The Editors of this volume were keen to discuss with Stanley Johnson some past, present and future core issues around Brexit how the UK has handled coronavirus pandemic. interview started in May 2021 during a conference on platform Microsoft Teams, titled “Post-Brexit political discourse at time COVID-19”, which Department Political Science University Bari Aldo Moro holds video. Two years on, w...

Figure 1. Anteroposterior view of the trunk with coa-lescing vesicobullous lesions.

For k ≥ 1, let I g (k) be the k term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k ≥ 1, there exists some Gk ≥ 0 such that I g (k) is generated by elements which are supported on subsurfaces whose genus is at most Gk. We also prove similar theorems for the Johnson filtration of Aut(Fn) and for certain mod-p analogu...

PrA∼D [∣∣‖Ax‖22 − 1∣∣ > ε] < δ. Lemma 2 implies Lemma 1, since we can set δ = 1/n2 then apply a union bound on the vectors (xi − xj)/‖xi − xj‖2 for all i < j. The first proof of Lemma 2 was given by [15]. Since then, several proofs have been given where D can be taken as a distribution over matrices with independent Gaussian or Bernoulli entries, or even more generally, Ω(log(1/δ))-wise indepen...

Definition 1.1 Let N(0, 1) denote the one dimensional normal distribution. This distribution has density n(x) = e−x 2/2/ √ 2π. LetNd(0, 1) denote the d-dimensional Gaussian distribution, induced by picking each coordinate independently from the standard normal distribution N(0, 1). Let Exp(λ) denote the exponential distribution, with parameter λ. The density function of the exponential distribu...