We say that two free p.m.p. actions of countable groups are Shannon orbit equivalent if there is an equivalence between them whose associated cocycle partitions have finite entropy. show the acting sofic and each has a w-normal amenable subgroup which neither locally nor virtually cyclic then implies same maximum This extends result Austin beyond finitely generated setting consequence Bernoulli...

Abstract Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, artificial intelligence. The hidden processes they generate notoriously complicated, however, even if the chain is finite state: no expression for their Shannon entropy rate exists, as set predictive features generically infinite. As such, date ...

This paper explores the utility of a discrete singular convolution (DSC) algorithm for beam analysis. Regularized Shannon and Dirichlet kernels are selected to illustrate the present algorithm. Three classes of benchmark beam problems, including bending, vibration and buckling, are utilized to test numerical accuracy and speed of convergence of the present approach. Numerical experiments indica...