113 citations · 136 across the 6 of their papers we have counts for
7 papers
Powers of Karpelevic arcs and their Sparsest Realising matrices
Priyanka Joshi, Stephen Kirkland, Helena Smigoc
The region in the complex plane containing the eigenvalues of all stochastic matrices of order n was described by Karpelevic in 1988, and it is since then known as the Karpelevic r…
Edge Addition and the Change in Kemeny's Constant
Stephen Kirkland, Yuqiao Li, John McAlister +1
Given a connected graph , Kemeny's constant measures the average travel time for a random walk to reach a randomly selected vertex. It is known that when an e…
State Transfer on Paths with Weighted Loops
Stephen Kirkland, Christopher M. van Bommel
We consider the fidelity of state transfer on an unweighted path on vertices, where a loop of weight has been appended at each of the end vertices. It is known that if …
Stochastic Matrices Realising the Boundary of the Karpelevi\v c Region
Stephen Kirkland, Helena Šmigoc
A celebrated result of Karpelevi\v c describes the collection of all eigenvalues arising from the stochastic matrices of order The boundary of consists of roots o…
alpha-Kuramoto partitions: graph partitions from the frustrated Kuramoto model generalise equitable partitions
Stephen Kirkland, Simone Severini
The Kuramoto model describes the collective dynamics of a system of coupled oscillators. An alpha-Kuramoto partition is a graph partition induced by the Kuramoto model, when the os…
Number-Theoretic Nature of Communication in Quantum Spin Systems
Chris Godsil, Stephen Kirkland, Simone Severini +1
The last decade has witnessed substantial interest in protocols for transferring information on networks of quantum mechanical objects. A variety of control methods and network top…
Spin systems dynamics and faults detection in threshold networks
Steve Kirkland, Simone Severini
We consider an agent on a fixed but arbitrary node of a known threshold network, with the task of detecting an unknown missing link/node. We obtain analytic formulas for the probab…