Related papers: Simplification Techniques for Maps in Simplicial T…
A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations of closed orientable surfaces. Those surfaces arise as the…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
Coverage path planning is a fundamental challenge in robotics, with diverse applications in aerial surveillance, manufacturing, cleaning, inspection, agriculture, and more. The main objective is to devise a trajectory for an agent that…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
Complexity one spaces are an important class of examples in symplectic geometry. Karshon and Tolman classify them in terms of combinatorial and topological data. In this paper, we compute the equivariant cohomology for any complexity one…
High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…
We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams.
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the `coarse' underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has…
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines,…
We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…
Affordances have been introduced in literature as action opportunities that objects offer, and used in robotics to semantically represent their interconnection. However, when considering an environment instead of an object, the problem…
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…
A novel algorithm for creating a mathematical model of curved shapes is introduced. The core of the algorithm is based on building a graph representation of the contoured image, which occupies less storage space than produced by raster…
It is declared that the aim of simplifying representations of coefficients of power series of classical statistical mechanics is to simplify a process of obtaining estimates of the coefficients using their simplified representations. The…
We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On…
Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…
A simple algorithm with quasi-linear time complexity and linear space complexity for the evaluation of the hypergeometric series with rational coefficients is constructed. It is shown that this algorithm is suitable in practical informatics…
We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some…
We give a particular choice of the higher Eilenberg-MacLane maps by a recursive formula.This choice leads to a simple description of the homotopy operations for simplicial Z/2-algebras.