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.

The noisy trigonometric moment problem for a finite linear combination of box functions is considered, and a research program, possibly leading to a superresolving method, is outlined and some initial steps are performed. The method is based on the remark that the poles of the Padè approximant to the Z-transform of the noiseless moments show, asymptotically, a regular pattern in the complex plane. The pattern can be described by a set of arcs, connecting points on the unit circle, and a pole density function defined on the arcs.

Deep neural networks are rapidly emerging as data analysis tools, often outperforming the conventional techniques used in complex microfluidic systems. One fundamental analysis frequently desired in microfluidic experiments is counting and tracking the droplets. Specifically, droplet tracking in dense emulsions is challenging due to inherently small droplets moving in tightly packed configurations. Sometimes, the individual droplets in these dense clusters are hard to resolve, even for a human observer.

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.

Drug-coated balloons (DCBs) are used commonly for delivering drug into diseased arteries. When applied on the inner surface of an artery, drug is transported from the balloon into the multilayer arterial wall through diffusion and advection, where it is ultimately absorbed through binding reactions. Mathematical modeling of these mass transport processes has the potential to help understand and optimize balloon-based drug delivery, thereby ensuring both safety and efficacy.

Objective: Customization of the rate of drug delivered based on individual patient requirements is of paramount importance in the design of drug delivery devices. Advances in manufacturing may enable multilayer drug delivery devices with different initial drug distributions in each layer. However, a robust mathematical understanding of how to optimize such capabilities is critically needed. The objective of this work is to determine the initial drug distribution needed in a spherical drug delivery device such as a capsule in order to obtain a desired drug release profile.

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.

Abstract In this paper the Bi-Objective k-Length-Bounded Critical Disruption Path (BO-kLB-CDP) optimization problem is proposed, aimed at maximizing the interdiction effects provided on a network by removing a simple path connecting a given source and destination whose length does not exceed a certain threshold. The BO-kLB-CDP problem extends the Critical Disruption Path (CDP) problem introduced by Granata et al. in [Granata, D. and Steeger, G.

Variational methods for image segmentation try to recover a piecewise smooth function together with a discontinuity set which represents the boundaries of the segmentation. This paper deals with a variational method that constrains the formation of discontinuities along smooth contours. The functional to be minimized, which involves the computation of the geometrical properties of the boundaries, is approximated by a sequence of functionals which can be discretized in a straightforward way. Computer examples of real images are presented to illustrate the feasibility of the method.