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#### Complete multipartite graphs and Braess edges

(Linear Algebra and its Applications 579, 284-301., 2019)

Given an irreducible stochastic matrix T, Kemeny's constant k(T)
measures the expected number of steps from any initial state to a
randomly chosen final state, and is thus regarded as an indicator of
the overall transit ...

#### Estimating random walk centrality in networks

(Computational Statistics & Data Analysis 138, pp. 190-200., 2019)

Random walk centrality (equivalently, the accessibility index) for the states of a time-homogeneous irreducible Markov chain on a finite state space is considered. It is known that the accessibility index for a particular ...

#### Switching and partially switching the hypercube while maintaining perfect state transfer

(Quantum Information and Computation 19, 0541-0554., 2019)

A graph is said to exhibit perfect state transfer (PST) if one of its corresponding Hamiltonian matrices, which are based on the vertex-edge structure of the graph, gives rise to PST in a quantum information-theoretic ...

#### Perfect quantum state transfer in weighted paths with potentials (loops) using orthogonal polynomials

(Linear and Multilinear Algebra 67, pp. 1043-1061., 2019)

A simple method for transmitting quantum states within a quantum computer is via a quantum spin chain – that is, a path on n vertices. Unweighted paths are of limited use, and so a natural generalization is to consider ...

#### Number of source patches required for population persistence in a source-sink metapopulation with explicit movement

(Bulletin of Mathematical Biology 81, pp. 1916–1942., 2019)

We consider a simple metapopulation model with explicit movement of individuals between patches, in which each patch is either a source or a sink. We prove that similarly to the case of patch occupancy metapopulations with ...