Related papers: Simplification Techniques for Maps in Simplicial T…
In this paper, we introduce complexity-aware planning for finite-horizon deterministic finite automata with rewards as outputs, based on Kolmogorov complexity. Kolmogorov complexity is considered since it can detect computational…
The problem of representing a class of maps in a form suited for application of normal form methods is revisited. It is shown that using the methods of Lie series and of Lie transform a normal form algorithm is constructed in a…
Schematic maps are in daily use to show the connectivity of subway systems and to facilitate travellers to plan their journeys effectively. This study surveys up-to-date algorithmic approaches in order to give an overview of the state of…
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…
We present a new approach to equivariant version of the topological complexity, called a symmetric topological complexity. It seems that the presented approach is more adequate for the analysis of an impact of symmetry on the the motion…
We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex…
Without leaving finite mathematics and using finite topological spaces only, we give a definition of homeomorphisms of finite abstract simplicial complexes or finite graphs. Besides exploring the definition in various contexts, we add some…
Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…
The central problem in computational algebraic topology is the computation of the homotopy groups of a given space, represented as a simplicial set. Algorithms have been found which achieve this, but the running times depend on the size of…
The aim of the paper is to clarify the nature of combinatorial structures associated with maps on closed compact surfaces. We prove that maps give rise to Lagrangian matroids representable in a setting provided by cohomology of the surface…
We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to numeric computation as an optimization problem.…
A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to computing structured pseudospectra and their extremal points, and…
For a smooth family of exact forms on a smooth manifold, an algorithm for computing a primitive family smoothly dependent on parameters is given. The algorithm is presented in the context of a diagram chasing argument in the \v{C}ech-de…
We study motion planning algorithms for collision free control of multiple objects in the presence of moving obstacles. We compute the topological complexity of algorithms solving this problem. We apply topological tools and use information…
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some…
Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…
We study the problem of path planning with soft homology constraints on a surface topologically equivalent to a disk with punctures. Specifically, we propose an algorithm, named $\Hstar$, for the efficient computation of a path homologous…
The paper describes a general glance to the use of element exchange techniques for optimization over permutations. A multi-level description of problems is proposed which is a fundamental to understand nature and complexity of optimization…
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…
This article has two purposes. The first is to give an expository account of the integrable systems approach to harmonic maps from surfaces to Lie groups and symmetric spaces, focusing on spectral curves for harmonic 2-tori. The most…