Mesh networks have become increasingly important because they can be easily implemented without much infrastructure and can support adequate bandwidth with a flexible multi-hop wireless communication among their routers serving the clients.
XZ=ZY is called the conjugacy equation. Given languages X and Y we are interested in knowing if there exists a non empty language Z which makes this equation true. This problem is undecidable in the general setting.
Suppose we have a polynomial $P$ in variables $X_1, \\ldots, X_n$ with coefficients from a field $F$, with total degree at most $d$. The polynomial $P$ is given in terms of some algebraic expression involving $X_1, \\ldots, X_n$.
I shall describe two approaches to the study of self-assembly. The first approach involves experiments with DNA molecules. We use DNA like a construction material --- akin to the uses of brick, cement, glass, etc. --- to form nanostructures.
Many stochastic systems are governed by events that, though they have a small probability of occurrence, are crucial to performance.
Large deviations is an asymptotic theory that allows
