Carlo Laing - Profile on Academia.edu (original) (raw)

Papers by Carlo Laing

Waves in Spatially-Disordered Neural Fields: A Case Study in Uncertainty Quantification

Studies in Mechanobiology, Tissue Engineering and Biomaterials, 2015

International Journal of Bifurcation and Chaos, 2013

Although variability is a ubiquitous characteristic of the nervous system, under appropriate cond... more Although variability is a ubiquitous characteristic of the nervous system, under appropriate conditions neurons can generate precisely timed action potentials. Thus considerable attention has been given to the study of a neuron's output in relation to its stimulus. In this study, we consider an increasingly popular spiking neuron model, the adaptive exponential integrateand-fire neuron. For analytical tractability, we consider its piecewise linear variant in order to understand the responses of such neurons to periodic stimuli. There exist regions in parameter space in which the neuron is mode locked to the periodic stimulus, and instabilities of the mode locked states lead to an Arnol'd tongue structure in parameter space. We analyze mode locked solutions and examine the bifurcations that define the boundaries of the tongue structures. The theoretical analysis is in excellent agreement with numerical simulations, and this study can be used to further understand the functional features related to responses of such a model neuron to biologically realistic inputs.

Numerical Bifurcation Theory for High-Dimensional Neural Models

The Journal of Mathematical Neuroscience, 2014

PDE Methods for Two-Dimensional Neural Fields

Neural Fields, 2014

We present a two-variable delay-differential-equation model of a pyramidal cell from the electros... more We present a two-variable delay-differential-equation model of a pyramidal cell from the electrosensory lateral line lobe of a weakly electric fish that is capable of burst discharge. It is a simplification of a six-dimensional ordinary differential equation model for such a cell whose bifurcation structure has been analyzed (Doiron et al., J. Comput. Neurosci., 12, 2002). We have modeled the effects of back-propagating action potentials by a delay, and use an integrate-and-fire mechanism for action potential generation. The simplicity of the model presented here allows one to explicitly derive a two-dimensional map for successive interspike intervals, and to analytically investigate the effects of time-dependent forcing on such a model neuron. Some of the effects discussed include 'burst excitability', the creation of resonance tongues under periodic forcing, and stochastic resonance. We also investigate the effects of changing the parameters of the model.

Siam Journal on Applied Mathematics, Jul 27, 2006

We study a partial integro-differential equation defined on a spatially extended domain that aris... more We study a partial integro-differential equation defined on a spatially extended domain that arises from the modeling of "working" or short-term memory in a neuronal network. The equation is capable of supporting spatially localized regions of high activity which can be switched "on" and "off" by transient external stimuli. We analyze the effects of coupling between units in the network, showing that if the connection strengths decay monotonically with distance, then no more than one region of high activity can persist, whereas if they decay in an oscillatory fashion, then multiple regions can persist.

Running title: “Different timings in neural field models” Corresponding author

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.

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.

We examine the existence and stability of spatially localized "bumps" of neuronal activity in a n... more We examine the existence and stability of spatially localized "bumps" of neuronal activity in a network of spiking neurons. Bumps have been proposed in mechanisms of visual orientation tuning, the rat head direction system, and working memory. We show that a bump solution can exist in a spiking network provided the neurons re asynchronously within the bump. We consider a parameter regime where the bump solution is bistable with an all-off state and can be initiated with a transient excitatory stimulus. We show that the activity pro le matches that of a corresponding population rate model. The bump in a spiking network can lose stability through partial synchronization to either a traveling wave or the all-off state. This can occur if the synaptic timescale is too fast through a dynamical effect or if a transient excitatory pulse is applied to the network. A bump can thus be activated and deactivated with excitatory inputs that may have physiological relevance.

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.

Multistability in spiking neuron models of delayed recurrent inhibitory loops

Lecture Notes in Physics, 2003

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.

GHOSTBURSTING: THE ROLE OF ACTIVE DENDRITES IN ELECTROSENSORY PROCESSING

The Genesis of Rhythm in the Nervous System, 2005

Physica D Nonlinear Phenomena

The complex Ginzburg-Landau (CGL) equation on a one-dimensional domain with periodic boundary con... more The complex Ginzburg-Landau (CGL) equation on a one-dimensional domain with periodic boundary conditions has a number of different symmetries, and solutions of the equation may or may not be fixed by the action of these symmetries. We investigate the stability of chaotic solutions that are spatially periodic with period L with respect to subharmonic perturbations that have a spatial period kL for some integer k > 1. This is done by considering the isotypic decomposition of the space of solutions and finding the dominant Lyapunov exponent associated with each isotypic component. We find a region of parameter space in which there exist chaotic solutions with spatial period L and homogeneous Neumann boundary conditions that are stable with respect to perturbations of period 2L. On varying the parameters it is possible to arrange for this solution to become unstable to perturbations of period 2L while remaining chaotic, leading to a supercritical subharmonic blowout bifurcation. For a large number of parameter values checked, chaotic solutions with spatial period L were found to be unstable with respect to perturbations of period 3L. We conclude that while periodic boundary conditions are often convenient mathematically, we would not expect to see chaotic, spatially periodic solutions forming starting with an arbitrary, non-periodic initial condition.

The Journal of Mathematical Neuroscience, 2015

The formation of oscillating phase clusters in a network of identical Hodgkin-Huxley neurons is s... more The formation of oscillating phase clusters in a network of identical Hodgkin-Huxley neurons is studied, along with their dynamic behavior. The neurons are synaptically coupled in an all-to-all manner, yet the synaptic coupling characteristic time is heterogeneous across the connections. In a network of N neurons where this heterogeneity is characterized by a prescribed random variable, the oscillatory single-cluster state can transition-through N − 1 (possibly perturbed) perioddoubling and subsequent bifurcations-to a variety of multiple-cluster states. The clustering dynamic behavior is computationally studied both at the detailed and the coarse-grained levels, and a numerical approach that can enable studying the coarsegrained dynamics in a network of arbitrarily large size is suggested. Among a number of cluster states formed, double clusters, composed of nearly equal sub-network sizes are seen to be stable; interestingly, the heterogeneity parameter in each of the doublecluster components tends to be consistent with the random variable over the entire network: Given a double-cluster state, permuting the dynamical variables of the neurons can lead to a combinatorially large number of different, yet similar "fine" states that appear practically identical at the coarse-grained level. For weak heterogeneity we find that correlations rapidly develop, within each cluster, between the neuron's "identity" (its own value of the heterogeneity parameter) and its dynamical state. For single-and double-cluster states we demonstrate an effective coarse-graining ap-Page 2 of 20 S.J. Moon et al. proach that uses the Polynomial Chaos expansion to succinctly describe the dynamics by these quickly established "identity-state" correlations. This coarse-graining approach is utilized, within the equation-free framework, to perform efficient computations of the neuron ensemble dynamics.

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, ...