Runge-Kutta Defect Control Using Hermite-Birkhoff Interpolation. - Desmond J. Higham (SIAM J. Sci. Comput., 1991)

Highly continuous Runge-Kutta interpolants. - Desmond J. Higham (ACM Trans. Math. Softw., 1991)

Remark on algorithm 669. - Desmond J. Higham (ACM Trans. Math. Softw., 1991)

Backward Error and Condition of Structured Linear Systems. - Desmond J. Higham; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1992)

Order Stars (A. Iserles and S. P. Nørsett). - Desmond J. Higham (SIAM Rev., 1992)

Reliability of local error control algorithms for initial value ordinary differential equations. - Desmond J. Higham (Quality of Numerical Software, 1996)

Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes. - Manuel Calvo; Desmond J. Higham; Juan I. Montijano; Luis Rández (Adv. Comput. Math., 1997)

Structured Backward Error and Condition of Generalized Eigenvalue Problems. - Desmond J. Higham; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1998)

Trust Region Algorithms and Timestep Selection. - Desmond J. Higham (SIAM J. Numer. Anal., 1999)

Matlab guide. - Desmond J. Higham; Nicholas J. Higham (SIAM, 2000)

Theta Method Dynamics. - Graeme J. Barclay; David F. Griffiths; Desmond J. Higham (LMS J. Comput. Math., 2000)

Mean-Square and Asymptotic Stability of the Stochastic Theta Method. - Desmond J. Higham (SIAM J. Numer. Anal., 2000)

Runge-Kutta Solutions of a Hyperbolic Conservation Law with Source Term. - Mark A. Aves; David F. Griffiths; Desmond J. Higham (SIAM J. Sci. Comput., 2000)

Phase Space Error Control for Dynamical Systems. - Desmond J. Higham; A. R. Humphries; R. J. Wain (SIAM J. Sci. Comput., 2000)

An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations. - Desmond J. Higham (SIAM Rev., 2001)

Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations. - Desmond J. Higham; Xuerong Mao; Andrew M. Stuart (SIAM J. Numer. Anal., 2002)

Nine Ways to Implement the Binomial Method for Option Valuation in MATLAB. - Desmond J. Higham (SIAM Rev., 2002)

Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations. - Desmond J. Higham; Xuerong Mao; Andrew M. Stuart (LMS J. Comput. Math., 2003)

A Matrix Perturbation View of the Small World Phenomenon. - Desmond J. Higham (SIAM J. Matrix Anal. Appl., 2003)

Black-Scholes for scientific computing students. - Desmond J. Higham (Comput. Sci. Eng., 2004)

Matlab guide, Second Edition. - Desmond J. Higham; Nicholas J. Higham (SIAM, 2005)

Google PageRank as mean playing time for pinball on the reverse web. - Desmond J. Higham (Appl. Math. Lett., 2005)

GeneRank: Using search engine technology for the analysis of microarray experiments. - Julie L. Morrison; Rainer Breitling; Desmond J. Higham; David R. Gilbert (BMC Bioinform., 2005)

Numerical methods for nonlinear stochastic differential equations with jumps. - Desmond J. Higham; Peter E. Kloeden (Numerische Mathematik, 2005)

A lock-and-key model for protein-protein interactions. - Julie L. Morrison; Rainer Breitling; Desmond J. Higham; David R. Gilbert (Bioinform., 2006)

A clustering coefficient for weighted networks, with application to gene expression data. - Gabriela Kalna; Desmond J. Higham (AI Commun., 2007)

Modelling the cAMP pathway using BioNessie, and the use of BVP techniques for solving ODEs. - Xu Gu; David R. Gilbert; Desmond J. Higham; Miles Houslay (BMC Syst. Biol., 2007)

Progression of oral carcinomas revealed by spectral reordering of a bipartite graph. - Gabriela Kalna; Johanna Thurlow; J. Keith Vass; Desmond J. Higham (BMC Syst. Biol., 2007)

