Given a graph $G$, let $\mathbb{P}_G$ denote the cone of positive semidefinite (psd) matrices, with non-negative entries, and zeros according to $G$. Which powers preserve psd-ness when applied entrywise to all matrices in $\mathbb{P}_G$?

We study the logistics system of eukaryotic cells, whose warehouses are micron-scale "organelles" and whose trucks are 10-nanometer-scale "vesicles". Organelles form the nodes and vesicle fluxes form the edges of a transport graph.

In a reasonable topological space, large deviation estimates essentially deal with probabilities of events that are asymptotically (exponentially) small, and in a certain sense, quantify the rate of these decaying probabilities.

In many applications such as cloud computing, managing server farm resources etc. an incoming task or job has to be matched with an appropriate server in order to minimise the latency or blocking associated with the processing.

We provide a systematic method for solving general Principal-Agent problems.