Related papers: Adding Machine Maps and Minimal Sets for Iterated …
We study contraction conditions for an iterated function system of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space,…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
We define a `tree of fusion systems' and give a sufficient condition for its completion to be saturated. We apply this result to enlarge an arbitrary fusion system by extending the automorphism groups of certain of its subgroups.
Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
An iterative map of the unit disc in the complex plane (Appendix) is used to explore certain aspects of selfdual, four dimensional gauge fields (quasi)periodic in the Euclidean time. These fields are characterized by two topological numbers…
We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…
A minimal system $(X,T)$ is topologically mildly mixing if all non-empty open subsets $U,V$, $\{n\in \Z: U\cap T^{-n}V\neq \emptyset\}$ is an IP$^*$-set. In this paper we show that if a minimal system is topologically mildly mixing, then it…
We study the connectedness locus $\mathcal{N}$ for the family of iterated function systems of pairs of homogeneous affine-linear maps in the plane. We prove this set is regular closed (i.e., it is the closure of its interior) away from the…
Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away.…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
Topological mating is an combination that takes two same-degree polynomials and produces a new map with dynamics inherited from this initial pair. This process frequently yields a map that is Thurston-equivalent to a rational map $F$ on the…
We study the topological complexity of work maps with respect to some subspaces of the configuration space and a workspace considered as the target set of the motion of robots. The motivation is to optimize and reduce the number of motion…
In this paper we analyze the relationship between o-minimal structures and the notion of \omega -saturated one dimensional t.t.t structures. We prove that if removing any point from such a structure splits it into more than one definably…
Understanding the topology of sublevel sets yields crucial insights into the optimization landscape of non-convex functions. If sublevel sets are connected, local search algorithms are less likely to be trapped in isolated valleys,…
This article presents a novel approach to identifying and classifying intersections for semantic and topological mapping. More specifically, the proposed novel approach has the merit of generating a semantically meaningful map containing…
Modern autonomous vehicles and robots utilize versatile sensors for localization and mapping. The fidelity of these maps is paramount, as an accurate environmental representation is a prerequisite for stable and precise localization. Factor…
We introduce two new characterizations of Meyer sets. A repetitive Delone set in $\R^d$ with finite local complexity is topologically conjugate to a Meyer set if and only if it has $d$ linearly independent topological eigenvalues, which is…
This paper brings cooperative protocols for multi-agent systems with agents having a finite state-space. Both scalar single-integrator consensus and general LTI systems synchronization are considered. Systems having a finite state-space…
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays…