Editorial Introduction to the Special Issue: Math Circles in Times of Physical Distancing

Editorial Introduction to the Journal of Math Circles Special Issue

Approaches to modelling the shape of nanocrystals.

Unlike in the bulk, at the nanoscale shape dictates properties. The imperative to understand and predict nanocrystal shape led to the development, over several decades, of a large number of mathematical models and, later, their software implementations. In this review, the various mathematical approaches used to model crystal shapes are first overviewed, from the century-old Wulff construction to the year-old (2020) approach to describe supported twinned nanocrystals, together with a discussion and disambiguation of the terminology. Then, the multitude of published software implementations of these Wulff-based shape models are described in detail, describing their technical aspects, advantages and limitations. Finally, a discussion of the scientific applications of shape models to either predict shape or use shape to deduce thermodynamic and/or kinetic parameters is offered, followed by a conclusion. This review provides a guide for scientists looking to model crystal shape in a field where ever-increasingly complex crystal shapes and compositions are required to fulfil the exciting promises of nanotechnology

“Stealth” tumors: Breast cancer cells shun NK-cells anti-tumor immunity

Breast cancers (BCs) comprise heterogeneous subtypes of various prognoses. An active anti-tumor immune profile usually correlated with a better survival. Two current major challenges of BC research are to understand the inter-relations between BC and anti-tumor immunity, and to identify candidates whose targeting would contribute to enhance anti-tumor efficiency

Cerebral Sinus Thrombosis: A Fatal Neurological Complication of Ulcerative Colitis

Cerebral sinus thrombosis has been reported as an uncommon complication of ulcerative colitis (UC), occurring in up to 7.5% of cases. It is suspected to be a consequence of genetic predisposition and the hypercoagulable state occurring during disease relapse. We report a case of a 23-year-old male patient with one-year history of UC. He presented to the Emergency Room with left-sided progressive hemiparesis, numbness, hemiparesthesia, and pain, which followed a recent exacerbation of UC. The patient died 3 days after admission and an autopsy revealed superior and inferior sagittal sinus and cortical vein thrombosis with associated cerebral edema, hemorrhagic infarction, and herniation. The gastrointestinal tract had continuous cobblestone appearance extending from rectum to cecum, with hemorrhage and ulceration, consistent with active UC. Awareness of this rare complication of UC can contribute to early recognition and attempts at treatment of this serious and often fatal condition