Prof. Peter Grindrod CBE
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Books
Peter Grindrod, Leading Within Digital Worlds, (2020) Emerald Points, Emerald Publishing Ltd (2020)
Peter Grindrod, Mathematical Underpinnings of Analytics, (2014) OUP, Oxford. ISBN: 9780198725091.
Peter Grindrod, Patterns and Waves, The Theory and Applications of Reaaction Diffusion Equations, OUP, Oxford. https://tinyurl.com/yprcktcz
Most Papers (since 2010)
P. Grindrod and K.M. Yim. Dynamical Systems on Generalised Klein Bottles, Entropy 2025, 27, 119. https://www.mdpi.com/1099-4300/27/2/119
O. Gafvert, P. Grindrod, H.A. Harrington, C.F. Higham, D. J. Higham and Ka Man Yim (2025). On the hidden layer-to-layer topology of the representations of reality realised within neural networks, Engineering Computations. https://www.emerald.com/insight/content/doi/10.1108/ec-06-2024-0508/full/html
C.E Bowman, P. Grindrod, G.M. Smith and A. Stasinakis (2024) The National Risk Register 2023: Some Reasoned Reflections
September 2024 Sustainable and Resilient Infrastructure, 1–15 Published online: 04 Oct 2024. https://doi.org/10.1080/23789689.2024.2404277
P Grindrod, D.J. Higham, and H.-L. de Kergorlay (2023), Estimating Network Dimension when the spectrum struggles, Roy. Soc. Open Science https://royalsocietypublishing.org/doi/10.1098/rsos.230898
P. Grindrod (2024). Wishful Thinking About Consciousness. https://www.igminresearch.com/articles/pdf/igmin180.pdf IgMin Res. May 02, 2024; 2(5): 302-308. IgMin ID: igmin180; DOI: 10.61927/igmin180; Available at: igmin.link/p180
P. Grindrod and M. Brennan (2023) Cognition and Cosciousness Entwined, Brain Sci. 2023, 13(6), 872; https://doi.org/10.3390/brainsci13060872
M. Brennan and P. Grindord (2023) Generalised Kuramoto models with time-delayed phase-resetting for k-dimensional clocks,
Brain Multiphysics, Volume 4, https://doi.org/10.1016/j.brain.2023.100070 .
C.E. Bowman and P.Grindrod (2023), Desperately searching for something, Communications in Nonlinear Science and Numerical Simulation 125, https://authors.elsevier.com/a/1hN5s3b6559ZNF .
Z. Cui and P. Grindrod (2023) Mappings, Dimensionality and Reversing Out of Deep Neural Networks, IMA Jour Appl Maths, https://academic.oup.com/imamat/advance-article-abstract/doi/10.1093/im…
P. Grindrod CBE and M. Beguerisse-Díaz (2023) The Social Customer, (reviewed) to appear in Proceedisng of CARMA, Seville, https://www.researchgate.net/publication/371126293_The_Social_Customer
A. Bovet and P. Grindrod (2022) Structure and evolution of the UK far-right network on Telegram.Appl Netw Sci. 2022;7(1):76. doi: 10.1007/s41109-022-00513-8. Epub 2022 Nov 15. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9667007/.
