# School of Mathematics

## Prof Grant D Lythe

Professor in Applied Mathematics

Applied Mathematics

### Contact details

Room: Satellite 10.11

Tel: +44 (0)113 3435132

Email: G.D.Lythe @ leeds.ac.uk

## Research interests

http://www1.maths.leeds.ac.uk/~grant

### Useful links

Marie Curie Initial Training Network: Quantitative T cell immunology

IndoEuropean Maths for health and disease

## Current postgraduate students

Luis De La Higuera Romero (2013)

Marco Ferrarini (2014)

Maria Nowicka (2012)

Remus Stana (2015)

## Publications

**Chu HH, Chan SW, Gosling JP, Blanchard N, Tsitsiklis A, Lythe G, Shastri N, Molina-París C, Robey EA** Continuous Effector CD8^{+}T Cell Production in a Controlled Persistent Infection Is Sustained by a Proliferative Intermediate Population *Immunity*, **45**, 159-171, 2016

DOI:10.1016/j.immuni.2016.06.013

View abstract

**Donavan GM, Lythe GD** T cell and reticular network co-dependence in HIV infection *Journal of Theoretical Biology*, **395**, 211-220, 2016

DOI:10.1016/j.jtbi.2016.01.040

View abstract

**Castro M, Lythe G, Molina-París C, Ribeiro RM** Mathematics in modern immunology *Interface Focus*, **6**, 14, 2016

DOI:10.1098/rsfs.2015.0093

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**Lythe G, Callard RE, Hoare RL, Molina-París C** How many TCR clonotypes does a body maintain? *Journal of Theoretical Biology*, **389**, 214-224, 2016

DOI:10.1016/j.jtbi.2015.10.016

View abstract

**Pham K, Shimoni R, Charnley M, Ludford-Menting MJ, Hawkins ED, Ramsbottom K, Oliaro J, Izon D, Ting SB, Reynolds J, Lythe G, Molina-Paris C, Melichar H, Robey E, Humbert PO, Gu M, Russell SM** Asymmetric cell division during T cell development controls downstream fate *Journal of Cell Biology*, **210**, 933-950, 2015

DOI:10.1083/jcb.201502053

View abstract

**Burrage K, Lythe G** Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations *Stochastic Partial Differential Equations: Analysis and Computations*, **2**, 262-280, 2014

DOI:10.1007/s40072-014-0032-8

View abstract

**Reynolds J, Amado IF, Freitas AA, Lythe G, Molina-París C** A mathematical perspective on CD4^{+}T cell quorum-sensing *Journal of Theoretical Biology*, **347**, 160-175, 2014

DOI:10.1016/j.jtbi.2013.12.019

View abstract

**Sawicka M, Stritesky GL, Reynolds J, Abourashchi N, Lythe G, Molina-París C, Hogquist KA** From pre-DP, post-DP, SP4, and SP8 thymocyte cell counts to a dynamical model of cortical and medullary selection *Frontiers in Immunology*, **5**, 2014

DOI:10.3389/fimmu.2014.00019

View abstract

**Castro M, van Santen HM, Férez M, Alarcón B, Lythe G, Molina-París C** Receptor pre-clustering and T cell responses: Insights into molecular mechanisms *Frontiers in Immunology*, **5**, 2014

DOI:10.3389/fimmu.2014.00132

View abstract

**Gillard J, Laws TR, Lythe G, Molina-París C** Modelling early events in Francisella tularensis pathogenesis *Frontiers in Cellular and Infection Microbiology*, **4**, 2014

DOI:10.3389/fcimb.2014.00169

View abstract

**Reynolds J, Coles M, Lythe G, Molina-París C** Mathematical model of naive T cell division and survival IL-7 thresholds *Frontiers in Immunology*, **4**, 2013

DOI:10.3389/fimmu.2013.00434

View abstract

**Celli S, Day M, Müller AJ, Molina-Paris C, Lythe G, Bousso P** How many dendritic cells are required to initiate a T-cell response? *Blood*, **120**, 3945-3948, 2012

