Fermionic QFT, Grassmann calculus, and combinatorics

In the first section of this chapter, we use Grassmann calculus, used in fermionic QFT, to give, first a reformulation of the Lingström–Gesse–Viennot lemma proof. We further show that this proof generalizes to graphs with cycles. We then use the same Grassmann calculus techniques to give new proofs of Stembridge's identities relating appropriate graph Pfaffians to sum over non-intersecting paths. The results presented here go further than the ones of Stembridge, because Grassmann algebra techniques naturally extend (without any cost!) to graphs with cycles. We thus obtain, instead of sums over non-intersecting paths, sums over non-intersecting paths and non-intersecting cycles. In the fifth section of the chapter, we give a generalization of these results. In the sixth section of this chapter we use Grassmann calculus to exhibit the relation between a multivariate version of Tutte polynomial and the Kirchhoff-Symanzik polynomials of the parametric representation of Feynman integrals, polynomials already introduced in Chapters 1 and Chapter 3.

Building Pandemic Resilience in Design: Space and Movement in Art Museums during Covid-19

The global pandemic of COVID-19 has posed challenges in relation to how buildings re-open to use, particularly buildings attracting large numbers of visitors, such as museums and galleries. As these institutions start to reopen across the UK and internationally, a number of social distance measures have been adopted in order to safely bring people into their premises and access their collections. Building on Bill Hillier’s theorical model of spatial types and spatial structures (2019), we explore the spatial-curatorial changes implicated in the re-opening of four art museums (The National Gallery, The Tate Britain and Tate Modern in London) and one American museum (The MoMA, New York). Our purpose is not to provide practical solutions, but to set the search for spatial approaches to the re-opening of museums within a theory of spatial structure in space syntax theory and inform the design future of public buildings. We present a model of a three-layered spatial system interfacing the global and local structure of these buildings. We argue that the presence of intersecting cycles of movement in spatial layouts determines their capability for adapting to the one-way routes imposed by the pandemic. The spatial organisation of the display is a second factor influencing the reopening strategies, either limiting or optimising available spatial sequences to meet curatorial criteria.