Application driven Topological Data Analysis

Lead Research Organisation: University of Oxford
Department Name: Mathematical Institute

Abstract

Modern science and technology generates data at an unprecedented rate. A major challenge is that this data is often complex, high dimensional, may include temporal and/or spatial information. The "shape" of the data can be important but it is difficult to extract and quantify it using standard machine learning or statistical techniques. For example, an image of blood vessels near a tumor looks very different than an image of healthy blood
vessels; statistics alone cannot quantify this shape because it is the shape that matters. The focus of this proposal is to study the shape of data, through the development of new mathematics and algorithms, and build on existing data science techniques in order to obtain and interpret the shape of data. A theoretical field of mathematics that enables the study of shapes is topology. The ability to compute the shape (its topology) of complicated shapes is only possible with advanced mathematics and algorithms. The field known as topological data analysis (TDA), enables one to use topology to study the shape of data, such as loops in a blood vessel network. In particular, an algorithm within TDA known as persistent homology, provides a topological summary of the shape of the data (e.g., features such as holes) at multiple scales. A key success of persistent homology is the ability to provide robust results, even if the data are noisy. There are theoretical and computational challenges in the application of these algorithms to large scale, real-world data.

The aim of this project is to build on current persistent homology tools, extending it theoretically, computationally, and adapting it for practical applications. Our core team is composed of experts in pure and applied mathematicians, computer scientists, and statisticians whose combined expertise covers cutting edge pure mathematics, mathematical modeling, algorithm design and data analysis. This core team will work closely with our collaborators in a range of scientific and industrial domains. Some of the application challenges we have set out include:

Can we detect a tumor by looking at the shape of images of blood vessels? Can we design new materials by looking at the shape of molecules using topology? How can we design such molecules? Can we detect anomalies in security data? And importantly, how can we accelerate algorithms to obtain topological characteristics of data in real time?

Planned Impact

IMPACT

The proposed centre involves a number of collaborators, providing some immediate pathways to impact. Each will provide access to appropriate data and will evaluate research and outcomes from the viewpoint of potential exploiters (potential users and investors) rather than only from mathematical and computing perspectives.

(1) GCHQ has pointed us towards relevant data sets within the public domain for security-research.

(2) BSMbench have supplied data sets appropriate to PH, from their own sector, including data previously used to benchmark other analytics methods.

(3) We have access to time series data sets; and are discussing interest in TDA with IFPEN.

We will arrange meetings with commercial data-analytics experts from a variety of commercial companies that have already expressed their need to understand the possibilities that TDA may hold. These include Tesco/Dunnhumby, Lloyds Bank, Morgan Stanley, GSK, HSBC, iProspect, Unilever, BT, and others.

We will work with one SME initially, delivering B2B services, while aiming to grow this further: Kognitio is a specialist in parallel processing.

To build upon the state-of-the-art in domain-specific data analysis techniques, we will also closely collaboration with the following academic end-users to maximise impact and translation of our research framework:

(4) High-resolution, spatio-temporal vascular image data, Dept of Oncology (Oxford)

(5) Databases of hypothetical nano-crystal structures from Materials Innovation Factory (Liverpool) and Laboratory of Molecular Simulations (EPFL)

(6) Data from Monte Carlo simulations of phases of matter, Dept of Physics (Swansea)

Through the co-creation of new theory that is implemented to provide scientific breakthroughs, such advances will impact the mathematical, computational, scientific, and corporate sectors.

The centre will host two large conferences for researchers and an international conference to propagate PH methods across UK HEIs. We will disseminate our research both in generalist journals as well as specialised journals so that the developed framework is widely disseminated. Our goal is to catalyse an active application-driven TDA community within the UK through annual meetings with presentation of progress and papers. We aim to build a strong UK community focussed on research and translation of next generation TDA concepts and technologies.

Organisations

 
Description Theoretical advances include development of two new invariants for multi-parameter persistence homology. One is an extension of persistence landscapes to the multi-parameter case; software has been developed to compute this; and it has been applied to digital pathology. Specifically this tool distinguishes between different immune cell locations in cancer, and is a stronger discriminator than tools used so far. A computable metric had theoretically been developed that is a local discriminator of multi-parameter persistent modules.
In another direction, the barcode transform has been given a differential structure. This opens the way to include persistent homology as part of machine learning algorithms -- the optimal filter function can now be 'learned'. Code has been written to test on bench data to give a proof of principle.
Random geometric complexes are studied to support null-hypothesis and in a major paper for the first time, manifolds with boundary are handled successfully.
Exploitation Route More efficient software could be built to allow faster and more accurate computations which in turn will be of more use and interest to the scientific community.
Sectors Chemicals,Healthcare,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Security and Diplomacy

 
Description DSTL Topological Analysis of Maritime Data
Amount £250,000 (GBP)
Organisation Alan Turing Institute 
Sector Academic/University
Country United Kingdom
Start 03/2020 
End 03/2020
 
Description PhD studentship "A rigorous identification of all metastable polymorphs for better and safer drugs" supervised by Dr Vitaliy Kurlin
Amount £34,000 (GBP)
Organisation Cambridge Crystallographic Data Centre 
Sector Academic/University
Country United Kingdom
Start 10/2020 
End 09/2023
 
Description PhD studentship "Data Driven Discovery of Functional Molecular Co-crystals" of Katerina Vriza co-supervised by Dr Vitaliy Kurlin
Amount £30,000 (GBP)
Organisation Cambridge Crystallographic Data Centre 
Sector Academic/University
Country United Kingdom
Start 10/2018 
End 09/2021
 
Description Royal Society International Exchanges with Prof Edelsbrunner
Amount £12,000 (GBP)
Funding ID IES/R2/170039 
Organisation The Royal Society 
Sector Charity/Non Profit
Country United Kingdom
Start 12/2017 
End 12/2019
 
Title Ball Mapper, tool for topological data analysis 
Description A tool for multi dimension data visualization 
Type Of Material Improvements to research infrastructure 
Year Produced 2019 
Provided To Others? Yes  
Impact Too soon to tell. 
URL https://cran.r-project.org/web/packages/BallMapper/index.html
 