DOI:10.1182/blood-2012-01-408260

View abstract

**Celli S, Day M, Muller AJ, Molina-Paris C, Lythe GD, Bousso P** How many dendritic cells are required to initiate a T cell response *Blood*, 2012

**Alemeida ARM, Amado IF, Reynolds J, Berges J, Lythe G, Molina-Paris C, Freitas AA** Quorum-Sensing in CD4+ T Cell Homeostasis: A Hypothesis and a Model *Frontiers in Immunology*, **3**, 2012

DOI:10.3389/fimmu.2012.00125

View abstract

**Reynolds J, Coles M, Lythe G, Molina-Pars C** Deterministic and stochastic naive T cell population dynamics: Symmetric and asymmetric cell division *Dynamical Systems*, **27**, 75-103, 2012

DOI:10.1080/14689367.2011.645447

View abstract

**Donovan GM, Lythe GD** T-cell movement on the reticular network *Journal of Theoretical Biology*, **295**, 59-67, 2012

DOI:10.1016/j.jtbi.2011.11.001

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**Molina Paris C ed. ** *Mathematical Models and Immune Cell Biology* 2011

View abstract

**Stirk ER, Lythe G, van den Berg HA, Molina-París C** Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire. *J Theor Biol*, **265**, 396-410, 2010

DOI:10.1016/j.jtbi.2010.05.004

View abstract

**Stirk ER, Lythe G, van den Berg HA, Hurst GAD, Molina-París C** The limiting conditional probability distribution in a stochastic model of T cell repertoire maintenance *Mathematical Biosciences*, **224**, 74-86, 2010

DOI:10.1016/j.mbs.2009.12.004

View abstract

**Stirk ER, Lythe G, van den Berg HA, Hurst GAD, Molina-París C** The limiting conditional probability distribution in a stochastic model of T cell repertoire maintenance *Mathematical biosciences*, **224**, 74-86, 2010

**Burrage K, Lythe G** Accurate stationary densities with partitioned numerical methods for stochastic differential equations *SIAM Journal on Numerical Analysis*, **47**, 1601-1601, 2009

**Castro M, Lythe G** Numerical Experiments on Noisy Chains: From Collective Transitions to Nucleation-Diffusion *SIAM Journal on Applied Dynamical Systems*, **7**, 207-219-207-219, 2008

DOI:10.1137/070695514

**Castro M, Lythe G** Numerical Experiments on Noisy Chains: From Collective Transitions to Nucleation-Diffusion *SIAM Journal on Applied Dynamical Systems*, **7**, 207-219-207-219, 2008

DOI:10.1137/070695514

**Burrage K, Lenane I, Lythe G** Numerical Methods for Second-Order Stochastic Differential Equations *SIAM Journal on Scientific Computing*, **29**, 245-264-245-264, 2007

DOI:10.1137/050646032

**Burrage K, Lenane I, Lythe G** Numerical Methods for Second-Order Stochastic Differential Equations *SIAM Journal on Scientific Computing*, **29**, 245-264-245-264, 2007

DOI:10.1137/050646032

**Lythe GD, Habib S** Kink stochastics *Computing in Science&Engineering*, **8**, 10-15, 2006

DOI:10.1109/MCSE.2006.43

View abstract

**Lythe G** Diffusion-limited reaction in one dimension *Physica D*, **222**, 159-163, 2006

DOI:10.1016/j.physd.2006.07.030

**Camassa R, Findikoglu A, Lythe GD** Transmission, Reflection, and Second-Harmonic Generation in a Nonlinear Waveguide *SIAM Journal on Applied Mathematics*, **66**, 1-28, 2005

DOI:10.1137/040615183

View abstract

**Jansons KM, Lythe GD** Multidimensional exponential timestepping with boundary test *SIAM J SCI COMPUT*, **27**, 793-808, 2005

**Lythe GD, Mertens F** Rice's ansatz for overdamped kinksat finite temperature *Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics)*, **67**, pp.027601, 2003

