We prove da Silva’s 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space. It follows from this result and a result of the third author that the positive matroid Grassmannian (or positive MacPhersonian) is homeomorphic to a closed ball.

Connector-Centric Design (XCD) is centred around a new formal architectural description language, focusing mainly on complex connectors. Inspired by Wright and BIP, XCD aims to cleanly separate in a modular manner the high-level functional, interaction, and control system behaviours. This can aid in both increasing the understandability of architectural specifications and the reusability of com...

We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) S when the measures are indexed by another poset A. We give counterexamples to show that the two notions are not always equivalent, but for various large classes of S we also present conditions on the poset A that are necessary and s...

A list of complex numbers is realizable if it is the spectrum of a nonnegative matrix. In 1949 Sulěımanova posed the nonnegative inverse eigenvalue problem (NIEP): the problem of determining which lists of complex numbers are realizable. The version for reals of the NIEP (RNIEP) asks for realizable lists of real numbers. In the literature there are many sufficient conditions or criteria for lis...

Let D be a digraph on [Formula: see text]. Then the sequence [Formula: see text] is called the degree sequence of D. For any given sequence of pairs of integers [Formula: see text], if there exists a k-arc strongly connected digraph D such that d is the degree sequence of D, then d is realizable and D is a realization of d. In this paper, characterizations for k-arc-connected realizable sequenc...