A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement-invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in our analysis is a new reduction principle for the relevant embeddings, showing their equivalence to a couple of considerably simpler one-dimensional inequalities.

Changes in blood epigenetic age have been associated with several pathological conditions and have recently been described to anticipate cancer development. In this work, we analyze a publicly available leukocytes methylation dataset to evaluate the relation between DNA methylation age and the prospective development of specific types of cancer.

Motivation: Cells derived by cellular engineering, i.e. differentiation of induced pluripotent stem cells and direct lineage reprogramming, carry a tremendous potential for medical applications and in particular for regenerative therapies. These approaches consist in the definition of lineage-specific experimental protocols that, by manipulation of a limited number of biological cues-niche mimicking factors, (in) activation of transcription factors, to name a few-enforce the final expression of cell-specific (marker) molecules.

We propose a multi-component discrete Boltzmann model (DBM) for premixed, nonpremixed, or partially premixed nonequilibrium reactive flows. This model is suitable for both subsonic and supersonic flows with or without chemical reaction and/or external force. A two-dimensional sixteen-velocity model is constructed for the DBM. In the hydrodynamic limit, the DBM recovers the modified Navier-Stokes equations for reacting species in a force field.

We present an entropic version of the lattice Boltzmann pseudo-potential approach for the simulation of multiphase flows. The method is shown to correctly simulate the dynamics of impinging droplets on hydrophobic surfaces and head-on and grazing collisions between droplets, at Weber and Reynolds number regimes not accessible to previous pseudo-potential methods at comparable resolution.

A key ecological parameter for planktonic copepod studies is their encounter rates within the same population as well as with other species. The encounter rate is partly determined by copepod's swimming behaviour and is strongly influenced by turbulence of the surrounding environment. A distinctive feature of copepods' motility is their ability to perform quick displacements, often termed jumps, by means of powerful swimming strokes. Such a reaction has been associated to an escape behaviour from flow disturbances due to predators or other external signals.

We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultrarelativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Juttner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices.

An intraguild predator-prey model with a carrying capacity proportional to the biotic resource, is generalized by introducing a Holling type II functional response. The longtime behaviour of solutions is analyzed and, in particular, absorbing sets in the phase space are determined. The existence of biologically meaningful equilibria (boundary and internal equilibria) has been investigated. Linear and nonlinear stability conditions for biologically meaningful equilibria are performed.

The geometry of passive tracer trajectories is studied in two different types of rotating turbulent flows; rotating Rayleigh-Bénard convection (RBC; experiments and direct numerical simulations) and rotating electromagnetically forced turbulence (EFT; experiments). This geometry is fully described by the curvature and torsion of trajectories, and from these geometrical quantities we can subtract information on the typical flow structures at different rotation rates.

We present LBsoft, an open-source software developed mainly to simulate the hydro-dynamics of colloidal systems based on the concurrent coupling between lattice Boltzmann methods for the fluid and discrete particle dynamics for the colloids. Such coupling has been developed before, but, to the best of our knowledge, no detailed discussion of the programming issues to be faced in order to attain efficient implementation on parallel architectures, has ever been presented to date.