Related papers: The Topological Complexity of Spaces of Digital Jo…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
Tropical geometry is a relatively recent field in mathematics created as a simplified model for certain problems in algebraic geometry. We introduce the definition of abstract and planar tropical curves as well as their properties,…
The paper proves a result on the convergence of discrete conformal maps to the Riemann mappings for Jordan domains. It is a counterpart of Rodin-Sullivan's theorem on convergence of circle packing mappings to the Riemann mapping in the new…
Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…
We investigate online network topology identification from smooth nodal observations acquired in a streaming fashion. Different from non-adaptive batch solutions, our distinctive goal is to track the (possibly) dynamic adjacency matrix with…
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…
In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are…
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
Topological photonics provides a robust and flexible platform for controlling light, enabling functionalities such as backscattering-immune edge transport and slow-light propagation. In this work, we design and characterize photonic…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we…
The Fr\'echet distance is a computational mainstay for comparing polygonal curves. The Fr\'echet distance under translation, which is a translation invariant version, considers the similarity of two curves independent of their location in…
While the dynamics of transcendental entire functions in periodic Fatou components and in multiply connected wandering domains are well understood, the dynamics in simply connected wandering domains have so far eluded classification. We…
Topological states in photonics offer novel prospects for guiding and manipulating photons and facilitate the development of modern optical components for a variety of applications. Over the past few years, photonic topology physics has…
A fundamental problem in computer vision is boundary estimation, where the goal is to delineate the boundary of objects in an image. In this paper, we propose a method which jointly incorporates geometric and topological information within…
We establish sharp upper bounds for the topological complexity of motion planning problem in spaces with small fundamental group, i.e. when it is finite of small order or has small cohomological dimension.
In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…