P. Grindrod (2022), Scaling laws for properties of random graphs that grow via successive combination, Journal of Complex Networks, Volume 10, Issue 3, June 2022, cnac024, https://doi.org/10.1093/comnet/cnac024
P. Grindrod and C. Lester (2021), Cortex-Like Complex Systems: What Occurs Within? , Frontiers in Applied Mathematics and Statistics, 7, p 51 https://www.frontiersin.org/article/10.3389/fams.2021.627236
C. Singleton and P. Grindrod (2021), Forecasting for Battery Storage: Choosing the Error Metric. Energies 2021,14,6274. https://www.mdpi.com/1996-1073/14/19/6274/pdf
P. Grindrod, On human consciousness: A mathematical perspective, Network Neuroscience issue 1 volume 2 page 23-40 (January 2018)
P. Grindrod, D.J. Higham, High Modularity Creates Scaling Laws, Scientific reports issue 1 volume 8 page 9737-(27 June 2018)
P. Grindrod, D.J. Higham, and V. Noferini (2017) The deformed graph Laplacian and its applications to network centrality analysis, accepted to appear, SIAM Journal on Matrix Analysis and Applications SIAM Journal on Matrix Analysis and Applications, issue 1 volume 39 page 310-341(2018)
F. Arrigo, P. Grindrod, D.J. Higham, and V. Noferini, (2018) Non-backtracking walk centrality for directed networks, Journal of Complex Networks issue 1 volume 6page 54-78 (1 February 2018)
P. Grindrod and T.E. Lee, (2017) On strongly connected networks with excitable-refractory dynamics and delayed coupling, Royal Society Open Science, 5th April 2017. http://rsos.royalsocietypublishing.org/content/4/4/160912
P. Grindrod (2016) Beyond Privacy and Exposure: Ethical Issues within Citizen-Facing Analytics, Roy. Soc. Phil. Trans. A, Published 14 November 2016.DOI: 10.1098/rsta.2016.0132 http://rsta.royalsocietypublishing.org/content/374/2083/20160132
P. Grindrod and T.E. Lee, (2016) Comparison of social structures within cities of very different sizes, Royal Society Open Science, 24 February 2016.DOI: 10.1098/rsos.150526 http://rsos.royalsocietypublishing.org/content/3/2/150526
P. Grindrod, D.J. Higham, P. Laflin, A. Otley, J.A. Ward, (2016) Inverse network sampling to explore on-line brand allegianvce, European Journal of Applied Mathematics, CJO 2016 doi:10.1017/S0956792516000085
N.Otter, M.A. Porter, U.Tillmann, P. Grindrod, H.A. Harrington, (2015) A roadmap for the computation of persistent homology, EPJ Data Sci. 6, 17 (2017). https://doi.org/10.1140/epjds/s13688-017-0109-5/
P. Grindrod and E.L. Patel, (2015) Phase locking to the n-torus, IMA Journal of Applied Mathematics 10/2015; DOI: 10.1093/imamat/hxv031.
S. Haben, C.P. Singleton and P. Grindrod, (2015) Analysis and Clustering of Residential Customers Energy Behavioral Demand Using Smart Meter Data, IEEE TRANSACTIONS ON SMART GRID, JANUARY 2015, DOI: 10.1109/TSG.2015.2409786.
Grindrod, P. and Higham, D.J., (2014) A dynamical systems view of network centrality. Proc. R. Soc. A 470: 20130835. http://dx.doi.org/10.1098/rspa.2013.0835.
Ward, J.A and Grindrod, P. (2014) Aperiodic dynamics in a deterministic adaptive network model of attitude formation in social groups Physica D: Nonlinear Phenomena Volume 282, 15 July 2014, Pages 27–33.
Haben, S., Ward, J., Greetham, D., Grindrod, P. and Singleton, C. (2014) A new error measure for forecasts of household-level, high resolution electrical energy consumption. International Journal of Forecasting, 30, pp. 246--256, 2014.
D.V. Greetham , Z.Stoyanov, P.Grindrod (2014) On the radius of centrality in evolving communication networks, Journal of Combinatorial Optimization 10/2014; 28(3).
Grindrod, P. and Higham, D. J. (2013) A matrix iteration for dynamic network summaries. SIAM Review, 55, 2013, 118--128.
Laflin, P, Mantzaris, AV, Ainley, F, Otley, A, Grindrod, P & Higham, D (2013), Discovering and validating influence in a dynamic online social network, Social Network Analysis and Mining, vol 3, no. 4, pp. 1311-1323., 10.1007/s13278-013-0143-7.
P. Grindrod, Z.V. Stoyanov, G.M. Smith, J.D. Saddy, (2013) Primary evolving networks and the comparative analysis of robust and fragile structures, Journal of Complex Networks, doi: 10.1093/comnet/cnt015, 2013.
Parsons, M. C. and Grindrod, P. (2012) Competing edge networks, PHYSICS LETTERS A 376(32):2167–2173, ISSN 0375-9601 (2012).
Grindrod, P., Higham, D. J. and Parsons, M. C. (2011), Bistability through triadic closure. Internet Mathematics, 8, 2012, 402--423.
