Suppose you are trying to build a circuit using limited number of AND, OR, NOT gates to compute some boolean function $f$ over inputs in $\{0,1\}^n$.

In this talk, we will see how to use variational inequalities to solve a particular optimal stopping problem under certain conditions on the underlying diffusion processes.

To describe searching in its simplest abstract setting, suppose we have some accumulated data (called the 'file') and some new data item (called the 'sample'). Then, searching consists of relating the sample to the file.

I will introduce a very simple social interaction model of information transmission, opinion formation and consensus formation by De Groot. We will study sufficient and necessary conditions to converge to a consensus in very simple networks.

Determining the chromatic number of a graph is known to be NP-hard. We will consider the problem of coloring a $k$-colorable graph on n vertices with $n^{\alpha}$ colors (where $\alpha < 1$).