This talk focuses on how to compress blocks of streaming video data into weighted finite automata, how to improve the compression ratio by changing the underlying automaton, methods of parallel decompression and which types of video streams can effectively be compressed. Algorithm for constructing two sequences of functions that are solutions of periodic boundary value problems for linear impulsive differential-difference equations is suggested. It is proved that these functions are lower and upper solutions of the given nonlinear problem and the sequences are convergent to the unique solution. It is shown that the convergence is quadratic. Increasing attention has developed in recent years in obtaining more realistic and applicable models where alternatives to the assumption of independence are considered.
Negative dependence is one alternative to the usual assumption of independence.
This talk will be a survey of recent laws of large numbers and central limit theorems for negatively dependence random variables. The classical results for independent random variables will be used a template for comparisons of results for negatively dependent random variables, and examples will be provided to illustrate the differences in the results as well as the sharpness of the results. It is well known that a self-similar measure is either absolutely continuous or purely singular with respect to Lebesgue measure. However, it is very difficult to determine the dichotomy. This problem has been studied for a long time in connection with the classical infinite Bernoulli convolutions.