Calcium ion is the ubiquitous messenger in cells and plays a key role in neuronal signaling and fusion of synaptic vesicles. These vesicles are typically ∼20-50 nm in diameter, and thus their interaction with calcium ions cannot be modeled faithfully with a conventional flat membrane bilayer setup. Within our newly developed molecular dynamics simulations setup, we characterize here interaction...

The notion of a negatively curved group is at first highly non-intuitive because it links two areas of mathematics that are not usually associated with one another. Curvature is generally a property that we associate with geometric objects like curves or surfaces in R, while a group is an algebraic structure that we associate with objects like integers or matrices. However, there is a way to de...

There are three essential ideas underlying general relativity (GR). The first is that spacetime may be described as a curved, four-dimensional mathematical structure called a pseudo-Riemannian manifold. In brief, time and space together comprise a curved fourdimensional non-Euclidean geometry. Consequently, the practitioner of GR must be familiar with the fundamental geometrical properties of c...

Let P be a non positively curved polygon of nite groups The group P acts on a contractible complex XP and we prove that this complex is a building if and only if the links have angular diameter When P has zero group theoretic curvature a geometric argument shows that the periodic apartments are dense in the set of all apartments