We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment.

Comparison results for solutions to the Dirichlet problems for a class of nonlinear, anisotropic parabolic equations are established. These results are obtained through a semidiscretization method in time after providing estimates for solutions to anisotropic elliptic problems with zero-order terms.

The class of Bipartite Distance Hereditary (BDH) graphs is the intersection between bipartite domino-free and chordal bipartite graphs. Graphs in both the latter classes have linearly many maximal bicliques, implying the existence of polynomial-time algorithms for computing the associated Galois lattice. Such a lattice can indeed be built in O(m?n)O(m?n)worst-case time for a domino-free graph with mm edges and nn vertices. In Apollonio et al. (2015), BDH graphs have been characterized as those bipartite graphs whose Galois lattice is tree-like.

The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attracting multiple immune cell species. The in silico model here proposed goes towards the construction of a "digital twin" of the experimental immune cells in the chip environment to better understand the complex mechanisms of immunosurveillance.

In this work, we study the impact of high-energy radiation induced by solar X-ray flares on the determination of the temporal change in precipitable water vapor (?PWV) as estimated using the synthetic aperture radar (SAR) meteorology technique. As recent research shows, this radiation can significantly affect the ionospheric D-region and induces errors in the estimation of the total electron content (TEC) by the applied models.

The existence of eigenfunctions for a class of fully anisotropic elliptic equations is estab- lished. The relevant equations are associated with constrained minimization problems for inte- gral functionals depending on the gradient of competing functions through general anisotropic Young functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called 2-condition. In particular, our analysis re- quires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces. This is a joint work with G.