Related papers: Topological complexity of the work map
In this paper we introduce the concepts of higher equivariant and invariant topological complexity; and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We…
Topological complexity $\TC{B}$ of a space $B$ is introduced by M. Farber to measure how much complex the space is, which is first considered on a configuration space of a motion planning of a robot arm. We also consider a stronger version…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
In classical spin systems with two largely different inherent time scales, the configuration of the fast spins almost instantaneously follows the slow-spin dynamics. We develop the emergent effective theory for the slow-spin degrees of…
We define the notion of near geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter's notion of geodesic complexity to non-geodesic spaces. This has potential application to topological…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
Multi-robot Motion Planning (MRMP) is an active research field which has gained attention over the years. MRMP has significant roles to improve the efficiency and reliability of multi-robot system in a wide range of applications from…
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…
Modern computer networks support interesting new routing models in which traffic flows from a source s to a destination t can be flexibly steered through a sequence of waypoints, such as (hardware) middleboxes or (virtualized) network…
Farber and Rudyak introduced topological complexity $\mathbf{TC}(X)$ of motion planning and its higher analogs $\mathbf{TC}_n(X)$ to measure the complexity of assigning paths to point tuples. Motivated by motion planning where a robotic…
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
Mapping is an essential task for mobile robots and topological representation often works as a basis for the various applications. In this paper, a novel framework that can build topological maps incrementally is proposed. The algorithm is…
We determine the topological complexity of unordered configuration spaces on almost all punctured surfaces (both orientable and non-orientable). We also give improved bounds for the topological complexity of unordered configuration spaces…
A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…