by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

In this article, network science is discussed from a methodological perspective, and two central theses are defended. The first is that network science exploits the very properties that make a system complex. Rather than using idealization techniques to strip those properties away, as is standard practice in other areas of science, network science brings them to the fore, and uses them to furni...

Let a “complex probability” be a normalizable complex distribution P (x) defined on R. A real and positive probability distribution p(z), defined on the complex plane C, is said to be a positive representation of P (x) if 〈Q(x)〉P = 〈Q(z)〉p, where Q(x) is any polynomial in R D and Q(z) its analytical extension on C. In this paper it is shown that every complex probability admits a real represent...