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List of Publications for D. J. Higham

Books

B7: An Introduction to the Numerical Simulation of Stochastic Differential Equations, D.J. Higham and P. E. Kloeden, SIAM, 2021.
B6: MATLAB Guide, D.J. Higham and N.J. Higham, Society for Industrial and Applied Mathematics, 3rd edition, 2017.
B5: Learning L^AT_EX, D.F. Griffiths and D.J. Higham, Society for Industrial and Applied Mathematics, 2nd edition, 2016.
B4: Numerical Methods for Ordinary Differential Equations, D. F. Griffiths and D. J. Higham, Springer, 2010.
B3: Network Science: Complexity in Nature and Technology, Edited by E. Estrada, M. Fox, D. J. Higham and G.-L. Oppo, Springer, 2010.
B2: An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, D.J. Higham, Cambridge University Press, 2004.
B1: Numerical Analysis 1997: Proceedings of the 17th Biennial Conference on Numerical Analysis, Edited by D.F. Griffiths, D.J. Higham and G.A. Watson, Pitman Research Notes in Mathematics, Longman Scientific and Technical, 1998.

Refereed Journal Papers
(In reverse chronological order of acceptance)

P168: Estimating network dimension when the spectrum struggles, P. Grindrod, D. J. Higham and H.-L. de Kergorlay, Royal Society Open Science, to appear, 2024.
P167: Higher-order connection Laplacians for directed simplicial complexes, X. Gong, D. J. Higham, K. Zygalakis and G. Bianconi, Journal of Physics: Complexity, to appear, 2024.
P166: Backward error analysis and the qualitative behaviour of stochastic optimization algorithms: Application to stochastic coordinate descent, S. Di Giovacchino, D. J. Higham and K. C. Zygalakis, Journal of Computational Dynamics, early access, 2024.
P165: Connectivity of random geometric hypergraphs, H.-L. de Kergorlay and D. J. Higham, Ergodicity (special issue on Higher-Order Networks), to appear, 2023.
P164: The feasibility and inevitability of stealth attacks, I.Y. Tyukin, D. J. Higham, A. Bastounis, E. Woldegeorgis, A. N. Gorban, The Institute of Mathematics and Its Applications (IMA) Journal of Applied Mathematics, to appear, 2023.
P163: Weighted enumeration of nonbacktracking walks on weighted graphs, F. Arrigo, D. J. Higham, V. Noferini and R. Wood, SIAM Journal on Matrix Analysis and Applications, to appear, 2023.
P162: Adversarial ink: Componentwise backward error attacks on deep learning, L. Beerens and D. J. Higham, The Institute of Mathematics and Its Applications (IMA) Journal of Applied Mathematics, to appear 2023.
P161: Generative hypergraph models and spectral embedding, X. Gong, D. J. Higham, K. Zygalakis, Scientific Reports, 13, 2023.
P160: Core-periphery detection in hypergraphs, F. Tudisco and D. J. Higham, SIAM J. on Mathematics of Data Science, 5, 2023.
P159: Dynamic Katz and related network measures, F. Arrigo, D. J. Higham and V. Noferini, R. Wood, Linear Algebra and Its Applications, 655, 2022. 159--185
P158: Mean field analysis of hypergraph contagion models, D. J. Higham and H.-L. de Kergorlay, SIAM J. Applied Mathematics, 82, 2022, 1987--2007.
P157: Disease extinction for susceptible-infected-susceptible models on dynamic graphs and hypergraphs, D. J. Higham and H.-L. de Kergorlay, Chaos, 32, 2022, 083131.
P156: A hierarchy of network models giving bistability under triadic closure, S. Di Giovacchino, D. J. Higham and K. Zygalakis, Multiscale Modeling and Simulation (SIAM), 20, 2022, 1394--1410.
P155: Directed network Laplacians and random graph models, X. Gong, D. J. Higham and K. Zygalakis, Royal Society Open Science, 8, 2021.
P154: Consistency of anchor-based spectral clustering, H.-.L de Kergorlay and D. J. Higham, Information and Inference: A Journal of the IMA, 11, 2022, 801--822.
P153: Epidemics on hypergraphs: Spectral thresholds for extinction, D. J. Higham and H.-L. de Kergorlay, Proceedings of the Royal Society, Series A, 477, 2021.
P152: Node and edge eigenvector centrality for hypergraphs, F. Tudisco and D. J. Higham, Communications Physics, 4, 2021.
P151: A theory for backtrack-downweighted walks, F. Arrigo, D. J. Higham and V. Noferini, SIAM Journal on Matrix Analysis and Applications, 42, 2021. 1229--1247.
P150: Random matrices generating large growth in LU factorization with pivoting, D. J. Higham, N. J. Higham and S. Pranesh, SIAM Journal on Matrix Analysis and Applications, 42, 2021, 185--201.
P149: Accurately computing the log-sum-exp and softmax functions, P. Blanchard, D. J. Higham and N. J. Higham, The Institute of Mathematics and Its Applications (IMA) Journal of Numerical Analysis, 41, 2021.
