D. Higham

发表

Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise

Jonathan C. Mattingly, A. Stuart, D. Higham, 2002 .

Stochastic Ordinary Differential Equations in Applied and Computational Mathematics

D. Higham, 2011 .

Changes in connectivity profiles define functionally distinct regions in human medial frontal cortex.

Timothy Edward John Behrens, P. Matthews, M. Rushworth, 2004, Proceedings of the National Academy of Sciences of the United States of America.

Large growth factors in Gaussian elimination with pivoting

N. Higham, D. Higham, 1989 .

Communicability across evolving networks.

Mark C. Parsons, Ernesto Estrada, D. Higham, 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

Accurately computing the log-sum-exp and softmax functions

N. Higham, D. Higham, Pierre Blanchard, 2020, IMA Journal of Numerical Analysis.

A Matrix Iteration for Dynamic Network Summaries

Peter Grindrod, Desmond J. Higham, D. Higham, 2013, SIAM Rev..

Opportunities at the Mathematics/Future Cities Interface pdf

Peter Grindrod, Desmond J. Higham, Robert S. MacKay, 2014, ArXiv.

The structured sensitivity of Vandermonde-like systems

Sven G. Bartels, D. Higham, 1992 .

Stiffness of ODEs

L. Trefethen, D. Higham, 1993 .

A Unified View of Spectral Clustering ∗

D. Higham, M. Kibble, 2004 .

A weighted communicability measure applied to complex brain networks

D. Higham, J. J. Crofts, 2009, Journal of The Royal Society Interface.

Time-stepping and preserving orthonormality

D. Higham, 1997 .

Multi-level Monte Carlo for stochastically modeled chemical kinetic systems

David F. Anderson, D. Higham, 2011 .

An Introduction to Financial Option Valuation: Option

D. Higham, 2004 .

Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm

Guillermo Ricardo Simari, D. Higham, M. Kibble, 2022 .

Matlab guide, Second Edition

Nicholas J. Higham, Desmond J. Higham, N. Higham, 2005 .

Multilevel Monte Carlo for Continuous Time Markov Chains, with Applications in Biochemical Kinetics

Desmond J. Higham, David F. Anderson, David F. Anderson, 2011, Multiscale Model. Simul..

Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay

D. Higham, T. Sardar, 1995 .

Beyond non-backtracking: non-cycling network centrality measures

D. Higham, V. Noferini, F. Arrigo, 2020, Proceedings of the Royal Society A.

NON-BACKTRACKING ALTERNATING WALKS \ast

D. Higham, V. Noferini, F. Arrigo, 2019 .

Non-Backtracking Alternating Walks | SIAM Journal on Applied Mathematics | Vol. 79, No. 3 | Society for Industrial and Applied Mathematics

D. Higham, F. Arrigo, 2019 .

Modelling protein–protein interaction networks via a stickiness index

Natasa Przulj, Desmond J Higham, D. Higham, 2006, Journal of The Royal Society Interface.

Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model

L. Szpruch, D. Higham, X. Mao, 2011 .

Strongly Nonlinear Ait-Sahalia-Type Interest Rate Model and its Numerical Approximation

L. Szpruch, D. Higham, X. Mao, 2009 .

Componentwise perturbation theory for linear systems with multiple right-hand sides

N. Higham, D. Higham, 1992 .

Periodic Reordering

D. Higham, P. Grindrod, G. Kalna, 2008 .

Spectral Reordering of a Range-Dependent Weighted Random Graph

D. Higham, 2005 .

A-Stability and Stochastic Mean-Square Stability

D. Higham, 2000 .

Convergence, Non-negativity and Stability of a New Milstein Scheme with Applications to Finance

L. Szpruch, D. Higham, X. Mao, 2012, 1204.1647.

Discretization Provides a Conceptually Simple Tool to Build Expression Networks

D. Higham, X. Mao, J. Vass, 2011, PloS one.

Communicability betweenness in complex networks

Ernesto Estrada, D. Higham, N. Hatano, 2009, 0905.4102.

Convergence of Monte Carlo Simulations involving the Mean-Reverting Square Root Process

D. Higham, X. Mao, 2005 .

CONVERGENCE AND STABILITY OF IMPLICIT METHODS FOR JUMP-DIFFUSION SYSTEMS

P. Kloeden, D. Higham, 2005 .

Exponential mean square stability of numerical solutions to stochastic differential equations

Desmond J. Higham, Xuerong Mao, Andrew M. Stuart, 2003 .

Long-Term Dynamics

Desmond J. Higham, D. Griffiths, D. Higham, 2010 .