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**Lythe G, Mertens FG** Rice's ansatz for overdampedφ^{4}kinks at finite temperature *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **67**, 276011, 2003

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**Lythe GD** Exponential timesepping for stochastic differential equations *SIAM Journal on Scientific Computing*, **24**, 2003

**Lythe G; Habib S ** *Kinks in a Stochastic PDE*IUTAM symposium on nonlinear stochastic dynamics, 435-444 2003

**Lythe G, Mertens F** Rice’s ansatz for overdamped $φ^4$ kinks at finite temperature *Physical Review E*, **67**, 027601-4-027601-4, 2003

**Jansons KM, Lythe GD** Exponential timestepping with boundary test for stochastic differential equations *SIAM J SCI COMPUT*, **24**, 1809-1822, 2003

**Finkikoglu A, Camassa R, Lythe GD, Jia QX** Dielectric nonlinearity and stochastic effects in strontium titanate *Applied Physics Letters*, **80**, 3391-3393, 2002

DOI:10.1063/1.1477278

**Lythe G** Defect formation in a dynamic transition *International Journal of Theoretical Physics*, **40**, 2309-2316, 2001

View abstract

**Habib S, Lindenberg K, Lythe GD, Molina-Paris C** Diffusion-limited reaction in one dimension: Paired and unpaired nucleation *Journal of Chemical Physics*, **115**, 73-89, 2001

DOI:10.1063/1.1372763

**Lythe G** Stochastic PDEs: convergence to the continuum? *J. Comp. Phys.*, 2001

**Habib S, Lindenberg K, Lythe G, Carmen M-PS** Diffusion-limited reaction in one dimension:paired and unpaired nucleation *J. Chem. Phys.*, **115**, 73-89-73-89, 2001

**Lythe G, Habib S** Stochastic PDEs: convergence to the continuum? *Computer Physics Communications*, **142**, 29-35, 2001

**Jansons KM, Lythe GD** Efficient numerical solution of stochastic differential equations using exponential timestepping *Journal of Statistical Physics*, **100**, 1097-1109, 2000

View abstract

**Habib S, Lythe GD** Dynamics of Kinks: Nucleation, Diffusion and Annihilation *Physical Review Letters*, **84**, 1070-1073, 2000

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**Jansons KM, Lythe GD** Efficient Numerical Solution of Stochastic Differential Equations Using Exponential Timestepping *Journal of Statistical Physics*, **100**, 1097-1109, 2000

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**Habib S, Lythe G** Dynamics of kinks: nucleation, diffusion and annihilation *Physical Review Letters*, **84**, 1070-1073-1070-1073, 2000

**Bettencourt LMA, Habib S, Lythe G** Controlling one-dimensional Langevin dynamics on the lattice *Physical Review D - Particles, Fields, Gravitation and Cosmology*, **60**, 1-9, 1999

View abstract

**Bettencourt L, Habib S, Lythe G** Controlling one-dimensional Langevin dynamics on the lattice *Physical Review D*, **60**, 105039-47-105039-47, 1999

**Moro E, Lythe G** Dynamics of defect formation *Physical Review E*, **59**, R1303-6, 1999

**Lythe G, Proctor MRE** Predictabilty of noise-controlled dynamics *Physica D*, **133**, 362---362--, 1999

**Findikoglu AT, Jia QX, Reagor DW, Fan Y, Lythe GD, Camassa RA, Cai D, Gronbech-Jensen N, Bishop AR** New potential applications of nonlinear dielectrics: Microwave solitons and stochastic resonance *Integrated Ferroelectrics*, **22**, 259-268, 1998

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**Jansons KM, Lythe GD** Stochastic Stokes Drift *Physical Review Letters*, **81**, 3136-3139, 1998

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**Jansons KM, Lythe GD** Stochastic calculus: dynamic bifurcations and threshold crossings *J. Stat. Phys.*, **90**, 227-251, 1998

**Celet JC, Dangoisse D, Glorieux P, Lythe G, Erneux T** Slowly passing through resonance strongly depends on noise *Physical Review Letters*, **81**, 975-978, 1998

