All Outputs (24)

New percolation crossing formulas and second-order modular forms (2009)
Journal Article
Diamantis, N., & Kleban, P. (2009). New percolation crossing formulas and second-order modular forms. Communications in Number Theory and Physics, 3(4), 677–696. https://doi.org/10.4310/cntp.2009.v3.n4.a4

We consider the three crossing probability densities for percolation recently found via conformal field theory [23]. We prove that all three of them (i) may be simply expressed in terms of Cardy’s [4] and Watts’ [24] crossing probabilities, (ii) are... Read More about New percolation crossing formulas and second-order modular forms.

Second-order elliptic PDE with discontinuous boundary data (2009)
Journal Article
Houston, P., & Wihler, T. P. Second-order elliptic PDE with discontinuous boundary data. Manuscript submitted for publication

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point... Read More about Second-order elliptic PDE with discontinuous boundary data.

Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity (2009)
Journal Article
Ohl, T., & Schenkel, A. (2009). Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity. Journal of High Energy Physics, 2009, https://doi.org/10.1088/1126-6708/2009/10/052

We derive noncommutative Einstein equations for abelian twists and their solutions in consistently symmetry reduced sectors, corresponding to twisted FRW cosmology and Schwarzschild black holes. While some of these solutions must be rejected as model... Read More about Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity.

An integrative computational model for intestinal tissue renewal (2009)
Journal Article
Van Leeuwen, I. M., Mirams, G. R., Walter, A., Fletcher, A., Murray, P., Osborne, J., …Byrne, H. M. (2009). An integrative computational model for intestinal tissue renewal. Cell Proliferation, 42(5), 617-636. https://doi.org/10.1111/j.1365-2184.2009.00627.x

Objectives: The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoreti... Read More about An integrative computational model for intestinal tissue renewal.

Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity (2009)
Journal Article
Schenkel, A. (2009). Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity. Acta Physica Polonica B Proceedings Supplement, 2(3), 657-667

We review the noncommutative gravity of Wess et al. and discuss its physical applications. We define noncommutative symmetry reduction and construct deformed symmetric solutions of the noncommutative Einstein equations. We apply our framework to find... Read More about Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity.

Kernels of L-functions of cusp forms (2009)
Journal Article
Diamantis, N., & O’Sullivan, C. (2010). Kernels of L-functions of cusp forms. Mathematische Annalen, 346, 897–929. https://doi.org/10.1007/s00208-009-0419-4

Chaste: A test-driven approach to software development for biological modelling (2009)
Journal Article
Pitt-Francis, J., Pathmanathan, P., Bernabeu, M. O., Bordas, R., Cooper, J., Fletcher, A. G., …Gavaghan, D. J. (2009). Chaste: A test-driven approach to software development for biological modelling. Computer Physics Communications, 180(12), 2452-2471. https://doi.org/10.1016/j.cpc.2009.07.019

Chaste ('Cancer, heart and soft-tissue environment') is a software library and a set of test suites for computational simulations in the domain of biology. Current functionality has arisen from modelling in the fields of cancer, cardiac physiology an... Read More about Chaste: A test-driven approach to software development for biological modelling.

Bounds on fake weighted projective space (2009)
Journal Article
Kasprzyk, A. M. (2009). Bounds on fake weighted projective space. https://doi.org/10.2996/kmj/1245982903

A fake weighted projective space X is a Q-factorial toric variety with Picard number one. As with weighted projective space, X comes equipped with a set of weights (\lambda_0,...,\lambda_n). We see how the singularities of P(\lambda_0,...,\lambda_n)... Read More about Bounds on fake weighted projective space.

Delays in activity-based neural networks (2009)
Journal Article
Coombes, S., & Laing, C. (2009). Delays in activity-based neural networks. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 367(1891), 1117-1129. https://doi.org/10.1098/rsta.2008.0256

In this paper, we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity-based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discu... Read More about Delays in activity-based neural networks.

A multiple timescale analysis of a mathematical model of the Wnt/?-catenin signalling pathway (2009)
Journal Article
Mirams, G. R., Byrne, H. M., & King, J. R. (2010). A multiple timescale analysis of a mathematical model of the Wnt/?-catenin signalling pathway. Journal of Mathematical Biology, 60(1), 131-160. https://doi.org/10.1007/s00285-009-0262-y

The Wnt signalling pathway is involved in stem cell maintenance, differentiation and tissue development. Its disregulation has also been implicated in many cancers. β-catenin is a protein that regulates both transcription of many genes and cell-cell... Read More about A multiple timescale analysis of a mathematical model of the Wnt/?-catenin signalling pathway.

Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes (2009)
Journal Article
Ohl, T., & Schenkel, A. (2009). Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes. Journal of High Energy Physics, 2009, Article JHEP01(2009)084. https://doi.org/10.1088/1126-6708/2009/01/084

As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations that are given by a twist of a Lie algebra acting on... Read More about Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes.

Mode locking in a spatially extended neuron model: Active soma and compartmental tree (2009)
Journal Article
Svensson, C. M., Svensson, C., & Coombes, S. (2009). Mode locking in a spatially extended neuron model: Active soma and compartmental tree. International Journal of Bifurcation and Chaos, 19(8), 2597-2607. https://doi.org/10.1142/S0218127409024347

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example, it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a c... Read More about Mode locking in a spatially extended neuron model: Active soma and compartmental tree.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics (2009)
Journal Article
Thul, R., Coombes, S., & Smith, G. (2009). Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics. Physica D: Nonlinear Phenomena, 238, https://doi.org/10.1016/j.physd.2009.08.011

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitl... Read More about Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics.

Gap Junctions and Emergent Rhythms (2009)
Book Chapter
Coombes, S., & Zachariou, M. (2009). Gap Junctions and Emergent Rhythms. In J. Rubin, K. Josic, M. Matias, & R. Romo (Eds.), Coherent Behavior in Neuronal Networks. Springer

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic ne... Read More about Gap Junctions and Emergent Rhythms.

A computational study of discrete mechanical tissue models (2009)
Journal Article
Pathmanathan, P., Cooper, J., Fletcher, A., Mirams, G., Murray, P., Osborne, J., …Chapman, S. J. (2009). A computational study of discrete mechanical tissue models. Physical Biology, 6(3), Article 036001. https://doi.org/10.1088/1478-3975/6/3/036001

A computational study of discrete 'cell-centre' approaches to modelling the evolution of a collection of cells is undertaken. The study focuses on the mechanical aspects of the tissue, in order to separate the passive mechanical response of the model... Read More about A computational study of discrete mechanical tissue models.

Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions (2009)
Journal Article
Zhu, L., Giani, S., Houston, P., & Schoetzau, D. Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. Manuscript submitted for publication

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a... Read More about Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions.

Towards a predictive model of Ca²⁺ puffs (2009)
Journal Article
Thul, R., Thurley, K., & Falcke, M. (2009). Towards a predictive model of Ca²⁺ puffs. Chaos, 19, https://doi.org/10.1063/1.3183809

We investigate key characteristics of Ca²⁺ puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP[subscript]3 receptor channel clusters. In a first step, we numerically study Ca²⁺ liberation in a three dim... Read More about Towards a predictive model of Ca²⁺ puffs.

Rotational symmetries of crystals with defects (2009)
Journal Article
Parry, G. P. (2009). Rotational symmetries of crystals with defects. Journal of Elasticity, 94(2), https://doi.org/10.1007/s10659-008-9188-7

I use the theory of Lie groups/algebras to discuss the symmetries of crystals with uniform distributions of defects.

Voltage and current spectra for matrix power converters (2009)
Journal Article
Cox, S. M., & Creagh, S. C. (2009). Voltage and current spectra for matrix power converters. SIAM Journal on Applied Mathematics, 69(5), https://doi.org/10.1137/080718863

Matrix power converters are used for transforming one alternating-current power supply to another, with different peak voltage and frequency. There are three input lines, with sinusoidally varying voltages which are 120? out of phase one from another... Read More about Voltage and current spectra for matrix power converters.

Nonlinear development of matrix-converter instabilities (2009)
Journal Article
Cox, S. M., & Clare, J. C. (2009). Nonlinear development of matrix-converter instabilities. Journal of Engineering Mathematics, https://doi.org/10.1007/s10665-009-9325-8

Matrix converters convert a three-phase alternating-current power supply to a power supply of a different peak voltage and frequency, and are an emerging technology in a wide variety of applications. However, they are susceptible to an instability,... Read More about Nonlinear development of matrix-converter instabilities.