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- Heidi Johansen-Berg, Timothy Edward John Behrens, +6 authors Paul M. Matthews
- Proceedings of the National Academy of Sciences…
- 2004

A fundamental issue in neuroscience is the relation between structure and function. However, gross landmarks do not correspond well to microstructural borders and cytoarchitecture cannot be… (More)

- Desmond J. Higham
- SIAM Review
- 2001

A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Euler’s method for deterministic differential… (More)

The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state… (More)

- Desmond J. Higham
- SIAM J. Numerical Analysis
- 2000

Stability analysis of numerical methods for ordinary differential equations (ODEs) is motivated by the question “for what choices of stepsize does the numerical method reproduce the characteristics… (More)

- Julie L. Morrison, Rainer Breitling, Desmond J. Higham, David R. Gilbert
- BMC Bioinformatics
- 2005

Interpretation of simple microarray experiments is usually based on the fold-change of gene expression between a reference and a "treated" sample where the treatment can be of many types from drug… (More)

- Desmond J. Higham
- SIAM Review
- 2008

Many students are familiar with the idea of modeling chemical reactions in terms of ordinary differential equations. However, these deterministic reaction rate equations are really a certain… (More)

- Desmond J. Higham, Xuerong Mao, Andrew M. Stuart
- SIAM J. Numerical Analysis
- 2002

Traditional finite-time convergence theory for numerical methods applied to stochastic differential equations (SDEs) requires a global Lipschitz assumption on the drift and diffusion coefficients. In… (More)

The identification of specialized, functional regions of the human cortex is a vital precondition for neuroscience and clinical neurosurgery. Functional imaging modalities are used for their… (More)

- Jonathan J. Crofts, Desmond J. Higham, +4 authors Heidi Johansen-Berg
- NeuroImage
- 2011

Changes in brain structure occur in remote regions following focal damage such as stroke. Such changes could disrupt processing of information across widely distributed brain networks. We used… (More)

- David F. Anderson, Desmond J. Higham
- Multiscale Modeling & Simulation
- 2012

Review This work is concerned with computational methods for continuous time Markov chains. The setting is the one pertaining to mesoscopic chemical kinetics, where the so-called “random time change”… (More)