Grindrod, P. and Higham, D. J. (2012) Models for evolving networks: with applications in telecommunication and online activities. IMA J of Management Maths, 23.
Grindrod, P. and Parsons, M. (2011) Social networks: evolving graphs with memory dependent edges. Physica A, 390, 2. pp. 3970-3981.
Grindrod, P., Parsons, M. C., Higham, D. J. and Estrada, E. (2011) Communicability across evolving networks. Physical Review E, 83 (4). 046120. ISSN 1539-3755.
Grindrod, P. (2011) Mathematical modelling for the digital society. IMA Journal of Applied Mathematics, 76 (3). pp. 475-492.
Grindrod, P. and Pinotsis, D. (2011) On the spectra of certain integro-differential-delay problems with applications in neurodynamics., Physica D, 240 (1), pp13-20.
Grindrod, P. and Higham, D. J. (2010) Evolving graphs: dynamical models, inverse problems and propagation. Proceedings of the Royal Society A, 466 (2115).
Grindrod, P., Higham, D. J. and Kalna, G. (2010) Periodic Reordering. IMA Journal of Numerical Analysis, 30 (1). pp. 195-207.
Grindrod, P. and Higham, D. (2010) Models for Evolving Networks: with Applications in Telecommunication and Online Activities. IMA J of Management Maths.
Preprints
Peter Grindrod (2022), Economic and Social Resilience and Vulnerability, https://tinyurl.com/ydjzn4bu
Peter Grindrod (2022), There is something it is like to be me, https://tinyurl.com/5n7s6h3a
Clive E. Bowman and Peter Grindrod (2022), Desperately seeking something, https://tinyurl.com/4xaawrpx
Lyuba V. Bozhilova, Peter Grindrod, Gesine Reinert, and Tadas Temcinas (2022), Principles and Consequences of Evolutionary ’Omic Development: a Topological Perspective, https://tinyurl.com/mrxnnw3e
Peter Grindrod and Martin Brennan (2022), Cortex-Like Systems via Range-Dependent Networks of Phase-Resetting k-Dimensional Clocks, https://tinyurl.com/2eb5dxda
Peter Grindrod (2021), Unconvetional AI, https://tinyurl.com/ap28x22y
Peter Grindrod (2021), Research Strategy and Strategic Options for Mathematics Departments, https://tinyurl.com/ymc3afnb
Alain Goriely and Peter Grindrod (2021), Lessons to be Learned from the Covid-19 Experience in the UK https://tinyurl.com/59he5w5p
Peter Grindrod (2020), On MOD AI and Data Science, https://tinyurl.com/2p8s85pu
Peter Grindrod (2020), Rigorously Rethinking Data, https://tinyurl.com/ykxs4uuu .
Peter Grindrod (2020), Lock-Down Decompression: Opportunities for management and differential control, https://tinyurl.com/ymrr8ata.
Clive E. Bowman, Robert C. Brown, Peter Grindrod, Heather Wardle (2020), Online Gambling: Hidden Markov Models for Behavioural Changes, https://tinyurl.com/yp44j3ar .
Clive E. Bowman and Peter Grindrod (2019), Kinship, familial searching and biometrics, https://tinyurl.com/2kzd3a7m
Clive E. Bowman and Peter Grindrod (2019), Trust Limitation, Conflation and Hype, https://tinyurl.com/mr3h4cr2
Peter Grindrod, Desmond J. Higham, Robert S. MacKay, (2014), Opportunities at the Mathematics/ Future Cities Interface arXiv:1409.1831. [1]
D.J. Higham, P.Grindrod, A.V. Mantzaris, A. Otley, P. Laflin, (2014) Anticipating Activity in Social Media Spikes, arXiv:1406.2017v1
Conference Papers
G. Smith, Z. Stoyanov, D.V. Greetham, P. Grindrod, J.D. Saddy, (2014) Towards the Computer-aided Diagnosis of Dementia based on the Geometric and Network Connectivity of Structural MRI Data, MICCAI 2014 workshop Challenge on Computer-Aided Diagnosis of Dementia Based on Structural MRI Data; 09/2014.
