We propose a generalization of higher-dimensional automata, partial HDA. Unlike HDA, and also extending event structures and Petri nets, partial HDA can model phenomena such as priorities or the disabling of an event by another event. Using open maps and unfoldings, we introduce a natural notion of (higher-dimensional) bisimilarity for partial HDA and relate it to history-preserving bisimilarit...

We introduce a new formalism of higher-dimensional timed automata, based on van Glabbeek’s higher-dimensional automata and Alur’s timed automata. We prove that their reachability is PSPACE-complete and can be decided using zone-based algorithms. We also show how to use tensor products to combat state-space explosion and how to extend the setting to higher-dimensional hybrid automata.

The aim of this paper is to present the notion of higher-dimensional syntax, which is a hierarchy of languages. Each term of a n-dimensional language will be typed by terms of the underlying n ? 1-dimensional language. This is an application of the emerging higher-dimensional category notions. On the lower dimensions live notions of syntax which are already known. So dimension zero corresponds ...

Lyubashenko has described enriched 2–categories as categories enriched over V–Cat, the 2–category of categories enriched over a symmetric monoidal V. Here I generalize this to a k–fold monoidal V. The latter is defined as by Balteanu, Fiedorowicz, Schwänzl and Vogt but with the addition of making visible the coherent associators α. The symmetric case can easily be recovered. The introduction of...

In 3-dimensional Euclidean space Scherk second surfaces are singly periodic embedded minimal surfaces with 4 planar ends. In this paper, we obtain a natural generalization of Scherk’s second surfaces in higher dimensional Euclidean spaces. In particular we show that, in higher dimensional Euclidean spaces R, for n ≥ 3, there exists n−1-periodic embedded minimal hypersurfaces with 4 hyperplanar ...

This paper describes a procedure to steer rapidly successive iterates of an initial condition on a chaotic attractor to a small target region about any prespecified point on the attractor using only small controlling perturbations. Such a procedure is called "targeting. " Previous work on targeting for chaotic attractors has been in the context of oneand two-dimensional maps. Here it is shown t...

Herein, with the aid of substantial symbolic computation, we solve previously open problems in the theory of n-dimensional box integrals Bn(s) := 〈|~r|〉; ~r ∈ [0, 1]. In particular we resolve an elusive integral called K5 that previously acted as a blockade against closed-form evaluation in n = 5 dimensions. In consequence we now know that Bn(integer) can be given a closed form for n = 1, 2, 3,...

The question of how distant starlight can be seen in a young Universe has received much attention within creationist research. But creationist cosmological models need to explain much else in addition to the passage of light across vast distances. On both large and small cosmic scales there is a diverse range of trends, patterns, and phenomena that beckon some kind of explanation. Many of these...