Related papers: Digital Topological Complexity of Digital Maps
Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger…
Complex systems have become a popular lens for analyzing cities and complexity theory has many implications for urban performance and resilience. This paper develops a typology of measures and indicators for assessing the physical…
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
Topological spaces - such as classifying spaces, configuration spaces and spacetimes - often admit extra temporal structure. Qualitative invariants on such directed spaces often are more informative yet more difficult to calculate than…
Getting precise aspects of road through segmentation from remote sensing imagery is useful for many real-world applications such as autonomous vehicles, urban development and planning, and achieving sustainable development goals. Roads are…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
Spatial road networks have been widely employed to model the structure and connectivity of cities. In such representation, the question of spatial scale of the entities in the network, i.e. what its nodes and edges actually embody in…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.
Computing layer similarities is an important way of characterizing multiplex networks because various static properties and dynamic processes depend on the relationships between layers. We provide a taxonomy and experimental evaluation of…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of…
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…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…
Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…