Asymmetry through time dependency

Alexander V. Mantzaris, Desmond J. Higham, D. Higham, 2016 .

Spectral algorithms for heterogeneous biological networks.

D. Higham, J. Vass, M. Mcdonald, 2012, Briefings in functional genomics.

Discovering bipartite substructure in directed networks

D. Higham, J. Vass, Alan Taylor, 2011, LMS J. Comput. Math..

Chemical master versus chemical langevin for first-order reaction networks

Desmond J. Higham, D. Higham, R. Khanin, 2008 .

Equilibrium states of adaptive algorithms for delay differential equations

Desmond J. Higham, Ioannis Th. Famelis, D. Higham, 1995 .

The tolerance proportionality of adaptive ODE solvers

Desmond J. Higham, D. Higham, 1993 .

Robust defect control with Runge-Kutta schemes

Desmond J. Higham, D. Higham, 1989 .

Finite differences in a small world

G. Watson, D. Griffiths, D. Higham, 2003 .

The Sleekest Link Algorithm

Desmond J. Higham, D. Higham, Alan Taylor, 2003 .

Error control for initial value problems with discontinuities and delays

D. Higham, 1993 .

On the Boundedness of Asymptotic Stability Regions for the Stochastic Theta Method

Desmond J. Higham, D. Higham, A. Bryden, 2003 .

Qualitative properties of modi"ed equations

A. Stuart, D. Higham, O. Gonzalez, 1999 .

Vienna 2013: DJH Lectures. Some References

D. Higham, 2013 .

Hybrid simulation of autoregulation within transcription and translation

L. Szpruch, D. Higham, X. Mao, 2011 .

Zero, one and two-switch models of gene regulation

D. Higham, Somkid Intep, 2010 .

Subanesthetic Ketamine Treatment Promotes Abnormal Interactions between Neural Subsystems and Alters the Properties of Functional Brain Networks

D. Higham, B. Morris, J. Pratt, 2014, Neuropsychopharmacology.

Higham, D.J. and Mao, X. and Yuan, C. (2007) Almost sure and moment exponential stability in the numerical simulation of stochastic differential

D. Higham, X. Mao, C. Yuan, 2018 .

MOMENT EXPONENTIAL STABILITY IN THE NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS

D. Higham, X. Mao, C. Yuan, 2018 .

Betweenness in time dependent networks

Desmond J. Higham, Ahmad Alsayed, D. Higham, 2015 .

NON-NEGATIVE MATRIX FACTORISATION FOR NETWORK REORDERING

D. Higham, J. Vass, D. Crowther, 2010 .

Mathematical Modelling of Polyamine Metabolism in Bloodstream-Form Trypanosoma brucei: An Application to Drug Target Identification

D. Higham, D. Reid, X. Gu, 2013, PloS one.

Mathematical modelling of polyamine metabolism in bloodstream-form T . brucei

D. Higham, D. Reid, X. Gu, 2012 .

Connectivity based anatomical parcellation of cortical grey matter

Desmond J. Higham, Heidi Johansen-Berg, Paul M. Matthews, 2004 .

Inverse network sampling to explore online brand allegiance†

Jonathan A. Ward, D. Higham, P. Grindrod, 2016, European Journal of Applied Mathematics.

Sustained NMDA receptor hypofunction induces compromised neural systems integration and schizophrenia-like alterations in functional brain networks.

D. Higham, B. Morris, J. Pratt, 2014, Cerebral cortex.

Edinburgh Block matrix formulations for evolving networks

D. Higham, 2016 .

Stiffness of ODEs

L. Trefethen, D. Higham, 1993, Spectra and Pseudospectra.

Stiiness of Odes

L. Trefethen, D. Higham, 1993 .

Edinburgh Research Explorer The sleekest link algorithm

D. Higham, Alan Taylor, 2016 .

Edinburgh Research Explorer Modeling and simulating chemical reactions

D. Higham, 2008 .

Multidimensional partitioning and bi-partitioning

D. Higham, J. Vass, 2022 .

Runge-Kutta stability on a Floquet problem

D. Higham, 1994 .

Communicability betweenness in complex networks

Ernesto Estrada, D. Higham, N. Hatano, 2009, 0905.4102.

Edinburgh Research Explorer Sparse matrix computations for dynamic network centrality

D. Higham, 2017 .

An Introduction to Financial Option Valuation by Desmond J. Higham

Desmond J. Higham, D. Higham, 2004 .

