Graph structures nowadays pervasive Big Data. It is often useful to regroup suchclusters data incan clusters, according distinctive node features, and use are a representative elementinfor each cluster. In many real-world cases, be identified by to a set of connected features, and share use a representative element for eachfunction, cluster.

We study some numerical properties of a nonconvex variational problem which arises as the continuous limit of a discrete optimization method designed for the smoothing of images with preservation of discontinuities. The functional that has to be minimized fails to attain a minimum value. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. The oscillations of the gradient exhibit analogies with microstructures in ordered materials. The pattern of the oscillations is analysed numerically by using discrete parametrized measures.

Drug delivery carriers are considered an encouraging approach for the localized treatment of disease with minimum effect on the surrounding tissue. Particularly, layer-by-layer releasing particles have gained increasing interest for their ability to develop multifunctional systems able to control the release of one or more therapeutical drugs and biomolecules. Although experimental methods can offer the opportunity to establish cause and effect relationships, the data collection can be excessively expensive or/and time-consuming.

Controlled release of a drug contained in a spherical polymer capsule is of significant interest in many fields of medicine. There is growing interest in tailoring the erosion properties of the drug to help control and optimize the drug release process. Theoretical understanding of the nature of drug release from a bioerodible capsule is, therefore, important for designing effective drug delivery systems.

The prediction of drug dissolution profiles is crucial for elucidating the pharmacokinetic behaviour of drugs and the bioavailability of dosage forms. In this work, we develop a mathematical model to describe the dissolution process of irregularly shaped particles. We use a complete dissolution model that accounts for both surface kinetics and convective diffusion. The mechanistic relationship between the mass transfer coefficient and the local curvature is derived from the fundamental physical laws governing these processes.

We study some properties of a nonconvex variational problem. The infimum of the functional that has to be minimized fails to be attained. Instead, minimizing sequences develop gradient oscillations which allow them to decrease the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original non perturbed problem is analyzed numerically.

In this perspective we take stock of the current state of the art of computational models for droplets microfluidics and we suggest some strategies which may open the way to the full-scale simulation of microfluidic phenomena with interfaces, from near-contact interactions to the device operational lengths.

The rate of drug delivery to cells and the subsequent rate of drug metabolism are dependent on the cell membrane permeability to the drug. In some cases, tissue may be composed of different types of cells that exhibit order of magnitude differences in their membrane permeabilities. This paper presents a brief review of the components of the tissue scale three-compartment pharmacokinetic model of drug delivery to single-cell-type populations. The existing model is extended to consider tissue composed of two different cell types.

This paper deals with finite-difference approximations of Euler equations arising in the variational formulation of image segmentation problems. We illustrate how they can be defined by the following steps: (a) definition of the minimization problem for the Mumford-Shah functional (MSf), (b) definition of a sequence of functionals Gamma-convergent to the MSf, and (c) definition and numerical solution of the Euler equations associated to the k-th functional of the sequence.

Mathematical models have the potential to contribute to design and evaluate the infectivity spreading and growth of human immunodeficiency virus (HIV). Providing a better understanding of the dynamics of HIV infection in vivo and the immune system interactions with the virus can improve the classification of the infected cells and drive to an early diagnosis of the disease and drug evaluations.