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Contour maps are an essential tool for exploring spatial features of the terrain, such as distance, directions, and surface gradient among the contour areas. User interactions in contour-based visualizations create approaches to visual…
Non-terrestrial networks (NTNs) are anticipated to be indispensable in extending coverage and enabling global communication access in next-generation wireless networks. With the extensive deployment of non-terrestrial platforms, evaluating…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
We test the hypothesis whether transforming a data matrix into a 3D shaded surface or even a volumetric display can be more appealing to humans than a scatterplot since it makes direct use of the innate 3D scene understanding capabilities…
A fundamental challenge in text-to-3D face generation is achieving high-quality geometry. The core difficulty lies in the arbitrary and intricate distribution of vertices in 3D space, making it challenging for existing models to establish…
Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge…
We investigate the performance of fully convolutional networks to simulate the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net architecture and analyse how well it generalises to geometric…
A flexible topological representation consisting of a two-layer graph structure built on-board an Unmanned Aerial Vehicle (UAV) by continuously filling the free space of an occupancy map with intersecting spheres is proposed in this…
Convolutional neural networks (CNNs) constructed natively on the sphere have been developed recently and shown to be highly effective for the analysis of spherical data. While an efficient framework has been formulated, spherical CNNs are…
When beamforming is applied at the transmitter, only part of reconfigurable intelligent surfaces (RISs) will be active, and it becomes indispensable to study the impact of RIS geometry. This letter aims at evaluating RIS geometry, ranging…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
We investigate properties of sparse and tight surface graphs. In particular we derive topological inductive constructions for $(2, 2)$-tight surface graphs in the case of the sphere, the plane, the twice punctured sphere and the torus. In…
With the explosive deployment of non-terrestrial networks (NTNs), the computational complexity of network performance analysis is rapidly escalating. As one of the most suitable mathematical tools for analyzing large-scale network…
The interconnection network comprises a significant portion of the cost of large parallel computers, both in economic terms and power consumption. Several previous proposals exploit large-radix routers to build scalable low-distance…
We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling…
Convolutional neural networks (CNNs) have been widely used in various vision tasks, e.g. image classification, semantic segmentation, etc. Unfortunately, standard 2D CNNs are not well suited for spherical signals such as panorama images or…
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…
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…
The graph layouts used for complex network studies have been mainly been developed to improve visualization. If we interpret the layouts in metric spaces such as Euclidean ones, however, the embedded spatial information can be a valuable…
Template 3D shapes are useful for many tasks in graphics and vision, including fitting observation data, analyzing shape collections, and transferring shape attributes. Because of the variety of geometry and topology of real-world shapes,…