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.

Abstrat: Current garbage collectors leave much heap-allocated data uncollected because they preserve data reachable from a root set.