P148: Modelling burglary in Chicago using a self-exciting point process with isotropic triggering, C. Gilmour and D. J. Higham, European Journal of Applied Mathematics, 33, 2022, 369--391.
P147: A framework for second-order eigenvector centralities and clustering coefficients, F. Arrigo, D. J. Higham and F. Tudisco, Proceedings of the Royal Society, Series A, 476, 2020.
P146: Beyond non-backtracking: Non-cycling network centrality measures, F. Arrigo, D. J. Higham and V. Noferini, Proceedings of the Royal Society, Series A, 476, 2020.
P145: A network model for polarization of political opinion, A. Mantzaris and D. J. Higham, Chaos, 30, 2020.
P144: Non-backtracking PageRank, F. Arrigo, D. J. Higham and V. Noferini, J. Scientific Computing, 80, 2019, 1419--1437.
P143: A fast and robust kernel optimization method for core-periphery detection in directed and weighted graphs, F. Tudisco and D. J. Higham, Applied Network Science, 4, 2019.
P142: Non-backtracking alternating walks, F. Arrigo, D. J. Higham and V. Noferini, SIAM J. Applied Mathematics, 79, 2019, 781--801.
P141: Deep learning: An introduction for applied mathematicians, C. F. Higham and D. J. Higham, SIAM Review, 61, 2019, 860--891.
P140: A nonlinear spectral method for core--periphery detection in networks, F. Tudisco and D. J. Higham, SIAM J. on Mathematics of Data Science, 2, 2019, 269--292.
P139: Centrality-friendship paradoxes: When our friends are more important than us, D. J. Higham, Journal of Complex Networks, 7, 2019, 515--528.
P138: On constrained Langevin equations and (bio)chemical reaction networks, D. F. Anderson, D. J. Higham, S. C. Leite and R. J. Williams, Multiscale Modeling and Simulation (SIAM), 17, 2019, 1--30.
P137: On the exponential generating function for non-backtracking walks, F. Arrigo, P. Grindrod, D. J. Higham and V. Noferini, Linear Algebra and its Applications, 556, 2018, 381--399.
P136: Computational complexity analysis for Monte Carlo approximations of classically scaled population processes, D. F. Anderson, D. J. Higham and Y. Sun, Multiscale Modeling and Simulation (SIAM), 16, 2018, 1206--1226.
P135: High modularity creates scaling laws, P. Grindrod and D. J. Higham, Scientific Reports, 8, 2018, 9737.
P134: The deformed graph Laplacian and its applications to network centrality analysis, P. Grindrod, D. J. Higham and V. Noferini, SIAM Journal on Matrix Analysis and Applications, 39, 2018, 310--341.
P133: Centrality analysis for modified lattices, M. Paton, K. Akartunali and D. J. Higham, SIAM Journal on Matrix Analysis and Applications, 38, 2017, 1055--1073.
P132: Nonbacktracking walk centrality for directed networks, F. Arrigo, P. Grindrod, D. J. Higham and V. Noferini, Journal of Complex Networks, 6, 2018, 54--78.
P131: Sparse matrix computations for dynamic network centrality, F. Arrigo and D. J. Higham, Applied Network Science, 2, 2017, 1--19.
P130: An overview of city analytics, D. J. Higham, M. Batty, L. M. A. Bettencourt, D. Vukadinovic Greetham and P. Grindrod, Royal Society Open Science, 4, 2017, 161063.
P129: Block matrix formulations for evolving networks, C. Fenu and D. J. Higham, SIAM Journal on Matrix Analysis and Applications, 38, 2017, 343--360.
P128: Multilevel Monte Carlo for stochastic differential equations with small noise, D. F. Anderson, D. J. Higham and Y. Sun, SIAM Journal on Numerical Analysis, 54, 2016, 505--529.
P127: Inverse network sampling to explore on-line brand allegiance, P. Grindrod, D. J. Higham, P. Laflin, A. Otley, J. A. Ward, European Journal of Applied Mathematics (Special Issue on Networks), 27, 2016, 958--970.
P126: Asymmetry through time dependency, A. V. Mantzaris and D. J. Higham, European Physics Journal B (Special issue on Temporal Networks), 89, 2016.
P125: Matching exponential-based and resolvent-based centrality measures, M. Aprahamian, D. J. Higham and N. J. Higham, Journal of Complex Networks, 4, 2015, 157--176.
P124: An introduction to multilevel Monte Carlo for option valuation, D. J. Higham, International Journal of Computer Mathematics (Special Issue on Computational Methods in Finance), 92, 2015, 2347--2360.
P123: Complexity of multilevel Monte Carlo tau-leaping, D. F. Anderson, D. J. Higham and Y. Sun, SIAM Journal on Numerical Analysis, 52, 2015, 3106--3127.
P122: Betweenness in time dependent networks, A. Alsayed and D. J. Higham, Chaos, Solitons and Fractals (Special Issue on Network Science), Volume 72, 2015, 35--48.
