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All Outputs (5)

Neural Fields: Localised States with Piece-Wise Constant Interactions (2018)
Book Chapter
Gökçe, A., Coombes, S., & Avitabile, D. (2018). Neural Fields: Localised States with Piece-Wise Constant Interactions. In Mathematical and Theoretical Neuroscience: Cell, Network and Data Analysis (111-121). Cham, Switzerland: Springer Nature. https://doi.org/10.1007/978-3-319-68297-6_7

Neural field models are typically cast as continuum integro-differential equations for describing the idealised coarse-grained activity of populations of interacting neurons. For smooth Mexican hat kernels, with short-range excitation and long-range... Read More about Neural Fields: Localised States with Piece-Wise Constant Interactions.

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.

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.

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.

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.