Identification of phenotypes in patient microarrays. - J. Keith Vass; Gabriela Kalna; Desmond J. Higham (BMC Syst. Biol., 2007)

Connectivity-based parcellation of human cortex using diffusion MRI: Establishing reproducibility, validity and observer independence in BA 44/45 and SMA/pre-SMA. - Johannes C. Klein; Timothy Edward John Behrens; Matthew D. Robson; Clare E. Mackay; Desmond J. Higham; Heidi Johansen-Berg (NeuroImage, 2007)

Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations. - Desmond J. Higham; Xuerong Mao; Chenggui Yuan (Numerische Mathematik, 2007)

Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations. - Desmond J. Higham; Xuerong Mao; Chenggui Yuan (SIAM J. Numer. Anal., 2007)

Fitting a geometric graph to a protein-protein interaction network. - Desmond J. Higham; Marija Rasajski; Natasa Przulj (Bioinform., 2008)

Multidimensional partitioning and bi-partitioning: analysis and application to gene expression data sets. - Gabriela Kalna; J. Keith Vass; Desmond J. Higham (Int. J. Comput. Math., 2008)

Modeling and Simulating Chemical Reactions. - Desmond J. Higham (SIAM Rev., 2008)

Asymptotic Stability of a Jump-Diffusion Equation and Its Numerical Approximation. - Graeme D. Chalmers; Desmond J. Higham (SIAM J. Sci. Comput., 2008)

Chemical Master Equation and Langevin regimes for a gene transcription model. - Raya Khanin; Desmond J. Higham (Theor. Comput. Sci., 2008)

Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff. - Michael B. Giles; Desmond J. Higham; Xuerong Mao (Finance Stochastics, 2009)

Switching and Diffusion Models for Gene Regulation Networks. - Somkid Intep; Desmond J. Higham; Xuerong Mao (Multiscale Model. Simul., 2009)

Comparing Hitting Time Behavior of Markov Jump Processes and Their Diffusion Approximations. - Lukasz Szpruch; Desmond J. Higham (Multiscale Model. Simul., 2009)

Geometric De-noising of Protein-Protein Interaction Networks. - Oleksii Kuchaiev; Marija Rasajski; Desmond J. Higham; Natasa Przulj (PLoS Comput. Biol., 2009)

CONTEST: A Controllable Test Matrix Toolbox for MATLAB. - Alan Taylor; Desmond J. Higham (ACM Trans. Math. Softw., 2009)

Numerical Methods for Ordinary Differential Equations - Initial Value Problems. - David F. Griffiths; Desmond J. Higham (Springer, 2010)

Complex Networks: An Invitation. - Ernesto Estrada; Maria Fox 001; Desmond J. Higham; Gian-Luca Oppo (Network Science, 2010)

NESSIE: Network Example Source Supporting Innovative Experimentation. - Alan Taylor; Desmond J. Higham (Network Science, 2010)

Network Properties Revealed through Matrix Functions. - Ernesto Estrada; Desmond J. Higham (SIAM Rev., 2010)

Exploring metabolic pathway disruption in the subchronic phencyclidine model of schizophrenia with the Generalized Singular Value Decomposition. - Xiaolin Xiao; Neil Dawson; Lynsey MacIntyre; Brian J. Morris; Judith A. Pratt; David G. Watson; Desmond J. Higham (BMC Syst. Biol., 2011)

Googling the Brain: Discovering Hierarchical and Asymmetric Network Structures, with Applications in Neuroscience. - Jonathan J. Crofts; Desmond J. Higham (Internet Math., 2011)

Discovering bipartite substructure in directed networks. - Alan Taylor; J. Keith Vass; Desmond J. Higham (LMS J. Comput. Math., 2011)

Network analysis detects changes in the contralesional hemisphere following stroke. - Jonathan J. Crofts; Desmond J. Higham; Rose Bosnell; Saâd Jbabdi; Paul M. Matthews; T. E. J. Behrens; Heidi Johansen-Berg (NeuroImage, 2011)

