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— Transmission of packets over computer networks is subject to packet-level errors, which appear as " bursts " of bit-level errors and are not well modeled by memoryless binary channels. Using a standard scrambling technique [1] transmission of packets can be modeled by the q-ary symmetric channel (q-SC) with alphabet size q and error probability p.(More)
We consider a path-following problem in which the goal is to ensure that the error between the system output and the geometric path be asymptotically less than a prespecified constant, while guaranteeing a forward motion along the path and boundedness of all states. A solution to this problem was given in [12] for a class of nonlinear systems and for paths(More)
As a model for multiscale systems under random influences on physical boundary, a stochastic partial differential equation under a fast random dynamical boundary condition is investigated. An effective equation is derived and justified by reducing the random dynamical boundary condition to a random static boundary condition. The effective system is still a(More)
We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a definable set. We prove that some consequences of Ramsey's Theorem for colorings of pairs could help in simplifying the(More)