P121: A dynamical systems view of network centrality, P. Grindrod and D. J. Higham, Proceedings of the Royal Society, Series A, 2014, 20130835.
P120: Subanaesthetic ketamine treatment promotes abnormal interactions between neural subsystems and alters the properties of functional brain networks, N. Dawson, M. McDonald, D. J. Higham, B. Morris and J. Pratt, Neuropsychopharmacology, 39 2014, 1786--1798.
P119: Discovering and validating influence in a dynamic online social network, P. Laflin, A. V. Mantzaris, P. Grindrod, F. Ainley, A. Otley and D. J. Higham, Social Network Analysis and Mining, 3, 2013, 1311--1323.
P118: Convergence, non-negativity and stability of a new Milstein scheme with applications to finance, D. J. Higham, X. Mao and L. Szpruch, Discrete and Continuous Dynamical Systems B, 2013, 2083--2100.
P117: Mathematical modelling of polyamine metabolism in bloodstream-form Trypanosoma brucei: An application to drug target identification, X. Gu, D. Reid, D. J. Higham and D. Gilbert, PLoS ONE, 8, 2013, e53734.
P116: Dynamic network centrality summarizes learning in the human brain, A. V. Mantzaris, D. S. Bassett, N. F. Wymbs, E. Estrada, M. A. Porter, P. J. Mucha, S. T. Grafton and D. J. Higham, Journal of Complex Networks, 1, 2013, 83--92.
P115: Mean exit times and the multi-level Monte Carlo method, D. J. Higham, X. Mao, M. Roj, Q. Song and G. Yin, Journal of Uncertainty Quantification (SIAM/ASA), 1, 2013, 2--18.
P114: Simultaneous non-negative matrix factorization for multiple large scale gene expression datasets in toxicology, C. M. Lee, M. A. V. Mudaliar, D. R. Haggart, C. R. Wolf, G. Miele, J. K. Vass, D. J. Higham and D. Crowther, PLoS ONE, 7, 2013, e48238.
P113: Sustained NMDA receptor hypofunction induces compromised neural systems integration and schizophrenia-like alterations in functional brain networks, N. Dawson, X. Xiao, D. J. Higham, B. Morris, J. Pratt, Cerebral Cortex, 2014, 452--464.
P112: A model for dynamic communicators, A. Mantzaris and D. J. Higham, European Journal of Applied Mathematics (Special Issue on Network Science), 23, 2012, 659--668.
P111: Bistability through triadic closure, P. Grindrod, D. J. Higham and M. C. Parsons, Internet Mathematics, 8, 2012, 402--423.
P110: Spectral algorithms for heterogeneous biological networks, M. McDonald, D. J. Higham and J. K. Vass, Briefings in Functional Genomics, 11, 2012, 457--468.
P109: A matrix iteration for dynamic network summaries, P. Grindrod and D. J. Higham, SIAM Review, 55, 2013, 118--128.
P108: Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics, D. F. Anderson and D. J. Higham, Multiscale Modeling and Simulation (SIAM), 10, 2012, 146-179.
P107: Googling the Brain: Discovering hierarchical and asymmetric network structures, with applications in neuroscience, J. J. Crofts and D. J. Higham, Internet Mathematics (Special Issue on Biological Networks), 7, 2011, 233-254.
P106: Exploring metabolic pathway disruption in the subchronic phencyclidine model of schizophrenia with the Generalized Singular Value Decomposition, X. Xiao, N. Dawson, L. MacIntyre, B. J. Morris, J. A. Pratt, D. G. Watson and D. J. Higham, BMC Systems Biology, 2011, 5:72.
P105: Discretization provides a conceptually simple tool to build expression networks, J. K. Vass, D. J. Higham, M. A. V. Mudaliar, X. Mao, D. J. Crowther, PLoS ONE 6(4), 2011, e18634.
P104: Communicability across evolving networks, P. Grindrod, D. J. Higham, M. C. Parsons and E. Estrada, Physical Review E, 83 2011, 046120.
P103: Hybrid simulation of autoregulation within transcription and translation, D. J. Higham, S. Intep, X. Mao and L. Szpruch, BIT Numerical Mathematics, 51, 2011, 177-196.
P102: Models for evolving networks: with applications in telecommunication and online activities, P. Grindrod and D. J. Higham, The Institute of Mathematics and Its Applications (IMA) Journal of Management Mathematics, 23, 2012, 1-16.
P101: Discovering bipartite substructure in directed networks, A. J. Taylor, J. K. Vass and D. J. Higham, London Mathematical Society J. Comput. and Math., 14, 2011, 72-86.
P100: Stochastic ordinary differential equations in applied and computational mathematics, D. J. Higham, The Institute of Mathematics and Its Applications (IMA) Journal of Applied Mathematics, special issue: "2020 visions of applied mathematics", 76, 2011, 449-474.
P99: Network analysis detects changes in the contralesional hemisphere following stroke, J. J. Crofts, D. J. Higham, R. Bosnell, S. Jbabdi, P. M. Matthews, T. E. J. Behrens; H. Johansen-Berg, NeuroImage, 54, 2011, 161-169.