Mean Exit Times and the Multilevel Monte Carlo Method

G. Yin, G. Yin, D. Higham, 2013, SIAM/ASA J. Uncertain. Quantification.

Core-periphery Partitioning and Quantum Annealing

Catherine F. Higham, D. Higham, Francesco Tudisco, 2022, KDD.

Generative hypergraph models and spectral embedding

K. Zygalakis, D. Higham, Xue Gong, 2022, Scientific Reports.

Edinburgh Research Explorer Non-backtracking PageRank

D. Higham, V. Noferini, F. Arrigo, 2022 .

Communicability and multipartite structures in complex networks at negative absolute temperatures.

Ernesto Estrada, D. Higham, N. Hatano, 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

NON-BACKTRACKING ALTERNATING

D. Higham, V. Noferini, F. Arrigo, 2018 .

Matlab guide

Nicholas J. Higham, Desmond J. Higham, N. Higham, 2000 .

Matching exponential-based and resolvent-based centrality measures

Nicholas J. Higham, Desmond J. Higham, Mary Aprahamian, 2016, J. Complex Networks.

Mean Exit Times and the Multilevel Monte Carlo Method

Desmond J. Higham, Xuerong Mao, Mikolaj Roj, 2013, SIAM/ASA J. Uncertain. Quantification.

Computing mean first exit times for stochastic processes using multi-level Monte Carlo

Desmond J. Higham, Mikolaj Roj, D. Higham, 2012, Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC).

Consistency of Anchor-based Spectral Clustering pdf

Henry-Louis de Kergorlay, Desmond John Higham, D. Higham, 2020, Information and Inference: A Journal of the IMA.

A Survey of the Explicit Runge-Kutta Method

Desmond J. Higham, Philip W. Sharp, W. H. Enright, 1995 .

Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

Andrew M. Stuart, Desmond J. Higham, Xuerong Mao, 2002, SIAM J. Numer. Anal..

Switching and Diffusion Models for Gene Regulation Networks

Desmond J. Higham, Somkid Intep, Xuerong Mao, 2009, Multiscale Model. Simul..

DNA meets the SVD

Peter Grindrod, Desmond J. Higham, Gabriela Kalna, 2008 .

GeneRank: Using search engine technology for the analysis of microarray experiments

Desmond J. Higham, David R. Gilbert, Rainer Breitling, 2005, BMC Bioinformatics.

Learning LaTeX

Desmond J. Higham, David F. Griffiths, D. Griffiths, 1997 .

Hierarchical dynamic walks

Alexander V. Mantzaris, Peter Grindrod, Desmond J. Higham, 2016 .

Googling the Brain: Discovering Hierarchical and Asymmetric Network Structures, with Applications in Neuroscience

Desmond J. Higham, Jonathan J. Crofts, D. Higham, 2011, Internet Math..

Node and Edge Eigenvector Centrality for Hypergraphs pdf

Desmond J. Higham, Francesco Tudisco, D. Higham, 2021, ArXiv.

Node and edge nonlinear eigenvector centrality for hypergraphs

Desmond J. Higham, Francesco Tudisco, D. Higham, 2021, Communications Physics.

Geometric De-noising of Protein-Protein Interaction Networks

Desmond J. Higham, Natasa Przulj, Oleksii Kuchaiev, 2009, PLoS Comput. Biol..

Fitting a geometric graph to a protein-protein interaction network

Desmond J. Higham, Natasa Przulj, Marija Rasajski, 2008, Bioinform..

Network Properties Revealed through Matrix Functions

Desmond J. Higham, Ernesto Estrada, Ernesto Estrada, 2010, SIAM Rev..

Mathematical and computational modelling of post-transcriptional gene regulation by microRNAs

Desmond J. Higham, Raya Khanin, D. Higham, 2009 .

Connectivity-based parcellation of human cortex using diffusion MRI: Establishing reproducibility, validity and observer independence in BA 44/45 and SMA/pre-SMA

Desmond J. Higham, Timothy Edward John Behrens, Matthew D. Robson, 2007, NeuroImage.

Divergent routes to oral cancer.

Gabriela Kalna, Pawel Herzyk, D. Higham, 2006, Cancer research.

A lock-and-key model for protein-protein interactions

Desmond J. Higham, David R. Gilbert, Rainer Breitling, 2006, Bioinform..

Random graph models and their application to protein-protein interaction networks

Desmond J. Higham, Natasa Przulj, D. Higham, 2011 .

A minimal mathematical model of post-transcriptional gene regulation by microRNAs ∗

D. Higham, R. Khanin, 2007 .

Network analysis detects changes in the contralesional hemisphere following stroke

Desmond J. Higham, Timothy Edward John Behrens, Heidi Johansen-Berg, 2011, NeuroImage.