Title Detecting interfaces/geometric anomalies in data (Heather Harrington, Vidit Nanda, Bernadette Stolz) 
Description Persistent co-homology detects annomalies in data, for example, intersections of two shapes 
Type Of Material Improvements to research infrastructure 
Year Produced 2019 
Provided To Others? Yes  
Impact We were able to detect annomalies in 24 dimensional dataset of cyclo-octane 
URL https://arxiv.org/abs/1908.09397
 
Description Accelerated Crystal Structure Prediction 
Organisation Cambridge Crystallographic Data Centre
Country United Kingdom 
Sector Academic/University 
PI Contribution Vitaliy Kurlin and his team at the University of Liverpool develops a continuous approach to a similarity of crystals, which were studied in the past only by discrete invariants such as symmetry groups
Collaborator Contribution Cambridge Crystallographic Data Centre has contributed £64K to 2 PhD projects supervised by Vitaliy Kurlin at the University of Liverpool, and provides advice on the state-of-the-art in Crystal Structure Prediction and access to the Cambridge Structural Database.
Impact Two PhD scholarships
Start Year 2019
 
Description Amit Pavel 
Organisation Colorado State University
Country United States 
Sector Academic/University 
PI Contribution Vidit Nanda contributed Higher persistence and stability.
Collaborator Contribution Amit Patel contributed bisheaves and local systems.
Impact As listed
Start Year 2019
 
Description Bernadette Stolz - Florian Lipsmeier, and Franziska Mech 
Organisation Roche Pharmaceuticals
Country Global 
Sector Private 
PI Contribution I extracted a data set from Roche from segmented images using machine learning software, analysed the data using TDA and a radial filtration and performed statistical analyses of the results.
Collaborator Contribution Roche funded part of my DPhil and provided a data set as well as feedback on my work.
Impact As listed.
Start Year 2014
 
Description Biagio Lucini, Davide Vadacchino 
Organisation National Institute for Nuclear Physics
Department National Institute for Nuclear Physics - Torino
Country Italy 
Sector Academic/University 
PI Contribution Pawel Dlotko, Tak-Shing Chan are investigating the use of cubical complexes for statistical physics
Collaborator Contribution BL and DV will be providing their statistical physics expertise including sharing their implementations, data and analysis
Impact As listed
Start Year 2019
 
Description Emilie Dufresne 
Organisation University of York
Country United Kingdom 
Sector Academic/University 
PI Contribution Lewis Marsh conducted a several model reductions and rigorously compared them, designed and implemented a Bayesian inference on this data
Collaborator Contribution Emilie Dufresne studied the identifiability of the model and its reductions
Impact As listed
Start Year 2019
 
Description Heather Harrington - Anna Seigal 
Organisation Harvard University
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact Hooke Research Fellowship, 2019
Start Year 2019
 
Description Heather Harrington - Christian Bick 
Organisation University of Exeter
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Dane Taylor 
Organisation University at Buffalo
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2018
 
Description Heather Harrington - Dimitra Kosta 
Organisation University of Glasgow
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2018
 
Description Heather Harrington - Emilie Dufresne 
Organisation University of York
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact London Mathematical Society Seminar
Start Year 2018
 
Description Heather Harrington - Fabian Ruehle 
Organisation European Organization for Nuclear Research (CERN)
Department Theoretical Physics Unit
Country Switzerland 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Kathryn Hess/Wojciech Reise 
Organisation Swiss Federal Institute of Technology in Lausanne (EPFL)
Country Switzerland 
Sector Public 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact Wojciech Reise research trip in collaboration with Spotify at Oxford Mathematics.
Start Year 2019
 
Description Heather Harrington - Lior Horesh 
Organisation IBM
Department IBM T. J. Watson Research Center, Yorktown Heights
Country United States 
Sector Private 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Maria Bruna 
Organisation University of Cambridge
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2018
 
Description Heather Harrington - Mariano Beguerisse 
Organisation Spotify
Country Sweden 
Sector Private 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed
Start Year 2018
 
Description Heather Harrington - Matthew Macauley 
Organisation Clemson University
Country United States 
Sector Academic/University 
PI Contribution Expertise/Intellectual input
Collaborator Contribution Expertise/Intellectual input
Impact As listed
Start Year 2019
 
Description Heather Harrington - Michael Schaub 
Organisation Massachusetts Institute of Technology
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed
Start Year 2019
 
Description Heather Harrington - Michael Schaub 
Organisation University of Oxford
Department Department of Engineering Science
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed
Start Year 2019
 
Description Heather Harrington - Nicolette Meshkat 
Organisation Santa Clara University
Country United States 
Sector Academic/University 
PI Contribution Expertise/Intellectual input
Collaborator Contribution Expertise/Intellectual input
Impact The following publications: 1) Joining and decomposing reaction networks 2020, 2) Identifiability and numerical algebraic geometry, Dec 2019, 3) A Parameter-Free Model Comparison Test Using Differential Algebra Feb 2019
Start Year 2016
 
Description Heather Harrington - Nina Otter 
Organisation University of California, Los Angeles (UCLA)
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2018
 
Description Heather Harrington - Peter Bubenik 
Organisation University of Florida
Department College of Liberal Arts and Sciences
Country United States 
Sector Academic/University 
PI Contribution Expert/intellectual input
Collaborator Contribution Expert/intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Priya Subramanian 
Organisation University of Oxford
Department Mathematical Institute Oxford
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Prof. Andreas Münch 
Organisation University of Oxford
Department Mathematical Institute Oxford
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Professor Anne J Shiu 
Organisation Texas A&M University
Country United States 
Sector Academic/University 
PI Contribution Expertise/Intellectual input
Collaborator Contribution Expertise/Intellectual input
Impact The following publications: 1) Joining and decomposing reaction networks,2020. 2) Linear compartmental models: input-output equations and operations that preserve identifiability, (2019). 3)
Start Year 2016
 
