Results 1  10
of
34
Multisector models
 In Handbook of Development Economics, eds., H. Chenery and T.N. Srinivasan
, 1989
"... To the best of my knowledge, this thesis contains no copy or paraphrase of work published by another person, except where duly acknowledged in the text. This thesis contains no material which has been presented for a degree at the University of Sydney or any other university. ..."
Abstract

Cited by 87 (10 self)
 Add to MetaCart
To the best of my knowledge, this thesis contains no copy or paraphrase of work published by another person, except where duly acknowledged in the text. This thesis contains no material which has been presented for a degree at the University of Sydney or any other university.
A neural mass model for MEG/EEG: coupling and neuronal dynamics
 NeuroImage
, 2003
"... Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequencyspecific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their func ..."
Abstract

Cited by 81 (21 self)
 Add to MetaCart
Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequencyspecific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their functional significance remains a matter of debate. Some of the mechanisms that generate these signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. The kinetics of the ensuing population dynamics determine the frequency of oscillations. In this work we extended the classical nonlinear lumpedparameter model of alpha rhythms, initially developed by Lopes da Silva and colleagues [Kybernetik 15 (1974) 27], to generate more complex dynamics. We show that the whole spectrum of MEG/EEG signals can be reproduced within the oscillatory regime of this model by simply changing the population kinetics. We used the model to examine the influence of coupling strength and propagation delay on the rhythms generated by coupled cortical areas. The main findings were that (1) coupling induces phaselocked activity, with a phase shift of 0 or &pi; when the coupling is bidirectional, and (2) both coupling and propagation delay are critical determinants of the MEG/EEG spectrum. In forthcoming articles, we will use this model to (1) estimate how neuronal interactions are expressed in MEG/EEG oscillations and establish the construct validity of various indices of nonlinear coupling, and (2) generate eventrelated transients to derive physiologically informed basis functions for statistical modelling of average evoked responses.
Stochastic neural field theory and the systemsize expansion
 SIAM J. Appl. Math
, 2009
"... Abstract. We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and tra ..."
Abstract

Cited by 30 (5 self)
 Add to MetaCart
(Show Context)
Abstract. We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit (N →∞)we recover standard activitybased or voltagebased rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen systemsize expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N) can be truncated to form a closed system of equations for the first and secondorder moments. Taking a continuum limit of the moment equations while keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the meanfield dynamics; such an analysis is not possible using the systemsize expansion since the latter cannot accurately determine exponentially small transitions. Key words. neural field theory, master equations, stochastic processes, systemsize expansion, path integrals
Stability and bifurcations in neural fields with finite propagation speed and general connectivity
 SIAM J. APPL. MATH
, 2005
"... A stability analysis is presented for neural field equations in the presence of finite propagation speed along axons and for a general class of connectivity kernels and synaptic properties. Sufficient conditions are given for the stability of equilibrium solutions. It is shown that the propagation ..."
Abstract