P98: Mapping directed networks, J. J. Crofts, E. Estrada, D. J. Higham and A. Taylor, Electronic Transactions on Numerical Analysis, 37, 2010, 337-350.
P97: Numerical simulation of a strongly nonlinear Ait-Sahalia type interest rate model, L. Szpruch, X. Mao, D. J. Higham and J. Pan, BIT Numerical Mathematics, 51, 2011, 405-425.
P96: Non-negative matrix factorisation for network reordering, C. Lee, D. J. Higham, D. Crowther and J. K. Vass, Monografias de la Real Academia de Ciencias de Zaragoza, (special issue honouring Manuel Calvo on his 65th birthday), 33, 2010, 39-53.
P95: Network properties revealed through matrix functions, E. Estrada and D. J. Higham, SIAM Review, 52, 2010, 696-714.
P94: Comparing hitting time behaviour of Markov jump processes and their diffusion approximations, L. Szpruch and D. J. Higham, Multiscale Modeling and Simulation (SIAM), 8, 2010, 605-621.
P93: Periodic reordering, P. Grindrod, D. J. Higham and G. Kalna, The Institute of Mathematics and Its Applications (IMA) Journal of Numerical Analysis (Special Issue in Honour of A. R. Mitchell), 30, 2010, 195-207.
P92: Evolving graphs: Dynamical models, inverse problems and propagation, P. Grindrod and D. J. Higham, Proceedings of the Royal Society, Series A, 466, 2010, 753-770.
P91: Zero, one and two-switch models of gene regulation, S. Intep and D. J. Higham, Discrete and Continuous Dynamical Systems, Series B, 14 (special issue in honour of Peter Kloeden), 2010, 495-513.
P90: Geometric de-noising of protein-protein interaction networks, O. Kuchaiev, M. Rasajski, D. J. Higham and N. Przulj, PLoS Computational Biology, 5, 2009, e1000454.
P89: Switching and diffusion models for gene regulation networks, S. Intep, D. J. Higham and X. Mao, Multiscale Modeling and Simulation (SIAM), 8, 2009, 30-45.
P88: First and second moment reversion for a discretised square root process with jumps, G. D. Chalmers and D. J. Higham, J. Difference Equations and Applications, 16 (special issue in honour of Peter Kloeden), 2010, 143-156.
P87: A weighted communicability measure applied to complex brain networks, J. J. Crofts and D. J. Higham, J. Royal Socety Interface, 33, 2009, 411-414.
P86: Communicability betweenness in complex networks, E. Estrada, D. J. Higham and N. Hatano, Physica A. 388, 2009, 764-774.
P85: Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff, M. Giles, D. J. Higham and X. Mao, Finance and Stochastics. 13, 2009, 403-413.
P84: Communicability and multipartite structures in complex networks at negative absolute temperatures, E. Estrada, D. J. Higham and N. Hatano, Physical Review E, 78, 2008, 026102.
P83: CONTEST: A Controllable Test Matrix Toolbox for MATLAB, A. Taylor and D. J. Higham, ACM Trans. Math. Software., 35, 2009, 26:1-26:17.
P82: Asymptotic stability of a jump-diffusion equation and its numerical approximation, G. D. Chalmers and D. J. Higham, SIAM Journal on Scientific Computing, 31, 2008, 1141-1155.
P81: Chemical master equation and Langevin regimes for a gene transcription model, R. Khanin and D. J. Higham, Theoretical Computer Science. 408, 2008, 31-40.
P80: Fitting a geometric graph to a protein-protein interaction network, D. J. Higham, M. Rasajski and N. Przulj, Bioinformatics, 2008.
P79: Chemical master versus chemical Langevin for first-order reaction networks, D. J. Higham and R. Khanin, The Open Applied Mathematics Journal, 2, 2008, 59-79.
P78: DNA meets the SVD, P. Grindrod, D. J. Higham, G. Kalna, A. Spence, Z. Stoyanov and J. K. Vass, The Institute of Mathematics and Its Applications (IMA) Mathematics Today, 44, 2008, 80-85.
P77: A clustering coefficient for weighted networks, with application to gene expression data, G. Kalna and D. J. Higham, AI Communications (The European Journal on Artificial Intelligence) special issue on Network Analysis in Natural Sciences and Engineering, 20, 2007, 263-271.
P76: Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations, D. J. Higham, X. Mao and C. Yuan, Numerische Mathematik, 108, 2007, 295-325.
P75: Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes, G. D. Chalmers and D. J. Higham, Discrete and Continuous Dynamical Systems B, 9, 2008, 47-64.
P74: Modeling and simulating chemical reactions, D. J. Higham, SIAM Review, Education Section, 50, 2008, 347-368.
P73: Comment on "Numerical methods for stochastic differential equations", K. Burrage, P. Burrage, D. J. Higham, P. E. Kloeden and E. Platen, Physical Review E, 74, 2006, 068701.
