Alice and Bob want to hold a conversation over a noisy channel on which adversarially chosen bits may be flipped. How can they communicate robustly despite such an attack?

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 will show that there is a family of n- variate polynomials of degree d = O(log^2 n), which can be computed by linear sized homogeneous depth-5 arithmetic circuits, where as any homogeneous depth-4 circuit computing it must have size at least n^

A set function on a ground set of size n is approximately modular if it satisfies every modularity requirement to within an additive error;approximate modularity is the set analog of approximate linearity.

Abstract: A threshold gate is a Boolean function that accepts its input based on whether some weighted linear combination of its inputs exceeds some fixed threshold value or not. A threshold circuit is a circuit made up of threshold gates.