Markets are of course, one of the oldest mechanism of exchanging commodities and cultural artifacts. While their history is over 5000 years old, their mathematical theory is rather recent. The first such models were by Fisher and Walras.
How does one partition the vertex set of a graph into two parts $(S,S^C)$, so that the ratio of edges going across to the Volume (number of edges incident on vertices in S) in the vertex set is as small as possible?
Web Usage Mining is the application of data mining techniques for discovery and analysis of user access patterns from the interaction generated by the users in the form of access logs, proxy-server logs, browser logs, etc.
In information theory rate distortion addresses the problem of determining the minimal number of bits per symbol, as measured by the rate $R$, that should be communicated over a channel, so that the source (input signal) can be approximately recon
In an atomic splittable routing game, each player controls a non-negligible, splittable flow in a network. Each edge has a delay that is a function of the total flow on the edge.
The method of variation of parameters, credited to J.L. Lagrange, expresses each solution of the perturbed system of differential equations, $x' = A(t)x + f(t)$, in terms of the solution of the associated homogeneous system, $y' = A(t)y$.
Inefficient use of radio spectrum is becoming a serious problem as more and more wireless systems are being developed to operate in crowded spectrum bands.
Human interaction is central to many computing systems that require a high level of assurance. We term such systems as "high-confidence interactive systems".
