Tim Rogers

Professor of Mathematics

Department of Mathematical Sciences
University of Bath
4 West 3.37


+44(0)1225 38 6457


I am interested in understanding and predicting the behaviour of complicated random events and processes, in particular when there is network or spatial structure involved. Most of my work is connected to the idea of emergence: how large scale order can be created out of the random interactions of individual particles or organisms. As you can see from the titles of my papers, the problems I work on come from a wide range of sources, ecology, biochemistry, random matrix theory, social dynamics, stochastic processes, and so on...

Publications and preprints

Fitness differences suppress the number of mating types in evolving isogamous species
Yvonne Krumbeck, George W. A. Constable, Tim Rogers
preprint (2019)
Universal hypotrochoidic law for random matrices with cyclic correlations
Pau Vilimelis Aceituno, Tim Rogers, Henning Schomerus
preprint (2019)
New framework for automated article selection applied to a literature review of Enhanced Biological Phosphorus Removal
Minh Nguyen Quang, Tim Rogers, Jan Hofman, Ana B. Lanham
PLOS One (2019)
Spectral Theory of Sparse Non-Hermitian Random Matrices
(Topical Review)
Izaak Neri, Fernando Metz, Tim Rogers
arXiv Journal of Physics A: Mathematical and Theoretical (2019)
The invasion speed of cell migration models with realistic cell cycle time distributions
Enrico Gavagnin, Matthew J. Ford, Richard L. Mort, Tim Rogers, Christian A. Yates
arXiv Journal of Theoretical Biology (2018)
The Nested Kingman Coalescent: Speed of Coming Down from Infinity
Airam Blancas Benítez, Tim Rogers, Jason Schweinsberg, Arno Siri-Jégousse
arXiv Annals of Applied Probability (2018)
The effect of population abundances on the stability of large random ecosystems
Theo Gibbs, Jacopo Grilli, Tim Rogers, Stefano Allesina
Phys Rev E arXiv (2018)
Noise-driven bias in the non-local voter model
Kevin Minors, Tim Rogers, Christian A Yates
Europhysics Letters arXiv (2018)
A re-entrant phase transition in the survival of secondary
infections on networks

Sam Moore, Peter Mörters and Tim Rogers
Journal of Statistical Physics arXiv (2017)
Demographic noise slows down cycles of dominance
Qian Yang, Tim Rogers, and Jonathan Dawes

Journal of Theoretical Biology arXiv (2017)
Heterogeneous micro-structure of percolation in sparse networks
Reimer Kühn and Tim Rogers

arXiv Europhysics Letters (2017)
Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology
Todd Parsons and Tim Rogers
Journal of Physics A (2017) "Highlight of 2017"
A phase transition in excursions from infinity of the "fast" fragmentation-coalescence process
Andreas Kyprianou, Steven Pagett, Tim Rogers and Jason Schweinsberg
Annals of Probability arXiv (2017)
Universality in a class of fragmentation-coalescence processes
Andreas Kyprianou, Steven Pagett, and Tim Rogers
AIHP arXiv (2017)
Dual-specificity phosphatase 5 controls the localized inhibition, propagation, and transforming potential of ERK signaling
Andrew M. Kidger, Linda K. Rushworth, Julia Stellzig, Jane Davidson, Christopher J. Bryant, Cassidy Bayley, Edward Caddye, Tim Rogers, Stephen M. Keyse, and Christopher J. Caunt

PNAS (2017)
Demographic noise can reverse the direction of deterministic selection
George Constable, Tim Rogers, Alan McKane and Corina Tarnita

PNAS (2016)
Modularity and stability in ecological communities
Jacopo Grilli, Tim Rogers and Stefano Allesina

