In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model- driven approaches have (sometimes complementary) advantages and drawbacks. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class of vehicle.

The ongoing reproducibility crisis in psychology and cognitive neuroscience has sparked increasing calls to re-evaluate and reshape scientific culture and practices. Heeding those calls, we have recently launched the EEGManyPipelines project as a means to assess the robustness of EEG research in naturalistic conditions and experiment with an alternative model of conducting scientific research.

Understanding brain function from magneto-electroencephalographic (M/EEG) measurements requires advanced mathematical and signal processing tools. Although the analysis of M/EEG data at sensors level sheds light on important brain mechanisms, full exploitation of the information contained in such brain data could be achieved by reconstructing the active neural sources from M/EEG measurements.

Magnetoencephalography and electroencephalography (M/EEG) seed-based connectivity analysis typically requires regions of interest (ROI)-based extraction of measures. M/EEG ROI-derived source activity can be treated in different ways. For instance, it is possible to average each ROI's time series prior to calculating connectivity measures. Alternatively one can compute connectivity maps for each element of the ROI, prior to dimensionality reduction to obtain a single map. The impact of these different strategies on connectivity estimation is still unclear.

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.

Following the methodology of Brasco (Adv Math 394:108029, 2022), we study the long-time behavior for the signed fractional porous medium equation in open bounded sets with smooth boundary. Homogeneous exterior Dirichlet boundary conditions are considered. We prove that if the initial datum has sufficiently small energy, then the solution, once suitably rescaled, converges to a nontrivial constant sign solution of a sublinear fractional Lane-Emden equation.

A new, highly parallelized, adaptive mesh refinement (AMR) library, equipped with an accurate immersed boundary (IB) method for solving the compressible Navier-Stokes system is presented. The library, named ADAM, is designed to efficiently exploit modern exascale GPU-accelerated supercomputers and it is implemented with a highly modular structure in order to make easy to leverage it for a wide range of CFD applications.

We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd?s-Rényi random graph that incorporates the community structure observed in many real systems. In the SBM, nodes are partitioned into two subsets, which represent different communities, and pairs of nodes are independently connected with a probability that depends on the communities they belong to.

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.