All Outputs (32)

Mathematical neuroscience: from neurons to networks (2015)
Book Chapter
Coombes, S. (2015). Mathematical neuroscience: from neurons to networks. In C. Dogbe (Ed.), Actes du colloque "EDP-Normandie" : Le Havre 2015. Fédération Normandie Mathématiques

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. T... Read More about Mathematical neuroscience: from neurons to networks.

Covariance weighted procrustes analysis (2015)
Book Chapter
Brignell, C. J., Dryden, I. L., & Browne, W. J. (2015). Covariance weighted procrustes analysis. In P. K. Turaga, & A. Srivastava (Eds.), Riemannian Computing in Computer Vision (189-209). https://doi.org/10.1007/978-3-319-22957-7_9

© Springer International Publishing Switzerland 2016. We revisit the popular Procrustes matching procedure of landmark shape analysis and consider the situation where the landmark coordinates have a completely general covariance matrix, extending pre... Read More about Covariance weighted procrustes analysis.

Spots: breathing, drifting and scattering in a neural field model (2014)
Book Chapter
Coombes, S., Schmidt, H., & Avitabile, D. (2014). Spots: breathing, drifting and scattering in a neural field model. In S. Coombs, P. Beim Graben, R. Potthast, & J. Wright (Eds.), Neural fields: theory and applications (187-211). Springer. https://doi.org/10.1007/978-3-642-54593-1_7

Two dimensional neural field models with short range excitation and long range inhibition can exhibit localised solutions in the form of spots. Moreover, with the inclusion of a spike frequency adaptation current, these models can also support breath... Read More about Spots: breathing, drifting and scattering in a neural field model.

Estimation of Conductivity Tensors from Human Ventricular Optical Mapping Recordings (2013)
Book Chapter
Walmsley, J., Mirams, G. R., Efimov, I. R., Burrage, K., & Rodriguez, B. (2013). Estimation of Conductivity Tensors from Human Ventricular Optical Mapping Recordings. In S. Ourselin, D. Rueckert, & N. Smith (Eds.), Functional Imaging and Modeling of the Heart: 7th International Conference, FIMH 2013, London, UK, June 20-22, 2013. Proceedings (224-231). Springer Verlag. https://doi.org/10.1007/978-3-642-38899-6_27

Experimental recordings of transmural activation in the human left ventricle show variability in recorded activation times. In this paper we demonstrate a framework for fitting the conductivity tensor of a monodomain model to reproduce activation tim... Read More about Estimation of Conductivity Tensors from Human Ventricular Optical Mapping Recordings.

Fano polytopes (2012)
Book Chapter
Kasprzyk, A. M., & Nill, B. (2012). Fano polytopes. In A. Rebhan, L. Katzarkov, J. Knapp, R. Rashkov, & E. Scheidegger (Eds.), Strings, gauge fields, and the geometry behind: the legacy of Maximilian Kreuzer (349-364). World Scientific. https://doi.org/10.1142/9789814412551_0017

Fano polytopes are the convex-geometric objects corresponding to toric Fano varieties. We give a brief survey of classification results for different classes of Fano polytopes.

Second-Order Modular Forms with Characters (2012)
Book Chapter
Blann, T., & Diamantis, N. (2012). Second-Order Modular Forms with Characters. In Fourier Analysis and Number Theory to Radon Transforms and Geometry (55-66). Springer. https://doi.org/10.1007/978-1-4614-4075-8_4

We introduce spaces of second-order modular forms for which the relevant action involves characters. We compute the dimensions of these spaces by constructing explicit bases.

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.

Multiscale modeling of colonic crypts and early colorectal cancer (2010)
Book Chapter
Fletcher, A. G., Mirams, G. R., Murray, P. J., Walter, A., Kang, J. W., Cho, K. H., …Byrne, H. M. (2010). Multiscale modeling of colonic crypts and early colorectal cancer. In T. S. Deisboeck, & G. Stamatakos (Eds.), Multiscale Cancer Modeling (111-131). CRC Press. https://doi.org/10.1201/b10407

© 2011 by Taylor & Francis Group, LLC. Colorectal cancer accounts for 13% of all cancers in the United Kingdom, with around 35,300 new diagnoses and 16,000 deaths occurring each year (http://info.cancerresearchuk.org). Colorectal cancer is predomin... Read More about Multiscale modeling of colonic crypts and early colorectal cancer.

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.

Building oscillations bottom up: Elemental time scales of intracellular calcium dynamics (2007)
Book Chapter
Thul, R., & Falcke, M. (2007). Building oscillations bottom up: Elemental time scales of intracellular calcium dynamics. In L. Schimansky-Geier, B. Fiedler, J. Kurths, & E. Schöll (Eds.), Analysis and control of complex nonlinear processes in physics, chemistry and biology (293-324). World Scientific. https://doi.org/10.1142/9789812706911_0011

We analyze the elemental time scale of intracellular calcium dynamics. It is determined by the time course of Ca2+ puffs, which represent the fundamental quantum of Ca2+ release from intracellular storage compartments. Since Ca2+ puffs are truly rand... Read More about Building oscillations bottom up: Elemental time scales of intracellular calcium dynamics.

Calcium oscillations (2007)
Book Chapter
Thul, R., Bellamy, T., Roderick, L., Bootman, M., & Coombes, S. (2007). Calcium oscillations. In M. Maroto, & N. Monk (Eds.), Cellular Oscillatory Mechanisms. Springer

Changes in cellular calcium concentration control a wide range of physiological processes, from the subsecond release of synaptic neurotransmitters, to the regulation of gene expression over months or years. Calcium can also trigger cell death throu... Read More about Calcium oscillations.

Error estimation and adaptive mesh refinement for aerodynamic flows
Book Chapter
Hartmann, R., & Houston, P. Error estimation and adaptive mesh refinement for aerodynamic flows. In H. Deconinck (Ed.), Proceedings of the 36THCFD/Adigma course on HP-adaptive and HP-multigrid methods. Von Karman Institute for Fluid Dynamics, Rhode Saint Genese, Belgium: von Karman Institute for Fluid Dynamics

This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compress... Read More about Error estimation and adaptive mesh refinement for aerodynamic flows.