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Instabilities in threshold-diffusion equations with delay (2008)
Journal Article
Laing, C. R., & Coombes, S. (2009). Instabilities in threshold-diffusion equations with delay. Physica D: Nonlinear Phenomena, 238(3), 264-272. https://doi.org/10.1016/j.physd.2008.10.014

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics, ranging from periodic solutions through to spatio-temporal chaos. In this paper, we consider a class of scal... Read More about Instabilities in threshold-diffusion equations with delay.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models (2008)
Journal Article
Coombes, S. (2008). Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models. SIAM Journal on Applied Dynamical Systems, 7(3), 1101–1129. https://doi.org/10.1137/070707579

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of the... Read More about Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models.

A two-fluid model for tissue growth within a dynamic flow environment (2008)
Journal Article
O'Dea, R. D., Waters, S. L., & Byrne, H. M. (2008). A two-fluid model for tissue growth within a dynamic flow environment. European Journal of Applied Mathematics, 19, https://doi.org/10.1017/S0956792508007687

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture... Read More about A two-fluid model for tissue growth within a dynamic flow environment.

The classification of higher-order cusp forms (2008)
Journal Article
Diamantis, N., & Sim, D. (2008). The classification of higher-order cusp forms. Journal für die reine und angewandte Mathematik, 2008(622), 121-153. https://doi.org/10.1515/CRELLE.2008.067

Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.

A Note on Palindromic ? -Vectors for Certain Rational Polytopes (2008)
Journal Article
Fiset, M., & Kasprzyk, A. M. (2008). A Note on Palindromic ? -Vectors for Certain Rational Polytopes. Electronic Journal of Combinatorics, 15, Article N18. https://doi.org/10.37236/893

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart ?-vector of P is palindromic. Perhaps less well-known is that a similar resu... Read More about A Note on Palindromic ? -Vectors for Certain Rational Polytopes.

Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis (2008)
Journal Article
Zachariou, M., Dissanayake, D. W. N., Coombes, S., Owen, M. R., & Mason, R. (in press). Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis. Cognitive Neurodynamics, 2, https://doi.org/10.1007/s11571-008-9050-4

Gating of sensory information can be assessed using an auditory conditioning-test paradigm which measures the reduction in the auditory evoked response to a test stimulus following an initial conditioning stimulus. Recording brainwaves from specific... Read More about Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis.

Democratization in a passive dendritic tree: An analytical investigation (2008)
Journal Article
Timofeeva, Y., Cox, S. J., Coombes, S., & Josic, K. (2008). Democratization in a passive dendritic tree: An analytical investigation. Journal of Computational Neuroscience, 25(2), 228-244. https://doi.org/10.1007/s10827-008-0075-9

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as "dendritic democr... Read More about Democratization in a passive dendritic tree: An analytical investigation.

A mixer design for the pigtail braid (2008)
Journal Article
Binder, B. J., & Cox, S. M. (2008). A mixer design for the pigtail braid. Fluid Dynamics Research, 40(1), 34-44. https://doi.org/10.1016/j.fluiddyn.2006.09.001

The stirring of a body of viscous fluid using multiple stirring rods is known to be particularly effective when the rods trace out a path corresponding to a nontrivial mathematical braid. The optimal braid is the so-called "pigtail braid", in which t... Read More about A mixer design for the pigtail braid.

Bayesian alignment of continuous molecular shapes using random fields (2008)
Journal Article
Czogiel, I., Dryden, I. L., & Brignell, C. J. Bayesian alignment of continuous molecular shapes using random fields. Manuscript submitted for publication

Statistical methodology is proposed for comparing molecular shapes. In order to account for the continuous nature of molecules, classical shape analysis methods are combined with techniques used for predicting random fields in spatial statistics. Ap... Read More about Bayesian alignment of continuous molecular shapes using random fields.

Modelling and analysis of planar cell polarity (2008)
Journal Article
Schamberg, S., Houston, P., Monk, N. A., & Owen, M. R. Modelling and analysis of planar cell polarity. Manuscript submitted for publication

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim i... Read More about Modelling and analysis of planar cell polarity.