Related papers: PETLS: PErsistent Topological Laplacian Software

TDA (topological data analysis) is a relatively new area of research related to importing classical ideas from topology into the realm of data analysis. Under the umbrella term TDA, there falls, in particular, the notion of persistent…

Topolectrical circuits provide a versatile platform for exploring and simulating modern physical models. However, existing approaches suffer from incomplete programmability and ineffective feature prediction and control mechanisms,…

Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…

Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…

Directed evolution is a molecular biology technique that is transforming protein engineering by creating proteins with desirable properties and functions. However, it is experimentally impossible to perform the deep mutational scanning of…

A suitable feature representation that can both preserve the data intrinsic information and reduce data complexity and dimensionality is key to the performance of machine learning models. Deeply rooted in algebraic topology, persistent…

In recent years, cosmic shear has emerged as a powerful tool to study the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods like peak count statistics…

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…

The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity…

Let's HPC (www.letshpc.org) is an open-access online platform to supplement conventional classroom oriented High Performance Computing (HPC) and Parallel & Distributed Computing (PDC) education. The web based platform provides online…

Periodic time series (PTS) forecasting plays a crucial role in a variety of industries to foster critical tasks, such as early warning, pre-planning, resource scheduling, etc. However, the complicated dependencies of the PTS signal on its…

Software libraries for Topological Data Analysis (TDA) offer limited support for interactive visualization. Most libraries only allow to visualize topological descriptors (e.g., persistence diagrams), and lose the connection with the…

Path homology proposed by S.-T.Yau and his co-workers provides a new mathematical model for directed graphs and networks. Persistent path homology (PPH) extends the path homology with filtration to deal with asymmetry structures. However,…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…

Topological data analysis (TDA) delivers invaluable and complementary information on the intrinsic properties of data inaccessible to conventional methods. However, high computational costs remain the primary roadblock hindering the…

Topology is the foundation for many industrial applications ranging from CAD to simulation analysis. Computational topology mostly focuses on structured data such as mesh, however unstructured dataset such as point set remains a virgin land…

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss…