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Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…

Algebraic Topology · Mathematics 2025-10-23 Aleksei Luchinsky , Umar Islambekov

Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…

Computational Geometry · Computer Science 2022-12-27 Brittany Terese Fasy , Samuel Micka , David L. Millman , Anna Schenfisch , Lucia Williams

In this work, we propose an efficient algorithm for the calculation of the Betti matching, which can be used as a loss function to train topology aware segmentation networks. Betti matching loss builds on techniques from topological data…

Algebraic Topology · Mathematics 2024-07-08 Nico Stucki , Vincent Bürgin , Johannes C. Paetzold , Ulrich Bauer

The diffusion of minimally invasive, endovascular interventions motivates the development of visualization methods for complex vascular networks. We propose a planar representation of blood vessel trees which preserves the properties that…

Image and Video Processing · Electrical Eng. & Systems 2025-10-23 Guillaume Houry , Tom Boeken , Stéphanie Allassonnière , Jean Feydy

A persistence module $M$, with coefficients in a field $\mathbb{F}$, is a finite-dimensional linear representation of an equioriented quiver of type $A_n$ or, equivalently, a graded module over the ring of polynomials $\mathbb{F}[x]$. It is…

Algebraic Topology · Mathematics 2025-11-06 Alessandro De Gregorio , Marco Guerra , Sara Scaramuccia , Francesco Vaccarino

Large-scale numerical simulations of planetary interiors require dedicated visualization algorithms that are able to efficiently extract a large amount of information in an interactive and user-friendly way. Here we present a software…

In this paper, we present Hi-D maps, a novel method for the visualization of multi-dimensional categorical data. Our work addresses the scarcity of techniques for visualizing a large number of data-dimensions in an effective and…

Graphics · Computer Science 2025-07-11 Radi Muhammad Reza , Benjamin A Watson

We present a row reduction algorithm to compute the barcode decomposition of persistence modules. This algorithm dualises the standard persistence one and clarifies the symmetry between clear and compress optimisations.

Computational Geometry · Computer Science 2021-03-12 Barbara Giunti

In Topological Data Analysis, a common way of quantifying the shape of data is to use a persistence diagram (PD). PDs are multisets of points in $\mathbb{R}^2$ computed using tools of algebraic topology. However, this multi-set structure…

Computer Vision and Pattern Recognition · Computer Science 2021-09-20 Kit C. Chan , Umar Islambekov , Alexey Luchinsky , Rebecca Sanders

Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…

Algebraic Topology · Mathematics 2026-02-13 R. Gonzalez-Diaz , M. Soriano-Trigueros , A. Torras-Casas

The complexity of modern Just-In-Time (JIT) compiler optimization poses significant challenges for developers seeking to understand and debug intermediate representation (IR) behavior. This work introduces JITScope, an interactive…

Software Engineering · Computer Science 2025-05-29 Kyra Dalbo , Yumna Ahmed , HeuiChan Lim

A robust evaluation toolset has been designed for Naval Research Laboratory's Real-Time Ocean Forecasting System RELO with the purpose of facilitating an adaptive sampling strategy and providing more educated guidance for routing underwater…

Robotics · Computer Science 2024-09-24 Edward Holmberg

Material node graphs are programs that generate the 2D channels of procedural materials, including geometry such as roughness and displacement maps, and reflectance such as albedo and conductivity maps. They are essential in computer…

Computer Vision and Pattern Recognition · Computer Science 2026-05-18 Jonas Belouadi , Tamy Boubekeur , Adrien Kaiser

The past few years have witnessed vibrant efforts in discovering new two-dimensional (2D) semiconductor materials from both academia and the industry, due to their promising potential in resolving the severe performance deterioration of…

Human-Computer Interaction · Computer Science 2026-05-07 Kavinda Athapaththu , Shiwei Chen , Yuan Fang , Sanchali Mitra , Yee Sin Ang , Yong Wang

We present vivid, an R package for visualizing variable importance and variable interactions in machine learning models. The package provides a range of displays including heatmap and graph-based displays for viewing variable importance and…

Computation · Statistics 2024-10-15 Alan Inglis , Andrew Parnell , Catherine Hurley

Vision Transformers (ViTs) have established new performance benchmarks in vision tasks such as image recognition and object detection. However, these advancements come with significant demands for memory and computational resources,…

Hardware Architecture · Computer Science 2026-02-10 Cong Wang , Zexin Fu , Jiayi Huang , Shanshi Huang

In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology,…

Algebraic Topology · Mathematics 2024-04-04 Toshitaka Aoki , Emerson G. Escolar , Shunsuke Tada

Advanced manufacturing creates increasingly complex objects with material compositions that are often difficult to characterize by a single modality. Our collaborating domain scientists are going beyond traditional methods by employing both…

Several visualization schemes have been developed for imaging materials at the atomic level through atom probe tomography. The main shortcoming of these tools is their inability to parallel process data using multi-core computing units to…

Materials Science · Physics 2012-02-07 Hari Dahal , Michael Stukowski , Matthias J. Graf , Alexander V. Balatsky , Krishna Rajan

Pursuing a continuous visual representation that offers flexible frequency modulation and fast rendering speed has recently garnered increasing attention in the fields of 3D vision and graphics. However, existing representations often rely…

Computer Vision and Pattern Recognition · Computer Science 2025-08-20 Wenhao Zhang , Hao Zhu , Delong Wu , Di Kang , Linchao Bao , Xun Cao , Zhan Ma