Spatiotemporal multi-resolution approximation of the Amari type neural field model

Aram, Parham; Freestone, Dean R.; Dewar, Michael; Scerri, Kenneth; Jirsa, Viktor K.; Grayden, David B.; Kadirkamanathan, Visakan

doi:10.1016/j.neuroimage.2012.10.039

Cited by 8 publications

(13 citation statements)

References 62 publications

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“…Perhaps one of the most famous applications of the IDE is with the Wilson and Cowan or Amari neural field model of the neocortex [33,34]. In the Amari neural field model (and many others), the spatial mixing kernel represents the neural connectivity function and the disturbance covariance represents the receptive field for subcortical input [35,36].…”

Section: Resultsmentioning

confidence: 99%

Estimation of the mixing kernel and the disturbance covariance in IDE-based spatiotemporal systems

Aram

Freestone

2016

Signal Processing

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The integro-difference equation (IDE) is an increasingly popular mathematical model of spatiotemporal processes, such as brain dynamics, weather systems, disease spread and others. We present an efficient approach for system identification based on correlation techniques for linear temporal systems that extended to spatiotemporal IDE-based models. The method is derived from the average (over time) spatial correlations of observations to calculate closed-form estimates of the spatial mixing kernel and the disturbance covariance function. Synthetic data are used to demonstrate the performance of the estimation algorithm.

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Section: Resultsmentioning

confidence: 99%

Estimation of the mixing kernel and the disturbance covariance in IDE-based spatiotemporal systems

Aram

Freestone

2016

Signal Processing

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“…A solution, therefore, to this problem is to use an iterative two-stage state-parameter estimation algorithm: a step of Kalman filtering (or smoothing) to estimate the state sequence, followed by a step of parameter estimation by LS [3], [18]. We extend this algorithm here to a sparse version where we use lasso in the parameter estimation step.…”

Section: A Joint Sparse Parameter and State Estimationmentioning

confidence: 99%

“…S PATIOTEMPORAL systems modelling is becoming an important area of study in such diverse areas as meteorology [1], biomedical signal processing [2], the neurosciences [3], epidemiology [4], and mobile sensor networks [5]. In order to fully describe the underlying dynamics of such processes, it is generally recognised that space and time data should not be treated as statistically independent variables [6].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal System Identification With Continuous Spatial Maps and Sparse Estimation

Aram

Kadirkamanathan

Anderson

2015

IEEE Trans. Neural Netw. Learning Syst.

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Abstract-In this paper we present a framework for the identification for spatiotemporal linear dynamical systems. We use a state-space model representation, which has the following attributes: the number of spatial observation locations are decoupled from the model order; the model allows for spatial heterogeneity; the model representation is continuous-over-space; the model parameters can be identified in a simple, sparse estimation procedure. The model identification procedure we propose has four steps: (i) decomposition of the continuous spatial field using a finite set of basis functions. Spatial frequency analysis is used to determine basis function width and spacing such that the main spatial frequency contents of the underlying field can be captured; (ii) initialisation of states in closed form; (iii) initialisation of state-transition and input matrix model parameters using sparse regression -the least absolute shrinkage and selection operator (lasso) method; (iv) joint state and parameter estimation using an iterative Kalman-filter/sparseregression algorithm. To investigate the performance of the proposed algorithm we use data generated by the Kuramoto model of spatiotemporal cortical dynamics. The identification algorithm performs successfully, predicting the spatiotemporal field with high accuracy, whilst the sparse regression leads to a compact model.

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“…For example, although the derivation is complex, the closed-form estimator presented in Eq. (15) is algorithmically straightforward when compared to alternative algorithms Scerri et al, 2009;Freestone et al, 2011;Aram et al, 2012). Furthermore, by using the closedform solution, one can see how errors in the knowledge of other parameters of the model that are assumed to be known will affect the estimates.…”

Section: Advantages Over Other Estimation Algorithmsmentioning

confidence: 99%

“…There are several data-driven frameworks recently presented in the literature Schiff and Sauer, 2008;Ullah and Schiff, 2010;Sedigh-Sarvestani et al, 2012;Pinotsis et al, 2013;Gorzelic et al, 2013;Turner et al, 2013;Aram et al, 2012;Freestone et al, 2011Freestone et al, , 2013Freestone et al, , 2014. These frameworks utilize system identification techniques to solve the problem of inferring parameters from data.…”

Section: Introductionmentioning

confidence: 99%

Model-based estimation of intra-cortical connectivity using electrophysiological data

et al. 2015

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This paper provides a new method for model-based estimation of intra-cortical connectivity from electrophysiological measurements. A novel closed-form solution for the connectivity function of the Amari neural field equations is derived as a function of electrophysiological observations. The resultant intra-cortical connectivity estimate is driven from experimental data, but constrained by the mesoscopic neurodynamics that are encoded in the computational model. A demonstration is provided to show how the method can be used to image physiological mechanisms that govern cortical dynamics, which are normally hidden in clinical data from epilepsy patients. Accurate estimation performance is demonstrated using synthetic data. Following the computational testing, results from patient data are obtained that indicate a dominant increase in surround inhibition prior to seizure onset that subsides in the cases when the seizures spread.

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Spatiotemporal multi-resolution approximation of the Amari type neural field model

Cited by 8 publications

References 62 publications

Estimation of the mixing kernel and the disturbance covariance in IDE-based spatiotemporal systems

Estimation of the mixing kernel and the disturbance covariance in IDE-based spatiotemporal systems

Spatiotemporal System Identification With Continuous Spatial Maps and Sparse Estimation

Model-based estimation of intra-cortical connectivity using electrophysiological data

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