Vertices arrive sequentially in space and are joined to existing vertices at random according to a preferential rule combining degree and spatial proximity. We investigate phase transitions in the ...

The Annals of Applied Probability, Vol. 28, No. 4 (August 2018), pp. 2003-2062 (60 pages) Given a graph, the popular “modularity” clustering method specifies a partition of the vertex set as the ...

These are not the kinds of objects that concern Scott Sheffield. Sheffield, a professor of mathematics at the Massachusetts Institute of Technology, studies shapes that are constructed by random ...

In Raiders of the Lost Ark, Indiana Jones must find a secret chamber that contains the legendary Ark of the Covenant. To identify its exact location, Indy must uncover a special map that’s only ...

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures. These are not the kinds of objects that concern Scott Sheffield.

Unveiling a new chapter in the understanding of human genetics, scientists have discovered a hidden geometric code within our DNA. This code, embedded in the three-dimensional structure of DNA, goes ...