Demonstration of Dynamic Targeting in an Online Social Medium. - Peter Laflin; Fiona Ainley; Amanda Otley; Alexander V. Mantzaris; Desmond J. Higham (SocInfo, 2012)

Dynamic Targeting in an Online Social Medium. - Peter Laflin; Alexander V. Mantzaris; Fiona Ainley; Amanda Otley; Peter Grindrod; Desmond J. Higham (SocInfo, 2012)

Computing mean first exit times for stochastic processes using multi-level Monte Carlo. - Desmond J. Higham; Mikolaj Roj (WSC, 2012)

Bistability through Triadic Closure. - Peter Grindrod; Desmond J. Higham; Mark C. Parsons (Internet Math., 2012)

Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics. - David F. Anderson; Desmond J. Higham (Multiscale Model. Simul., 2012)

Dynamic network centrality summarizes learning in the human brain. - Alexander V. Mantzaris; Danielle S. Bassett; Nicholas F. Wymbs; Ernesto Estrada; Mason A. Porter; Peter J. Mucha; Scott T. Grafton; Desmond J. Higham (J. Complex Networks, 2013)

Dynamical Systems to Monitor Complex Networks in Continuous Time. - Peter Grindrod; Desmond J. Higham (CoRR, 2013)

Mean Exit Times and the Multilevel Monte Carlo Method. - Desmond J. Higham; Xuerong Mao; Mikolaj Roj; Qingshuo Song; George Yin 001 (SIAM/ASA J. Uncertain. Quantification, 2013)

A Matrix Iteration for Dynamic Network Summaries. - Peter Grindrod; Desmond J. Higham (SIAM Rev., 2013)

Survey and Review. - Desmond J. Higham (SIAM Rev., 2013)

Discovering and validating influence in a dynamic online social network. - Peter Laflin; Alexander V. Mantzaris; Fiona Ainley; Amanda Otley; Peter Grindrod; Desmond J. Higham (Soc. Netw. Anal. Min., 2013)

Opportunities at the Mathematics/Future Cities Interface. - Peter Grindrod; Desmond J. Higham; Robert S. MacKay (CoRR, 2014)

Anticipating Activity in Social Media Spikes. - Desmond J. Higham; Peter Grindrod; Alexander V. Mantzaris; Amanda Otley; Peter Laflin (CoRR, 2014)

Complexity of Multilevel Monte Carlo Tau-Leaping. - David F. Anderson; Desmond J. Higham; Yu Sun (SIAM J. Numer. Anal., 2014)

An introduction to multilevel Monte Carlo for option valuation. - Desmond J. Higham (Int. J. Comput. Math., 2015)

Learning LaTeX (2. ed.). - David F. Griffiths; Desmond J. Higham (SIAM, 2016)

Preserving Sparsity in Dynamic Network Computations. - Francesca Arrigo; Desmond J. Higham (COMPLEX NETWORKS, 2016)

Commentary on Dehmer and Mowshowitz. - Michele Benzi; Desmond J. Higham (Complex., 2016)

Matching exponential-based and resolvent-based centrality measures. - Mary Aprahamian; Desmond J. Higham; Nicholas J. Higham (J. Complex Networks, 2016)

Multilevel Monte Carlo for Stochastic Differential Equations with Small Noise. - David F. Anderson; Desmond J. Higham; Yu Sun (SIAM J. Numer. Anal., 2016)

Sparse matrix computations for dynamic network centrality. - Francesca Arrigo; Desmond J. Higham (Appl. Netw. Sci., 2017)

Block Matrix Formulations for Evolving Networks. - Caterina Fenu; Desmond J. Higham (SIAM J. Matrix Anal. Appl., 2017)

Centrality Analysis for Modified Lattices. - Martin Paton; Kerem Akartunali; Desmond J. Higham (SIAM J. Matrix Anal. Appl., 2017)

Non-backtracking walk centrality for directed networks. - Francesca Arrigo; Peter Grindrod; Desmond J. Higham; Vanni Noferini (J. Complex Networks, 2018)