Description Heather Harrington - Professor Antonis Papachristodoulou 
Organisation University of Oxford
Department Department of Engineering Science
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/intellectual input
Collaborator Contribution Expert/intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Professor Balazs Szendroi 
Organisation University of Oxford
Department Mathematical Institute Oxford
Country United Kingdom 
Sector Academic/University 
PI Contribution Expterise/Intellectual input
Collaborator Contribution Expterise/Intellectual input
Impact As listed
Start Year 2019
 
Description Heather Harrington - Professor Bernd Sturmfels 
Organisation Max Planck Society
Department Max Planck Society Leipzig
Country Germany 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2018
 
Description Heather Harrington - Professor Elizabeth Gross 
Organisation University of Hawai'i at Manoa
Country United States 
Sector Academic/University 
PI Contribution Expertise/Intellectual input
Collaborator Contribution Expertise/Intellectual input
Impact The following publications: 1) Joining and decomposing reaction networks, with Heather Harrington, Nicolette Meshkat, and Anne Shiu, 2) Linear compartmental models: input-output equations and operations that preserve identifiability, with Heather Harrington, Nicolette Meshkat, and Anne Shiu, SIAM Journal on Applied Mathematics.
Start Year 2016
 
Description Heather Harrington - Professor Jared Tanner 
Organisation University of Oxford
Department Mathematical Institute Oxford
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2018
 
Description Heather Harrington - Professor Joe Howard 
Organisation Yale University
Department Howard Lab
Country United States 
Sector Academic/University 
PI Contribution Expertise/Intellectual input
Collaborator Contribution Expertise/Intellectual input
Impact The Howard Lab is a highly interdisciplinary group of biologists, physicists, chemists and engineers, combining optical, mechanical and biochemical experiments with theory and computation.
Start Year 2018
 
Description Heather Harrington - Professor Jon Hauenstein 
Organisation University of Notre Dame
Country United States 
Sector Academic/University 
PI Contribution Expertise/Intellectual input
Collaborator Contribution Expertise/Intellectual input
Impact As listed.
Start Year 2018
 
Description Heather Harrington - Professor Konstantin Michaikow 
Organisation Rutgers University
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Professor Marc Lackenby 
Organisation University of Oxford
Department Mathematical Institute Oxford
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Marc Lackenby
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Professor Martin Wuhr 
Organisation Princeton University
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Professor Mauricio Barahona 
Organisation Imperial College London
Country United Kingdom 
Sector Academic/University 
PI Contribution Expertise / intellectual input
Collaborator Contribution Expertise / intellectual input
Impact As listed.
Start Year 2018
 
Description Heather Harrington - Professor Michael E. Stillman 
Organisation Cornell University
Country United States 
Sector Academic/University 
PI Contribution Expert/intellectual input
Collaborator Contribution Expert/intellectual input
Impact As listed
Start Year 2019
 
Description Heather Harrington - Professor Panos Kevrekedis 
Organisation University of Massachusetts Amherst
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact Professor Kevrekedis has spent a year in Oxford Mathematics to give a colloquium, a seminar and in collaboration on aspects of research
Start Year 2019
 
Description Heather Harrington - Professor Sharad Ramanathan 
Organisation Harvard University
Department Department of Stem Cell and Regenerative Biology
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Professor Shelby Wilson 
Organisation University of Maryland, College Park
Country United States 
Sector Academic/University 
PI Contribution Expertise/Intellectual input
Collaborator Contribution Expertise/Intellectual input
Impact None as yet
Start Year 2018
 
Description Heather Harrington - Professor Stanislav Shvartsman 
Organisation Princeton University
Country United States 
Sector Academic/University 
PI Contribution My expertise, and intellectual input.
Collaborator Contribution Expertise, and intellectual input.
Impact Publications as listed.
Start Year 2018
 
Description Heather Harrington - Professor Stephen Taylor 
Organisation University of Oxford
Department Weatherall Institute of Molecular Medicine (WIMM)
Country United Kingdom 
Sector Academic/University 
PI Contribution Expertise/intellectual input
Collaborator Contribution Expertise/intellectual input
Impact Molecular biology, data science, data visualisation, computational biology.
Start Year 2018
 
Description Heather Harrington - Rachel Neville 
Organisation University of Arizona
Department Department of Mathematics
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington - Sarah Filippi 
Organisation Imperial College London
Country United Kingdom 
Sector Academic/University 
PI Contribution Expertise/Intellectual input
Collaborator Contribution Expertise/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington, Helen Byrne - Xin Liu 
Organisation Chinese Academy of Sciences
Department State Key Laboratory of Scientific and Engineering Computing (LSEC)
Country China 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington, Helen Byrne, Bernadette Stolz-Pretzer - Professor Ruth Muschel 
Organisation University of Oxford
Department CRUK/MRC Oxford Institute for Radiation Oncology
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington, Helen Byrne, Oliver Vipond - Chris Pugh 
Organisation University of Oxford
Department Nuffield Department of Medicine
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed
Start Year 2019
 
Description Heather Harrington, Helen Byrne, Oliver Vipond - Joshua Adam Bull 
Organisation University of Oxford
Department Mathematical Institute Oxford
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed
Start Year 2019
 
Description Heather Harrington, Helen Byrne, Oliver Vipond - Philip Macklin 
Organisation University of Oxford
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Heather Harrington, Kelly Spendlove - Professor Doyne Farmer 
Organisation University of Oxford
Department Oxford Martin School
Country United Kingdom 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2020
 
Description Heather Harrinton - Richard Tanburn 
Organisation Google
Country United States 
Sector Private 
PI Contribution Expert/intellectual input
Collaborator Contribution Expert/intellectual input
Impact As listed.
Start Year 2019
 
Description Heather harrington - Rosanna Neuhausler 
Organisation University of California, Berkeley
Country United States 
Sector Academic/University 
PI Contribution Expert/Intellectual input
Collaborator Contribution Expert/Intellectual input
Impact As listed.
Start Year 2019
 
