Outputs (50)

Synchrony in networks of Franklin bells (2019)
Journal Article
Sayli, M., Lai, Y. M., Thul, R., & Coombes, S. (2019). Synchrony in networks of Franklin bells. IMA Journal of Applied Mathematics, 84(5), 1001-1021. https://doi.org/10.1093/imamat/hxz023

The Franklin bell is an electro-mechanical oscillator that can generate a repeating chime in the presence of an electric field. Benjamin Franklin famously used it as a lightning detector. The chime arises from the impact of a metal ball on a metal be... Read More about Synchrony in networks of Franklin bells.

Complex patterns of subcellular cardiac alternans (2019)
Journal Article
Veasy, J., Lai, Y. M., Coombes, S., & Thul, R. (2019). Complex patterns of subcellular cardiac alternans. Journal of Theoretical Biology, 478, 102-114. https://doi.org/10.1016/j.jtbi.2019.06.016

Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A... Read More about Complex patterns of subcellular cardiac alternans.

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling (2018)
Journal Article
Falcke, M., Moein, M., Tilunaite, A., Thul, R., & Skupin, A. (2018). On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling. Chaos, 28(4), Article 045115. https://doi.org/10.1063/1.5021073

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems, and is the basis of the predictive power of theoretical physics. While physicists have confidence... Read More about On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling.

Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals (2018)
Journal Article
McIvor, E., Coombes, S., & Thul, R. (2018). Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals. Cell Calcium, 73, https://doi.org/10.1016/j.ceca.2018.03.006

The spatial organisation of Orai channels and SERCA pumps within ER-PM junctions is important for enhancing the versatility and specificity of subcellular Ca2+ signals generated during store operated Ca2+ entry (SOCE). In this paper we present a nove... Read More about Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals.

Networks of piecewise linear neural mass models (2018)
Journal Article
Coombes, S., Lai, Y. M., Sayli, M., & Thul, R. (2018). Networks of piecewise linear neural mass models. European Journal of Applied Mathematics, 29(Special issue 5), 869-890. https://doi.org/10.1017/S0956792518000050

Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ordinary differential equations with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlase... Read More about Networks of piecewise linear neural mass models.

A Bayesian approach to modelling heterogeneous calcium responses in cell populations (2017)
Journal Article
Tilunaite, A., Croft, W., Russell, N. A., Bellamy, T. C., & Thul, R. (2017). A Bayesian approach to modelling heterogeneous calcium responses in cell populations. PLoS Computational Biology, 13(10), Article e1005794. https://doi.org/10.1371/journal.pcbi.1005794

Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding i... Read More about A Bayesian approach to modelling heterogeneous calcium responses in cell populations.

Evolution of moments and correlations in non-renewal escape-time processes (2017)
Journal Article
Braun, W., Thul, R., & Longtin, A. (in press). Evolution of moments and correlations in non-renewal escape-time processes. Physical Review E, 95, https://doi.org/10.1103/PhysRevE.95.052127

The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained... Read More about Evolution of moments and correlations in non-renewal escape-time processes.

Sign changes as a universal concept in first-passage-time calculations (2017)
Journal Article
Braun, W., & Thul, R. (2017). Sign changes as a universal concept in first-passage-time calculations. Physical Review E, 95(12114), https://doi.org/10.1103/PhysRevE.95.012114

First-passage-time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage-time calculations have p... Read More about Sign changes as a universal concept in first-passage-time calculations.

Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function (2016)
Journal Article
Coombes, S., & Thul, R. (2016). Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function. European Journal of Applied Mathematics, 27(6), 904-922. https://doi.org/10.1017/S0956792516000115

The master stability function is a powerful tool for determining synchrony in high-dimensional networks of coupled limit cycle oscillators. In part, this approach relies on the analysis of a low-dimensional variational equation around a periodic orbi... Read More about Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function.

Neural field models with threshold noise (2016)
Journal Article
Thul, R., Coombes, S., & Laing, C. R. (2016). Neural field models with threshold noise. Journal of Mathematical Neuroscience, 6, Article 3. https://doi.org/10.1186/s13408-016-0035-z

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate funct... Read More about Neural field models with threshold noise.