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20 Dec 2019: Here we describe the concept of quasi-reversibility, provide new examples of quasi-reversible nodes, discuss the range of arrival rates for which a node remains quasi-reversible, and analyse a

14 Nov 2019: You may need to read slightly ahead of the lectures to do the questions on theIsing and random-cluster models, but nothing new is needed beyond the requireddefinitions.

10 Nov 2019: A further outstanding question for explicit congestion control is the scale of the step-change in rate that is necessary at a resource to accommodate a new flow.

22 May 2019: systems, ‘influence’ requires a new definition, and this is provided in [19, 20]in the context of the Ising and random-cluster models (see [22]).

5 Dec 2019: Therefore, y ̸= z2, and hence y is a ‘new’ vertex, and z = w1. ... Since G is infinite, it containssome ‘new’ edge e with exactly one endpoint in S.