Related papers: Topology across Scales on Heterogeneous Cell Data
Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional definitions of structure or sequence similarity always involve superposition or…
Topological data analysis (TDA) uncovers crucial properties of objects in medical imaging. Methods based on persistent homology have demonstrated their advantages in capturing topological features that traditional deep learning methods…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…
Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…
Photon-Counting Computed Tomography (PCCT) is a novel imaging modality that simultaneously acquires volumetric data at multiple X-ray energy levels, generating separate volumes that capture energy-dependent attenuation properties.…
We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data.…
Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints. However, node-link diagrams may fail to convey insights regarding graph…
A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (in our case, a simplicial complex). Modern packages for persistent homology often construct Vietoris--Rips or other…
Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…
Persistent homology is a branch of computational algebraic topology that studies shapes and extracts features over multiple scales. In this paper, we present an unsupervised approach that uses persistent homology to study divergent behavior…
This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
Protein fold classification is a classic problem in structural biology and bioinformatics. We approach this problem using persistent homology. In particular, we use alpha shape filtrations to compare a topological representation of the data…
The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…
The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…
Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…
Pathological lung segmentation (PLS) is an important, yet challenging, medical image application due to the wide variability of pathological lung appearance and shape. Because PLS is often a pre-requisite for other imaging analytics,…
The combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from…
Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians…
Fields exhibit a variety of topological properties, like different topological charges, when field space in the continuum is composed by more than one topological sector. Lattice treatments usually encounter difficulties describing those…