P72: Multidimensional partitioning and bi-partitioning: analysis and application to gene expression datasets, G. Kalna, J. K. Vass and D. J. Higham, International Journal of Computer Mathematics, 85, 2008, 475-485.
P71: Spectral analysis of two-signed microarray expression data, D. J. Higham, G. Kalna and J. K. Vass, IMA Mathematical Medicine and Biology, 24, 2007, 131-148.
P70: Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations, D. J. Higham, X. Mao and C. Yuan, SIAM J. Numer. Anal., 45, 2007, 592-609.
P69: A matrix perturbation view of the small world phenomenon, D. J. Higham, SIAM Review, 49, 2007, 91-108 (chosen as a SIGEST article, based on [P49]).
P68: Connectivity-based parcellation of human cortex using diffusion MRI: establishing reproducibility, validity and observer-independence in BA 44/45 and SMA/pre-SMA, J. C. Klein, T. E. J. Behrens, M. D. Robson, C. E. Mackay, D. J. Higham, H. Johansen-Berg, NeuroImage, 34, 2007, 204-211.
P67: Modelling protein-protein interaction networks via a stickiness inde, N. Przulj and D. J. Higham, J. Royal Society Interface, 3, 2006, 711-716.
P66: Divergent routes to oral cancer, K. D. Hunter, J. K. Thurlow, J. Fleming, P. J. H. Drake, J. K. Vass, G. Kalna, D. J. Higham, P. Herzyk, D. G. MacDonald, E. K. Parkinson, P. R. Harrison, Cancer Research, 66, 2006, 7405-7413.
P65: A lock-and-key model for protein-protein interactions, J. L. Morrison, R. Breitling, D. J. Higham and D. R. Gilbert, Bioinformatics, 22, 2006, 2012-2019.
P64: Nonnormality and stochastic differential equations, D. J. Higham and X. Mao, BIT Numerical Mathematics. 46, 525-532, 2006.
P63: Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems, D. J. Higham and P. E. Kloeden, J. Computational and Applied Math. 205, 2007, 949-956.
P62: Greedy pathlengths and small world graphs, D. J. Higham, Linear Algebra and Its Applications, 416, 2006, 745-758.
P61: Spectral clustering and its use in bioinformatics, D. J. Higham, G. Kalna, and M. Kibble, J. Computational and Applied Math., 204, 2007, 25-37.
P60: Convergence and stability of implicit methods for jump-diffusion systems, D. J. Higham and P. E. Kloeden, International Journal of Numerical Analysis & Modeling, 3, 2006, 125-140.
P59: GeneRank: Using search engine technology for the analysis of microarray experiments, J. L. Morrison, R. Breitling, D. J. Higham and D. R. Gilbert, BMC Bioinformatics 2005, 6:233.
P58: Numerical methods for nonlinear stochastic differential equations with jumps, D. J. Higham and P. E. Kloeden, Numerische Mathematik, 101, 2005, 101-119.
P57: Convergence of Monte Carlo simulations involving the mean-reverting square root process, D. J. Higham and X. Mao, Journal of Computational Finance. 8, 2005, 35-61.
P56: Google PageRank as mean playing time for pinball on the reverse web,, D. J. Higham, Applied Mathematics Letters, 18, 2005, 1359-1362.
P55: Spectral reordering of a range-dependent weighted random graph,, D. J. Higham, The Institute of Mathematics and Its Applications (IMA) Journal of Numerical Analysis. 25, 2005, 443-457.
P54: Black-Scholes for scientific computing students, D. J. Higham, Computing in Science and Engineering (Education Section), 6, 2004, 72-79.
P53: Changes in connectivity profiles define functionally-distinct regions in human medial frontal cortex, H. Johansen-Berg, T. E. J. Behrens, M. D. Robson, I. Drobnjak, M. F. S. Rushworth, J. M. Brady, S. M. Smith, D. J. Higham and P. M. Matthews, Proceedings of the National Academy of Sciences (PNAS), vol. 101 (no. 26), 2004, 13335-13340.
P52: Numerical simulation of a linear stochastic oscillator with additive noise, A. H. Strømmen Melbø and D. J. Higham, Applied Numerical Mathematics, 51, 2004, 89-99.
P51: The sleekest link algorithm, D. J. Higham and A. Taylor, The Institute of Mathematics and Its Applications (IMA) Mathematics Today, 39, 2003, 192-197.
P50: Exponential mean square stability of numerical solutions to stochastic differential equations, D. J. Higham, X. Mao and A. M. Stuart, London Mathematical Society J. Comput. and Math., 6, 2003, 297-313.
P49: A matrix perturbation view of the small world phenomenon, D. J. Higham, SIAM Journal on Matrix Analysis and Applications, 25, 2003, 429-444.
P48: Unravelling small world networks, D. J. Higham, J. Computational and Applied Math., 158, 2003, 61-74.
P47: On the boundedness of asymptotic stability regions for the stochastic theta method, A. Bryden and D. J. Higham. BIT Numerical Mathematics, 43, 2003, 1-7.
