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Using a set of $\Lambda$CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We…

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…

Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…

Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about…

Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…

We study structural feature and evolution of the Internet at the autonomous systems level. Extracting relevant parameters for the growth dynamics of the Internet topology, we construct a toy model for the Internet evolution, which includes…

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 describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may…

Topological quantum sensing leverages unique topological features to suppress noise and improve the precision of parameter estimation, emerging as a promising tool in both fundamental research and practical application. In this Letter, we…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…

We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…

Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Comprehensive understanding of dynamic scenes is a critical prerequisite for intelligent robots to autonomously operate in their environment. Research in this domain, which encompasses diverse perception problems, has primarily been focused…

We propose and study a method called FLOT that estimates scene flow on point clouds. We start the design of FLOT by noticing that scene flow estimation on point clouds reduces to estimating a permutation matrix in a perfect world. Inspired…

Three novel applications of computational topology in the field of fusion science are developed. A procedure for the automatic classification of the orbits of magnetic field lines into topologically distinct classes using Vietoris-Rips…

Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…

Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…

We present HyperFLINT (Hypernetwork-based FLow estimation and temporal INTerpolation), a novel deep learning-based approach for estimating flow fields, temporally interpolating scalar fields, and facilitating parameter space exploration in…