Simultaneous Non-Negative Matrix Factorization for Multiple Large Scale Gene Expression Datasets in Toxicology

Desmond J. Higham, Gino Miele, D. Higham, 2012, PloS one.

Core-periphery detection in hypergraphs

D. Higham, Francesco Tudisco, 2022, SIAM J. Math. Data Sci..

Modeling and Simulating Chemical Reactions

Desmond J. Higham, D. Higham, 2008, SIAM Rev..

An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations

Desmond J. Higham, D. Higham, 2001, SIAM Rev..

Backward Error and Condition of Structured Linear Systems

Nicholas J. Higham, Desmond J. Higham, N. Higham, 1992, SIAM J. Matrix Anal. Appl..

Multidimensional partitioning and bi-partitioning: analysis and application to gene expression data sets

Desmond J. Higham, Gabriela Kalna, J. Keith Vass, 2008, Int. J. Comput. Math..

Non-backtracking walk centrality for directed networks

Peter Grindrod, Desmond J. Higham, Vanni Noferini, 2018, J. Complex Networks.

A Hierarchy of Network Models Giving Bistability Under Triadic Closure pdf

Desmond J. Higham, Konstantinos C. Zygalakis, Stefano Di Giovacchino, 2021, Multiscale Model. Simul..

Exploring metabolic pathway disruption in the subchronic phencyclidine model of schizophrenia with the Generalized Singular Value Decomposition

Desmond J. Higham, David G. Watson, Xiaolin Xiao, 2011, BMC Systems Biology.

A Nonlinear Spectral Method for Core-Periphery Detection in Networks pdf

Desmond J. Higham, Francesco Tudisco, D. Higham, 2018, SIAM J. Math. Data Sci..

An overview of city analytics

Michael Batty, Peter Grindrod, Desmond J. Higham, 2017, Royal Society Open Science.

Adaptive Step Size Selection

D. Griffiths, D. Higham, 2010 .

Linear Multistep Methods—V: Solving Implicit Methods

D. Griffiths, D. Higham, 2010 .

Structured Backward Error and Condition of Generalized Eigenvalue Problems

Nicholas J. Higham, Desmond J. Higham, N. Higham, 1999, SIAM J. Matrix Anal. Appl..

CONTEST: A Controllable Test Matrix Toolbox for MATLAB

Desmond J. Higham, Alan Taylor, D. Higham, 2009, TOMS.

Reordering diffusion-based connectivity matrices to define anatomical networks of the human brain

Desmond J. Higham, Stephen M. Smith, Heidi Johansen-Berg, 2004 .

Higher-order Network Analysis Takes Off, Fueled by Classical Ideas and New Data pdf

Desmond J. Higham, David F. Gleich, Austin R. Benson, 2021, ArXiv.

Trust Region Algorithms and Timestep Selection

Desmond J. Higham, D. Higham, 1999, SIAM J. Numer. Anal..

Regular Runge-Kutta pairs

D. Higham, 1997 .

Does Error Control Suppress Spuriosity

Desmond J. Higham, David F. Griffiths, Mark A. Aves, 1997 .

Models for evolving networks: with applications in telecommunication and online activities

Peter Grindrod, Desmond J. Higham, D. Higham, 2012 .

Greedy pathlengths and small world graphs

Desmond J. Higham, D. Higham, 2006 .

Mantzaris, Alexander

Alexander V. Mantzaris, Desmond J. Higham, D. Higham, 2019 .

Analysis of the dynamics of local error control via a piecewise continuous residual

Desmond J. Higham, Andrew M. Stuart, A. Stuart, 1998 .

Nonnormality Effects in a Discretised Nonlinear Reaction-Convection-Diffusion Equation

Desmond J. Higham, Brynjulf Owren, D. Higham, 1996 .

Reliability of local error control algorithms for initial value ordinary differential equations

Desmond J. Higham, D. Higham, 1996, Quality of Numerical Software.

Non-normality Eeects in a Discretised Nonlinear Reaction-convection-diusion Equation

D. Higham, 1995 .

Numerical Methods for Ordinary Differential Equations - Initial Value Problems

Desmond J. Higham, David F. Griffiths, D. Griffiths, 2010, Springer undergraduate mathematics series.

