What is the minimum possible number of vertices of a graph that contains every k-vertex graph as an induced subgraph? What is the minimum possible number of edges in a graph that contains every k-vertex graph with maximum degree 3 as a subgraph? These questions and related one were initiated by Rado in the 60s,…

In many practical applications information is conveyed by means of electromagnetic radiation and a natural question concerns the fundamental limits of this process. Identifying information with entropy, one can ask about the maximum amount of entropy associated to the propagating wave. The standard statistical physics approach to compute entropy is to take the logarithm of…

In the past couple of decades, non-smooth convex optimization has emerged as a powerful tool for the recovery of structured signals (sparse, low rank, finite constellation, etc.) from possibly noisy measurements in a variety applications in statistics, signal processing and machine learning. While the algorithms (basis pursuit, LASSO, etc.) are often fairly well established, rigorous…