We study a generalisation of the Hatano-Nelson Hamiltonian in which a periodic modulation of the site energies is present in addition to the usual random distribution. The system can then become localized by disorder or develop a band gap, and the eigenspectrum shows a wide variety of...

Let S = (1/n) [Sigma]t=1n X(t) X(t)', where X(1), ..., X(n) are p - 1 random vectors with mean zero. When X(t) (t = 1, ..., n) are independently and identically distributed (i.i.d.) as multivariate normal with mean vector 0 and covariance matrix [Sigma], many authors have investigated the...

This paper deals with the problem of classifying a multivariate observation X into one of two populations [Pi]1: p(x; w(1)) [set membership, variant] S and [Pi]2: p(x; w(2)) [set membership, variant] S, where S is an exponential family of distributions and w(1) and w(2) are unknown parameters....