Carlo Laing | Massey University (original) (raw)

Papers by Carlo Laing

Research paper thumbnail of Waves in Spatially-Disordered Neural Fields: A Case Study in Uncertainty Quantification

Studies in Mechanobiology, Tissue Engineering and Biomaterials, 2015

Research paper thumbnail of PERIODICALLY FORCED PIECEWISE-LINEAR ADAPTIVE EXPONENTIAL INTEGRATE-AND-FIRE NEURON

International Journal of Bifurcation and Chaos, 2013

Research paper thumbnail of Numerical Bifurcation Theory for High-Dimensional Neural Models

The Journal of Mathematical Neuroscience, 2014

Research paper thumbnail of PDE Methods for Two-Dimensional Neural Fields

Research paper thumbnail of A Two-Variable Model of Somatic-Dendritic Interactions in a Bursting Neuron

Research paper thumbnail of Multiple Bumps in a Neuronal Model of Working Memory

Siam Journal on Applied Mathematics, Jul 27, 2006

Research paper thumbnail of Running title: “Different timings in neural field models” Corresponding author

Research paper thumbnail of Periodically-forced finite networks of heterogeneous globally-coupled oscillators: A low-dimensional approach

Physica D Nonlinear Phenomena, Feb 29, 2008

We study a network of 500 globally-coupled modified van der Pol oscillators. The value of a param... more We study a network of 500 globally-coupled modified van der Pol oscillators. The value of a parameter associated with each oscillator is drawn from a normal distribution, giving a heterogeneous network. For strong enough coupling the oscillators all have the same period, and we consider periodic forcing of the network when it is in this state. By exploiting the correlations that quickly develop between the state of an oscillator and the value of its parameter we obtain an approximate low-dimensional description of the system in terms of the first few coefficients in a polynomial chaos expansion. Standard bifurcation analysis can then be performed on the low-dimensional system which results from this computational coarse-graining, and the results obtained from this predict very well the behaviour of the high-dimensional system for any set of realisations of the random parameter. Situations in which the method begins to fail are also discussed.

Research paper thumbnail of Solvable Model of Spiral Wave Chimeras

Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coup... more Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral can occur, with a circular core consisting of desynchronized oscillators running at full amplitude. Here we provide the first analytical description of such a spiral wave chimera, and use perturbation theory to calculate its rotation speed and the size of its incoherent core.

Research paper thumbnail of Stationary Bumps in Networks of Spiking Neurons

Research paper thumbnail of Periodically-forced finite networks of heterogeneous coupled oscillators: a low-dimensional approach

Ispd, 2006

We study a network of 500 coupled modified van der Pol oscillators. The value of a parameter asso... more We study a network of 500 coupled modified van der Pol oscillators. The value of a parameter associated with each oscillator is drawn from a normal distribution, giving a heterogeneous network. For strong enough coupling the oscillators all have the same period, and we consider periodic forcing of the network when it is in this state. By exploiting the correlations that quickly develop between the state of an oscillator and the value of its parameter we obtain an approximate low-dimensional description of the system in terms of the first few coefficients in a polynomial chaos expansion. Standard bifurcation analysis can then be performed on this low-dimensional system, and the results obtained from this predict very well the behaviour of the high-dimensional system for any set of realisations of the random parameter. Situations in which the method begins to fails are also discussed.

Research paper thumbnail of Multistability in spiking neuron models of delayed recurrent inhibitory loops

Research paper thumbnail of Journal of Computational Neuroscience 12, 5--25, 2002 c

Research paper thumbnail of Correlations and Memory in Neurodynamical Systems

Lecture Notes in Physics, 2003

Research paper thumbnail of Identification of Surface Electromyography Signals with Continuous Wavelet Entropy Transform

Continuous wavelet transform with focus placed on wavelet time entropy and wavelet frequency entr... more Continuous wavelet transform with focus placed on wavelet time entropy and wavelet frequency entropy in identifying human muscles action through sEMG signals is presented in this paper. It is found and demonstrated in calibrated experiments that the complex Shannon wavelet is the best candidate to identify the biceps and flexor digitorum superficialis (FDS) muscles activities due to its lowest wavelet time entropy values and its consistency over the time-variant signal. The finding presented in this paper has engineering implication in biomedical engineering and bio-robotic applications.