S. Haben, M. Rowe, D.V. Greetham, P. Grindrod, W. Holderbaum, B. Potter, C. Singleton, (2013) Mathematical solutions for electricity networks in a low carbon future, Electricity Distribution (CIRED 2013), 22nd International Conference and Exhibition.
P. Laflin, A.V. Mantzaris, F. Ainley, A. Otley, P. Grindrod, D.J. Higham, (2012) Dynamic targeting in an online social medium, Proceedings of the 4th international conference on Social Informatics; 12/2012.
Laflin, P., Mantzaris, A.V., Higham, D.J., Grindrod, P., Ainley, F. and Otley, A., 2012. Twitter’s big hitters. In Proceedings of 2012 Digital Economy All Hands Conference, Aberdeen, Scotland.
Chapters in a books
P. Grindrod, (2015) Evolving social networks, attitudes and beliefs and counter terrorism. In: The Princeton Companion to Applied Mathematics. Edited by Nicholas J. Higham; Mark R. Dennis, Paul Glendinning, Paul A. Martin, Fadil Santosa & Jared Tanner, associate editors, 2015.
P. Grindrod, D.J. Higham and P. Laflin, (2016) The Graph Whisperers, UK Success Stories in Industrial Mathematics. Edited by P.J. Aston, A.J. Mulholland, K.M.M. Tant, Springer. 2016.
I am an innovator and a strategist.
My recent research includes novel ideas for neuromorphic information processing: developing whole cortex simulations via Kuramoto-types of models. Previously we have used supercomputers to make 10B neuron simutaions of the human cortex: these experiments are computationally expensive and take a lot of time - whereas if we exploit the brain's natural "network-of-networks" architecture we can use a sparse network of only 1M neural columns, where each column is a multi-dimensional "clock" representing say 10k neurons. As a result simulations can be made on a laptop, with similar results to the full simulations. Applications are to next generation (non-binary) neuromorphic computation, and to novel forms of AI.
I am also interested in the inner working of AI: both in supervised classification using ML/DL and in the use of generative models. The topology of the layer-by-layer representation of inputs can explian why these applications may be spooffed by strange, specific, perturbations of the inputs (that a human would regard as irrelevant), or being subject to adversarial attacks.
Scientific research strategy and research funding prioritization; encouraging uncoventional and non-consensual research; developing high risk and high impact research outcomes; coporate and academic collaborations.
Leadership for R&D teams in both commercial and academic research groups.
Start-ups, enterprise, and innovation
Mathematics of consciousness, Mathematics for Online Threats and Harms, Network theory and Digital Marketing, Trust and ethics in analytics and AI
Founding Trustee of The Alan Turing Institute; Chairman and founder of Hare Analytics Lmited; Chairman and founder of GTTA Limited; Director and founder of CountingLab Limited; Founder and former Director of Numbercraft Limited; Former Independent member of MOD Defence Scientific Advisory Council; Former member of EPSRC Council; Former member of BBSRC Council; Former member for RCUK Digital Economy programme advisory board; Former President of the Instutute of Mathematics and its Applications.
Cortex-like comnplex systems: what occurs within? https://vimeo.com/500916728
Leading within Digital worlds. https://www.youtube.com/watch?v=6gv9B0dSpKU&t=1987s
Urban Analytics https://www.youtube.com/watch?v=xAhzQQ5Hc0A
Why get into Data Science? Data Science at work https://www.youtube.com/watch?v=mH4mjF9ONy8
"The Mathematical Underpinnings of Analytics" OUP (2015) see video at http://www.amazon.com/Peter-Grindrod/e/B001KD6IK2/ref=dp_byline_cont_bo…;The book is aimed at final year and graduate students as well as early career professionals within analytics teams.
Strategy for scinetific research mechanisms and research funding: uncoventional and non consensual research.
The theory and applications of dynamically evolving networks, including nonlinear node-based dynamics, fully coupled through time dependent network dynamics. Stochastic modelling and classification of behaviour within evolving peer-to-peer communication and social networks. Memory dependent network dynamics. Generalisations of centrality to continuous time networks.
Applications of mathematics to social media, digital media and marketing, and the digital economy. Design of algorithms that run in real time over vast peer-to-peer networks. Applications of mathematics to the emergence of social norms and attitudes.
