Entries of a random matrix are random variables but a random matrix is equivalently considered as a probability measure on the set of matrices. A simple example of random matrix has independent identically distributed entries. In this paper random unitary matrices are studied whose entries must be correlated. A unitary matrix U = (Uij) is a matrix with complex entries and UU ∗ = UU = I. In term...

Given a sequence S of n symbols over some alphabet Σ of size σ, we develop new compression methods that are (i) very simple to implement; (ii) provide O(1) time random access to any symbol (or short substring) of the original sequence. Our simplest solution uses at most 2h + o(h) bits of space, where h = n(H0(S) + 1), and H0(S) is the zeroth-order empirical entropy of S. We discuss a number of ...

We consider random logic programs with two-literal rules and study their properties. In particular, we obtain results on the probability that random “sparse” and “dense” programs with two-literal rules have answer sets. We study experimentally how hard it is to compute answer sets of such programs. For programs that are constraint-free and purely negative we show that the easy-hard-easy pattern...