We study the consistency and the oracle properties of the adaptive Lasso estimator for the coefficients of a linear AR(p) time series with a strictly stationary white noise (not necessarily described by i.i.d. r.v.'s). We apply the results to INAR(p) time series and to the non-parametric inference of the fertility function of a Hawkes point process. We present some numerical simulations to emphasize the advantages of the proposed procedure with respect to more classical ones and finally we apply it to a set of epidemiological data

This paper investigates the model for pedestrian flow firstly proposed in [Cristiani, Priuli, and Tosin, SIAM J. Appl. Math., 75:605-629, 2015]. The model assumes that each individual in the crowd moves in a known domain, aiming at minimizing a given cost functional. Both the pedestrian dynamics and the cost functional itself depend on the position of the whole crowd. In addition, pedestrians are assumed to have predictive abilities, but limited in time.

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.

This contribution outlines current research aimed at developing models for personalized type 2 diabetes mellitus (T2D) prevention in the framework of the European project PRAESIIDIUM (Physics Informed Machine Learn-ing-Based Prediction and Reversion of Impaired Fasting Glucose Management) aimed at building a digital twin for preventing T2D in patients at risk.

Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an overview of some techniques for Shape-from-Shading problems as well as for 3D printing with an emphasis on the approaches based on nonlinear partial differential equations and optimization. We also sketch possible couplings to complete the process of object manufacturing starting from one or more images of the object and ending with its final 3D print.

The Dirichlet-Ferguson measure is a cornerstone in nonparametric Bayesian statistics and the study of distributional properties of expectations with respect to such measure is an important line of research. In this paper we provide explicit upper bounds for the d2, the d3 and the convex distance between vectors whose components are means of the Dirichlet-Ferguson measure and a Gaussian random vector.

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.

A new technique for nonparametric regression of multichannel signals is presented. The technique is based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with a tunable Q-factor able to provide sparse representations of functions with different oscillations persistence. In particular, two different frames are obtained by two RADWT with different Q-factors that give sparse representations of functions with low and high resonance.

Dissolution of drug from its solid form to a dissolved form is an important consideration in the design and optimization of drug delivery devices, particularly owing to the abundance of emerging compounds that are extremely poorly soluble. When the solid dosage form is encapsulated, for example by the porous walls of an implant, the impact of the encapsulant drug transport properties is a further confounding issue. In such a case, dissolution and diffusion work in tandem to control the release of drug.