Research paper thumbnail of GHOSTBURSTING: THE ROLE OF ACTIVE DENDRITES IN ELECTROSENSORY PROCESSING

The Genesis of Rhythm in the Nervous System, 2005

Research paper thumbnail of Symmetry and chaos in the complex ginzburg-landau equatio. II: translational symmetries

Physica D Nonlinear Phenomena

Research paper thumbnail of Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons

The Journal of Mathematical Neuroscience, 2015

Research paper thumbnail of Derivation of a neural field model from a network of theta neurons

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Neural field models are used to study macroscopic spatiotemporal patterns in the cortex. Their de... more Neural field models are used to study macroscopic spatiotemporal patterns in the cortex. Their derivation from networks of model neurons normally involves a number of assumptions, which may not be correct. Here we present an exact derivation of a neural field model from an infinite network of theta neurons, the canonical form of a type I neuron. We demonstrate the existence of a "bump" solution in both a discrete network of neurons and in the corresponding neural field model.

Research paper thumbnail of A dynamic dendritic refractory period regulates burst discharge in the electrosensory lobe of weakly electric fish

The Journal of neuroscience : the official journal of the Society for Neuroscience, Jan 15, 2003

Na+-dependent spikes initiate in the soma or axon hillock region and actively backpropagate into ... more Na+-dependent spikes initiate in the soma or axon hillock region and actively backpropagate into the dendritic arbor of many central neurons. Inward currents underlying spike discharge are offset by outward K+ currents that repolarize a spike and establish a refractory period to temporarily prevent spike discharge. We show in a sensory neuron that somatic and dendritic K+ channels differentially control burst discharge by regulating the extent to which backpropagating dendritic spikes can re-excite the soma. During repetitive discharge a progressive broadening of dendritic spikes promotes a dynamic increase in dendritic spike refractory period. A leaky integrate-and-fire model shows that spike bursts are terminated when a decreasing somatic interspike interval and an increasing dendritic spike refractory period synergistically act to block backpropagation. The time required for the somatic interspike interval to intersect with dendritic refractory period determines burst frequency, ...

Research paper thumbnail of Waves in Spatially-Disordered Neural Fields: A Case Study in Uncertainty Quantification

Studies in Mechanobiology, Tissue Engineering and Biomaterials, 2015

Research paper thumbnail of PERIODICALLY FORCED PIECEWISE-LINEAR ADAPTIVE EXPONENTIAL INTEGRATE-AND-FIRE NEURON

International Journal of Bifurcation and Chaos, 2013

Research paper thumbnail of Numerical Bifurcation Theory for High-Dimensional Neural Models

The Journal of Mathematical Neuroscience, 2014

Research paper thumbnail of PDE Methods for Two-Dimensional Neural Fields

Research paper thumbnail of A Two-Variable Model of Somatic-Dendritic Interactions in a Bursting Neuron

Research paper thumbnail of Multiple Bumps in a Neuronal Model of Working Memory

Siam Journal on Applied Mathematics, Jul 27, 2006

Research paper thumbnail of Running title: “Different timings in neural field models” Corresponding author

Research paper thumbnail of Periodically-forced finite networks of heterogeneous globally-coupled oscillators: A low-dimensional approach

Physica D Nonlinear Phenomena, Feb 29, 2008

We study a network of 500 globally-coupled modified van der Pol oscillators. The value of a param... more We study a network of 500 globally-coupled modified van der Pol oscillators. The value of a parameter associated with each oscillator is drawn from a normal distribution, giving a heterogeneous network. For strong enough coupling the oscillators all have the same period, and we consider periodic forcing of the network when it is in this state. By exploiting the correlations that quickly develop between the state of an oscillator and the value of its parameter we obtain an approximate low-dimensional description of the system in terms of the first few coefficients in a polynomial chaos expansion. Standard bifurcation analysis can then be performed on the low-dimensional system which results from this computational coarse-graining, and the results obtained from this predict very well the behaviour of the high-dimensional system for any set of realisations of the random parameter. Situations in which the method begins to fail are also discussed.

