48 citations · 109 across the 12 of their papers we have counts for
13 papers
A computational approach to maximum likelihood thresholds for colored Gaussian graphical models
Roser Homs, Olga Kuznetsova, Bernadette J. Stolz
Gaussian graphical models (GGMs) are essential tools for interpretable structure learning. However, in high-dimensional, small-sample regimes, the available data is often insuffici…
From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
Juliette Murris, Bernadette Stolz, Karsten Borgwardt
Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing th…
Magnitude-Based Features for Multispecies Spatial Data
Julia Sollberger, Joshua Bull, Sara Kališnik +1
Multispecies spatial data arise in many applications where interactions between different entities are central to system behaviour, including biomedical imaging, geospatial analysi…
Topological model selection: a case-study in tumour-induced angiogenesis
Robert A McDonald, Helen M Byrne, Heather A Harrington +2
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models…
Communities in the Kuramoto Model: Dynamics and Detection via Path Signatures
Tâm Johan Nguyên, Darrick Lee, Bernadette Jana Stolz
The behavior of multivariate dynamical processes is often governed by underlying structural connections that relate the components of the system. For example, brain activity, which…
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…
Outlier-robust subsampling techniques for persistent homology
Bernadette J. Stolz
In recent years, persistent homology (PH) has been successfully applied to real-world data in many different settings. Despite significant computational advances, PH algorithms do…
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…
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…
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…
The Topological "Shape" of Brexit
Bernadette J. Stolz, Heather A. Harrington, Mason A. Porter
Persistent homology is a method from computational algebraic topology that can be used to study the "shape" of data. We illustrate two filtrations --- the weight rank clique filtra…