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?
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.
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
- University of Oxford, United Kingdom (Collaboration, Lead Research Organisation)
- Spotify (Collaboration)
- University of California, Berkeley (Collaboration)
- Swiss Federal Institute of Technology in Lausanne (EPFL) (Collaboration)
- University of California Los Angeles, United States (Collaboration)
- Harvard University (Collaboration)
- IBM, United States (Collaboration)
- University of Udine (Collaboration)
- S&P Global (Collaboration)
- University of Padova (Collaboration)
- University of British Columbia, Canada (Collaboration)
- Massachusetts Institute of Technology (Collaboration)
- University of Wisconsin Madison, United States (Collaboration)
- George Mason University, United States (Collaboration)
- Max Planck Society (Collaboration)
- Gdansk University of Technology (Collaboration)
- Cambridge Crystallographic Data Centre, United Kingdom (Collaboration)
- Santa Clara University (Collaboration)
- GlaxoSmithKline (GSK) (Collaboration)
- Yeshiva University (Collaboration)
- University of Glasgow, United Kingdom (Collaboration)
- University of Malaysia, Terengganu (Collaboration)
- Colorado State University, United States (Collaboration)
- Cornell University (Collaboration)
- University of Strathclyde, United Kingdom (Collaboration)
- Yale University (Collaboration)
- University of Exeter, United Kingdom (Collaboration)
- Technical University of Munich (Collaboration)
- American University of Sharjah (Collaboration)
- University at Buffalo, United States (Collaboration)
- Texas A & M University, United States (Collaboration)
- The National Institute for Research in Computer Science and Control (INRIA) (Collaboration)
- Roche Pharmaceuticals (Collaboration)
- Southern Methodist University (Collaboration)
- North Carolina State University, United States (Collaboration)
- Bentley University (Collaboration)
- University of Southampton, United Kingdom (Collaboration)
- University of Arizona, United States (Collaboration)
- University of Florida, United States (Collaboration)
- University of Massachusetts Amherst, United States (Collaboration)
- Alan Turing Institute (Collaboration)
- Jagiellonian University, Poland (Collaboration)
- University of Hawaii at Manoa, United States (Collaboration)
- Bangor University, United Kingdom (Collaboration)
- Ohio State University, United States (Collaboration)
- Chinese Academy of Sciences (Collaboration)
- Ludwig Institute for Cancer Research (Collaboration)
- Princeton University, United States (Collaboration)
- Queen Mary, University of London, United Kingdom (Collaboration)
- Unlisted (Collaboration)
- University of Notre Dame (Collaboration)
- Rutgers University (Collaboration)
- University of Maryland, United States (Collaboration)
- NTNU University Museum (Collaboration)
- Australian National University (ANU) (Collaboration)
- Imperial College London, United Kingdom (Collaboration)
- Technion Israel Institue of Technology, Israel (Collaboration)
- Queen's University of Belfast, United Kingdom (Collaboration)
- University of Cambridge, United Kingdom (Collaboration)
- University of York, United Kingdom (Collaboration)
- European Organization for Nuclear Research (CERN) (Collaboration)
- National Institute for Nuclear Physics, Italy (Collaboration)
- St. Pölten University of Applied Sciences (Collaboration)
- Clemson University (Collaboration)
- Swansea University, United Kingdom (Collaboration)
- Free University of Amsterdam (Collaboration)
- University of Bremen (Collaboration)
- Technical University Berlin (Collaboration)
- Google (Collaboration)
- IFP New Energy (Project Partner)
- Swiss Federal Inst of Technology (EPFL), Switzerland (Project Partner)
- GlaxoSmithKline PLC (Project Partner)
- University of Ulster, United Kingdom (Project Partner)
- BSMBench Limited (Project Partner)
- GCHQ, United Kingdom (Project Partner)
- University of Sheffield, United Kingdom (Project Partner)
- Unilever Corporate Research, United Kingdom (Project Partner)
- Kognitio Limited (Project Partner)
Publications
Bartosz Zielinsk
(2019)
Persistence Bag-of-Words for Topological Data Analysis
Bozhilova LV
(2019)
Measuring rank robustness in scored protein interaction networks.
in BMC bioinformatics
Bright M
(2020)
Encoding and topological computation on textile structures
in Computers & Graphics
Byrne Helen M
(2019)
Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature
in arXiv e-prints
De Kergorlay Henry-Louis
(2019)
Random Cech Complexes on Manifolds with Boundary
in arXiv e-prints
Devraj Basu
(2020)
The Four Seasons of Commodity Futures: Insights from Topological Data Analysis
in SSRN
Dlotko P
(2019)
Fake Conductivity or Cohomology: Which to Use When Solving Eddy Current Problems With $h$ -Formulations?
in IEEE Transactions on Magnetics
Dlotko Pawel
(2019)
An Economic Topology of the Brexit vote
in arXiv e-prints
Dufresne Emilie
(2018)
Sampling real algebraic varieties for topological data analysis
in arXiv e-prints
Heather Harrington
(2019)
Topology Characterises Tumour Vasculature
in Mathematics Today.
Kališnik S
(2019)
A higher-dimensional homologically persistent skeleton
in Advances in Applied Mathematics
Kurlin V
(2020)
Persistence-based resolution-independent meshes of superpixels
in Pattern Recognition Letters
Kurlin Vitaliy
(2019)
Skeletonisation Algorithms with Theoretical Guarantees for Unorganised Point Clouds with High Levels of Noise
in arXiv e-prints
Lee Y
(2018)
High-Throughput Screening Approach for Nanoporous Materials Genome Using Topological Data Analysis: Application to Zeolites.
in Journal of chemical theory and computation
Mosca M
(2020)
Voronoi-Based Similarity Distances between Arbitrary Crystal Lattices
in Crystal Research and Technology
Nanda V
(2019)
Discrete Morse theory and localization
in Journal of Pure and Applied Algebra
Nanda V
(2019)
Local Cohomology and Stratification
in Foundations of Computational Mathematics
Qiu W
(2020)
Refining understanding of corporate failure through a topological data analysis mapping of Altman's Z-score model
in Expert Systems with Applications
Stolz Bernadette J
(2019)
Geometric anomaly detection in data
in arXiv e-prints
Stolz Bernadette J
(2019)
Geometric anomaly detection in data
in arXiv e-prints
Stolz Bernadette J.
(2018)
Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia
in arXiv e-prints
| 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 |
| Description | TOPMAP Platform for predicting biomarkers for patient stratification |
| Amount | $200,000 (USD) |
| Organisation | Emerson Collective |
| Sector | Private |
| Country | United States |
| Start | 12/2019 |
| End | 12/2021 |
| 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 | |
| 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 |