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The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study (2006)
Journal Article
Zachariou, M., Dissanayake, D., Owen, M. R., Mason, R., & Coombes, S. The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study. Neurocomputing, 70(10/12), https://doi.org/10.1016/j.neucom.2006.10.065

Gating of sensory (e.g. auditory) information has been demonstrated as a reduction in the auditory-evoked potential responses recorded in the brain of both normal animals and human subjects. Auditory gating is perturbed in schizophrenic patients and... Read More about The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study.

Persistent localized states for a chaotically mixed bistable reaction (2006)
Journal Article
Cox, S. M. (2006). Persistent localized states for a chaotically mixed bistable reaction. Physical Review E, 74(5),

We describe the evolution of a bistable chemical reaction in a closed two-dimensional chaotic laminar flow, from a localized initial disturbance. When the fluid mixing is sufficiently slow, the disturbance may spread and eventually occupy the entire... Read More about Persistent localized states for a chaotically mixed bistable reaction.

Spatio-temporal filtering properties of a dendritic cable with active spines: A modeling study in the spike-diffuse-spike framework (2006)
Journal Article
Timofeeva, Y., Lord, G., & Coombes, S. (2006). Spatio-temporal filtering properties of a dendritic cable with active spines: A modeling study in the spike-diffuse-spike framework. Journal of Computational Neuroscience, 21(3), 293-306. https://doi.org/10.1007/s10827-006-8776-4

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modeled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. In th... Read More about Spatio-temporal filtering properties of a dendritic cable with active spines: A modeling study in the spike-diffuse-spike framework.

Iterated integrals and higher order automorphic forms (2006)
Journal Article
Diamantis, N., & Sreekantan, R. (2006). Iterated integrals and higher order automorphic forms. Commentarii Mathematici Helvetici, 81(2), 481–494. https://doi.org/10.4171/cmh/60

Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's theory, we pro... Read More about Iterated integrals and higher order automorphic forms.

Frequency of elemental events of intracellular Ca²⁺ dynamics (2006)
Journal Article
Thul, R., & Falcke, M. (2006). Frequency of elemental events of intracellular Ca²⁺ dynamics. Physical Review E, 73, Article 061923. https://doi.org/10.1103/PhysRevE.73.061923

The dynamics of intracellular Ca²⁺ is driven by random events called Ca²⁺ puffs, in which Ca²⁺ is liberated from intracellular stores. We show that the emergence of Ca²⁺ puffs can be mapped to an escape process. The mean first passage times that corresp... Read More about Frequency of elemental events of intracellular Ca²⁺ dynamics.

The structure of uniform discrete defective crystals (2006)
Journal Article
Cermelli, P., & Parry, G. P. (2006). The structure of uniform discrete defective crystals. Continuum Mechanics and Thermodynamics, 18(1-2), https://doi.org/10.1007/s00161-006-0019-4

In the continuum context, a uniform crystal has dislocation density tensor constant in space. A simple iteration procedure generates an infinite set of points which is associated with uniform defective crystals. When certain necessary conditions are... Read More about The structure of uniform discrete defective crystals.

Toric Fano three-folds with terminal singularities (2006)
Journal Article
Kasprzyk, A. M. (2006). Toric Fano three-folds with terminal singularities. TÔhoku Mathematical Journal, 58(1), 101-121. https://doi.org/10.2748/tmj/1145390208

This paper classifies all toric Fano 3-folds with terminal singularities. This is achieved by solving the equivalent combinatoric problem; that of finding, up to the action of GL(3,Z), all convex polytopes in Z^3 which contain the origin as the only... Read More about Toric Fano three-folds with terminal singularities.

Class-D audio amplifiers with negative feedback (2006)
Journal Article
Cox, S. M., & Candy, B. H. (2006). Class-D audio amplifiers with negative feedback. SIAM Journal on Applied Mathematics, 66(2),

There are many different designs for audio amplifiers. Class-D, or switching, amplifiers generate their output signal in the form of a high-frequency square wave of variable duty cycle (ratio of on time to off time). The square-wave nature of the ou... Read More about Class-D audio amplifiers with negative feedback.

A bistable reaction-diffusion system in a stretching flow (2006)
Journal Article
Cox, S. M., & Gottwald, G. A. (2006). A bistable reaction-diffusion system in a stretching flow. Physica D: Nonlinear Phenomena, 216(2),

We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODEs) for the dynamics of the governing advection-reaction-diffu... Read More about A bistable reaction-diffusion system in a stretching flow.

Reduced models of chemical reaction in chaotic flows (2006)
Journal Article
Vikhansky, A., & Cox, S. M. (2006). Reduced models of chemical reaction in chaotic flows. Physics of Fluids, 18(3), https://doi.org/10.1063/1.2182373

We describe and evaluate two reduced models for nonlinear chemical reactions in a chaotic laminar flow. Each model involves two separate steps to compute the chemical composition at a given location and time. The “manifold tracking model” first track... Read More about Reduced models of chemical reaction in chaotic flows.