On Adversarial Examples and Stealth Attacks in Artificial Intelligence Systems

I. Tyukin, D. Higham, A. Gorban, 2020, 2020 International Joint Conference on Neural Networks (IJCNN).

Anticipating Activity in Social Media Spikes pdf

Alexander V. Mantzaris, Peter Grindrod, Desmond J. Higham, 2014, Proceedings of the International AAAI Conference on Web and Social Media.

Directed network Laplacians and random graph models

Desmond J. Higham, Konstantinos Zygalakis, Xue Gong, 2021, Royal Society Open Science.

Non-Backtracking Alternating Walks

Desmond J. Higham, Vanni Noferini, Francesca Arrigo, 2019, SIAM J. Appl. Math..

Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff

Desmond J. Higham, Xuerong Mao, Michael B. Giles, 2009, Finance Stochastics.

Mapping directed networks

Desmond J. Higham, Ernesto Estrada, Jonathan J. Crofts, 2010 .

Dynamic network centrality summarizes learning in the human brain

Mason A. Porter, Alexander V. Mantzaris, Desmond J. Higham, 2012, J. Complex Networks.

A clustering coefficient for weighted networks, with application to gene expression data

Desmond J. Higham, Gabriela Kalna, D. Higham, 2007, AI Commun..

Mean-Square and Asymptotic Stability of the Stochastic Theta Method

Desmond J. Higham, D. Higham, 2000, SIAM J. Numer. Anal..

Numerical methods for nonlinear stochastic differential equations with jumps

Desmond J. Higham, Peter E. Kloeden, P. Kloeden, 2005, Numerische Mathematik.

On Constrained Langevin Equations and (Bio)Chemical Reaction Networks

Desmond J. Higham, Saul de Castro Leite, Ruth J. Williams, 2019, Multiscale Model. Simul..

Analysis of the Enright-Kamel Partitioning Method for Stiff Ordinary Differential Equations

Desmond J. Higham, D. Higham, 1989 .

Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems

Desmond J. Higham, Peter E. Kloeden, P. Kloeden, 2007 .

Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations

Desmond J. Higham, Xuerong Mao, Chenggui Yuan, 2007, SIAM J. Numer. Anal..

An Introduction to Financial Option Valuation

Desmond J. Higham, D. Higham, 2004 .

Preserving exponential mean-square stability in the simulation of hybrid stochastic differential equations

Desmond J. Higham, Xuerong Mao, Chenggui Yuan, 2007, Numerische Mathematik.

Edinburgh Research Explorer Deep learning: an introduction for applied mathematicians pdf

Desmond J. Higham, Catherine F. Higham, D. Higham, 2022 .

Runge-Kutta type methods for orthogonal integration

Desmond J. Higham, D. Higham, 1996 .

Testing a QUBO Formulation of Core-periphery Partitioning on a Quantum Annealer pdf

Desmond J. Higham, Catherine F. Higham, Francesco Tudisco, 2022, arXiv.org.

High Modularity Creates Scaling Laws

D. Higham, P. Grindrod, 2018, Scientific Reports.

COMMUNICABILITY IN COMPLEX BRAIN NETWORKS

Desmond J. Higham, Jonathan J. Crofts, D. Higham, 2008, 0811.0769.

Progression of oral carcinomas revealed by spectral reordering of a bipartite graph

Desmond J. Higham, Gabriela Kalna, J. Keith Vass, 2007, BMC Systems Biology.

NESSIE: Network Example Source Supporting Innovative Experimentation

Desmond J. Higham, Alan Taylor, D. Higham, 2010, Network Science.

ANALYSIS OF THE SINGULAR VALUE DECOMPOSITION AS A TOOL FOR PROCESSING MICROARRAY EXPRESSION DATA

Desmond J. Higham, Gabriela Kalna, J. K. Vass, 2005 .

Nine Ways to Implement the Binomial Method for Option Valuation in MATLAB

Desmond J. Higham, D. Higham, 2002, SIAM Rev..

Epidemics on hypergraphs: spectral thresholds for extinction

D. Higham, Henry-Louis de Kergorlay, 2021, Proceedings of the Royal Society A.

Parallel defect control

Desmond J. Higham, Wayne H. Enright, D. Higham, 1991 .

Global error versus tolerance for explicit Runge-Kutta methods

Desmond J. Higham, D. Higham, 1991 .

Non-backtracking PageRank

Desmond J. Higham, Vanni Noferini, Francesca Arrigo, 2019, J. Sci. Comput..

On the exponential generating function for non-backtracking walks

Peter Grindrod, Desmond J. Higham, Vanni Noferini, 2018, Linear Algebra and its Applications.

MATLAB Guide, Third Edition

Nicholas J. Higham, Desmond J. Higham, Nicholas J. Higham, 2016 .

