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Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where they tend to be over-parameterized. As a consequence, different solutions have been proposed, often relying on matrix decompositions or variable selection strategies. Recently, a methodological link between Gaussian graphical models and finite mixtures has been established, paving the way for penalized model-based clustering in the presence of large precision matrices. Notwithstanding, current methodologies implicitly assume similar levels of sparsity across the classes, not accounting for different degrees of association between the variables across groups. We overcome this limitation by deriving group-wise penalty factors, which automatically enforce under or over-connectivity in the estimated graphs. The approach is entirely data-driven and does not require additional hyper-parameter specification. Analyses on synthetic and real data showcase the validity of our proposal., Comment: 41 pages, 11 figures

Between the years 2015 and 2019, members of the Horizon 2020-funded Innovative Training Network named "AMVA4NewPhysics" studied the customization and application of advanced multivariate analysis methods and statistical learning tools to high-energy physics problems, as well as developed entirely new ones. Many of those methods were successfully used to improve the sensitivity of data analyses performed by the ATLAS and CMS experiments at the CERN Large Hadron Collider; several others, still in the testing phase, promise to further improve the precision of measurements of fundamental physics parameters and the reach of searches for new phenomena. In this paper, the most relevant new tools, among those studied and developed, are presented along with the evaluation of their performances., Comment: 101 pages, 21 figures, submitted to Elsevier. [v2]: Updated to published version (in 'Reviews in Physics')

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data we need to account for relations among both time instants and variables and, at the same time, for subjects heterogeneity. We propose a new co-clustering methodology for clustering individuals and variables simultaneously that is designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the Shape Invariant Model in the Latent Block Model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that could be chosen on substantive grounds and provides parsimonious summaries of complex longitudinal or functional data by partitioning data matrices into homogeneous blocks., Comment: 21 pages, 7 figures

The family of edge-sharing tri-coordinated iridates and ruthenates has emerged in recent years as a major platform for Kitaev spin liquid physics, where spins fractionalize into emergent magnetic fluxes and Majorana fermions with Dirac-like dispersions. While such exotic states are usually pre-empted by long-range magnetic order at low temperatures, signatures of Majorana fermions with long coherent times have been predicted to manifest at intermediate and higher energy scales, similar to the observation of spinons in quasi-1D spin chains. Here we present a Resonant Inelastic X-ray Scattering study of the magnetic excitations of the hyperhoneycomb iridate $\beta$-Li$_2$IrO$_3$ under a magnetic field with a record-high-resolution spectrometer. At low-temperatures, dispersing spin waves can be resolved around the predicted intertwined incommensurate spiral and field-induced zigzag orders, whose excitation energy reaches a maximum of 16meV. A 2T magnetic field softens the dispersion around ${\bf Q}=0$. The behavior of the spin waves under magnetic field is consistent with our semiclassical calculations for the ground state and the dynamical spin structure factor, which further predicts that the ensued intertwined uniform states remain robust up to very high fields (100 T). Most saliently, the low-energy magnon-like mode is superimposed by a broad continuum of excitations, centered around 35meV and extending up to 100meV. This high-energy continuum survives up to at least 300K -- well above the ordering temperature of 38K -- and gives evidence for pairs of long-lived Majorana fermions of the proximate Kitaev spin liquid., Comment: 8 pages, 4 figures

In recent years animal diet has been receiving increased attention, in particular examining the impact of pasture-based feeding strategies on the quality of milk and dairy products, in line with the increased prevalence of grass-fed dairy products appearing on market shelves. To date, there are limited testing methods available for the verification of grass-fed dairy therefore these products are susceptible to food fraud and adulteration. Hence statistical tools studying potential differences among milk samples coming from animals on different feeding systems are required, thus providing increased security around the authenticity of the products. Infrared spectroscopy techniques are widely used to collect data on milk samples and to predict milk related traits. While these data are routinely used to predict the composition of the macro components of milk, each spectrum provides a reservoir of unharnessed information about the sample. The interpretation of these data presents a number of challenges due to their high-dimensionality and the relationships amongst the spectral variables. In this work we propose a modification of the standard factor analysis to induce a parsimonious summary of spectroscopic data. The procedure maps the observations into a low-dimensional latent space while simultaneously clustering observed variables. The method indicates possible redundancies in the data and it helps disentangle the complex relationships among the wavelengths. A flexible Bayesian estimation procedure is proposed for model fitting, providing reasonable values for the number of latent factors and clusters. The method is applied on milk mid-infrared spectroscopy data from dairy cows on different pasture and non-pasture based diets, providing accurate modelling of the data correlation, the clustering of variables and information on differences between milk samples from cows on different diets., Comment: 23 pages, 6 figures