P46: Nine ways to implement the binomial method for option valuation in MATLAB, D. J. Higham. SIAM Review, Education Section, 44, 2002, 661-677.
P45: Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise, J. Mattingly, A. M. Stuart and D. J. Higham. Stochastic Processes and their Appl., 101, 2002, 185-232.
P44: Strong convergence of Euler-type methods for nonlinear stochastic differential equations, D. J. Higham, X. Mao and A. M. Stuart. SIAM J. Num Anal., 40, 2002, 1041-1063.
P43: Error analysis of QR algorithms for computing Lyapunov exponents, E. J. McDonald and D. J. Higham, Electronic Transactions on Numerical Analysis, 12, 2001, 234-251.
P42: An algorithmic introduction to numerical simulation of stochastic differential equations, D. J. Higham, SIAM Review, Education Section, 43, 2001, 525-546.
P41: MacCormack's method for advection-reaction equations, D. F. Griffiths and D. J. Higham, Journal of the Japan Society of Computational Fluid Dynamics, 9, 2000.
P40: Mean-square and asymptotic stability of numerical methods for stochastic ordinary differential equations, D. J. Higham, SIAM J. Num Anal, 38, 2000, 753-769.
P39: Theta method dynamics, G. J. Barclay, D. F. Griffiths and D. J. Higham, London Mathematical Society J. Comput. and Math., 3, 2000, 27-43.
P38: A-stability and stochastic mean-square stability, D. J. Higham, BIT, 40, 2000, 404-409.
P37: Runge-Kutta solutions of a hyperbolic conservation law with source term, M. A. Aves, D. F. Griffiths and D. J. Higham, SIAM Journal on Scientific Computing, 22, 2000, 20-38.
P36: The effect of quadrature on the dynamics of a discretised nonlinear integro-differential equation, M. A. Aves, P. J. Davies and D. J. Higham, Applied Numerical Mathematics, 32, 2000, 1-20.
P35: Phase space error control for dynamical systems, D. J. Higham, A. R. Humphries and R. J. Wain, SIAM Journal on Scientific Computing, 21, 2000, 2275-2294.
P34: Trust region algorithms and timestep selection, D. J. Higham, SIAM Journal on Numerical Analysis, 37, 1999, 194-210.
P33: Qualitative properties of modified equations, O. Gonzalez, A. M. Stuart and D. J. Higham, IMA Journal of Numerical Analysis, 19, 1999, 169-190.
P32: Structured backward error and condition of generalized eigenvalue problems, D. J. Higham and N. J.Higham, SIAM Journal on Matrix Analysis and Applications, 20, 1998, 493-512.
P31: Analysis of the dynamics of local error control via a piecewise continuous residual, D. J. Higham and A. M. Stuart, BIT, 38, 1998, 44-57.
P30: Regular Runge-Kutta pairs, D. J. Higham, Applied Numerical Mathematics, 25, 1997, 229-241.
P29: Time-stepping and preserving orthonormality, D. J. Higham, BIT, 37, 1997, 24-36.
P28: Does error control suppress spuriosity? M. A. Aves, D. F. Griffiths and D. J. Higham, SIAM Journal on Numerical Analysis, 34, 1997, 756-778.
P27: Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes, M. C. Calvo, D. J. Higham, J. M. Montijano and L. Rández, Advances in Computational Mathematics, 7, 1997, 361-382.
P26: Dynamics of constant and variable stepsize methods for a nonlinear population model with delay, D. J. Higham and T. Sardar, Applied Numerical Mathematics, 24, 1997, 425-438.
P25: Runge-Kutta type methods for orthogonal integration, D. J. Higham, Applied Numerical Mathematics, 22, 1996, 217-223.
P24: Non-normality effects in a discretised, nonlinear, reaction-convection-diffusion equation, D. J. Higham and B. Owren, Journal of Computational Physics, 124, 1996, 309-323.
P23: Global error estimation with adaptive explicit Runge-Kutta methods, M. C. Calvo, D. J. Higham, J. M. Montijano and L. Rández, IMA Journal of Numerical Analysis, 16, 1996, 47-63.
P22: Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay, D. J. Higham and T. Sardar, Applied Numerical Mathematics, 18, 1995, 155-173.
P21: Equilibrium states of adaptive algorithms for delay differential equations, D. J. Higham and I.Th. Famelis, Journal of Computational and Applied Mathematics, 58, 1995, 151-169.
P20: Condition numbers and their condition numbers, D. J. Higham, Linear Algebra and Its Applications, 214, 1995, 193-214.
P19: Runge-Kutta stability on a Floquet problem, D. J. Higham, BIT, 34, 1994, 88-98.
P18: Error control for initial value problems with discontinuities and delays, D. J.Higham, Applied Numerical Mathematics, 12, 1993, 315-330.
P17: Stiffness of ODEs, D. J. Higham and L. N. Trefethen, BIT, 33, 1993, 285-303.
P16: The tolerance proportionality of adaptive ODE solvers, D. J. Higham, Journal of Computational and Applied Mathematics, 45, 1993, 227-236.
