Robert A. M. Gregson

Cognitive load as a determinant of the dimensionality of the electroencephalogram: A replication study

A sequel study to that reported by Gregson, Britton, Campbell and Gates (1990), partially replicating and extending findings which relate estimates of the dimensionality of the EEG to the complexity of task load in a visual scanning task, is described. The correlation dimensionality D2 of the attractor was computed using a variant of the Grassberger-Procaccia algorithm, and was shown to change in the expected direction, increasing as the task became more complicated. The effects are slight but consistent, and may be attenuated by nonstationarity over time, and by idiosyncratic factors. The results are numerically and qualitatively compatible with other recent reported studies, and support an interpretation linking brain dynamics to implied cognitive processes.

Comparisons of the nonlinear dynamics of electroencephalograms under various task loading conditions : a preliminary report

Comparison of the characteristics of electroencephalogram (EEG) records treated as realizations from a nonlinear process were compared under four different conditions: eyes shut resting, and three silent observation instructions to predict the patterns of randomly generated lights which illuminated every 10 seconds. The correlation dimension of the EEG was calculated by a method involving finding the correlation integral in m-dimensional space, and found to show some variations within time series. The degree and directions of changes in the dimensionality of the process varied between observers and did not clearly confirm some earlier reported findings, but it is demonstrable that the measures of nonlinear brain dynamics can be correlated with psychological variables. Reasons for this are discussed.

Nonlinear dynamical systems analysis for the behavioral sciences using real data

Introduction to Nonlinear Dynamical Systems Analysis, R.A.M. Gregson and S.J. Guastello Principles of Time Series Analysis, R.A.M. Gregson Frequency Distributions and Error Functions, S.J. Guastello Phase Space Analysis and Unfolding, M. Shelhamer Nonlinear Dynamical Analysis of Noisy Time Series, A. Heathcote and D. Elliott The Effects of the Irregular Sample and Missing Data in Time Series Analysis, D.M. Kreindler and C.J. Lumsden A Dynamical Analysis via the Extended-Return-Map, J.-S. Li, J. Krauth, and J.P. Huston Adjusting Behavioral Methods When Applying Nonlinear Dynamical Measures to Stimulus Rates, B.B. Frey Entropy, S.J. Guastello Analysis of Recurrence: Overview and Application to Eye-Movement Behavior, D.J. Aks Discontinuities and Catastrophes with Polynomial Regression, S.J. Guastello Nonlinear Regression and Structural Equations, S.J. Guastello Catastrophe Models with Nonlinear Regression, S.J. Guastello Catastrophe Model for the Prospect-Utility Theory Question, T.A. Oliva and S.R. McDade Measuring the Scaling Properties of Temporal and Spatial Patterns: From the Human Eye to the Foraging Albatross, M.S. Fairbanks and R.P. Taylor Oscillators with Differential Equations, J. Butner and T.N. Story Markov Chains for Identifying Nonlinear Dynamics, S.J. Merrill Markov Chain Example: Transitions between Two Pictorial Attractors, R.A.M. Gregson Identifying Ill-Behaved Nonlinear Processes without Metrics: Use of Symbolic Dynamics, R.A.M. Gregson Information Hidden in Signals and Macromolecules I: Symbolic Time-Series Analysis, M.A. Jimenez-Montano, R. Feistel, and O. Diez-Martinez Orbital Decomposition: Identification of Dynamical Patterns in Categorical Data, S.J. Guastello Orbital Decomposition for Multiple Time-Series Comparisons, D. Pincus, D.L. Ortega, and A.M. Metten The Danger of Wishing for Chaos, P.E. McSharry Methodological Issues in the Application of Monofractal Analyses in Psychological and Behavioral Research, D. Delignieres, K. Torre, and L. Lemoine Frontiers of Nonlinear Methods, R.A.M. Gregson Index

A cusp catastrophe analysis of changes to adolescent smoking behaviour in response to smoking prevention programs

The efficacy of smoking prevention programs aimed at adolescent smoking behaviour is widely debated in the health psychology literature. In general, however, these are not seen to be particularly effective in eliminating this acknowledged health risk behaviour. Even when positive results are presented, they frequently assume a linear association between exposure to some prevention or other and the dynamics of subsequent smoking behaviour change. Clair (1998) demonstrated that for alcohol consumption behaviour in adolescents, at least, this was not necessarily so. A nonlinear model, and in Clairs particular case, a Cusp Catastrophe Model (CCM) provided a better fit for the data than did any of a number of simple or interactive linear models. The present paper reports the use of precisely the same analysis for change in adolescent smoking behaviour following exposure to one or other of three smoking prevention programs of different orientations. While changes to adolescent smoking behaviour were evident following intervention, the reported analyses suggested that unlike alcohol consumption behaviour, CCMs were not necessarily the best nonlinear representation of the data.

Cascades and fields in perceptual psychophysics

Fundamental assumptions of nonlinear psychophysics nonlinear psycho-physics, response surface identification, and cross-entropy properties of nonlinear dynamics underlying the generation of cascades and fields unidimensional cascades and the case of perceived time estimation phase space changes and cascaded noise in fields more fields generated from lattices in (n x n)rk evolutions other field and cascade representations - isosimilarities, instabilities and inductions postscript - psychophysics or events in the real brain?

A nonlinear systems approach to Fechner's Paradox

It is possible to predict the topology of isointensity plots under conditions of extreme imbalance of the stimulus inputs, without making any assumptions specific to the circumstances in which Fechners Paradox is sometimes observed. This is done by extending a nonlinear model for a sensory channel, by postulating a form of cross-coupling or interference between two channels which represents other phenomena in psychophysics. It is noted that the form in which data are usually reported is not an adequate basis for testing all the predictions of a nonlinear model in sensory psychophysics. The physiologist Panum (1958), and later Fechner (1860) reported that the apparent brightness of an object viewed binocularly could, under conditions where the input to one eye was diminished by filtering, be less than its brightness viewed monocularly by the unfiltered eye. To a first approximation, binocular brightness is more like an averaging of two monocular inputs than a summation of those same inputs. For over 120 years this phenomenon, which came to be called “Fechners Paradox”, though Panum should perhaps have had some credit, has been the subject of experimental investigation and associated mathematical modelling. If one consults a dictionary of psychological terms, for example Evans (1978), one may read something like Fechners Paradox: The name give to the observation that something [which is] viewed binocularly seems to increase in brightness when one eye is closed. And yet we now know that this definition is misleading, because the same phenomenon in pooling two sensory inputs has its analogues in audition (Lehky 1983) and in olfaction (Gregson 1986). Gilchrist and McIver (1985) have now shown an analogue of the paradox exists in ocular contrast sensitivity. The definition also goes awry when the input luminance to one eye is zero, or when the luminance and ocular adaptation are closely matched for the two eyes. It is wiser, in the light of results reporting individual differences in the existence and extent of the paradox, and its sensitivity to stimulus conditions, to side with Blake and Fox (1973) when they observed that it is not unreasonable to suppose that various stimulus conditions might yield varying amounts of summation or even inhibition. Empirical reviews of relevant data in vision have been given by Roelofs and Zeeman (1914), Blake and Fox (1973), and Blake et al. (1981), but a theoretical model of interest as a starting point is that of Lehky (1983).

Nonlinear dynamics in a complex cubic one-dimensional model for sensory psychophysics

A cubic recursion with complex variable, has different properties in the phase spases of the reals and the imaginaries. The separation of the dynamics of the parts may be interpretable in terms of sensory intensity signal transmission through higher neural networks in man.

Effects of Random Noise and Internal Delay in Nonlinear Psychophysics

The effects of introducing second-order random noise on to parameters, so that they are unstable over time, and the effects of internal delay in a deterministic and therefore noise-free Γ recursion are compared. This is done by examining changes in the shape of the escarpment region which corresponds to the traditional psychometric function in sensation intensity or threshold experiments. Some of the grosser psychophysical response surface features are preserved, but only over a limited region of the parameter space. The system is robust against low noise and very brief internal delays, but will lose information and stability outside the region corresponding to low inputs and medium stability. This finding is compatible with what is reported on nonlinear cellular neural networks, for which a few analytical results on stability have been derived.

The size-weight illusion in 2-D nonlinear psychophysics

An extension of unidimensional nonlinear psychophysics is postulated by using forms of crosscoupling between the parameters of the two single-channel recursions, which have already been shown to model some perceptual phenomena. The size-weight illusion is shown to be reproducible in the topology of its relations, and it is suggested that some so-called illusions are in fact the natural consequences of nonlinear cross-coupling. The conditions that produce the illusion involve partially compensating the cross-coupling of sensory dimensions, and a second equilibrium with no cross-coupling, resembling simpler veridical perception, also exists in the behavior of some subjects.

Julia sets for the gamma recursion in nonlinear psychophysics

Julia sets for the map z→a(z−ie)(1−z)(z+ie) are illustrated for some attractors of interest. This work extends previous analyses of the cubic complex polynomial and considers dynamics in regions which may be associated with the modelling of the results of overload in sensory inputs.