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.

Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s->1^- of the Gagliardo-Slobodeckij fractional seminorm are established in the Orlicz space setting. The results hold for fractional Orlicz-Sobolev spaces built upon general Young functions, as well. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation. An extended version of the Maz'ya-Shaposhnikova theorem on the limit as s->0^+ of the Gagliardo-Slobodeckij fractional seminorm is established in the Orlicz space setting.

We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^-, and of the Maz'ya-Shaposhnikova theorem on the limit as s-> 0^+ , dealing with classical fractional Sobolev spaces. As regards the limit as s->1^-, Young functions with an asymptotic linear growth are also considered in connection with the space of functions of bounded variation. Concerning the limit as s-> 0^+, Young functions fulfilling the \Delta_2-condition are admissible.

Asymptotically convolution Volterra equations are characterized by kernel functions which exponentially decay to convolution ones. Their importance in the applications motivates a numerical analysis of the asymptotic behavior of the solution. Here the quasi-convolution nature of the kernel is exploited in order to investigate the stability of .; / methods for general systems and in some particular cases.

Background and limitations Impaired wound healing (WH) and chronic inflammation are hallmarks of non-communicable diseases (NCDs). However, despite WH being a recognized player in NCDs, mainstream therapies focus on (un)targeted damping of the inflammatory response, leaving WH largely unaddressed, owing to three main factors. The first is the complexity of the pathway that links inflammation and wound healing; the second is the dual nature, local and systemic, of WH; and the third is the limited acknowledgement of genetic and contingent causes that disrupt physiologic progression of WH.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants.

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix's symmetry and the graphs' joint learning.

Unsupervised learning approaches are frequently employed to stratify patients into clinically relevant subgroups and to identify biomarkers such as disease-associated genes.

We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s ->1^-, and of the Maz'ya-Shaposhnikova theorem on the limit as s->0^-, dealing with classical fractional Sobolev spaces. As regards the limit as s ->1^-, Young functions with an asymptotic linear growth are also considered in connection with the space of functions of bounded variation. Concerning the limit as s->0^+, Young functions fulfilling the \Delta_2-condition are admissible.

The crack density within a fault's damage zone is thought to vary as seismic rupture is approached, as well as in the postseismic period. Moreover, external stress loads, seasonal or tidal, may also change the crack density in rocks, and all such processes can leave detectable signatures on seismic attenuation. Here we show that attenuation time histories from the San Andreas Fault at Parkfield are affected by seasonal loading cycles, as well as by 1.5-3-year periodic variations of creep rates, consistent with Turner et al.