People Who Read this Article Also Read . . . : Part I

Ernesto Estrada, D. Higham, P. Grindrod, 2011 .

Comment on "Numerical methods for stochastic differential equations".

Kevin Burrage, Eckhard Platen, Pamela Burrage, 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

An Algorithmic Introduction to Numerical Simulation of

Desmond J. Higham, D. Higham, 2001 .

A Theory for Backtrack-Downweighted Walks pdf

Desmond J. Higham, Vanni Noferini, Francesca Arrigo, 2020, SIAM J. Matrix Anal. Appl..

A fast and robust kernel optimization method for core–periphery detection in directed and weighted graphs

Desmond J. Higham, Francesco Tudisco, D. Higham, 2019, Appl. Netw. Sci..

Centrality-Friendship Paradoxes: When Our Friends Are More Important Than Us pdf

Desmond J. Higham, D. Higham, 2018, J. Complex Networks.

Centrality Analysis for Modified Lattices

Desmond J. Higham, Kerem Akartunali, Martin Paton, 2017, SIAM J. Matrix Anal. Appl..

A framework for second-order eigenvector centralities and clustering coefficients

D. Higham, F. Arrigo, Francesco Tudisco, 2019, Proceedings of the Royal Society A.

The Feasibility and Inevitability of Stealth Attacks

Alexander N Gorban, I. Tyukin, D. Higham, 2021, IMA Journal of Applied Mathematics.

Phase Space Error Control for Dynamical Systems

Desmond J. Higham, A. R. Humphries, R. J. Wain, 1999, SIAM J. Sci. Comput..

Stepsize selection for tolerance proportionality in explicit Runge–Kutta codes

Desmond J. Higham, Manuel Calvo, Juan I. Montijano, 1997, Adv. Comput. Math..

Runge–Kutta Method—I: Order Conditions

D. Griffiths, D. Higham, 2010 .

Euler’s Method

D. Griffiths, D. Higham, 2010 .

Linear Multistep Methods—II: Convergence and Zero-Stability

D. Griffiths, D. Higham, 2010 .

Global error estimation with adaptive explicit Runge-Kutta methods

Desmond J. Higham, Manuel Calvo, Luis Rández, 1996 .

Adversarial Ink: Componentwise Backward Error Attacks on Deep Learning

D. Higham, Lucas Beerens, 2023, IMA Journal of Applied Mathematics.

Uniform-in-diffusivity Chaotic Mixing and the Batchelor Spectrum

I. Tyukin, D. Higham, Christian Hansen, 2021 .

Sparse matrix computations for dynamic network centrality

Desmond J. Higham, Francesca Arrigo, D. Higham, 2017, Appl. Netw. Sci..

Block Matrix Formulations for Evolving Networks

Desmond J. Higham, Caterina Fenu, D. Higham, 2015, SIAM J. Matrix Anal. Appl..

A dynamical systems view of network centrality

Peter Grindrod, Desmond J Higham, D. Higham, 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Dynamic Communicability Predicts Infectiousness

Alexander V. Mantzaris, Desmond J. Higham, D. Higham, 2013 .

Runge-Kutta Defect Control Using Hermite-Birkhoff Interpolation

Desmond J. Higham, D. Higham, 1991, SIAM J. Sci. Comput..

Discovering and validating influence in a dynamic online social network

Alexander V. Mantzaris, D. Higham, P. Grindrod, 2013, Social Network Analysis and Mining.

Complex Networks: An Invitation

Desmond J. Higham, Maria Fox, Ernesto Estrada, 2010, Network Science.

Evolving graphs: dynamical models, inverse problems and propagation

Peter Grindrod, Desmond J. Higham, D. Higham, 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Unravelling small world networks

Desmond J. Higham, D. Higham, 2003 .

An Introduction to the Numerical Simulation of Stochastic Differential Equations

P. Kloeden, D. Higham, 2021 .

Multilevel Monte Carlo for Stochastic Differential Equations with Small Noise

Yu Sun, Desmond J. Higham, David F. Anderson, 2014, SIAM J. Numer. Anal..

Comparing Hitting Time Behavior of Markov Jump Processes and Their Diffusion Approximations

LUKASZ SZPRUCH, DESMOND J. HIGHAM, L. Szpruch, 2010, Multiscale Model. Simul..

Chemical Master Equation and Langevin regimes for a gene transcription model

Desmond J. Higham, Raya Khanin, D. Higham, 2007, Theor. Comput. Sci..