Computational Complexity Analysis for Monte Carlo Approximations of Classically Scaled Population Processes. - David F. Anderson; Desmond J. Higham; Yu Sun (Multiscale Model. Simul., 2018)

The Deformed Graph Laplacian and Its Applications to Network Centrality Analysis. - Peter Grindrod; Desmond J. Higham; Vanni Noferini (SIAM J. Matrix Anal. Appl., 2018)

A fast and robust kernel optimization method for core-periphery detection in directed and weighted graphs. - Francesco Tudisco; Desmond J. Higham (Appl. Netw. Sci., 2019)

Centrality-friendship paradoxes: when our friends are more important than us. - Desmond J. Higham (J. Complex Networks, 2019)

Accurate Computation of the Log-Sum-Exp and Softmax Functions. - Pierre Blanchard; Desmond J. Higham; Nicholas J. Higham (CoRR, 2019)

A framework for second order eigenvector centralities and clustering coefficients. - Francesca Arrigo; Desmond J. Higham; Francesco Tudisco (CoRR, 2019)

Non-backtracking PageRank. - Francesca Arrigo; Desmond J. Higham; Vanni Noferini (J. Sci. Comput., 2019)

On Constrained Langevin Equations and (Bio)Chemical Reaction Networks. - David F. Anderson; Desmond J. Higham; Saul C. Leite; Ruth J. Williams (Multiscale Model. Simul., 2019)

Non-Backtracking Alternating Walks. - Francesca Arrigo; Desmond J. Higham; Vanni Noferini (SIAM J. Appl. Math., 2019)

Deep Learning: An Introduction for Applied Mathematicians. - Catherine F. Higham; Desmond J. Higham (SIAM Rev., 2019)

A Nonlinear Spectral Method for Core-Periphery Detection in Networks. - Francesco Tudisco; Desmond J. Higham (SIAM J. Math. Data Sci., 2019)

On Adversarial Examples and Stealth Attacks in Artificial Intelligence Systems. - Ivan Yu. Tyukin; Desmond J. Higham; Alexander N. Gorban (IJCNN, 2020)

Consistency of Anchor-based Spectral Clustering. - Henry-Louis de Kergorlay; Desmond John Higham (CoRR, 2020)

A Personal Perspective on Numerical Analysis and Optimization. - Desmond J. Higham (CoRR, 2020)

Node and Edge Eigenvector Centrality for Hypergraphs. - Francesco Tudisco; Desmond J. Higham (CoRR, 2021)

Higher-order Network Analysis Takes Off, Fueled by Classical Ideas and New Data. - Austin R. Benson; David F. Gleich; Desmond J. Higham (CoRR, 2021)

Epidemics on Hypergraphs: Spectral Thresholds for Extinction. - Desmond John Higham; Henry-Louis de Kergorlay (CoRR, 2021)

The Feasibility and Inevitability of Stealth Attacks. - Ivan Yu. Tyukin; Desmond J. Higham; Eliyas Woldegeorgis; Alexander N. Gorban (CoRR, 2021)

Directed Network Laplacians and Random Graph Models. - Xue Gong; Desmond John Higham; Konstantinos Zygalakis (CoRR, 2021)

A Theory for Backtrack-Downweighted Walks. - Francesca Arrigo; Desmond J. Higham; Vanni Noferini (SIAM J. Matrix Anal. Appl., 2021)

Random Matrices Generating Large Growth in LU Factorization with Pivoting. - Desmond J. Higham; Nicholas J. Higham; Srikara Pranesh (SIAM J. Matrix Anal. Appl., 2021)

Core-periphery Partitioning and Quantum Annealing. - Catherine F. Higham; Desmond J. Higham; Francesco Tudisco (KDD, 2022)

Testing a QUBO Formulation of Core-periphery Partitioning on a Quantum Annealer. - Catherine F. Higham; Desmond J. Higham; Francesco Tudisco (CoRR, 2022)

Generative Hypergraph Models and Spectral Embedding. - Xue Gong; Desmond J. Higham; Konstantinos Zygalakis (CoRR, 2022)

