The least-mean-squares (LMS) algorithm is analysed as a feedback control system. It is shown that despite the fact that LMS is a time-variant system that in fact it behaves much as a linear time-invariant (LTI) closed-loop control system. Therefore, it is possible to treat the LMS algorithm as a control system in the classical sense and define properties such as bandwidth to determine how fast ...

We study actions of countable discrete groups which are amenable in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups of amenable actions which allow us to relate the first `-Betti number of G with that of the stabilizer subgroups. An analogous relationship is also shown to ...