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Neural fields with sigmoidal firing rates: Approximate solutions (2010)
Journal Article
Coombes, S., & Schmidt, H. (2010). Neural fields with sigmoidal firing rates: Approximate solutions. Discrete and Continuous Dynamical Systems - Series A, 28(4), 1369-1379. https://doi.org/10.3934/dcds.2010.28.1369

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of... Read More about Neural fields with sigmoidal firing rates: Approximate solutions.

A hybrid approach to multi-scale modelling of cancer (2010)
Journal Article
Osborne, J. M., Walter, A., Kershaw, S. K., Mirams, G. R., Fletcher, A. G., Pathmanathan, P., …Byrne, H. M. (2010). A hybrid approach to multi-scale modelling of cancer. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 368(1930), 5013-5028. https://doi.org/10.1098/rsta.2010.0173

In this paper, we review multi-scale models of solid tumour growth and discuss a middleout framework that tracks individual cells. By focusing on the cellular dynamics of a healthy colorectal crypt and its invasion by mutant, cancerous cells, we comp... Read More about A hybrid approach to multi-scale modelling of cancer.

Phenomenological modeling of cell-to-cell and beat-to-beat variability in isolated guinea pig ventricular myocytes (2010)
Conference Proceeding
Walmsley, J., Mirams, G., Bahoshy, M., Bollensdorff, C., Rodriguez, B., & Burrage, K. (2010). Phenomenological modeling of cell-to-cell and beat-to-beat variability in isolated guinea pig ventricular myocytes. In 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology, (1457-1460). https://doi.org/10.1109/IEMBS.2010.5626858

Experimental action potential (AP) recordings in isolated ventricular myoctes display significant temporal beatto- beat variability in morphology and duration. Furthermore, significant cell-to-cell differences in AP also exist even for isolated cells... Read More about Phenomenological modeling of cell-to-cell and beat-to-beat variability in isolated guinea pig ventricular myocytes.

Household epidemic models with varying infection response (2010)
Journal Article
Ball, F. G., Britton, T., & Sirl, D. J. (2011). Household epidemic models with varying infection response. Journal of Mathematical Biology, 63(2), 309-337

This paper is concerned with SIR (susceptible--infected--removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different mode... Read More about Household epidemic models with varying infection response.

High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing (2010)
Journal Article
Schenkel, A., & F. Uhlemann, C. (2010). High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing. Physics Letters B, 694(3), 258-260. https://doi.org/10.1016/j.physletb.2010.09.066

We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which -- in contrast to the well known Moyal-Weyl deformation -- lead to a theory with modified kinetic te... Read More about High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing.

Sloshing and slamming oscillations in a collapsible channel flow (2010)
Journal Article
Stewart, P. S., Waters, S. L., Jensen, O. E., & Heil, M. (2010). Sloshing and slamming oscillations in a collapsible channel flow. Journal of Fluid Mechanics, 662, 288-319. https://doi.org/10.1017/s0022112010003277

We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to a linear external pressure dist... Read More about Sloshing and slamming oscillations in a collapsible channel flow.

Modelling spatially regulated ?-catenin dynamics and invasion in intestinal crypts (2010)
Journal Article
Murray, P. J., Kang, J. W., Mirams, G. R., Shin, S. Y., Byrne, H. M., Maini, P. K., & Cho, K. H. (2010). Modelling spatially regulated ?-catenin dynamics and invasion in intestinal crypts. Biophysical Journal, 99(3), 716-725. https://doi.org/10.1016/j.bpj.2010.05.016

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from... Read More about Modelling spatially regulated ?-catenin dynamics and invasion in intestinal crypts.

Field Theory on Curved Noncommutative Spacetimes (2010)
Journal Article
Schenkel, A., & F. Uhlemann, C. (2010). Field Theory on Curved Noncommutative Spacetimes. Symmetry, Integrability and Geometry: Methods and Applications, 6, Article 061. https://doi.org/10.3842/SIGMA.2010.061

We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative spacetimes by us... Read More about Field Theory on Curved Noncommutative Spacetimes.

Spacetime Noncommutativity in Models with Warped Extradimensions (2010)
Journal Article
Ohl, T., Schenkel, A., & F. Uhlemann, C. (2010). Spacetime Noncommutativity in Models with Warped Extradimensions. Journal of High Energy Physics, Article 29. https://doi.org/10.1007/JHEP07%282010%29029

We construct consistent noncommutative (NC) deformations of the Randall-Sundrum spacetime that solve the NC Einstein equations with a non-trivial Poisson tensor depending on the fifth coordinate. In a class of these deformations where the Poisson ten... Read More about Spacetime Noncommutativity in Models with Warped Extradimensions.

Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes (2010)
Journal Article
Ohl, T., & Schenkel, A. (2010). Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes. General Relativity and Gravitation, 42(12), 2785–2798. https://doi.org/10.1007/s10714-010-1016-2

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals and compu... Read More about Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes.

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem (2010)
Journal Article
Cliffe, A., Hall, E., Houston, P., Phipps, E. T., & Salinger, A. G. (2010). Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem. Communications in Computational Physics, 8(4), 845-865. https://doi.org/10.4208/cicp.290709.120210a

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, base... Read More about Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem.

Preferred foliation effects in Quantum General Relativity (2010)
Journal Article
Koslowski, T., & Schenkel, A. (2010). Preferred foliation effects in Quantum General Relativity. Classical and Quantum Gravity, 27(13), Article 135014. https://doi.org/10.1088/0264-9381/27/13/135014

We investigate the infrared (IR) effects of Lorentz violating terms in the gravitational sector using functional renormalization group methods similar to Reuter and collaborators. The model we consider consists of pure quantum gravity coupled to a pr... Read More about Preferred foliation effects in Quantum General Relativity.

The influence of bioreactor geometry and the mechanical environment on engineered tissues (2010)
Journal Article
Osborne, J., O'Dea, R. D., Whiteley, J., Byrne, H., & Waters, S. (2010). The influence of bioreactor geometry and the mechanical environment on engineered tissues. Journal of Biomechanical Engineering, 132(5), Article 051006. https://doi.org/10.1115/1.4001160

A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium and porous scaffold are treated as distinct phases. The bioreactor system is... Read More about The influence of bioreactor geometry and the mechanical environment on engineered tissues.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry (2010)
Journal Article
Cliffe, A., Hall, E., Houston, P., Phipps, E. T., & Salinger, A. G. Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry. Manuscript submitted for publication

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particula... Read More about Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry.

Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks (2010)
Journal Article
Hlinka, J., Hlinka, J., & Coombes, S. (2010). Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks. Physical Review Letters, 104(6), https://doi.org/10.1103/PhysRevLett.104.068101

Ultraslow fluctuations (0.01-0.1 Hz) are a feature of intrinsic brain activity of as yet unclear origin. We propose a candidate mechanism based on retrograde endocannabinoid signaling in a synaptically coupled network of excitatory neurons. This is k... Read More about Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks.

Normed algebras of differentiable functions on compact plane sets (2010)
Journal Article
Dales, H., & Feinstein, J. (2010). Normed algebras of differentiable functions on compact plane sets. Indian Journal of Pure and Applied Mathematics, 41(1), https://doi.org/10.1007/s13226-010-0005-1

We investigate the completeness and completions of the normed algebras (D(1)(X),∥•∥) for perfect, compact plane sets X. In particular, we construct a radially self-absorbing, compact plane set X such that the normed algebra (D(1)(X),∥•∥) is not compl... Read More about Normed algebras of differentiable functions on compact plane sets.

A new method for conditioning stochastic groundwater flow models in fractured media (2010)
Journal Article
Milne, A., Cliffe, A., Holton, D., Houston, P., Jackson, C. P., & Joyce, S. A new method for conditioning stochastic groundwater flow models in fractured media. Manuscript submitted for publication

Many geological formations consist of crystalline rocks that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposa... Read More about A new method for conditioning stochastic groundwater flow models in fractured media.

Large-scale neural dynamics: Simple and complex (2010)
Journal Article
Coombes, S. (2010). Large-scale neural dynamics: Simple and complex. NeuroImage, 52(3), 731-739. https://doi.org/10.1016/j.neuroimage.2010.01.045

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models... Read More about Large-scale neural dynamics: Simple and complex.

High-order hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows (2010)
Book Chapter
Giani, S., & Houston, P. (2010). High-order hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. In N. Kroll, H. Bieler, H. Deconinck, V. Couallier, H. van der Ven, & K. Sorensen (Eds.), ADIGMA - a European initiative on the development of adaptive higher-order variational methods for aerospace applications. Springer. https://doi.org/10.1007/978-3-642-03707-8_28

This article is concerned with the construction of general isotropic and anisotropic adaptive strategies, as well as hp-mesh refinement techniques, in combination with dual-weighted-residual a posteriori error indicators for the discontinuous Galerki... Read More about High-order hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows.