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no code implementations • 5 Dec 2022 • 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.

no code implementations • 16 Nov 2022 • David Beers, Heather A. Harrington, Alain Goriely

These results guarantee that persistence images of topological morphology descriptors are stable against the same set of perturbations and reliable.

1 code implementation • 19 Sep 2022 • Robert A. McDonald, Rosanna Neuhausler, Martin Robinson, Laurel G. Larsen, Heather A. Harrington, Maria Bruna

A complex interplay between species governs the evolution of spatial patterns in ecology.

no code implementations • 22 Aug 2022 • Christian Goodbrake, David Beers, Travis B. Thompson, Heather A. Harrington, Alain Goriely

This sequence of edges defines a filtration of the graph.

1 code implementation • 15 Jun 2022 • Renee S. Hoekzema, Lewis Marsh, Otto Sumray, Thomas M. Carroll, Xin Lu, Helen M. Byrne, Heather A. Harrington

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.

no code implementations • 7 Apr 2022 • David Beers, Despoina Goniotaki, Diane P. Hanger, Alain Goriely, Heather A. Harrington

We introduce {topological morphology functions}, a class of functions similar to Sholl functions, that can be recovered from the associated topological morphology descriptor.

no code implementations • 1 Dec 2021 • Lewis Marsh, Emilie Dufresne, Helen M. Byrne, Heather A. Harrington

The MEK/ERK signalling pathway is involved in cell division, cell specialisation, survival and cell death.

1 code implementation • 26 Aug 2021 • Thomas Thorne, Paul D. W. Kirk, Heather A. Harrington

Here we focus on recent work using topological data analysis to study different regimes of parameter space for a well-studied model of angiogenesis.

1 code implementation • 2 Jan 2021 • John T. Nardini, Bernadette J. Stolz, Kevin B. Flores, Heather A. Harrington, Helen M. Byrne

Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data.

1 code implementation • 19 Aug 2020 • Bernadette J. Stolz, Jakob Kaeppler, Bostjan Markelc, Franziska Mech, Florian Lipsmeier, Ruth J. Muschel, Helen M. Byrne, Heather A. Harrington

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 quantification is an active area of research.

1 code implementation • 25 Aug 2019 • Bernadette J. Stolz, Jared Tanner, Heather A. Harrington, Vidit Nanda

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data.

Algebraic Topology Algebraic Geometry 57N80

no code implementations • 22 Sep 2018 • Bernadette J. Stolz, Tegan Emerson, Satu Nahkuri, Mason A. Porter, Heather A. Harrington

With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions.

1 code implementation • 21 Feb 2018 • Emilie Dufresne, Parker B. Edwards, Heather A. Harrington, Jonathan D. Hauenstein

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points.

Algebraic Topology Algebraic Geometry Numerical Analysis

no code implementations • 24 Aug 2017 • Heather A. Harrington, Nina Otter, Hal Schenck, Ulrike Tillmann

A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way.

Algebraic Topology Commutative Algebra 55B55, 68U05, 68Q17, 13P25 (primary)

no code implementations • 24 Dec 2016 • Anna Seigal, Mariano Beguerisse-Díaz, Birgit Schoeberl, Mario Niepel, Heather A. Harrington

Our clustering method is general and can be tailored to a variety of applications in science and industry.

1 code implementation • 30 Jun 2015 • Nina Otter, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, Heather A. Harrington

We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH.

Algebraic Topology Computational Geometry Data Analysis, Statistics and Probability Quantitative Methods

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