794 citations · 1.8k across the 40 of their papers we have counts for
52 papers
Relational persistent homology for multispecies data with application to the tumor microenvironment
Bernadette J. Stolz, Jagdeep Dhesi, Joshua A. Bull +3
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 focu…
Topological classification of tumour-immune interactions and dynamics
Jingjie Yang, Heidi Fang, Jagdeep Dhesi +5
The complex and dynamic crosstalk between tumour and immune cells results in tumours that can exhibit distinct qualitative behaviours - elimination, equilibrium, and escape - and i…
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…
Equivariant vector bundles on Drinfeld's halfspace over a finite field
Sascha Orlik
Let be Drinfeld's halfspace over a finite field and let be a homogeneous vector bundle on . The paper deals w…
Differential elimination for dynamical models via projections with applications to structural identifiability
Ruiwen Dong, Christian Goodbrake, Heather A Harrington +1
Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are o…
Topological Approximate Bayesian Computation for Parameter Inference of an Angiogenesis Model
Thomas Thorne, Paul D. W. Kirk, Heather A. Harrington
Inferring the parameters of models describing biological systems is an important problem in the reverse engineering of the mechanisms underlying these systems. Much work has focuse…
What are higher-order networks?
Christian Bick, Elizabeth Gross, Heather A. Harrington +1
Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based pe…
Principal Components along Quiver Representations
Anna Seigal, Heather A. Harrington, Vidit Nanda
Quiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of ve…
Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis
John T. Nardini, Bernadette J. Stolz, Kevin B. Flores +2
Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound heali…
Multiscale Topology Characterises Dynamic Tumour Vascular Networks
Bernadette J. Stolz, Jakob Kaeppler, Bostjan Markelc +5
Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops, and their qu…
Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology
Agnese Barbensi, Daniele Celoria, Heather A. Harrington +2
Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether…
Geometric anomaly detection in data
Bernadette J Stolz, Jared Tanner, Heather A Harrington +1
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the t…
Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature
Helen M Byrne, Heather A Harrington, Ruth Muschel +3
Understanding how the spatial structure of blood vessel networks relates to their function in healthy and abnormal biological tissues could improve diagnosis and treatment for dise…