All Outputs (81)

Complex patterns of subcellular cardiac alternans (2019)
Journal Article

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.

Next-generation neural field model: The evolution of synchrony within patterns and waves (2019)
Journal Article

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue... Read More about Next-generation neural field model: The evolution of synchrony within patterns and waves.

How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes (2018)
Journal Article

Functional networks obtained from magnetoencephalography (MEG) from different frequency bands show distinct spatial patterns. It remains to be elucidated how distinct spatial patterns in MEG networks emerge given a single underlying structural networ... Read More about How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes.

Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony (2018)
Journal Article

Integrate-and-fire networks have proven remarkably useful in modelling the dynamics of real world phenomena ranging from earthquakes, to synchrony in neural networks, to cascading activity in social networks. The reset process means that such models... Read More about Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony.

Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals (2018)
Journal Article

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.

Clusters in nonsmooth oscillator networks (2018)
Journal Article

© 2018 American Physical Society. For coupled oscillator networks with Laplacian coupling, the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory... Read More about Clusters in nonsmooth oscillator networks.

Networks of piecewise linear neural mass models (2018)
Journal Article

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.

The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions (2017)
Journal Article

© 2017, The Author(s). Continuum neural field equations model the large-scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded as well as unbounde... Read More about The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions.

An analysis of waves underlying grid cell firing in the medial enthorinal cortex (2017)
Journal Article

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an I_h current in response to hyperpolarising synaptic input. A computational... Read More about An analysis of waves underlying grid cell firing in the medial enthorinal cortex.

A mean field model for movement induced changes in the beta rhythm (2017)
Journal Article

In electrophysiological recordings of the brain, the transition from high amplitude to low amplitude signals are most likely caused by a change in the synchrony of underlying neuronal population firing patterns. Classic examples of such modulations... Read More about A mean field model for movement induced changes in the beta rhythm.

Standing and travelling waves in a spherical brain model: the Nunez model revisited (2017)
Journal Article

The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or... Read More about Standing and travelling waves in a spherical brain model: the Nunez model revisited.

Combining spatial and parametric working memory in a dynamic neural field model (2016)
Journal Article

We present a novel dynamic neural field model consisting of two coupled fields of Amari-type which supports the existence of localized activity patterns or “bumps” with a continuum of amplitudes. Bump solutions have been used in the past to model spa... Read More about Combining spatial and parametric working memory in a dynamic neural field model.

Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function (2016)
Journal Article

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

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.

Mathematical frameworks for oscillatory network dynamics in neuroscience (2016)
Journal Article

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting nov... Read More about Mathematical frameworks for oscillatory network dynamics in neuroscience.

Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes (2015)
Journal Article

Atrial myocytes in a number of species lack transverse tubules. As a consequence the intracellular calcium signals occurring during each heartbeat exhibit complex spatio-temporal dynamics. These calcium patterns arise from saltatory calcium waves tha... Read More about Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes.

Travelling waves in models of neural tissue: from localised structures to periodic waves (2014)
Journal Article

We consider travelling waves (fronts, pulses and periodics) in spatially extended one dimensional neural field models. We demonstrate for an excitatory field with linear adaptation that, in addition to an expected stable pulse solution, a stable anti... Read More about Travelling waves in models of neural tissue: from localised structures to periodic waves.

Travelling waves in a neural field model with refractoriness (2013)
Journal Article

At one level of abstraction neural tissue can be regarded as a medium for turning local synaptic activity into output signals that propagate over large distances via axons to generate further synaptic activity that can cause reverberant activity in n... Read More about Travelling waves in a neural field model with refractoriness.

A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition (2013)
Journal Article

Memories are believed to be represented in the synaptic pathways of vastly interconnected networks of neurons. The plasticity of synapses, that is, their strengthening and weakening depending on neuronal activity, is believed to be the basis of lea... Read More about A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition.

Limitations of perturbative techniques in the analysis of rhythms and oscillations (2013)
Journal Article

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when... Read More about Limitations of perturbative techniques in the analysis of rhythms and oscillations.