Preservation of the angle of reflection when an internal gravity wave hits a sloping boundary generates a focusing mechanism if the angle between the direction of propagation of the incident wave and the horizontal is close to the slope inclination (near-critical reflection). This paper provides an explicit description of the leading approximation of the unique Leray solution to the near-critical reflection of internal waves from a slope in the form of a beam wave.

Given a random sample drawn from a Multivariate Bernoulli Variable (MBV), we consider the problem of estimating the structure of the undirected graph for which the distribution is pairwise Markov and the parameters' vector of its exponential form. We propose a simple method that provides a closed form estimator of the parameters' vector and through its support also provides an estimate of the undirected graph associated with the MBV distribution. The estimator is proved to be asymptotically consistent but it is feasible only in low-dimensional regimes.

Electrophysiological source imaging (ESI) aims at reconstructing the precise origin of brain activity from measurements of the electric field on the scalp. Across laboratories/research centers/hospitals, ESI is performed with different methods, partly due to the ill-posedness of the underlying mathematical problem. However, it is difficult to find systematic comparisons involving a wide variety of methods. Further, existing comparisons rarely take into account the variability of the results with respect to the input parameters.

In this paper, we study fluctuations and precise deviations of cumulative INAR time series, both in a non-stationary and in a stationary regime. The theoretical results are based on the recent mod- convergence theory as presented in Féray et al., 2016. We apply our findings to the construction of approximate confidence intervals for model parameters and to quantile calculation in a risk management context.

Machine learning (ML) is increasingly used in cognitive, computational and clinical neuroscience. The reliable and efficient application of ML requires a sound understanding of its subtleties and limitations. Training ML models on datasets with imbalanced classes is a particularly common problem, and it can have severe consequences if not adequately addressed.

We derive bounds on the Kolmogorov distance between the dis- tribution of a random functional of a {0, 1}-valued random sequence and the normal distribution. Our approach, which relies on the general framework of stochastic analysis for discrete-time normal martingales, extends existing results obtained for independent Bernoulli (or Rademacher) sequences. In particular, we obtain Kolmogorov distance bounds for the sum of normalized random sequences without any independence assumption.

The accurate characterization of cortical functional connectivity from Magnetoencephalography (MEG) data remains a challenging problem due to the subjective nature of the analysis, which requires several decisions at each step of the analysis pipeline, such as the choice of a source estimation algorithm, a connectivity metric and a cortical parcellation, to name but a few. Recent studies have emphasized the importance of selecting the regularization parameter in minimum norm estimates with caution, as variations in its value can result in significant differences in connectivity estimates.

The aim of this work was to characterize the palette and painting technique used for the realization of three late sixteenth century paintings from "Galleria dell'Accademia Nazionale di San Luca" in Rome attributed to Cavalier d'Arpino (Giuseppe Cesari), namely "Cattura di Cristo" (Inv. 158), "Autoritratto" (Inv. 546) and "Perseo e Andromeda" (Inv. 221).

We prove the strong ill-posedness of the two-dimensional Boussinesq system in vorticity form in L8pR2q without boundary, building upon the method that Shikh Khalil & Elgindi arXiv:2207.04556v1 developed for scalar equations. We provide examples of initial data with vorticity and density gradient of small L8pR2q size, for which the horizontal density gradient has a strong L8pR2q-norm inflation in infinitesimal time, while the vorticity and the vertical density gradient remain bounded.