P15: Componentwise perturbation theory for linear systems with multiple right-hand sides, D. J. Higham and N. J. Higham, Linear Algebra and Its Applications, 174, 1992, 111-130.
P14: The structured sensitivity of Vandermonde-like systems, S. G. Bartels and D. J. Higham, Numerische Mathematik, 62, 1992, 17-33.
P13: Monotonic piecewise cubic interpolation, with applications to ODE plotting, D. J. Higham, Journal of Computational and Applied Mathematics, 39, 1992, 287-294.
P12: Backward error and condition of structured linear systems, D. J. Higham and N. J. Higham, SIAM Journal on Matrix Analysis and Applications, 13, 1992, 162-175.
P11: Parallel defect control, W. H. Enright and D. J. Higham, BIT, 31, 1991, 647-663.
P10: Global error versus tolerance for explicit Runge-Kutta methods, D. J. Higham, IMA Journal of Numerical Analysis, 11, 1991, 457-480.
P9: Remark on Algorithm 669, D. J. Higham, ACM Transactions on Mathematical Software, 17, 1991, 424-426.
P8: Runge-Kutta defect control using Hermite-Birkhoff interpolation, D. J. Higham, SIAM Journal on Scientific and Statistical Computing, 12, 1991, 991-999.
P7: Highly continuous Runge-Kutta interpolants, D. J. Higham, ACM Transactions on Mathematical Software, 17, 1991, 368-386.
P6: Embedded Runge-Kutta formulae with stable equilibrium states, D. J. Higham and G. Hall, Journal of Computational and Applied Mathematics, 29, 1990, 25-33.
P5: Robust defect control with Runge-Kutta schemes, D. J. Higham, SIAM Journal on Numerical Analysis, 26, 1989, 1175-1183.
P4: Defect estimation in Adams PECE codes, D. J. Higham, SIAM Journal on Scientific and Statistical Computing, 10, 1989, 964-976.
P3: Large growth factors in Gaussian elimination with pivoting, N. J. Higham and D. J. Higham, SIAM Journal on Matrix Analysis and Applications, 10, 1989, 155-164.
P2: Analysis of the Enright-Kamel partitioning method for stiff ODEs, D. J. Higham, IMA Journal of Numerical Analysis, 9, 1989, 1-14.
P1: Analysis of stepsize selection schemes for Runge-Kutta codes, G. Hall and D. J. Higham, IMA Journal of Numerical Analysis, 8, 1988, 305-310.

Refereed Conference Papers

C14: The boundaries of verifiable accuracy, robustness, and generalisation in deep learning, Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen, Desmond J. Higham, Danil Prokhorov, Oliver Sutton, Ivan Y. Tyukin, Qinghua Zhou, Artificial Neural Networks and Machine Learning – ICANN 2023, 2023, Crete
C13: Core-periphery partitioning and quantum annealing, C. F. Higham, D. J Higham and F. Tudisco, Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2020, Washington D.C.
C12: On adversarial examples and stealth attacks in artificial intelligence systems, I. Y. Tyukin, D. J. Higham and A. N. Gorban, in IEEE International Joint Conference on Neural Networks, 2020, Glasgow.
C11: Modelling and inferring the triggering function in a self-exciting point process, C. Gilmour and D. J. Higham, in Proceedings of 5th International Conference on Numerical Analysis and Optimization, Editors: Mehiddin Al-Baali, Anton Purnama, Lucio Grandinetti, pages 121-133, 2020, Oman.
C10: Preserving sparsity in dynamic network computations, F. Arrigo and D. J. Higham, in International Workshop on Complex Networks and their Applications, 2016, Milan.
C9: Dynamic targeting in an online social medium, P. Laflin, A. V. Mantzaris, P. Grindrod, F. Ainley, A. Otley and D. J. Higham, in Social Informatics 2012, Lausanne.
C8: Demonstration of dynamic targeting in an online social medium, P. Laflin, A. V. Mantzaris, P. Grindrod, F. Ainley, A. Otley and D. J. Higham, real time demonstration and demo paper in Social Informatics 2012, Lausanne.
C7: Computing mean first exit times for stochastic processes using multilevel Monte Carlo, D. J. Higham and M. Roj, Proceedings of the 2012 Winter Simulation Conference, edited by C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose and A. M. Uhrmacher, 2012, Berlin.
C6: Analysis of the singular value decomposition as a tool for processing microarray expression data, D. J. Higham, G. Kalna and J. K. Vass, Proceedings of ALGORITMY 2005, Conference on Scientific Computing, Slovak University of Technology, 250-259, Slovakia, 2005.
C5: Reordering diffusion-based connectivity matrices to define anatomical networks of the human brain, T. E. J. Behrens, H. Johansen-Berg, S. M. Smith, I. Drobnjak, J. M. Brady, P. M. Matthews and D. J. Higham, Proceedings of the International Society for Magnetic Resonance in Medicine 12th Scientific Meeting, Kyoto, 2004.