Description Henry-Louis de Kergolay 
Organisation Alan Turing Institute
Country United Kingdom 
Sector Academic/University 
PI Contribution Oliver Vipond - Random Geometric Complexes Paper joint work (expertise algebraic topology)
Collaborator Contribution Henry-Louis de Kergolay - Random Geometric Complexes Paper joint work (expertise probability)
Impact As listed
Start Year 2018
 
Description Integrating barcodes 
Organisation Bentley University
Country United States 
Sector Academic/University 
PI Contribution This is a theoretical project to give a new kind of invariants for multiparameter persistence problems. Jeffrey Giansiracusa has been working out the algebraic foundations for these invariants.
Collaborator Contribution Noah Giansiracusa (Bentley University), Chul Moon (Southern Methodist University, USA). CM will be proving computational expertise in developing an R/Python package implementation of these invariants. NG collaborates on mathematical ideas.
Impact As listed
Start Year 2018
 
Description Integrating barcodes 
Organisation Southern Methodist University
Country United States 
Sector Academic/University 
PI Contribution This is a theoretical project to give a new kind of invariants for multiparameter persistence problems. Jeffrey Giansiracusa has been working out the algebraic foundations for these invariants.
Collaborator Contribution Noah Giansiracusa (Bentley University), Chul Moon (Southern Methodist University, USA). CM will be proving computational expertise in developing an R/Python package implementation of these invariants. NG collaborates on mathematical ideas.
Impact As listed
Start Year 2018
 
Description Josh Bull, Philip Macklin 
Organisation Ludwig Institute for Cancer Research
Country United Kingdom 
Sector Academic/University 
PI Contribution Oliver Vipon contributed Topological Data Analusis on Histology data.
Collaborator Contribution Philip Macklin provides clinical data. Josh Bull develops algorithms to convert raw data to point cloud data.
Impact As listed
Start Year 2018
 
Description Kelly Spendlove - Matt Kahle, Professor Bob MacPherson, Professor Ulrich Bauer, Hannah Alpert 
Organisation Ohio State University
Country United States 
Sector Academic/University 
PI Contribution Computational Morse Theory
Collaborator Contribution Homology of Configuration Spaces
Impact As listed
Start Year 2019
 
Description Kelly Spendlove - Matt Kahle, Professor Bob MacPherson, Professor Ulrich Bauer, Hannah Alpert 
Organisation Princeton University
Department Institute for Advanced Study
Country United States 
Sector Academic/University 
PI Contribution Computational Morse Theory
Collaborator Contribution Homology of Configuration Spaces
Impact As listed
Start Year 2019
 
Description Kelly Spendlove - Matt Kahle, Professor Bob MacPherson, Professor Ulrich Bauer, Hannah Alpert 
Organisation Technical University of Munich
Country Germany 
Sector Academic/University 
PI Contribution Computational Morse Theory
Collaborator Contribution Homology of Configuration Spaces
Impact As listed
Start Year 2019
 
Description Kelly Spendlove - Matt Kahle, Professor Bob MacPherson, Professor Ulrich Bauer, Hannah Alpert 
Organisation University of British Columbia
Country Canada 
Sector Academic/University 
PI Contribution Computational Morse Theory
Collaborator Contribution Homology of Configuration Spaces
Impact As listed
Start Year 2019
 
Description Kelly Spendlove - Professor Rob VanderVorst 
Organisation Free University of Amsterdam
Country Netherlands 
Sector Academic/University 
PI Contribution Sharing expertise and intellectual inputs on Computational Connection Matrix Theory.
Collaborator Contribution Sharing expertise and intellectual inputs Braid Floer Homology.
Impact As listed
Start Year 2017
 
Description Lewis Marsh - Sarah Filippi 
Organisation Imperial College London
Country United Kingdom 
Sector Academic/University 
PI Contribution Lewis Marsh conducted a several model reductions and rigorously compared them, designed and implemented a Bayesian inference on this data
Collaborator Contribution Sarah Filippi assisted with design of Bayesian inference
Impact As listed
Start Year 2019
 
Description Lewis Marsh - Stanislav Y Shvartsman, Eyan Yeung, Sarah McFann, Martin Wuhr 
Organisation Princeton University
Country United States 
Sector Academic/University 
PI Contribution Lewis Marsh conducted several model reductions and rigorously compared them, designed and implemented a Bayesian inference on this data
Collaborator Contribution Princeton (no direct financial contribution; resulted in a publication, research on the shared data still ongoing)
Impact As listed
Start Year 2019
 
Description Martin Helmer 
Organisation Australian National University (ANU)
Country Australia 
Sector Academic/University 
PI Contribution Vidit Nanda contributed Euler obstructions
Collaborator Contribution Martin Helmer contributed Cellular models for 2-vector bundles
Impact As listed
Start Year 2019
 
Description Nicola Richmond 
Organisation GlaxoSmithKline (GSK)
Department GlaxoSmithKline Medicines Research Centre
Country United Kingdom 
Sector Private 
PI Contribution Sharing expertise, intellectual input. Visualization of biochemical design.
Collaborator Contribution Nicola Richmond is a member of our Scientific Advisory Board.
Impact None
Start Year 2019
 
Description Omer Bobrowski 
Organisation Technion - Israel Institute of Technology
Country Israel 
Sector Academic/University 
PI Contribution Oliver Vipond contributed random geometric complexes
Collaborator Contribution Omer also contributed random geometric complexes
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Alex Smith 
Organisation University of Wisconsin-Madison
Department Department of Biochemistry
Country United States 
Sector Academic/University 
PI Contribution Topological signatures in molecular simulation
Collaborator Contribution How to discriminate different chemical compounds
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Bartosz Zielinski 
Organisation Jagiellonian University
Country Poland 
Sector Academic/University 
PI Contribution Vectorizations of persistence diagrams
Collaborator Contribution How to interface topology to machine learning
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Berent Smit 
Organisation Swiss Federal Institute of Technology in Lausanne (EPFL)
Country Switzerland 
Sector Public 
PI Contribution Topological descriptors of nanoporous materials
Collaborator Contribution Building better tools to compare databases of materials
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Davide Gurnari 
Organisation University of Padova
Department Department of Mathematics
Country Italy 
Sector Academic/University 
PI Contribution Supported an Erasmus financed Masters student
Collaborator Contribution Distributed computations of Euler characteristics
Impact As lited.
Start Year 2020
 