Research paper thumbnail of Solvable Model of Spiral Wave Chimeras

Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coup... more Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral can occur, with a circular core consisting of desynchronized oscillators running at full amplitude. Here we provide the first analytical description of such a spiral wave chimera, and use perturbation theory to calculate its rotation speed and the size of its incoherent core.

Research paper thumbnail of Stationary Bumps in Networks of Spiking Neurons

Research paper thumbnail of Periodically-forced finite networks of heterogeneous coupled oscillators: a low-dimensional approach

Ispd, 2006

We study a network of 500 coupled modified van der Pol oscillators. The value of a parameter asso... more We study a network of 500 coupled modified van der Pol oscillators. The value of a parameter associated with each oscillator is drawn from a normal distribution, giving a heterogeneous network. For strong enough coupling the oscillators all have the same period, and we consider periodic forcing of the network when it is in this state. By exploiting the correlations that quickly develop between the state of an oscillator and the value of its parameter we obtain an approximate low-dimensional description of the system in terms of the first few coefficients in a polynomial chaos expansion. Standard bifurcation analysis can then be performed on this low-dimensional system, and the results obtained from this predict very well the behaviour of the high-dimensional system for any set of realisations of the random parameter. Situations in which the method begins to fails are also discussed.

Research paper thumbnail of Multistability in spiking neuron models of delayed recurrent inhibitory loops

Research paper thumbnail of Journal of Computational Neuroscience 12, 5--25, 2002 c

Research paper thumbnail of Correlations and Memory in Neurodynamical Systems

Lecture Notes in Physics, 2003

Research paper thumbnail of Identification of Surface Electromyography Signals with Continuous Wavelet Entropy Transform

Continuous wavelet transform with focus placed on wavelet time entropy and wavelet frequency entr... more Continuous wavelet transform with focus placed on wavelet time entropy and wavelet frequency entropy in identifying human muscles action through sEMG signals is presented in this paper. It is found and demonstrated in calibrated experiments that the complex Shannon wavelet is the best candidate to identify the biceps and flexor digitorum superficialis (FDS) muscles activities due to its lowest wavelet time entropy values and its consistency over the time-variant signal. The finding presented in this paper has engineering implication in biomedical engineering and bio-robotic applications.

Research paper thumbnail of GHOSTBURSTING: THE ROLE OF ACTIVE DENDRITES IN ELECTROSENSORY PROCESSING

The Genesis of Rhythm in the Nervous System, 2005

Research paper thumbnail of Symmetry and chaos in the complex ginzburg-landau equatio. II: translational symmetries

Physica D Nonlinear Phenomena

Research paper thumbnail of Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons

The Journal of Mathematical Neuroscience, 2015

Research paper thumbnail of Derivation of a neural field model from a network of theta neurons

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Neural field models are used to study macroscopic spatiotemporal patterns in the cortex. Their de... more Neural field models are used to study macroscopic spatiotemporal patterns in the cortex. Their derivation from networks of model neurons normally involves a number of assumptions, which may not be correct. Here we present an exact derivation of a neural field model from an infinite network of theta neurons, the canonical form of a type I neuron. We demonstrate the existence of a "bump" solution in both a discrete network of neurons and in the corresponding neural field model.

Research paper thumbnail of A dynamic dendritic refractory period regulates burst discharge in the electrosensory lobe of weakly electric fish

The Journal of neuroscience : the official journal of the Society for Neuroscience, Jan 15, 2003

Na+-dependent spikes initiate in the soma or axon hillock region and actively backpropagate into ... more Na+-dependent spikes initiate in the soma or axon hillock region and actively backpropagate into the dendritic arbor of many central neurons. Inward currents underlying spike discharge are offset by outward K+ currents that repolarize a spike and establish a refractory period to temporarily prevent spike discharge. We show in a sensory neuron that somatic and dendritic K+ channels differentially control burst discharge by regulating the extent to which backpropagating dendritic spikes can re-excite the soma. During repetitive discharge a progressive broadening of dendritic spikes promotes a dynamic increase in dendritic spike refractory period. A leaky integrate-and-fire model shows that spike bursts are terminated when a decreasing somatic interspike interval and an increasing dendritic spike refractory period synergistically act to block backpropagation. The time required for the somatic interspike interval to intersect with dendritic refractory period determines burst frequency, ...