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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 

We report the first double-differential cross section measurement of neutral-current neutral pion ( $\mathrm{NC}{\pi }^0$) production in neutrino-argon scattering, as well as single-differential measurements of the same channel in terms of final states with and without protons. The kinematic variables of interest for these measurements are the ${\pi }^0$momentum and the ${\pi }^0$scattering angle with respect to the neutrino beam. A total of 4971 candidate $\mathrm{NC}{\pi }^0$events fully contained within the MicroBooNE detector are selected using data collected at a mean neutrino energy of $\sim 0.8\mathrm{GeV}$from $6.4\times {10}^{20}$protons on target from the Booster Neutrino Beam at the Fermi National Accelerator Laboratory. After extensive data-driven model validation to ensure unbiased unfolding, the Wiener-singular-value-decomposition method is used to extract nominal flux-averaged cross sections. The results are compared to predictions from commonly used neutrino event generators, which tend to overpredict the measured $\mathrm{NC}{\pi }^0$cross section, especially in the $0.2–0.5\mathrm{GeV}/\mathrm{c}$ ${\pi }^0$momentum range and at forward scattering angles. Events with at least one proton present in the final state are also underestimated. This data will help improve the modeling of $\mathrm{NC}{\pi }^0$production, which represents a major background in measurements of charge-parity violation in the neutrino sector and in searches for new physics beyond the standard model. 

The EIC Comprehensive Chromodynamics Experiment (ECCE) detector has been designed to address the full scope of the proposed Electron Ion Collider (EIC) physics program as presented by the National Academy of Science and provide a deeper understanding of the quark–gluon structure of matter. To accomplish this, the ECCE detector offers nearly acceptance and energy coverage along with excellent tracking and particle identification. The ECCE detector was designed to be built within the budget envelope set out by the EIC project while simultaneously managing cost and schedule risks. This detector concept has been selected to be the basis for the EIC project detector. 

We present a measurement of neutral pion production in charged-current interactions using data recorded with the MicroBooNE detector exposed to Fermilab’s booster neutrino beam. The signal comprises one muon, one neutral pion, any number of nucleons, and no charged pions. Studying neutral pion production in the MicroBooNE detector provides an opportunity to better understand neutrino-argon interactions, and is crucial for future accelerator-based neutrino oscillation experiments. Using a dataset corresponding to $6.86\times {10}^{20}$protons on target, we present single-differential cross sections in muon and neutral pion momenta, scattering angles with respect to the beam for the outgoing muon and neutral pion, as well as the opening angle between the muon and neutral pion. Data extracted cross sections are compared to generator predictions. We report good agreement between the data and the models for scattering angles, except for an over-prediction by generators at muon forward angles. Similarly, the agreement between data and the models as a function of momentum is good, except for an underprediction by generators in the medium momentum ranges, 200–400 MeV for muons and 100–200 MeV for pions. Published by the American Physical Society2024