Description Pawel Dlotko - Dmitry Feichtner-Kozlov 
Organisation University of Bremen
Country Germany 
Sector Academic/University 
PI Contribution Explore the relations of Morse theory and persistence
Collaborator Contribution How hard instances in Morse theory correspond to hard instances in persistence
Impact As listed.
Start Year 2019
 
Description Pawel Dlotko - Florian Pausinger 
Organisation Queen Mary University of London
Department School of Mathematical Sciences
Country United Kingdom 
Sector Academic/University 
PI Contribution Geographical time series
Collaborator Contribution Examine how to reconstruct the dymanics leading geographical processes
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Frank H. Lutz 
Organisation Technical University Berlin
Country Germany 
Sector Academic/University 
PI Contribution Explore the relation of Morse theory and persistence
Collaborator Contribution How hard instances in Morse theory correspond to hard instances in persistence
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Jacek Brodzki 
Organisation University of Southampton
Country United Kingdom 
Sector Academic/University 
PI Contribution Topology of neural networks
Collaborator Contribution Interactions of topology and ANNs
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Michael Grinfeld 
Organisation University of Strathclyde
Department Mathematics and Statistics Strathclyde
Country United Kingdom 
Sector Academic/University 
PI Contribution Phase separation in alloys
Collaborator Contribution Topological signatures of phase separations
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Professor Fred Chazal 
Organisation The National Institute for Research in Computer Science and Control (INRIA)
Department Saclay
Country France 
Sector Charity/Non Profit 
PI Contribution Creating a Topological Data Analysis library - the Gudhi library resource.
Collaborator Contribution Requested the development of a open source library of topological data analysis tutorials.
Impact In progress
Start Year 2019
 
Description Pawel Dlotko - Professor Grzegorz Graff 
Organisation Gdansk University of Technology
Department Faculty of Appied Physics and Mathematics
Country Poland 
Sector Academic/University 
PI Contribution Time series of breaching
Collaborator Contribution Using TDA to predict pulmunology diseases
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Professor Marian Gidea 
Organisation Yeshiva University
Country United States 
Sector Academic/University 
PI Contribution Topology of time series
Collaborator Contribution Measuring the predictability of financial crashes
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Professor Matthias Zeppelzauer 
Organisation St. Pölten University of Applied Sciences
Country Austria 
Sector Academic/University 
PI Contribution Vectorizations of persistence diagrams
Collaborator Contribution How to interface topology to machine learning
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Professor Ruben Specogna 
Organisation University of Udine
Country Italy 
Sector Academic/University 
PI Contribution Topology to speed up Maxwells equations computations
Collaborator Contribution Providing new tools for better electromagnetic modelling
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Professor Slawomir Nasuto 
Organisation University of Reading
Department School of Biological Sciences Reading
Country United Kingdom 
Sector Academic/University 
PI Contribution Sharing expertise and intellectual inputs on the application of topological networks to neurons and complicated systems
Collaborator Contribution Sharing expertise and intellectual inputs on applying topological measures to networks and artificially grown neurons
Impact As listed.
Start Year 2019
 
Description Pawel Dlotko - Radmila Sazdanovic 
Organisation North Carolina State University
Country United States 
Sector Academic/University 
PI Contribution Properties of knots
Collaborator Contribution How different knot invariants interact
Impact As listed
Start Year 2019
 
Description Pawel Dlotko - Reem Khalil 
Organisation American University of Sharjah
Country United Arab Emirates 
Sector Academic/University 
PI Contribution Shape of pyramidal neurons
Collaborator Contribution Determining distribution of different piramidal neurons
Impact As listed
Start Year 2020
 
Description Pawel Dlotko - Sadok Kallel 
Organisation American University of Sharjah
Country United Arab Emirates 
Sector Academic/University 
PI Contribution Topological descriptor of graphs
Collaborator Contribution How to plot a graph to a learning procedure
Impact As listed.
Start Year 2018
 
Description Pawel Dlotko - Simon Rudkin 
Organisation Swansea University
Department School of Management
Country United Kingdom 
Sector Academic/University 
PI Contribution Sharing expertise and intellectual inputs into the applications of topology to economics
Collaborator Contribution Sharing expertise and intellectual inputs into the applications of topology to economics
Impact As listed.
Start Year 2019
 
Description Pawel Dlotko - Thomas Wanner 
Organisation George Mason University
Country United States 
Sector Academic/University 
PI Contribution Rigorous approximation of topology of function
Collaborator Contribution How to approximate with controled error bound topology of functions
Impact As lited.
Start Year 2019
 
Description Pawel Dlotko - Yuri Katz 
Organisation S&P Global
Country United States 
Sector Private 
PI Contribution Toplogy of time series
Collaborator Contribution Measuring the predictability of financial crashes
Impact As listed.
Start Year 2019
 
Description Professor Frances Kirwan FRS 
Organisation University of Oxford
Department Mathematical Institute Oxford
Country United Kingdom 
Sector Academic/University 
PI Contribution Vidit Nanda contributed Symplectic quotients of persistence modules
Collaborator Contribution Frances Kirwan contributed interactions of geometric invariant theory with persistent homology
Impact As listed
Start Year 2019
 
Description Professor Nils Baas 
Organisation NTNU University Museum
Country Norway 
Sector Charity/Non Profit 
PI Contribution Vidit Nanda contributed Persistent K-theory
Collaborator Contribution Nil Baas contributed Cellular models for 2-vector bundles
Impact As listed
Start Year 2019
 
