Related papers: GPU Computation of the Euler Characteristic Curve …

Vector graphics includes both filled and stroked paths as the main primitives. While there are many techniques for rendering filled paths on GPU, stroked paths have proved more elusive. This paper presents a technique for performing stroke…

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…

Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…

Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers…

Cosmological measurements require the calculation of nontrivial quantities over large datasets. The next generation of survey telescopes (such as DES, PanSTARRS, and LSST) will yield measurements of billions of galaxies. The scale of these…

We equip dynamic geometry software (DGS) with a user-friendly method that enables massively parallel calculations on the graphics processing unit (GPU). This interplay of DGS and GPU opens up various applications in education and…

We recently proposed a new ensemble clustering algorithm for graphs (ECG) based on the concept of consensus clustering. We validated our approach by replicating a study comparing graph clustering algorithms over benchmark graphs, showing…

Analysis of processing time and similarity of images generated between CPU and GPU architectures and sequential and parallel programming. For image processing a computer with AMD FX-8350 processor and an Nvidia GTX 960 Maxwell GPU was used,…

Three-dimensional neutron transport calculations using the Method of Characteristics (MOC) are highly regarded for their exceptional computational efficiency, precision, and stability. Nevertheless, when dealing with extensive-scale…

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

The Euler calculus -- an integral calculus based on Euler characteristic as a valuation on constructible functions -- is shown to be an incisive tool for answering questions about injectivity and invertibility of recent transforms based on…

A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…

Graph contrastive learning (GCL) aims to align the positive features while differentiating the negative features in the latent space by minimizing a pair-wise contrastive loss. As the embodiment of an outstanding discriminative unsupervised…

Real-time, energy-efficient inference on edge devices is essential for graph classification across a range of applications. Hyperdimensional Computing (HDC) is a brain-inspired computing paradigm that encodes input features into…

General Purpose Graphics Processing Unit (GPGPU) computing plays a transformative role in deep learning and machine learning by leveraging the computational advantages of parallel processing. Through the power of Compute Unified Device…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…

Hybrid computational architectures based on the joint power of Central Processing Units and Graphic Processing Units (GPUs) are becoming popular and powerful hardware tools for a wide range of simulations in biology, chemistry, engineering,…

Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by [Thomassen '89] and a linear-time fixed-parameter algorithm has been obtained by [Mohar '99]. Despite extensive…