The 2-point correlation function of the galaxy spatial distribution is a major cosmological observable that enables constraints on the dynamics and geometry of the Universe. The Euclid mission aims at performing an extensive spectroscopic survey of approximately 20--30 million H$\alpha$-emitting galaxies up to about redshift two. This ambitious project seeks to elucidate the nature of dark energy by mapping the 3-dimensional clustering of galaxies over a significant portion of the sky. This paper presents the methodology and software developed for estimating the 3-dimensional 2-point correlation function within the Euclid Science Ground Segment. The software is designed to overcome the significant challenges posed by the large and complex Euclid data set, which involves millions of galaxies. Key challenges include efficient pair counting, managing computational resources, and ensuring the accuracy of the correlation function estimation. The software leverages advanced algorithms, including kd-tree, octree, and linked-list data partitioning strategies, to optimise the pair-counting process. The implementation also includes parallel processing capabilities using shared-memory open multi-processing to further enhance performance and reduce computation times. Extensive validation and performance testing of the software are presented. The results indicate that the software is robust and can reliably estimate the 2-point correlation function, which is essential for deriving cosmological parameters with high precision. Furthermore, the paper discusses the expected performance of the software during different stages of the Euclid Wide Survey observations and forecasts how the precision of the correlation function measurements will improve over the mission's timeline, highlighting the software's capability to handle large data sets efficiently.

A serious concern for semi-analytical galaxy formation models, aiming to simulate multi-wavelength surveys and to thoroughly explore the model parameter space, is the extremely time consuming numerical solution of the radiative transfer of stellar radiation through dusty media. To overcome this problem, we have implemented an artificial neural network algorithm in the radiative transfer code GRASIL, in order to significantly speed up the computation of the infrared SED. The ANN we have implemented is of general use, in that its input neurons are defined as those quantities effectively determining the shape of the IR SED. Therefore, the training of the ANN can be performed with any model and then applied to other models. We made a blind test to check the algorithm, by applying a net trained with a standard chemical evolution model (i.e. CHE_EVO) to a mock catalogue extracted from the SAM MORGANA, and compared galaxy counts and evolution of the luminosity functions in several near-IR to sub-mm bands, and also the spectral differences for a large subset of randomly extracted models. The ANN is able to excellently approximate the full computation, but with a gain in CPU time by $\sim 2$ orders of magnitude. It is only advisable that the training covers reasonably well the range of values of the input neurons in the application. Indeed in the sub-mm at high redshift, a tiny fraction of models with some sensible input neurons out of the range of the trained net cause wrong answer by the ANN. These are extreme starbursting models with high optical depths, favorably selected by sub-mm observations, and difficult to predict a priori.

The dwarf spheroidal galaxy Ursa Major II (UMaII) is believed to be one of the most dark-matter dominated systems among the Milky Way satellites and represents a suitable target for indirect dark matter (DM) searches. The MAGIC telescopes carried out a deep observation campaign on UMaII between 2014 and 2016, collecting almost one hundred hours of good-quality data. This campaign enlarges the pool of DM targets observed at very high energy (E$\gtrsim$50GeV) in search for signatures of dark matter annihilation in the wide mass range between $\sim$100 GeV and $\sim$100 TeV. To this end, the data are analyzed with the full likelihood analysis, a method based on the exploitation of the spectral information of the recorded events for an optimal sensitivity to the explored dark matter models. We obtain constraints on the annihilation cross-section for different channels that are among the most robust and stringent achieved so far at the TeV mass scale from observations of dwarf satellite galaxies.