Related papers: Topological Data Analysis for Particulate Gels

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

This paper explores the use of Topological Data Analysis (TDA) to investigate patterns in zonal-mean zonal winds of the Arctic, which make up the polar vortex, in order to better explain polar vortex dynamics. We demonstrate how TDA reveals…

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…

Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited to the field of financial time series primarily and as a method for…

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…

Soft particulate gels include materials we can eat, squeeze, or 3D print. From foods to bio-inks to cement hydrates, these gels are composed of a small amount of particulate matter (proteins, polymers, colloidal particles, or agglomerates…

Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…

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…

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…

Particles added to a fluid interface can be used as a surface stabilizer in the food, oil and cosmetic industries. As an alternative to rigid particles, it is promising to consider highly deformable particles that can adapt their…

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…

The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between plastic dynamics and the structure of a particle's…

Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important…

This paper concerns a theoretical approach that combines topological data analysis (TDA) and sheaf theory. Topological data analysis, a rising field in mathematics and computer science, concerns the shape of the data and has been proven…

Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these…

Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…

Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…