Description R.U. Gobithaasan 
Organisation University of Malaysia, Terengganu
Country Malaysia 
Sector Academic/University 
PI Contribution Pawel Dlotko, Tak-Shing Chan have been awarded a joint grant from the Malaysian government to use TDA to examine meteorological time series.
Collaborator Contribution Malaysian government have supported this financially
Impact Not as yet
Start Year 2019
 
Description Topological measurements geospatial habitat data 
Organisation Bangor University
Country United Kingdom 
Sector Academic/University 
PI Contribution Jeffrey Giansiracusa is developing topological descriptors for measuring habitat integrity and fragmentation using persistent homology.
Collaborator Contribution Florian Pausinger (Queens Belfast), Isabel Rosa (Bangor). This collaboration has brought in-kind access to geospatial data. IR provides datasets, domain knowledge. FP collaborates on mathematical ideas.
Impact as listed
Start Year 2020
 
Description Topological measurements geospatial habitat data 
Organisation Queen's University Belfast
Country United Kingdom 
Sector Academic/University 
PI Contribution Jeffrey Giansiracusa is developing topological descriptors for measuring habitat integrity and fragmentation using persistent homology.
Collaborator Contribution Florian Pausinger (Queens Belfast), Isabel Rosa (Bangor). This collaboration has brought in-kind access to geospatial data. IR provides datasets, domain knowledge. FP collaborates on mathematical ideas.
Impact as listed
Start Year 2020
 
Title Ball Mapper (MATLAB) (Tak-Shing Chan) 
Description MATLAB version of Ball Mapper 
Type Of Technology Software 
Year Produced 2019 
Open Source License? Yes  
Impact MATLAB version of Ball Mapper 
 
Title Ball Mapper algorithm 
Description Ball Mapper algorithm, R package published on CRAN (The Comprehensive R Archive Network). A GPL tool to visualize and analyze high dimensional datasets. 
Type Of Technology Webtool/Application 
Year Produced 2019 
Open Source License? Yes  
Impact See listed. 
URL https://CRAN.R-project.org/package=BallMapper
 
Title Ball Mapper algorithm, R package published on CRAN (The Comprehensive R Archive Network) 
Description A GPL tool to visualize and analyze high dimensional datasets. 
Type Of Technology Software 
Year Produced 2019 
Open Source License? Yes  
Impact Accessible to statisticians. 
 
Title DESR (Heather Harrington, Siddarth Kumar) 
Description Symmetry reduction of dynamical systems and nondimensionalisation 
Type Of Technology Software 
Year Produced 2020 
Open Source License? Yes  
Impact Enables automatic nondimensionalisation 
 
Title Epsilon-dense samples for TDA given equations (Heather Harrington) 
Description provides epsilon-dense samples for TDA 
Type Of Technology Software 
Year Produced 2020 
Open Source License? Yes  
Impact provides epsilon-dense samples for TDA 
 
Title HoPeS: Homologically Persistent Skeleton 
Description For a given 2D cloud of points, the HoPeS algorithm computes a Homologically Persistent Skeleton that optimally captures 1-dimensional cycles corresponding to all dots in the 1D persistence diagram as described in the paper by Philip Smith, Vitaliy Kurlin. Skeletonisation Algorithms with Theoretical Guarantees for Unorganised Point Clouds with High Levels of Noise, https://arxiv.org/abs/1901.03319. 
Type Of Technology Software 
Year Produced 2019 
Impact none yet 
URL https://arxiv.org/abs/1901.03319
 
Title PRIM: Persistence-based Resolution-Independent Meshes (Vitaly Kurlin) 
Description For a given image and a number k of line segments, the PRIM algorithms finds k most persistent line segments and extends them to a polygonal mesh 
Type Of Technology Software 
Year Produced 2019 
Open Source License? Yes  
Impact For a given image and a number k of line segments, the PRIM algorithms finds k most persistent line segments and extends them to a polygonal mesh 
 
Title PyCHomP/Conley-Morse Sheaf (Kelly Spendlove) 
Description Enables connection matrix computation over parameter space 
Type Of Technology Software 
Year Produced 2020 
Open Source License? Yes  
Impact Enables connection matrix computation over parameter space 
 
Description AI @ Oxford 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact TITLE:
ABSTRACT:
Discussed possible spinout of TDA
Year(s) Of Engagement Activity 2019
URL https://www.mpls.ox.ac.uk/upcoming-events/ai-oxford-conference
 
Description Biological and Biomedical Physics Seminar, Cambridge (Helen Byrne) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact TALK TITLE: Multiscale approaches to modelling vascular tumour growth. ABSTRACT: Understanding how vascular networks deliver nutrients and chemotherapy to solid tumours, how these networks evolve and how they may be manipulated to improve patient outcomes remain a major focus of cancer research. Such knowledge is important accurately to predict a tumour's response to radiotherapy and for establishing whether a particular patient's response can be enhanced by treatment with vascular targeting agents. Mathematical and computational models have the potential to provide valuable insight into the biophysical mechanisms that regulate tumour blood flow, transport and vascular remodelling, and a variety of models have been proposed. In this talk, I will explain how integrating data from in vitro and in vivo experiments within multiscale computational models can be used: (i) to propose new mechanisms for tumour hypoxia, and (ii) to characterise the morphology of vascular networks.

This talk is part of the Biological and Biomedical Physics series.
Year(s) Of Engagement Activity 2020
URL https://www.talks.cam.ac.uk/talk/index/132559
 
Description Can calculus cure cancer, Sydney University, (Helen Byrne) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact How can mathematical modelling and calculus help us understand how tumours grow and respond to treatments? A public lecture part of the Public Talks at Sydney University, is co-presented with the Sydney Mathematical Research Institute (Faculty of Science, University of Sydney).
Year(s) Of Engagement Activity 2019
URL https://www.facebook.com/sydney.ideas/videos/live-sydney-ideas-can-calculus-cure-cancer/271010400482...
 
