Related papers: Digital Shy Maps
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…
A common approach for describing classes of functions and probability measures on a topological space $\mathcal{X}$ is to construct a suitable map $\Phi$ from $\mathcal{X}$ into a vector space, where linear methods can be applied to address…
Complex, dynamic networks underlie many systems, and understanding these networks is the concern of a great span of important scientific and engineering problems. Quantitative description is crucial for this understanding yet, due to a…
This is an expository article about the topological theory of digital images, and a gamification of a research project.
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
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…
This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…
We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a…
Maps are an important medium that enable people to comprehensively understand the configuration of cultural activities and natural elements over different times and places. Although massive maps are available in the digital era, how to…
We describe the relation of $r$-similarity and finite-order invariants on the homotopy set $[S^1,Y]=\pi_1(Y)$.
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
In this article, we show how the recent statistical techniques developed in Topological Data Analysis for the Mapper algorithm can be extended and leveraged to formally define and statistically quantify the presence of topological…
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…
Digital terrain models (DTMs) are pivotal in remote sensing, cartography, and landscape management, requiring accurate surface representation and topological information restoration. While topology analysis traditionally relies on smooth…
This article examines the inverse problem for a lossy quantum graph that is internally excited and sensed. In particular, we supply an algorithmic methodology for deducing the topology and geometric structure of the underlying metric graph.…
We present a method for inferring dense depth maps from images and sparse depth measurements by leveraging synthetic data to learn the association of sparse point clouds with dense natural shapes, and using the image as evidence to validate…