Nature Communications, 7, 12031 (2016)
Network Inoculation: Heteroclinics and phase transitions in an epidemic model
Hui Yang, Tim Rogers and Thilo Gross
Chaos, Volume 26, Issue 8 10.1063/1.4961249
From empirical data to time-inhomogeneous continuous Markov processes
Pedro Lencastre, Frank Raischel, Tim Rogers, and Pedro G. Lind
Phys. Rev. E 93, 032135 (2016)
Scale-invariant geometric random graphs
Zheng Xie and Tim Rogers
Phys. Rev. E 93, 032310 (2016)
Assessing node risk and vulnerability to epidemics on networks
Tim Rogers
Free to read until 31 December 2016 at EPL, also on arXiv:1502.00901
Europhys. Lett. 109, 28005 (2015) "Editor's Choice"
Modes of competition and the fitness of evolved populations
Tim Rogers, Alan McKane
Phys. Rev. E 92, 032708 (2015) "Editor's Suggestion"
Growth-induced breaking and unbreaking of ergodicity in fully-connected spin systems
Richard Morris, Tim Rogers
J. Phys. A: Math. Theor. 47 342003 (2014)
Current noise-removal methods can create false signals in ecogenomic data
Axel G Rossberg, Tim Rogers, Alan J McKane
Full text
Proc. R. Soc. B: Biol. (2014) 281, 1783
Null models for dynamic centrality in temporal networks
Tim Rogers
Full text
Journal of Complex Networks (2014)
Stochastic pattern formation and spontaneous polarisation: the linear noise approximation and beyond
Alan J McKane, Tommaso Biancalani, Tim Rogers
Bull. Math. Biol. 76, 4, pp 895-921 (2014)
Consensus time and conformity in the adaptive voter model
Tim Rogers, Thilo Gross
Phys. Rev. E 88, 030102(R) (2013)
Are there species smaller than 1mm?
Axel G Rossberg, Tim Rogers, Alan J McKane
Open access
Proc. R. Soc. B: Biol. (2013) 280, 1767
Stochastic dynamics on slow manifolds
George W A Constable, Alan J McKane, Tim Rogers
J. Phys. A: Math. Theor. 46, 295002 (2013)
Voter models with conserved dynamics
Fabio Caccioli, Luca Dall'Asta, Tobias Galla, Tim Rogers
Phys. Rev. E. 87, 052114 (2013)
Spontaneous genetic clustering in populations of competing organisms
Tim Rogers, Alan J McKane, Axel G Rossberg
Phys. Biol. 9, 066002 (2012)
Stochastic oscillations of adaptive networks:
application to epidemic modelling

Tim Rogers, William Clifford-Brown, Catherine Mills, Tobias Galla
J. Stat. Mech. P08018 (2012)
Noise-induced metastability in biochemical networks
Tommaso Biancalani, Tim Rogers, Alan J McKane
Phys. Rev. E 86, 010106 (Rapid Communications) (2012)
Jamming and pattern formation in models of segregation
Tim Rogers, Alan J McKane
Phys. Rev. E 85, 041136 (2012)
Demographic noise can lead to the spontaneous formation of species
Tim Rogers, Alan J McKane, Axel G Rossberg
Europhys. Lett. 97, 40008 (2012) "Editor's Choice"
A unified framework for Schelling's model of segregation
Tim Rogers, Alan J McKane
J. Stat. Mech. P07006 (2011)
Maximum-entropy moment-closure for stochastic systems on networks
Tim Rogers
J. Stat. Mech. P05007 (2011)
Universal sum and product rules for random matrices
Tim Rogers
J. Math. Phys. 51, 093304 (2010)
Spectral density of random graphs with topological constraints
Tim Rogers, Conrad Pérez Vicente, Koujin Takeda, Isaac Pérez Castillo
J. Phys. A: Math. Theor. 43 195002, (2010)
Cavity approach to the spectral density of non-Hermitian sparse matrices
Tim Rogers, Isaac Pérez Castillo
Phys. Rev. E. 79, 012101 (2009)
Cavity approach to the spectral density of sparse symmetric random matrices
Tim Rogers, Koujin Takeda, Isaac Pérez Castillo, Reimer Kühn
Phys. Rev. E. 78, 031116 (2008)
PhD Thesis - New Results on the Spectral Density of Random Matrices
Tim Rogers
King's College London (2010)

Art & Popular Science

9:1 profliferation: movement, 4 stages, 1,723 steps
Leonie Bradley
Print artwork based on my work with Kit Yates and Enrico Gavagnin on cell proliferation.
Click here too see a video of the process, or here to read about how the work was made.
Debunking the selfish myth
Tim Rogers and George Constable

Positive News
Adam Evans and Alec Morton
Video art piece created by Adam Evans and Alec Morton for Fringe Arts Bath, exploring the themes of my research into stochastic effects in evolution.
Click here for the video.
"The Species Paradox"
Ignite talk: watch the video
University of Bath, December 2013
How, if and why species form
Axel G Rossberg, Tim Rogers, Alan J McKane
Popular science article
The Scientist, November 2013 Issue
Make your own patterns with the Swift-Hohenberg equation
Interactive demo made for Manchester Museum
(you'll need an up-to-date version of Firefox or Chrome)

PhD Students

Yvonne Krumbeck
Co-supervised with George Constable
Project: Randomness in biological populations
Enrico Gavagnin
Co-supervised with Kit Yates
Project: Cell migration and collective behaviour
Sam Moore
Co-supervised with Peter Mörters
Project: Contagion on networks
Minh Nguyen Quang
Co-supervised with Ana Lanham
Project: Microbial community structure in biological phosphorus removal systems
Qian Yang
Co-supervised with Jonathan Dawes
Project: Cyclic dominance
Kevin Minors
Co-supervised with Jonathan Dawes
Project: Invasive species
Steven Pagett
Co-supervised with Andreas Kyprianou
Project: Fragmentation-coalescence processes


MA30245: Graphs & Networks
University of Bath, Spring 2015, 2016, 2017

Epidemics and Networks
Complex Systems Modelling "Masterclass"
King's Collect London, Spring 2015
Download the notes
Bayesian Data Analysis
Manchester University, Autumn 2011
Download the worked examples
(you'll need Mathematica)