We give a permutation approach to validation (estimation of out-sample error). One typical use of validation is model selection. We establish the legitimacy of the proposed permut...
Ellul, Krawetz, Shallit and Wang prove an exponential lower bound on the size of any context-free grammar generating the language of all permutations over some alphabet. We genera...
A k-signed r-set on [n] = {1, ..., n} is an ordered pair (A, f), where A is an rsubset of [n] and f is a function from A to [k]. Families A1, ..., Ap are said to be cross-intersec...
Abstract—We derive a simple general parametric representation of the rate–distortion function of a memoryless source, where both the rate and the distortion are given by integr...
—In this paper, we propose a communication model of evolution and investigate its information-theoretic bounds. The process of evolution is modeled as the retransmission of infor...