Description Curing Cancer with Calculus by integrating information from bench to bedside (Helen Byrne) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Talk title: Mathematical approaches to modelling and remodelling biological tissues
Year(s) Of Engagement Activity 2019
URL https://gregynogwmc.github.io/Gregynog2019Timetable.pdf
 
Description Heather Harrington - Applied Algebra and Geometry Glasgow 8th Meeting 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Study participants or study members
Results and Impact Heather contributes time to this research network brings together UK academics who are interested in applications of algebra and geometry, and related algebraically-minded fields, be it commutative algebra, representation theory, group theory, process algebras, as well as algebraic geometry, category theory, and algebraic topology. The scope extends to computational algebra for applications including data-science, biology, medicine, engineering, physics, etc.
Year(s) Of Engagement Activity 2019
URL https://sites.google.com/view/appliedalgebraandgeometry/home/8th-meeting-glasgow
 
Description Heather Harrington - Harvard CMSA Colloquium & Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact TALK TITLE: Algebra, Geometry and Topology of ERK Enzyme Kinetics
ABSTRACT: In this talk I will analyse ERK time course data by
developing mathematical models of enzyme kinetics. I will present
how we can use differential algebra and geometry for model
identifiability and topological data analysis to study these the wild type
dynamics of ERK and ERK mutants. This work is joint with Lewis
Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.
Year(s) Of Engagement Activity 2019
URL https://cmsa.fas.harvard.edu/dynamics-and-randomness/
 
Description Heather Harrington - ICIAM Mini-symposium on Higher-order Networks, Valencia 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact TITLE: Topological data analysis for investigation of dynamics and biological networks
ABSTRACT: Persistent homology (PH) is a technique in topological data
analysis that allows one to examine features in data across multiple
scales in a robust and mathematically principled manner, and it is being
applied to an increasingly diverse set of applications. We investigate
applications of PH to dynamic biological networks.
1
Year(s) Of Engagement Activity 2019
URL https://iciam2019.org/images/site/news/ICIAM2019_PROGRAM_ABSTRACTS_BOOK.pdf
 
Description Heather Harrington - QMUL Women in Maths 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Engaged with students interested in maths
Year(s) Of Engagement Activity 2019
URL https://doctoralcollege.wordpress.com/2019/03/11/women-in-mathematics-2019-where-could-maths-take-yo...
 
Description Heather Harrington - SIAM Applied Algebraic Geometry, Bern 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact I was a member of the Programming Committee for the event. I also gave several talks and chaired several sessions.

TALK 1: Algebraic geometry in topological data analysis - with Parker Edwards, Emilie Dufresne, Jonathan D. Hauenstein.
TALK 1 ABSTRACT: I will discuss an adaptive algorithm for finding provably dense samples of points on a real algebraic variety given the variety's defining polynomials as input. Our algorithm utilizes methods from numerical algebraic geometry to give formal guarantees about the density of the sampling and it also employs geometric heuristics to reduce the size of the sample. As persistent homology methods consume significant computational resources that scale poorly in the number of sample points, our sampling minimization makes applying these methods more feasible. I will also present results of applying persistent homology to point samples generated by an implementation of the algorithm.

CHAIR 1 TITLE: Algebraic geometry, data science and fundamental physics. - with Yang-Hui He, Fabian Ruehle.
CHAIR 1 ABSTRACT: There has been an increasing interaction between computational algebraic geometry, data science and fundamental theoretical physics. This is rooted in the tradition that the 2 pillars of theoretical physics- general relativity and the standard model of particle physics, as well as their best candiate unified theory of superstrings - are physical realizations of the study of gauge connections and Riemannian metrics on manifolds. In the last couple of years, problems such as mapping the Calabi-Yau landscape, translating problems in particle theory to precise problems in algebraic and differential geometry, using the latest techniques in machine-learning, etc., have taken off in the theoretical physics community.

CHAIR 2&3 TITLE: Geometry and topology in applications - with Jacek Brodzki. Part 1 & 2

CHAIR 2 ABSTRACT for Parts 1 & 2: This symposium will bring together leading practitioners, mid-carreer scientists as well as PhD students and postdoctoral fellows who are interested in the theory and practice of the applications of geometry and topology in real life problems. The spectrum of possible applications is very wide, and covers the sciences, biology, medicine, materials science, and many others. The talks will address the theoretical foundations of the methodology as well as the state of the art of geometric and topological modelling.

Impact reported is not listed: As programme committee, I saw the major advances in applied algebra and topology.
Year(s) Of Engagement Activity 2019,2020
URL https://mathsites.unibe.ch/siamag19/
 
Description Heather Harrington - SIAM Conference on Applications of Dynamical Systems - MS87 Topological Data Analysis and Applications in Dynamical Systems - Part I of II 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact TITLE: Topological Data Analysis for Investigation of Dynamics and Biological Networks.
ABSTRACT: Topological Data Analysis for Investigation of Dynamics and Biological Networks
Persistent homology (PH) is a technique in topological data
analysis that allows one to examine features in data across
multiple scales in a robust and mathematically principled
manner, and it is being applied to an increasingly diverse
set of applications. We investigate applications of PH to
dynamic biological networks.
Year(s) Of Engagement Activity 2020
URL https://www.siam.org/conferences/cm/program/program-and-abstracts/ds19-program-abstracts
 
Description Heather Harrington - SIAM Keynote Workshop on Network Science: Topological Data Analysis for Investigating Dynamics on and of Biological Networks 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact Keynote lecture
Year(s) Of Engagement Activity 2019
 