Estimating network dimension when the spectrum struggles

Henry-Louis de Kergorlay, D. Higham, P. Grindrod, 2023, Royal Society Open Science.

Condition numbers and their condition numbers

Desmond J. Higham, D. Higham, 1995 .

The Deformed Graph Laplacian and Its Applications to Network Centrality Analysis

Peter Grindrod, Desmond J. Higham, Vanni Noferini, 2018, SIAM J. Matrix Anal. Appl..

MacCormack's method for advection-reaction equations

D. Griffiths, D. Higham, 2000 .

ALTERATIONS IN FUNCTIONAL BRAIN NETWORK STRUCTURE INDUCED BY SUBCHRONIC PHENCYCLIDINE (PCP) TREATMENT PARALLEL THOSE SEEN IN SCHIZOPHRENIA

D. Higham, B. Morris, J. Pratt, 2010, Schizophrenia Research.

Node and edge nonlinear eigenvector centrality for hypergraphs

D. Higham, Francesco Tudisco, 2021, Communications Physics.

Dynamic Targeting in an Online Social Medium

Alexander V. Mantzaris, Peter Grindrod, Desmond J. Higham, 2012, SocInfo.

A model for dynamic communicators

Alexander V. Mantzaris, Desmond J. Higham, D. Higham, 2012, European Journal of Applied Mathematics.

Edinburgh Research Explorer A model for dynamic communicators

Alexander V. Mantzaris, D. Higham, 2011 .

Accurate Computation of the Log-Sum-Exp and Softmax Functions pdf

Nicholas J. Higham, Desmond J. Higham, Pierre Blanchard, 2019, ArXiv.

High Modularity Creates Scaling Laws

Peter Grindrod, Desmond J. Higham, D. Higham, 2018, Scientific Reports.

2 Organization and Funding 3 Registered Participants and Lectures Implicit-explicit Methods for Time-dependent Pdes Alternating Direction Orthogonal Spline Collocation Methods for Initial/boundary Value Prob- Lems Adaptive and Parallel Computational Techniques with Applications in Materials Science

J. M. Sanz-Serna, Hyman, J. Flaherty, 2007 .

A network model for polarization of political opinion.

Desmond J. Higham, Alexander V. Mantzaris, D. Higham, 2020, Chaos.

Mean Field Analysis of Hypergraph Contagion Models

Desmond J. Higham, Henry-Louis de Kergorlay, D. Higham, 2021, SIAM J. Appl. Math..

Stochastic Ordinary Differential Equations in Applied and Computational Mathematics

D. Higham, 2011 .

An introduction to multilevel Monte Carlo for option valuation

Desmond J. Higham, D. Higham, 2015, Int. J. Comput. Math..

Computational Complexity Analysis for Monte Carlo Approximations of Classically Scaled Population Processes

Desmond J. Higham, Yu Sun, David F. Anderson, 2015, Multiscale Model. Simul..

Numerical simulation of a linear stochastic oscillator with additive noise

Desmond J. Higham, D. Higham, Aslaug H. Strommen Melbo, 2004 .

Multilevel Monte Carlo for Stochastic Differential Equations with Small Noise

D. Higham, Yu Sun, D. F. Anderson, 2014, SIAM J. Numer. Anal..

Convergence, Non-negativity and Stability of a New Milstein Scheme with Applications to Finance

D. Higham, Xuerong Mao, Lukasz Szpruch, 2012, 1204.1647.

Connectivity of Random Geometric Hypergraphs

Henry-Louis de Kergorlay, D. Higham, 2023, Entropy.

Network Science: Complexity in Nature and Technology

D. Higham, E. Estrada, G. Oppo, 2010 .

Runge-Kutta Solutions of a Hyperbolic Conservation Law with Source Term

Mark A. Aves, D. Griffiths, D. Higham, 2000, SIAM Journal on Scientific Computing.

Runge–kutta Solutions of a Hyperbolic Conservation Law with Source Term *

Mark A. Aves, D. Higham, David F Griiths, 1998 .

Theta method dynamics

D. Griffiths, D. Higham, G. J. Barclay, 2000 .

Runge-Kutta and MacCormack dynamics

D. Griffiths, D. Higham, 1999 .

London Mathematical Society Theta Method Dynamics

D. Griffiths, D. Higham, G. J. Barclay, 2000 .

Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes

Desmond J. Higham, Graeme D. Chalmers, D. Higham, 2007 .

Numerical Analysis 1997

Desmond J. Higham, G. A. Watson, David F. Griffiths, 1997 .

Linear Multistep Methods—I: Construction and Consistency

Desmond J. Higham, David F. Griffiths, D. Griffiths, 2010 .

