Suppose you want to find the least congested route in an ad hoc network. Each link's rate is unknown and stochastic, and each time you get to see the minimum rate (i.e., bottleneck) along any route you pick.
Networks of chemical reactions have natural underlying combinatorial structure, allowing them to be represented as graphs or digraphs, perhaps with additional vertex or edge colourings/labellings.
In this talk we will discuss about the role played by smooth Renyi quantities in non-asymptotic information theory. In particular, we will discuss about various source coding and channel coding problems in the non-asymptotic regime.
We analyze large random matching markets with unequal numbers of men and women. We find that being on the short side of the market confers a large advantage.
We present a new approach to showing that random graphs are nearly optimal expanders. This approach is based on deep results from combinatorial group theory. It applies both to regular and irregular random graphs.
