Bezem, Coquand, and Huber have recently given a constructively valid model of higher type theory in a category of nominal cubical sets satisfying a novel condition, called the uniform Kan condition (UKC), which generalizes the standard cubical Kan condition (as considered by, for example, Williamson in his survey of combinatorial homotopy theory) to admit phantom “additional” dimensions in open...

In this paper we describe a model of concurrency enjoying an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with neither loops nor branchings. Such programs are given a semantics using cubical areas that we call geometric. The collection of all cubical areas admits a structure of tensor product in the c...

We establish sufficient conditions implying semistability and connectivity at infinity properties for CAT(0) cubical complexes. We use this, along with the geometry of cubical K(π, 1)’s to give a complete description of the higher connectivity at infinity properties of right angled Artin groups. Among other things, this determines which right angled Artin groups are duality groups. Applications...

Title of Document: SEPARATING THE EFFECTS OF GROUP SIZE, DENSITY, AND ENCLOSURE SIZE ON MOVEMENT AND USE OF SPACE IN DOMESTIC FOWL (Gallus gallus domesticus) Erin Hoerl Leone, Ph.D., 2008 Directed By: Professor Inmaculada Estevez, Department of Animal and Avian Science This project was designed to separate the confounded effects of group size, density, and enclosure size, and to examine the rol...

Cubical type theory provides a constructive justification of homotopy theory. A crucial ingredient cubical is path lifting operation which explained computationally by induction on the involving several non-canonical choices. We present in this article two canonicity results, both proved sconing argument: result, every natural number equal to numeral, even if we take away equations defining str...