794 citations · 1.8k across the 40 of their papers we have counts for
12 papers · 1 filter
Detecting Temporal shape changes with the Euler Characteristic Transform
Lewis Marsh, Felix Y. Zhou, Xiao Qin +3
Organoids are multi-cellular structures which are cultured in vitro from stem cells to resemble specific organs (e.g., brain, liver) in their three-dimensional composition. Dynamic…
Topological Data Analysis Detects Percolation Thresholds in Arctic Melt-Pond Evolution
Wilfred Offord, Michael Coughlan, Ian J. Hewitt +2
During the summer melt period, ponds form on the surface of Arctic sea ice as it melts, with important consequences for ice evolution and marine ecology. Due to the ice-albedo feed…
Multiscale topology classifies and quantifies cell types in subcellular spatial transcriptomics
Katherine Benjamin, Aneesha Bhandari, Zhouchun Shang +7
Spatial transcriptomics has the potential to transform our understanding of RNA expression in tissues. Classical array-based technologies produce multiple-cell-scale measurements r…
Algebraic network reconstruction of discrete dynamical systems
Heather A. Harrington, Mike Stillman, Alan Veliz-Cuba
We present a computational algebra solution to reverse engineering the network structure of discrete dynamical systems from data. We use monomial ideals to determine dependencies b…
Stability of topological descriptors for neuronal morphology
David Beers, Heather A. Harrington, Alain Goriely
The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descri…
Grounded persistent path homology: a stable, topological descriptor for weighted digraphs
Thomas Chaplin, Heather A. Harrington, Ulrike Tillmann
Weighted digraphs are used to model a variety of natural systems and can exhibit interesting structure across a range of scales. In order to understand and compare these systems, w…
Hypergraphs for multiscale cycles in structured data
Agnese Barbensi, Iris H. R. Yoon, Christian Degnbol Madsen +3
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 man…
Zigzag persistence for coral reef resilience using a stochastic spatial model
Robert A. McDonald, Rosanna Neuhausler, Martin Robinson +3
A complex interplay between species governs the evolution of spatial patterns in ecology. An open problem in the biological sciences is characterising spatio-temporal data and unde…
Brain Chains as Topological Signatures for Alzheimer's Disease
Christian Goodbrake, David Beers, Travis B. Thompson +2
We propose a topological framework to study the evolution of Alzheimer's disease, the most common neurodegenerative disease. The modeling of this disease starts with the representa…
Multiscale methods for signal selection in single-cell data
Renee S. Hoekzema, Lewis Marsh, Otto Sumray +4
Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters.…
Barcodes distinguish morphology of neuronal tauopathy
David Beers, Despoina Goniotaki, Diane P. Hanger +2
The geometry of neurons is known to be important for their functions. Hence, neurons are often classified by their morphology. Two recent methods, persistent homology and the topol…
Homology of homologous knotted proteins
Katherine Benjamin, Lamisah Mukta, Gabriel Moryoussef +4
Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here we develop a mathematical pipeline that systema…