In the previous lecture, we showed that Shannon constructed a code, which was a one-to-one mapping, that took a stream of data X = (X1, ..., Xn) generated iid from a distribution P (X) over a finite alphabet A = (a1, ..., aA) of size A, and compressed it using ≈ nH(X) bits in total or ≈ H(X) bits per symbol, on average (for sufficiently large n). The code was based considering a special subset ...

introduction: in early typical language development, children understand words before they are able to use them in speech. children with autism spectrum disorders (asd) generally show impairments in both the comprehension and the production of language. however, the relative degree of delay or impairment in each of these sub-domains may also be atypical and remains less well-understood. materia...

AWract-The entropies and combinatorics of trees that branch according to fixed but finite numbers of rules are studied. Context-free grammars are used to categorize the ways in which nodes branch to yield daughter nodes, thus providing an organized setting to examine the entropies for random branching processes whose realizations are trees and whose probabilities are determined by probabilities...