GAGG:Ce (Cerium-doped Gadolinium Aluminium Gallium Garnet) is a promising new scintillator crystal. A wide array of interesting features, such as high light output, fast decay times, almost non-existent intrinsic background and robustness, make GAGG:Ce an interesting candidate as a component of new space-based gamma-ray detectors. As a consequence of its novelty, literature on GAGG:Ce is still lacking on points crucial to its applicability in space missions. In particular, GAGG:Ce is characterized by unusually high and long-lasting delayed luminescence. This afterglow emission can be stimulated by the interactions between the scintillator and the particles of the near-Earth radiation environment. By contributing to the noise, it will impact the detector performance to some degree. In this manuscript we summarize the results of an irradiation campaign of GAGG:Ce crystals with protons, conducted in the framework of the HERMES-TP/SP (High Energy Rapid Modular Ensemble of Satellites - Technological and Scientific Pathfinder) mission. A GAGG:Ce sample was irradiated with 70 MeV protons, at doses equivalent to those expected in equatorial and sun-synchronous Low-Earth orbits over orbital periods spanning 6 months to 10 years, time lapses representative of satellite lifetimes. We introduce a new model of GAGG:Ce afterglow emission able to fully capture our observations. Results are applied to the HERMES-TP/SP scenario, aiming at an upper-bound estimate of the detector performance degradation due to the afterglow emission expected from the interaction between the scintillator and the near-Earth radiation environment., Comment: 8 pages, 3 figures. Proceedings of SPIE "Astronomical Telescopes and Instrumentation" 2020

In the high spin-orbit coupled Sr2IrO4, the high sensitivity of the ground state to the details of the local lattice structure shows a large potential for the manipulation of the functional properties by inducing local lattice distortions. We use epitaxial strain to modify the Ir-O bond geometry in Sr2IrO4 and perform momentum-dependent Resonant Inelastic X-ray Scattering (RIXS) at the metal and at the ligand sites to unveil the response of the low energy elementary excitations. We observe that the pseudospin-wave dispersion for tensile-strained Sr2IrO4 films displays large softening along the [h,0] direction, while along the [h,h] direction it shows hardening. This evolution reveals a renormalization of the magnetic interactions caused by a strain-driven crossover from anisotropic to isotropic interactions between the magnetic moments. Moreover, we detect dispersive electron-hole pair excitations which shift to lower (higher) energies upon compressive (tensile) strain, manifesting a reduction (increase) in the size of the charge gap. This behavior shows an intimate coupling between charge excitations and lattice distortions in Sr2IrO4, originating from the modified hopping elements between the t2g orbitals. Our work highlights the central role played by the lattice degrees of freedom in determining both the pseudospin and charge excitations of Sr2IrO4 and provides valuable information towards the control of the ground state of complex oxides in the presence of high spin-orbit coupling., Comment: Published in Proceedings of the National Academy of Sciences, September 2020

Although ultrafast manipulation of magnetism holds great promise for new physical phenomena and applications, targeting specific states is held back by our limited understanding of how magnetic correlations evolve on ultrafast timescales. Using ultrafast resonant inelastic x-ray scattering we demonstrate that femtosecond laser pulses can excite transient magnons at large wavevectors in gapped antiferromagnets, and that they persist for several picoseconds which is opposite to what is observed in nearly gapless magnets. Our work suggests that materials with isotropic magnetic interactions are preferred to achieve rapid manipulation of magnetism., Comment: 6 pages, 4 figures, not including supplemental material; accepted in PNAS

With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging landscape. In fact, basing predictions and inference on a single model may be limiting if not harmful; ensemble approaches, which combine different models, have been proposed to overcome the selection step, and proven fruitful especially in the supervised learning framework. Conversely, these approaches have been scantily explored in the unsupervised setting. In this work we focus on the model-based clustering formulation, where a plethora of mixture models, with different number of components and parametrizations, is typically estimated. We propose an ensemble clustering approach that circumvents the single best model paradigm, while improving stability and robustness of the partitions. A new density estimator, being a convex linear combination of the density estimates in the ensemble, is introduced and exploited for group assignment. As opposed to the standard case, where clusters are typically associated to the components of the selected mixture model, we define partitions by borrowing the modal, or nonparametric, formulation of the clustering problem, where groups are linked with high-density regions. Staying in the density-based realm we thus show how blending together parametric and nonparametric approaches may be beneficial from a clustering perspective.

We present a study of resonant inelastic X-ray scattering (RIXS) spectra collected at the rare-earth $L$ edges of divalent hexaborides YbB$_6$ and EuB$_6$. In both systems, RIXS-active features are observed at two distinct resonances separated by $\sim10$ eV in incident energy, with angle-dependence suggestive of distinct photon scattering processes. RIXS spectra collected at the divalent absorption peak strongly resemble the unoccupied 5$d$ density of states calculated using density functional theory, an occurrence we ascribe to transitions between weakly-dispersing 4$f$ and strongly dispersing 5$d$ states. In addition, anomalous resonant scattering is observed at higher incident energy, where no corresponding absorption feature is present. Our results suggest the far-reaching utility of $L$-edge RIXS in determining the itinerant-state properties of $f$-electron materials.

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering.