Bi-allelic hypomorphic mutations in DNMT3B disrupt DNA methyltransferase activity and lead to immunodeficiency, centromeric instability, facial anomalies syndrome, type 1 (ICF1). Although several ICF1 phenotypes have been linked to abnormally hypomethylated repetitive regions, the unique genomic regions responsible for the remaining disease phenotypes remain largely uncharacterized.

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.

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.