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Higher analogues of discrete topological complexity
In this paper, we introduce the n th discrete topological complexity and study its properties such as its relation with simplicial...
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Group actions and higher topological complexity of lens spaces
In this paper, we obtain an upper bound on the higher topological complexity of the total spaces of fibrations. As an application, we improve the...
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Topological Complexity: Entropy Point, Metric Mean Dimension in Control Systems
We introduce two new notions to describe the topological complexity of control systems. We first introduce a notion called entropy point to...
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On the LS-category and topological complexity of projective product spaces
We determine the Lusternik-Schnirelmann category of the projective product spaces introduced by D. Davis. We also obtain an upper bound for the...
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Geodesic complexity of a cube
The topological (resp. geodesic) complexity of a topological (resp. metric) space is roughly the smallest number of continuous rules required to...
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The pressure of intricacy and average sample complexity for amenable group actions
Let ( X , G ) be a G -system, where G is an infinite countable discrete amenable group and X is a compact metric space with a metric d . In this paper, we...
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A Topological Approach to Vortex Knots and Links
Here we review some recent developments in the topological study of vortex knots and links. We start from fundamental properties of kinetic helicity,...
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Khovanov homology, wedges of spheres and complexity
Our main result has topological, combinatorial and computational flavor. It is motivated by a fundamental conjecture stating that computing Khovanov...
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Topological Entropy of Iterated Set-Valued Dynamical Systems
This paper studies topological entropy and pseudo-entropy of iterated set-valued function systems. Firstly, the notions of topological entropy...
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Quantum Fibrations: Quantum Computation on an Arbitrary Topological Space
Using operator algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space. Quantum...
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Fast topological signal identification and persistent cohomological cycle matching
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are...
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Brain chains as topological signatures for Alzheimer’s disease
Topology is providing new insights for neuroscience. For instance, graphs, simplicial complexes, directed graphs, flag complexes, persistent homology...
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Localized Topological Pressure for Random Dynamical Systems
This paper is devote to the investigation of fiber localized topological pressure for random dynamical systems. By establishing Katok’s pressure...
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Topological Art in Simple Galleries
Let P be a simple polygon, then the art gallery problem is looking for a minimum set of points (guards) that can see every point in P . We say two...
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Topological representations of simplicial complexes and their applications
Topological models can be used to represent complex systems which originate in the real life world. The aim of this paper is to show the equivalence...