A Hierarchy of Network Models Giving Bistability Under Triadic Closure. - Stefano Di Giovacchino; Desmond J. Higham; Konstantinos C. Zygalakis (Multiscale Model. Simul., 2022)

Mean Field Analysis of Hypergraph Contagion Models. - Desmond John Higham; Henry-Louis de Kergorlay (SIAM J. Appl. Math., 2022)

The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning. - Alexander Bastounis; Alexander N. Gorban; Anders C. Hansen; Desmond J. Higham; Danil V. Prokhorov; Oliver J. Sutton; Ivan Yu. Tyukin; Qinghua Zhou (ICANN (1), 2023)

Componentwise Adversarial Attacks. - Lucas Beerens; Desmond J. Higham (ICANN (1), 2023)

Adversarial Ink: Componentwise Backward Error Attacks on Deep Learning. - Lucas Beerens; Desmond J. Higham (CoRR, 2023)

Estimating Network Dimension When the Spectrum Struggles. - Peter Grindrod; Desmond John Higham; Henry-Louis de Kergorlay (CoRR, 2023)

Can We Rely on AI? - Desmond J. Higham (CoRR, 2023)

Backward error analysis and the qualitative behaviour of stochastic optimization algorithms: Application to stochastic coordinate descent. - Stefano Di Giovacchino; Desmond J. Higham; Konstantinos Zygalakis (CoRR, 2023)

Vulnerability Analysis of Transformer-based Optical Character Recognition to Adversarial Attacks. - Lucas Beerens; Desmond J. Higham (CoRR, 2023)

Core-Periphery Detection in Hypergraphs. - Francesco Tudisco; Desmond J. Higham (SIAM J. Math. Data Sci., 2023)

Connectivity of Random Geometric Hypergraphs. - Henry-Louis de Kergorlay; Desmond J. Higham (Entropy, 2023)

Stealth edits to large language models. - Oliver J. Sutton; Qinghua Zhou; Wei Wang 357; Desmond J. Higham; Alexander N. Gorban; Alexander Bastounis; Ivan Tyukin (NeurIPS, 2024)

Higher-order Connection Laplacians for Directed Simplicial Complexes. - Xue Gong; Desmond J. Higham; Konstantinos Zygalakis; Ginestra Bianconi (CoRR, 2024)

Stealth edits for provably fixing or attacking large language models. - Oliver J. Sutton; Qinghua Zhou; Wei Wang 357; Desmond J. Higham; Alexander N. Gorban; Alexander Bastounis; Ivan Yu. Tyukin (CoRR, 2024)

How adversarial attacks can disrupt seemingly stable accurate classifiers. - Oliver J. Sutton; Qinghua Zhou; Ivan Yu. Tyukin; Alexander N. Gorban; Alexander Bastounis; Desmond J. Higham (Neural Networks, 2024)

Adaptive Stepsize Algorithms for Langevin Dynamics. - Alix Leroy; Benedict J. Leimkuhler; Jonas Latz; Desmond J. Higham (SIAM J. Sci. Comput., 2024)

Weighted Enumeration of Nonbacktracking Walks on Weighted Graphs. - Francesca Arrigo; Desmond J. Higham; Vanni Noferini; Ryan Wood (SIAM J. Matrix Anal. Appl., 2024)

Deceptive Diffusion: Generating Synthetic Adversarial Examples. - Lucas Beerens; Catherine F. Higham; Desmond J. Higham (SSVM (1), 2025)

Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians. - Catherine F. Higham; Desmond J. Higham; Peter Grindrod (SIAM Rev., 2025)

Rethinking Oversmoothing in Graph Neural Networks: A Rank-Based Perspective. - Kaicheng Zhang; Piero Deidda; Desmond J. Higham; Francesco Tudisco (CoRR, 2025)

Embedding Hidden Adversarial Capabilities in Pre-Trained Diffusion Models. - Lucas Beerens; Desmond J. Higham (CoRR, 2025)