This paper reports from a user requirement, design and evaluation study on supporting collaborative learning by visual perception in the medical education domain. Establishing the user requirements has been based on the Cognitive Systems Engineering approach. The user requirements laid the foundation for designing the software system CANTOR (Converging Agreement by Networking Telematics for Obj...

We prove that for any separable Banach space X, there exists a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space contains a complemented subspace isomorphic to X. As a consequence we give an example of a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space fails the approximation property and we prove that ther...

A ‘symbolic dynamical system’ is a continuous transformation Φ : X−→X of closed perfect subset X ⊆ A, where A is a finite set and V is countable. (Examples include subshifts, odometers, cellular automata, and automaton networks.) The function Φ induces a directed graph structure on V, whose geometry reveals information about the dynamical system (X ,Φ). The ‘dimension’ dim(V) is an exponent des...

We review some aspects of the spectral theory of the Almost Mathieu operator (acting on`2 (Z)): where ; ; 2 R. We concentrate on the spectrum as a set, and describe the partial results obtained so far on the conjectures that, for irrational , it is a Cantor set and has Lebesgue measure j4 ? 2jjj.

First, we answer a question of Pestov, by proving that the full group of a sofic equivalence relation is a sofic group. Then, we give a short proof of the theorem of Grigorchuk and Medynets that the topological full group of a minimal Cantor homeomorphism is LEF. Finally, we show that for certain non-amenable groups all the generalized lamplighter groups are sofic.

In this paper we study conditions under which a free minimal Zaction on the Cantor set is a topological extension of the action of d rotations, either on the product T of d 1-tori or on a single 1-torus T. We extend the notion of linearly recurrent systems defined for Z-actions on the Cantor set to Z-actions and we derive in this more general setting, a necessary and sufficient condition, which...

We describe all possible ways of bi-ordering Thompson group F: its space of bi-orderings is made up of eight isolated points and four canonical copies of the Cantor set.

We specify exactly which groups can act geometrically on CAT(0) spaces whose visual boundary is homeomorphic to either a circle or a suspension of a Cantor set.

We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We introduce here a larger class of condensation groups, called infinitely independently presentable groups, and establish criteria which allow one to infer that ...

The study of properties for the patterns obtained when two Cantor grids are superimposed is important for establishing the relationships between the geometry of each fractal grating and the corresponding structure of the superposition. Here, we obtain the mathematical expressions for the characteristic parameters (period and direction of fringes) for the moiré effect, when Cantor grids, built w...