Universities, economic development and ‘levelling up’ – how can universities make a positive impact on their local areas?

Based on the findings of a recent report into the ways in which higher education institutions contribute to the development of their local regions. Mark Tewdwr-Jones and Louise Kempton, discuss the complexity of aligning the goals of higher education to regional economic initiatives, such as the UK government’s levelling up agenda. They also highlight how good policy for productive regional engagements, is long-term, recognises diversity within regions and higher education and cuts a balance between universities as important, but not always central, actors in regional development

Zero Forcing on 2-connected Outerplanar Graphs

We determine upper and lower bounds on the zero forcing number of 2-connected outerplanar graphs in terms of the structure of the weak dual. We show that the upper bound is always at most half the number of vertices of the graph. This work generalizes work of Hern\'andez, Ranilla and Ranilla-Cortina who proved a similar result for maximal outerplanar graphs

Non-Backtracking Random Walks and a Weighted Ihara’s Theorem

We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-backtracking walk to the transition matrix for the usual random walk. This allows us to determine the spectrum of the transition probability matrix of a non-backtracking random walk in the case of regular graphs and biregular graphs. As a corollary, we obtain a result of Alon et. al. in [1] that in most cases, a nonbacktracking random walk on a regular graph has a faster mixing rate than the usual random walk. In addition, we obtain an analogous result for biregular graphs.Mathematic