**Lythe G; Erneux T; Gavrielides A; Kovanis V ** *Quasi-periodicity in semiconductor lasers*Proceedings of SPIE - The International Society for Optical Engineering, 624-635 1997

View abstract

**Gavrielides A, Kovanis V, Varangis PM, Erneux T, Lythe G** Coexisting periodic attractors in injection-locked diode lasers *Journal of Optics B: Quantum and Semiclassical Optics*, **9**, 785-796, 1997

View abstract

**Lythe G, Erneux T, Gavrielides A, Kovanis V** Low pump limit of the bifurcation to periodic intensities in a semiconductor laser subject to external optical feedback *Physical Review A*, **55**, 4443-4448-4443-4448, 1997

**Lythe GD** Domain formation in transitions with noise and a time-dependent bifurcation parameter *Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, **53**, 1996

View abstract

**Lythe GD** Domain Formation in Transitions with Noise and a Time-dependent Bifurcation Parameter *Physical Review A*, **53**, 4271-4274, 1996

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**Lythe G** Domain formation in dynamic transitions with noise *Physical Review E*, **53**, R4271-4274, 1996

**Celet JC; Dangoisse O; Glorieux P; Lythe G; Erneux T ** *Slow passage through resonance in a periodically modulated laser*Technical Digest - European Quantum Electronics Conference, 31 1996

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**Gavrielides A; Kovanis V; Lythe G; Erneux T ** *Quasiperiodic intensity oscillations in a laser subject to optical feedback*Technical Digest - European Quantum Electronics Conference, 166 1996

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**Lythe GD** Dynamics controlled by additive noise *Il Nuovo Cimento D*, **17**, 855-861, 1995

DOI:10.1007/BF02451843

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**PROCTOR MRE; LYTHE GD ** *Noise and Resonant Mode Interactions*Annals of the New York Academy of Sciences, 42-53 1993

DOI:10.1111/j.1749-6632.1993.tb24680.x

Noise and slow-fast dynamics in a three-wave resonance problem *Physical Review E*, **47**, 3122-3127, 1993

**WH A, IA B, BUDDING E, MJ C, DANIEL A, KB F, FUJII H, FUJII Z, HAYASHIDA N, HIBINO K, HONDA M, JE H, KABE S, KASAHARA K, KIFUNE T, GD L, MASAIKE A, MATSUBARA Y, MITSUI K, MIURA Y, MORI M, MURAKI Y, NAGANO M, NAKAMURA T, NISHIZAWA M, PM M, OGIO S, SAITO T, SAKATA M, SATO H, HM S, SPENCER M, JR S, TANIMORI T, TESHIMA M, TORII S, WADSWORTH A, WATASE Y, MD W, YAMAMOTO Y, PCM Y, YUDA T** SEARCH FOR POINT SOURCES OF ULTRAHIGH-ENERGY GAMMA-RAYS IN THE SOUTHERN SKY *Physica D*, **48**, 466-478, 1993

**WH A, IA B, BUDDING E, MJ C, DANIEL A, KB F, FUJII H, FUJII Z, HAYASHIDA N, HIBINO K, HONDA M, JE H, KABE S, KASAHARA K, KIFUNE T, GD L, MASAIKE A, MATSUBARA Y, MITSUI K, MIURA Y, MORI M, MURAKI Y, NAGANO M, NAKAMURA T, NISHIZAWA M, PM M, OGIO S, SAITO T, SAKATA M, SATO H, HM S, SPENCER M, JR S, TANIMORI T, TESHIMA M, TORII S, WADSWORTH A, WATASE Y, MD W, YAMAMOTO Y, PCM Y, YUDA T** SEARCH FOR POINT SOURCES OF ULTRAHIGH-ENERGY GAMMA-RAYS IN THE SOUTHERN SKY *Astrophysical Journal*, **344**, L14-L17-L14-L17, 1989

**Lythe GD** A stochastic T cell response criterion *Journal of the Royal Society Interface*

Lythe G *Stochastic slow-fast dynamics*

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