Strathprints Institutional Repository

D. Higham, Xuerong Mao, 2012 .

Dynamics of constant and variable stepsize methods for a nonlinear population model with delay

Desmond J. Higham, D. Higham, T. Sardar, 1997 .

Vulnerability Analysis of Transformer-based Optical Character Recognition to Adversarial Attacks

D. Higham, Lucas Beerens, 2023, ArXiv.

Numerical Methods for Ordinary Differential Equations - Initial Value Problems

D. Griffiths, D. Higham, 2010, Springer undergraduate mathematics series.

Backward error analysis and the qualitative behaviour of stochastic optimization algorithms: Application to stochastic coordinate descent

Stefano Di Giovacchino, K. Zygalakis, D. Higham, 2023, Journal of Computational Dynamics.

Edinburgh Research Explorer Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics

D. Higham, D. F. Anderson, 2022 .

Weighted Enumeration of Nonbacktracking Walks on Weighted Graphs

D. Higham, V. Noferini, F. Arrigo, 2022, SIAM Journal on Matrix Analysis and Applications.

6. Operators and Flow Control

Nicholas J. Higham, Desmond J. Higham, N. Higham, 2005 .

Dynamic Katz and Related Network Measures

Desmond J. Higham, Vanni Noferini, Francesca Arrigo, 2021, Linear Algebra and its Applications.

ARRIGO, FRANCESCA; HIGHAM, DESMOND J.; NOFERINI, VANNI A theory for backtrack-downweighted walks

D. Higham, 2021 .

Analysis of stepsize selection schemes for Runge-Kutta codes

Desmond J. Higham, D. Higham, George Hall, 1988 .

Numerical Schemes for Stochastic Differential Equation Models

P. Kloeden, D. Higham, 2008 .

ODEs—An Introduction

D. Griffiths, D. Higham, 2010 .

Complexity of Multilevel Monte Carlo Tau-Leaping

D. Higham, Yu Sun, D. F. Anderson, 2013, SIAM J. Numer. Anal..

The dynamics of a discretised nonlinear delay differential equation

G. Watson, D. Griffiths, D. Higham, 1993 .

Convergence, Non-negativity and Stability of a New Milstein Scheme with Applications to Finance

D. Higham, Xuerong Mao, Lukasz Szpruch, 2012, 1204.1647.

Black-Scholes for scientific computing students

D. Higham, 2004, Comput. Sci. Eng..

Black-Scholes option valuation for scientific computing students

Desmond J. Higham, D. Higham, 2004 .

MAPLE and MATLAB for stochastic differential equations in finance

Desmond J. Higham, Peter E. Kloeden, P. Kloeden, 2002 .

Highly continuous Runge-Kutta interpolants

Desmond J. Higham, D. Higham, 1991, TOMS.

Mathematical and computational modelling of post-transcriptional gene regulation by microRNAs

D. Higham, R. Khanin, 2009 .

Bistability through Triadic Closure

Peter Grindrod, Desmond J. Higham, Mark C. Parsons, 2012, Internet Math..

Asymmetry through time dependency

D. Higham, A. Mantzaris, 2016, The European Physical Journal B.

Deep Learning: An Introduction for Applied Mathematicians | SIAM Review | Vol. 61, No. 4 | Society for Industrial and Applied Mathematics

Catherine F. Higham, D. Higham, 2019 .

Asymptotic Stability of a Jump-Diffusion Equation and Its Numerical Approximation

Desmond J. Higham, Graeme D. Chalmers, D. Higham, 2008, SIAM J. Sci. Comput..

Google PageRank as mean playing time for pinball on the reverse web

D. Higham, 2005, Appl. Math. Lett..

Google Pagerank as Mean Playing Time for Pinball on the Reverse Web * 1 the Pagerank System

D. Higham, 2022 .

Sparse matrix computations for dynamic network centrality

D. Higham, F. Arrigo, 2017, Applied Network Science.

Preserving Sparsity in Dynamic Network Computations

Desmond J. Higham, Francesca Arrigo, D. Higham, 2016, COMPLEX NETWORKS.

Communicability and Bipartivity in Complex Networks at Negative Temperatures

Desmond J. Higham, Ernesto Estrada, Naomichi Hatano, 2008 .

Infering and calibrating triadic closure in a dynamic network

D. Higham, A. Mantzaris, 2013 .

Publisher Correction: Node and edge nonlinear eigenvector centrality for hypergraphs

D. Higham, Francesco Tudisco, 2021, Communications Physics.