The threshold model is widely used to study the propagation of opinions and technologies in social networks. In this model individuals adopt the new behavior based on how many neighbors have already chosen it.

We develop new techniques for rounding packing integer programs using iterative randomized rounding. It is based on a novel application of multidimensional Brownian motion in $\mathbb{R}^n$.

We introduce a new information-theoretic complexity measure IC∞ for 2-party functions which is a lower-bound on communication complexity, and has the two leading lower-bounds on communication complexity as its natural relaxations: (external) infor

One of the basic questions in complexity theory is how the complexity of computing $k$ instances of a function relates to the complexity of computing a single instance.

The compactness theorem states that there is a model for an infinite set S of propositional formulas, if and only if, there is a model for every finite subset of S.