We give a necessary and sufficient condition for the validity of the strong maximum principle in one space dimension.

Background Cell organization is governed and maintained via specific interactions among its constituent macromolecules. Comparison of the experimentally determined protein interaction networks in different model organisms has revealed little conservation of the specific edges linking ortholog proteins. Nevertheless, some topological characteristics of the graphs representing the networks - namely non-random degree distribution and high clustering coefficient - are shared by networks of distantly related organisms.

We study the Poiseuille flow of a soft-glassy material above the jamming point, where the material flows like a complex fluid with Herschel-Bulkley rheology. Microscopic plastic rearrangements and the emergence of their spatial correlations induce cooperativity flow behavior whose effect is pronounced in presence of confinement. With the help of lattice Boltzmann numerical simulations of confined dense emulsions, we explore the role of geometrical roughness in providing activation of plastic events close to the boundaries.

We consider a cell growth model involving a nonlinear system of partial differential equations which describes the growth of two types of cell populations with contact inhibition. Numerical experiments show that there is a parameter regime where, for a large class of initial data, the large time behaviour of the solutions is described by a segregated travelling wave solution with positive wave speed c.

We correct an error in the proof of Theorem 4.1 of the paper "Boundedness of solutions to anisotropic variational problems" [Comm. Part. Diff. Eq. 36 (2011); 470-486].

We consider an initial-boundary value problem for a degenerate pseudoparabolic regularization of a nonlinear forward-backward-forward parabolic equation, with a bounded nonlinearity which is increasing at infinity. We prove existence of suitably defined nonnegative solutions of the problem in a space of Radon measures. Solutions satisfy several monotonicity and regularization properties; in particular, their singular part is nonincreasing and may disappear in finite time.

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes.

ElectroCOrticoGraphy (ECoG) is an invasive neuroimaging technique that measures electrical potentials produced by brain currents via an electrode grid implanted on the cortical surface. A full interpretation of ECoG data is difficult because it requires solving the inverse problem of reconstructing the spatio-temporal distribution of neural currents responsible of the recorded ECoG signals, which is ill-posed. Only in the last few years novel computational methods to solve this inverse problem have been developed. This study describes a beamformer method for ECoG source modeling.

We establish a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.