Cited by 26 (5 self)
 Add to MetaCart
(Show Context)
A stability analysis is presented for neural field equations in the presence of finite propagation speed along axons and for a general class of connectivity kernels and synaptic properties. Sufficient conditions are given for the stability of equilibrium solutions. It is shown that the propagation delays play a significant role in nonstationary bifurcations of equilibria, whereas the stationary bifurcations depend only on the connectivity kernel. In the case of nonstationary bifurcations, bounds are determined on the frequencies of the resulting oscillatory solutions. A perturbative scheme is used to calculate the types of bifurcations leading to spatial patterns, oscillations, and traveling waves. For high propagation speeds a simple method is derived that allows the determination of the bifurcation type by visual inspection of the Fourier transforms of the kernel and its first moment. Results are numerically illustrated on a class of neurologically plausible systems with combinations of Gaussian excitatory and inhibitory connections.
Dynamic instabilities in scalar neural field equations with spacedependent delays
 PHYSICA D
, 2007
"... In this paper we consider a class of scalar integral equations with a form of spacedependent delay. These nonlocal models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homoge ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
In this paper we consider a class of scalar integral equations with a form of spacedependent delay. These nonlocal models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled meanfield Ginzburg–Landau equations describing a Turing–Hopf bifurcation with modulation group velocity of O(1). Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatiotemporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatiotemporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin–Feir instabilities.
Existence and properties of solutions for neural field equations
, 2007
"... The first goal of this work is to study solvability of the neural field equation ∂u(x, t) τ − u(x, t) = w(x, y)f(u(y, t)) dy, x ∈ R ∂t m, t> 0, R m which is an integrodifferential equation in m+1 dimensions. In particular, we show the existence of global solutions for smooth activation function ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
(Show Context)
The first goal of this work is to study solvability of the neural field equation ∂u(x, t) τ − u(x, t) = w(x, y)f(u(y, t)) dy, x ∈ R ∂t m, t> 0, R m which is an integrodifferential equation in m+1 dimensions. In particular, we show the existence of global solutions for smooth activation functions f with values in [0, 1] and L 1 kernels w via the Banach fixpoint theorem. For a Heaviside type activation function f we show that the above approach fails. However, with slightly more regularity on the kernel function w (we use Hölder continuity with respect to the argument x) we can employ compactness arguments, integral equation techniques and the results for smooth nonlinearity functions to obtain a global existence result in a weaker space. Finally, general estimates on the speed and durability of waves are derived. We show that compactly supported waves with directed kernels (i.e. w(x, y) ≤ 0 for x ≤ y) decay exponentially after a finite time and that the field has a well defined finite speed. 1
Toward a Complementary Neuroscience: Metastable Coordination Dynamics of the Brain
"... Abstract. Metastability has been proposed as a new principle of behavioral and brain function and may point the way to a truly complementary neuroscience. From elementary coordination dynamics we show explicitly that metastability is a result of a symmetry breaking caused by the subtle interplay of ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Metastability has been proposed as a new principle of behavioral and brain function and may point the way to a truly complementary neuroscience. From elementary coordination dynamics we show explicitly that metastability is a result of a symmetry breaking caused by the subtle interplay of two forces: the tendency of the components to couple together and the tendency of the components to express their intrinsic independent behavior. The metastable regime reconciles the wellknown tendencies of specialized brain regions to express their autonomy (segregation) and the tendencies for those regions to work together as a synergy (integration). Integration ~ segregation is just one of the complementary pairs (denoted by the tilde (~) symbol) to emerge from the science of coordination dynamics. We discuss metastability in the brain by describing the favorable conditions existing for its emergence and by deriving some predictions for its empirical characterization in neurophysiological recordings.
Emerging consciousness as a result of complexdynamical interaction process. Eprint physics/0409140
"... A quite general interaction process within a multicomponent system is analysed by the extended effective potential method liberated from usual limitations of perturbation theory or integrable model. The obtained causally complete solution of the manybody problem reveals the phenomenon of dynamic m ..."
Abstract

Cited by 6 (6 self)
 Add to MetaCart
A quite general interaction process within a multicomponent system is analysed by the extended effective potential method liberated from usual limitations of perturbation theory or integrable model. The obtained causally complete solution of the manybody problem reveals the phenomenon of dynamic multivaluedness, or redundance, of emerging, incompatible system realisations and dynamic entanglement of system components within each realisation. The ensuing concept of dynamic complexity (and related intrinsic chaoticity) is absolutely universal and can be applied to the problem of consciousness that emerges now as a high enough, properly specified level of unreduced complexity of a suitable interaction process. This complexity level can be identified with the appearance of bound, permanently localised states in the multivalued brain dynamics from strongly chaotic states of unconscious intelligence, by analogy with classical behaviour emergence from quantum states at much lower levels of world dynamics. We show that the main properties of this dynamically emerging consciousness (and intelligence, at the preceding complexity level) correspond to empirically derived properties and criteria of their natural versions and obtain causally substantiated conclusions about their artificial realisation, including the fundamentally justified paradigm of genuine machine consciousness. This rigorously defined machine consciousness is different by its basic design from both natural consciousness and any mechanistic, dynamically singlevalued imitation of the latter. We use then the same, truly universal concept of complexity to derive equally rigorous conclusions about mental and social implications of the machine consciousness paradigm, demonstrating its indispensable role in the next stage of progressive civilisation development.