What if artificial intelligence (AI) could be used to spur discovery in areas such as biotechnology, drug discovery and fluid dynamics? Using geometric graphs and innovative methodologies, AI can ...

Six years ago, Afonso Bandeira and Shuyang Ling were attempting to come up with a better way to discern clusters in enormous data sets when they stumbled into a surreal world. Ling realized that the ...

Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established between two ...

This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...

This is a graduate topics course on learning in networks, focusing in particular on fundamental statistical and computational limits. Topics include the planted clique problem, community detection, ...

In the random geometric graph G(n, rn), n vertices are placed randomly in Euclidean d-space and edges are added between any pair of vertices distant at most rn from each other. We establish strong ...

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 ...