E-Mail IMAGE: Topology-based machine learning classifies how human cells organize into spatial patterns based on the presence of persistent topological loops around empty regions, which can be used to infer cellular behaviors... view more Credit: Wong lab/Brown University PROVIDENCE, R.I. [Brown University] -- The field of mathematical topology is often described in terms of donuts and pretzels. To most of us, the two differ in the way they taste or in their compatibility with morning coffee. But to a topologist, the only difference between the two is that one has a single hole and the other has three. There's no way to stretch or contort a donut to make it look like a pretzel -- at least not without ripping it or pasting different parts together, both of which are verboten in topology. The different number of holes make two shapes that are fundamentally, inexorably different.