parameter, and formally establish the consistency of the maximum like- lihood estimate and the asymptotic optimality of the best linear unbiased predictor. The circle is studied as a specific example of compact Riemannian manifolds with numerical experiments to illustrate and corroborate the theory 

Abstract Two different types of monoclinic HfO 2 nanocrystals were employed in this work to study the effect of nanocrystal shape and crystallinity on the structural defects in the YBa2Cu3O7−δ (YBCO) matrix as it leads to an enhancement of pinning performances of solution-derived YBCO nanocomposite films. In this work the nanorod-like HfO 2 nanocrystals obtained from surfactant-controlled synthesis led to short intergrowths surrounding the particles, while spherical HfO 2 nanocrystals from the solvent-controlled synthesis led to the formation of long stacking faults in the YBCO matrix. It means that the small difference in crystallinity, lattice parameters, nanocrystal structures, core diameter of preformed nanocrystals in colloidal solutions have a strong influence on the formation of the structural defects around the particles in the YBCO matrix, leading to different pinning performances. 

X-ray free electron laser (XFEL) sources coupled to high-power laser systems offer an avenue to study the structural dynamics of materials at extreme pressures and temperatures. The recent commissioning of the DiPOLE 100-X laser on the high energy density (HED) instrument at the European XFEL represents the state-of-the-art in combining x-ray diffraction with laser compression, allowing for compressed materials to be probed in unprecedented detail. Here, we report quantitative structural measurements of molten Sn compressed to 85(5) GPa and ∼3500 K. The capabilities of the HED instrument enable liquid density measurements with an uncertainty of ∼1% at conditions which are extremely challenging to reach via static compression methods. We discuss best practices for conducting liquid diffraction dynamic compression experiments and the necessary intensity corrections which allow for accurate quantitative analysis. We also provide a polyimide ablation pressure vs input laser energy for the DiPOLE 100-X drive laser which will serve future users of the HED instrument.

 

We examine the capacity of the Large Hadron Collider to determine the mean proper lifetime of long-lived particles assuming different decay final states. We mostly concentrate on the high luminosity runs of the LHC, and therefore, develop our discussion in light of the high amount of pile-up and the various upgrades for the HL-LHC runs. We employ model-dependent and model-independent methods in order to reconstruct the proper lifetime of neutral long- lived particles decaying into displaced leptons, potentially accompanied by missing energy, as well as charged long- lived particles decaying ihnto leptons and missing energy. We also present a discussion for lifetime estimation of neu- tral long-lived particles decaying into displaced jets, along with the challenges in the high PU environment of HL-LHC. After a general discussion, we illustrate and discuss these methods using several new physics models. We conclude that the lifetime can indeed be reconstructed in many concrete cases. Finally, we discuss to which extent including timing information, which is an important addition in the Phase-II upgrade of CMS, can improve such an analysis.