Description Heather Harrington - Sheffield Applied Math Colloquium 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact TITLE: Comparing models and biological data using computational algebra and topology
ABSTRACT: Many biological problems, such as tumor-induced angiogenesis (the growth of blood vessels to provide nutrients to a tumor), or signaling pathways involved in the dysfunction of cancer (sets of molecules that interact that turn genes on/off and ultimately determine whether a cell lives or dies), can be modeled using differential equations. There are many challenges with analyzing these types of mathematical models, for example, rate constants, often referred to as parameter values, are difficult to measure or estimate from available data. I will present mathematical methods we have developed to enable us to compare mathematical models with experimental data. Depending on the type of data available, and the type of model constructed, we have combined techniques from computational algebraic geometry and topology, with statistics, networks and optimization to compare and classify models without necessarily estimating parameters. Specifically, I will introduce our methods that use computational algebraic geometry (e.g., Gröbner bases) and computational algebraic topology (e.g., persistent homology). I will present applications of our methodology on datasets involving cancer. Time permitting, I will conclude with our current work for analyzing spatio-temporal datasets with multiple parameters using computational algebraic topology. Mathematically, this is studying a module over a multivariate polynomial ring, and finding discriminating and computable invariants.
Year(s) Of Engagement Activity 2019
URL http://maths.dept.shef.ac.uk/maths/sem_history_2019.html
 
Description IBIN/3DbioNet Meeting, London (Helen Byrne) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Conducted the workshop, 'Unravelling biological complexity with mathematical modelling'
Year(s) Of Engagement Activity 2020
URL https://3dbionet.org/2019/11/26/full-agenda-for-upcoming-joint-ibin-3dbionet-meeting/
 
Description IBM Workshop, Oxford (Heather Harrington) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Study participants or study members
Results and Impact Developed experimental collaborations with Joe Howard and Sharad Ramanathan
Year(s) Of Engagement Activity 2019
 
Description Invited Lecture at Conference: 10 years SYM Copenhagen (U Tillmann) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Conference talk -- communication and dissemination of research
Year(s) Of Engagement Activity 2019
URL https://www.math.ku.dk/english/research/conferences/2019/sym-10-year-anniversary/
 
Description Invited lecture: National Academy of Montenegro 29 October 2019 (U Tillmann) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Invited talk to general audience of academy scientists
Year(s) Of Engagement Activity 2019
 
Description Invited plenary talk: Equivariant Topology and Derived Algebra, Trondheim (U Tillmann) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Plenary talk for large research conference.
Year(s) Of Engagement Activity 2019
URL https://www.commalg.org/2019/07/29/equivariant-topology-and-derived-algebra-in-honor-of-john-greenle...
 
Description Joint Mathematics Meeting - AMS Special Session on Topological Data Analysis: Theory and Applications (Heather Harrington) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact Invited speaker in the special session on Topological Data Analysis
Year(s) Of Engagement Activity 2019
URL http://jointmathematicsmeetings.org/meetings/national/jmm2019/2217_programindex
 
Description Maths in Action (Warwick) -- day of talks and activities for sixth formers (U Tillmann) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Schools
Results and Impact I gave a lecture on topology and data science.
Year(s) Of Engagement Activity 2018
URL https://www.thetrainingpartnership.org.uk/study-day/maths-in-action-14-11-2018/
 
Description Meeting and Conference of the Society for Mathematical Biology, Montreal (Helen Byrne) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited plenary title: Coming full circle in cancer modelling?
Year(s) Of Engagement Activity 2019
URL http://www.smb2019.org/
 
Description Modelling Challenges in Cancer and Immunology, Kings College (Helen Byrne) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact TITLE: Approaches to modelling tumour-immune interactions. ABSTRACT: While the presence of immune cells within solid tumours was initially viewed positively, as the host fighting to rid itself of a foreign body, we now know that the tumour can manipulate
immune cells so that they promote, rather than inhibit, tumour growth. Immunotherapy aims to
correct for this by boosting and/or restoring the normal function of the immune system.
Immunotherapy has delivered some extremely promising results. However the complexity of the
tumour-immune interactions means that it can be difficult to understand why one patient responds
well to immunotherapy while another does not. In this talk, we will show how mathematical
modelling can contribute to resolving this issue and present recent results which illustrate the
complementary insight that different modelling approaches can deliver.
Year(s) Of Engagement Activity 2019
URL https://mils.ghost.io/events/
 
Description Spires, Mathematical Institute, Oxford (All Members of TDA attended) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The purpose of this conference is to bring together international researchers working in topological data analysis and to discuss new developments and challenges that will shape the research in the future.
Year(s) Of Engagement Activity 2019
URL https://people.maths.ox.ac.uk/tillmann/TDA2019.html
 
Description Symposium on Machine Learning and Dynamical Systems, Imperial College (Heather Harrington) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Study participants or study members
Results and Impact TITLE: Topological data analysis for investigation of dynamics and networks

ABSTRACT: Persistent homology (PH) is a technique in topological data analysis that allows one to examine features in data across multiple scales in a robust and mathematically principled manner, and it is being applied to an increasingly diverse set of applications. We investigate applications of PH to dynamics and networks, focusing on two settings: dynamics on a network and dynamics of a network.

Dynamics on a network: a contagion spreading on a network is influenced by the spatial embeddedness of the network. In modern day, contagions can spread as a wave and through the appearance of new clusters via long-range edges, such as international flights. We study contagions by constructing 'contagion maps' that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast, and control of spreading processes.

Dynamics of a network: one can construct static graph snapshots to represent a network that changes in time (e.g. edges are added/removed). We show that partitionings of a network of random-graph ensembles into snapshots using existing methods often lack meaningful temporal structure that corresponds to features of the underlying system. We apply persistent homology to track the topology of a network over time and distinguish important temporal features from trivial ones. We define two types of topological spaces derived from temporal networks and use persistent homology to generate a temporal profile for a network. We show that the methods we apply from computational topology can distinguish temporal distributions and provide a high-level summary of temporal structure.

Together, these two investigations illustrate that persistent homology can be very illuminating in the study of networks and their applications.
Year(s) Of Engagement Activity 2019
URL https://sites.google.com/site/boumedienehamzi/symposium-on-machine-learning-for-dynamical-systems_20...
 
Description Women in Data Science (U Tillmann) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Other audiences
Results and Impact Conference for women in Data Science organised by the Alan Turing Institute.
Year(s) Of Engagement Activity 2018
URL https://www.turing.ac.uk/events/women-data-science-conference