Dynamical systems and Delay Differential Equations. Theory and appications of semilinear parabolic systems. Non-Fickian dispersion.
Inference and forecasting problems for the energy (smart meter) retail, consumer goods, and telecommunications sectors. Behaviour-based risk measures and targetted-marketing applications.
Models for counter terrorism and real time recognition of anomalies within vast communications data sets.
Strategy for investment in science and technology research and innovation. Knowledge exchange and balancing open public research with confidential commercial interests through open innovation.
http://scholar.google.co.uk/citations?user=CKmGEiwAAAAJ&hl=en
Please do not telephone me: please use grindrod@maths.ox.ac.uk
I am an innovator and a strategist.
My recent research includes novel ideas for neuromorphic information processing: developing whole cortex simulations via Kuramoto-types of models. Previously we have used supercomputers to make 10B neuron simutaions of the human cortex: these experiments are computationally expensive and take a lot of time - whereas if we exploit the brain's natural "network-of-networks" architecture we can use a sparse network of only 1M neural columns, where each column is a multi-dimensional "clock" representing say 10k neurons. As a result simulations can be made on a laptop, with similar results to the full simulations. Applications are to next generation (non-binary) neuromorphic computation, and to novel forms of AI.
I am also interested in the inner working of AI: both in supervised classification using ML/DL and in the use of generative models. The topology of the layer-by-layer representation of inputs can explian why these applications may be spooffed by strange, specific, perturbations of the inputs (that a human would regard as irrelevant), or being subject to adversarial attacks.
Scientific research strategy and research funding prioritization; encouraging uncoventional and non-consensual research; developing high risk and high impact research outcomes; coporate and academic collaborations.
Leadership for R&D teams in both commercial and academic research groups.
Start-ups, enterprise, and innovation
Mathematics of consciousness, Mathematics for Online Threats and Harms, Network theory and Digital Marketing, Trust and ethics in analytics and AI
Founding Trustee of The Alan Turing Institute; Chairman and founder of Hare Analytics Lmited; Chairman and founder of GTTA Limited; Director and founder of CountingLab Limited; Founder and former Director of Numbercraft Limited; Former Independent member of MOD Defence Scientific Advisory Council; Former member of EPSRC Council; Former member of BBSRC Council; Former member for RCUK Digital Economy programme advisory board; Former President of the Instutute of Mathematics and its Applications.
Cortex-like comnplex systems: what occurs within? https://vimeo.com/500916728
Leading within Digital worlds. https://www.youtube.com/watch?v=6gv9B0dSpKU&t=1987s
Urban Analytics https://www.youtube.com/watch?v=xAhzQQ5Hc0A
Why get into Data Science? Data Science at work https://www.youtube.com/watch?v=mH4mjF9ONy8
"The Mathematical Underpinnings of Analytics" OUP (2015) see video at http://www.amazon.com/Peter-Grindrod/e/B001KD6IK2/ref=dp_byline_cont_bo…;The book is aimed at final year and graduate students as well as early career professionals within analytics teams.
Strategy for scinetific research mechanisms and research funding: uncoventional and non consensual research.
The theory and applications of dynamically evolving networks, including nonlinear node-based dynamics, fully coupled through time dependent network dynamics. Stochastic modelling and classification of behaviour within evolving peer-to-peer communication and social networks. Memory dependent network dynamics. Generalisations of centrality to continuous time networks.
Applications of mathematics to social media, digital media and marketing, and the digital economy. Design of algorithms that run in real time over vast peer-to-peer networks. Applications of mathematics to the emergence of social norms and attitudes.
Dynamical systems and Delay Differential Equations. Theory and appications of semilinear parabolic systems. Non-Fickian dispersion.
Inference and forecasting problems for the energy (smart meter) retail, consumer goods, and telecommunications sectors. Behaviour-based risk measures and targetted-marketing applications.
Models for counter terrorism and real time recognition of anomalies within vast communications data sets.
Strategy for investment in science and technology research and innovation. Knowledge exchange and balancing open public research with confidential commercial interests through open innovation.
http://scholar.google.co.uk/citations?user=CKmGEiwAAAAJ&hl=en