C4: Connectivity based anatomical parcellation of cortical grey matter, H. Johansen-Berg, T. E. J. Behrens, I. Drobnjak, S. M. Smith, D. J. Higham and P. M. Matthews, Proceedings of the 10th International Conference for Functional Mapping of the Human Brain, Budapest, 2004.
C3: Runge-Kutta and MacCormack dynamics, D. F. Griffiths and D. J. Higham, Proceedings of the 8th International Symposium on Computational Fluid Dynamics (CD ROM format), Bremen, Sep. 1999.
C2: The reliability of standard local error control algorithms for initial value ordinary differential equations, D. J. Higham, Proceedings of the IFIP Conference on The Quality of Numerical Software, R.F. Boisvert, Ed. 1997, 315-325, Chapman & Hall.
C1: Runge-Kutta equilibrium theory for a mixed relative-absolute error measure, D. J. Higham and G. Hall, Proceedings of the 1989 IMA Conference on Computational ODEs, J.R. Cash and I. Gladwell, Eds 1992, 73-85, Oxford University Press.

Refereed Book Chapters

Bc7: The Graph Whisperers, P. Grindrod, D. J. Higham and P. Laflin, in UK Success Stories in Industrial Mathematics, edited by P. J. Aston, A. J. Mulholland and K. M. M. Tant, pp. 271--279, Springer, 2016.
Bc6: Dynamic Communicability Predicts Infectiousness, A. V. Mantzaris and D. J. Higham, in Temporal Networks, edited by P. Holme and J. Saramaki, pp. 283--294, Springer, 2013.
Bc5: Infering and Calibrating Triadic Closure in a Dynamic Network, A. V. Mantzaris and D. J. Higham, in Temporal Networks, edited by P. Holme and J. Saramaki, pp. 265--282, Springer, 2013.
Bc4: Is It Safe To Go Out Yet? Statistical Inference in a Zombie Outbreak Model, B. Calderhead, M. Girolami and D. J. Higham, in Mathematical Modelling of Zombies, edited by R. Smith, University of Ottawa Press, 2014, pp. 129--148.
Bc3: Random Graph Models and Their Application to Protein-Protein Interaction Networks, D. J. Higham and N. Przulj, Chapter 14, pages 290-308, Handbook of Statistical Systems Biology, edited by D. Balding, M. Girolami and M. Stumpf, Wiley. 2011.
Bc2: NESSIE: Network Example Source Supporting Innovative Experimentation, A. Taylor and D. J. Higham, Chapter 5, pages 85-106, in Network Science: Complexity in Nature and Technology, Chapter 1, pages 1-11, edited by E. Estrada, M. Fox, D. J. Higham and G.-L. Oppo, Springer, 2010.
Bc1: MAPLE and MATLAB for Stochastic Differential Equations in Finance, D. J. Higham and P. E. Kloeden, in Programming Languages and Systems in Computational Economics and Finance, Edited by S. Neilsen, Kluwer, 2002, 233-270.

Invited (Unrefereed) Contributions to Proceedings and Books

I7: A personal perspective on numerical analysis and optimization,, D. J. Higham, in Proceedings of 5th International Conference on Numerical Analysis and Optimization, Editors: Mehiddin Al-Baali, Anton Purnama, Lucio Grandinetti, pages xix-xxiii, 2020, Oman.
I6: Complex networks: An invitation, by E. Estrada, M. Fox, D. J. Higham and G.-L. Oppo, in Network Science: Complexity in Nature and Technology, Chapter 1, pages 1-11, edited by E. Estrada, M. Fox, D. J. Higham and G.-L. Oppo, Springer, 2010.
I5: Mathematical and computational modeling of post-transcriptional gene regulation by microRNAs, R Khanin and D. J. Higham, in MicroRNA Profiling in Cancer: A Bioinformatics Perspective, Chapter 10, pages 197-216, edited by Yuriy Gusev, World Scientific, 2009.
I4: Multidimensional partitioning and bi-partitioning: analysis and application to gene expression datasets, D. J. Higham, G. Kalna and J. K. Vass, in Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2006, Editors R. Criado, D. Estep, M. A. Pérez Garcia, J. Vigo-Aguiar, Madrid, pages 414-425, 2006. Extended version appeared in International Journal of Computer Mathematics: see [P72]
I3: Finite differences in a small world, D.J. Higham, in the Proceedings of the 20th Biennial Conference on Numerical Analysis, Dundee, D.F. Griffiths and G.A. Watson, Eds, 2003.
I2: Fixed points and spurious modes of a nonlinear infinite-step map, M. A. Aves, P. J. Davies and D. J. Higham, in Numerical Analysis: A.R. Mitchell 75th Birthday Volume, D.F. Griffiths and G.A. Watson, Eds 1996, 21-38, World Scientific.
I1: The dynamics of a discretised nonlinear delay differential equation, D. J. Higham, in the Proceedings of the 15th Biennial Conference on Numerical Analysis, Dundee, G.A. Watson and D.F. Griffiths, Eds 1993, Pitman Research Notes in Mathematics, Volume 303, pages 167-179, Longman Scientific and Technical.