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Spiraling and Folding: The Topological View
For every n , we construct two arcs in the plane that intersect at least n times and do not form spirals. The construction is in three stages: we...
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On the complexity of the theory of a computably presented metric structure
We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric...
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A complexity of compact 3-manifolds via immersed surfaces
We generalise the surface-complexity of closed 3-manifolds to the compact case. This generalisation preserves the (natural generalisation of the)...
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The Categorical Basis of Dynamical Entropy
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical...
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Variational Principle for Topological Pressure on Subsets of Free Semigroup Actions
We investigate the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure-theoretic pressure of Borel probability...
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Complexity of distances: Reductions of distances between metric and Banach spaces
We show that all the standard distances from metric geometry and functional analysis, such as Gromov—Hausdorff distance, Banach—Mazur distance,...
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Measuring the Formal Complexity of Architectural Curved Surfaces Based on 3D Box-Counting Dimension
In fractal structures, the box-counting dimension is used to characterize the un-evenness of geometric objects or spaces. In architecture it can be...
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Topological methods for symbolic discrepancy
In this lecture, we discuss the notion of bounded symbolic discrepancy for infinite words and subshifts, both for letters and factors, from a...
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Classical versus fractional difference equations: the logistic case
This paper aims to highlight the differences between two dynamical processes which produce similar bifurcation diagrams. We establish some...
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A topological shuttle between inequalities and pseudoinequalities
Topological procedures to relate pseudoinequalities that define a pseudovariety of ordered algebras with inequalities that ultimately define it, and...
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Mathematical analysis of topological and random m-order spread models
This paper focuses on the analysis of two particular models, from deterministic and random perspective respectively, for spreading processes. With a...
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Topological Complexity of Configuration Spaces of Fully Articulated Graphs and Banana Graphs
We determine the topological complexity of configuration spaces of graphs that are not necessarily trees, which was a crucial assumption in previous...
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A Topological Bound on the Cantor–Bendixson Rank of Meromorphic Differentials
In translation surfaces of finite area (corresponding to holomorphic differentials), directions of saddle connections are dense in the unit circle....
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Calculating the Mind Change Complexity of Learning Algebraic Structures
This paper studies algorithmic learning theory applied to algebraic structures. In previous papers, we have defined our framework, where a learner,...
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Topological Multiple Recurrence of Weakly Mixing Minimal Systems for Generalized Polynomials
Let ( X, T ) be a weakly mixing minimal system, p 1 , …, p d be integer-valued generalized polynomials and ( p 1 , p 2 , …, p d ) be non-degenerate. Then there...
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Topological Equisingularity: Old Problems from a New Perspective (with an Appendix by G.-M. Greuel and G. Pfister on SINGULAR)
Among the various notions of equisingularity and equivalence of singularities, topological equisingularity is one of the oldest an easiest to define,...