The generic linear function ax + b of a real variable, with a, b, x ∈ R, is usually evaluated as a scale function (product) followed by a translation (sum). Our main result shows that when such a function is variously combined with rounding functions (floor and ceiling), exactly 67 inequivalent rounded generic linear functions result, of which 38 are integer-valued and 29 are not. Several relat...

Rounded-amoeboid cancer cells use actomyosin contractility driven by Rho-ROCK and JAK-STAT3 to migrate efficiently. It has been suggested that rounded-amoeboid cancer cells do not require matrix metalloproteinases (MMPs) to invade. Here we compare MMP levels in rounded-amoeboid and elongated-mesenchymal melanoma cells. Surprisingly, we find that rounded-amoeboid melanoma cells secrete higher le...

A lattice is called well-rounded, if its lattice vectors of minimal length span the ambient space. We show that there are interesting connections between the existence of well-rounded sublattices and coincidence site lattices (CSLs). Furthermore, we count the number of well-rounded sublattices for several planar lattices and give their asymptotic behaviour.