Related papers: Continuity up to a Covering and Connectedness
In this work, we will introduce the notion of generalized topological groups using generalized topological structure and generalized continuity defined by ?A. Cs?asz?ar [2]. We will discuss some basic properties of this kind of structures…
Inspired by the concept of hyperconvexity and its relation to curvature, we translate geometric properties of a metric space encoded by the curvature inequalities into the persistent homology induced by the \v{C}ech filtration of that…
We investigate and quantify the interplay between topology and ability to send specific signals in complex networks. We find that in a majority of investigated real-world networks the ability to communicate is favored by the network…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions…
Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space…
The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
In the literature, various types of points and meager sets whose complements are connected have been studied, such as colocally connected points, non-weak cut points/sets, non-block points/sets, shore points/sets, etc. We extend that study,…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…
Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly.…
We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…
The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…
We study the problem of controlling a general complex network towards an assigned synchronous evolution, by means of a pinning control strategy. We define the pinning-controllability of the network in terms of the spectral properties of an…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…
Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the…