794 citations · 1.8k across the 40 of their papers we have counts for
16 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…
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…
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…
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.…
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…
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…
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…
Coloured Noise from Stochastic Inflows in Reaction-Diffusion Systems
Michael F Adamer, Heather A Harrington, Eamonn A Gaffney +1
In this paper we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show ho…
Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia
Bernadette J. Stolz, Tegan Emerson, Satu Nahkuri +2
We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI tim…
Tensor clustering with algebraic constraints gives interpretable groups of crosstalk mechanisms in breast cancer
Anna Seigal, Mariano Beguerisse-Díaz, Birgit Schoeberl +2
We introduce a tensor-based clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. This framework is designed to enable detec…
Numerical algebraic geometry for model selection and its application to the life sciences
Elizabeth Gross, Brent Davis, Kenneth L. Ho +2
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization…
Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study
Adam L. MacLean, Heather A. Harrington, Michael P. H. Stumpf +1
The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt path…
Parameter-free methods distinguish Wnt pathway models and guide design of experiments
Adam L. MacLean, Zvi Rosen, Helen M. Byrne +1
The canonical Wnt signaling pathway, mediated by -catenin, is crucially involved in development, adult stem cell tissue maintenance and a host of diseases including cancer. We u…
A parameter-free model discrimination criterion based on steady-state coplanarity
Heather A. Harrington, Kenneth L. Ho, Thomas Thorne +1
We describe a novel procedure for deciding when a mass-action model is incompatible with observed steady-state data that does not require any parameter estimation. Thus, we avoid t…