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., Varma, S., Young, S. J., Cooper, J., Doyle, B., Pitt-Francis, J., Momtahan, L., Pathmanathan, P., Whiteley, J. P., Chapman, S. J., Gavaghan, D. J., Jensen, O. E., King, J. R., Maini, P. K., Waters, S. L., & 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., Mirams, G. R., Murray, P., Osborne, J. M., Walter, A., Chapman, S. J., Garny, A., van Leeuwen, I. M., Maini, P. K., Rodríguez, B., Waters, S. L., Whiteley, J. P., Byrne, H. M., & 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/β-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/β-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/β-catenin signalling pathway.