Symmetry-breaking, grouped images and multistability with transient unconsciousness.

Multistability in consciousness is characterised by transient switches in which the attributes of space and time are locally absent. An extensive number of studies has attempted to describe and predict the causes and duration of such switches, and many are obviously incomplete models or wrong, but some show promise. Models have, for example, drawn on neural network theory, psychophysics, signal detection theory, Markov matrices, and Shilnikov dynamics. Levels of macro-, meso- and micro-dynamics are employed by writers and contrasted. We compare some of those models and find problems in attempting to identify their properties and causality. Discontinuities in the observed local evolution of dynamical time series may be modelled in various ways; they are observed in multistability switches, in saddle-node bifurcations, and in cusp catastrophes. Three models, involving psychophysics, rapid recurrence, and neural networks, are considered as complementing rather than competing for representation.

Decision making with complex nonlinear systems: inference and identification in the context of DS22q11.2.

A rare gene deletion syndrome, that has in its associated phenome some possible cognitive and psychotic features, has been examined with DNA and fMRI for its causal basis within families and its statistical distribution in populations. Identification of its presence without DNA evidence is problematic as the condition is not stationary nor linear in its properties as the carrier grows older. Within a family its distribution is Mendelian, but there are also complications due to its complexity. A combined approach using both signal detection and an extension of Bayes theorem is a possible approach to discriminating between symptoms that have potentially a multi-causal basis, of which 22q11.2 deletion is only one possibility. Two later issues have arisen, one involving possibly at least two genetically different syndromes that result in similar autism in infancy, the other in statistical problems of prediction. Diagnosis of probable early DS 22q11.2 independent deaths as opposed to survival into adulthood can be wrongly thought to be a case of infanticide, and legal disputes have consequently arisen in the U.K., the USA, and Australia.

Multistable switching series in chaotic nets.

Examples of conscious and interpretable responses that have two or more forms alternating to the same stimuli have been known for centuries, and methods of describing how such situations arise have evolved in biological science. When switches between transient, perceptual or cognitive responses can occur and are mixed serially within time series exhibiting local terminal stability, then patterns arise where psychological data series are too brief to analyse empirically, and neurophysiological data and mathematical simulation are necessary. Modelling such conditions can be approached by using one modified Markov matrix, which we illustrate if we allow some singularities to exist in the dynamics. As soon as networks cease to be homogeneous and have a number of attractors present and operate with different local structures, then one or more response patterns may potentially exist at the same time. The patterns may be addressed within the behavioural dynamics by incorporating in turn very short transients that can be voluntary or involuntary, in sensory and cognitive data. Related software work for modelling, employing hierarchical Dirichlet structures projected into hidden Markov matrices is noted.

The Sheperd equation and chaos identification.

An equation created by Sheperd (1982) to model stability in exploited fish populations has been found to have a wider application, and it exhibits complicated internal dynamics, including phases of strict periodicity and of chaos. It may be potentially applicable to other psychophysiological contexts. The problems of determining goodness-of fit, and the comparative performance of alternative models including the Shephed model, are briefly addressed.

Conceptual problems in cardiological prediction.

The internal dynamics of cardiac activity are complex and can vary significantly over time, individuals may exhibit chaos, singularities, and nonstationarity at various time scales. The heart is one of the most studied psychobiological nonlinear systems, at various levels of mathematical and statistical sophistication. Some of its properties can be associated with morbidity or mortality. Prediction of when activity will terminate without acute clinical intervention is only possible at a statistical level over homogeneous groups of subjects under known conditions. Various consequent problems with data analysis at both individual and group levels are reviewed; the two related inferential issues, from individual dynamics to epidemiology, and from epidemiology to individual treatment issues, are critically examined.

Identifying ill-behaved nonlinear processes without metrics: use of symbolic dynamics.

Given ill-behaved psychological data that are unlikely to satisfy metric axioms, the use of encoding in symbolic dynamics, and hence leading into Markov analyses, is explored. Various measures of entropy are calculated. The tractability of entropic measures for categorizing the trajectories of nonlinear dynamics that may be present and chaotic is considered, with a focus on the case where there are two attractors and at least one heteroclinic orbit between them. Fast/slow dynamics are treated as a special case. The problem of identification is in other contexts the problem of diagnosis in time-varying pathologies. Some real data, selected for their psychological relevance in clinical, forensic and psychophysical processes, that are apparently edge-of chaos and nonstationary, are for comparison analysed both as metric and discrete and in symbolic encoding.

Transitions between two pictorial attractors.

Two experiments exploring similarity judgments on pairs and triplets of stimuli drawn from pictorial series are described. The stimuli are the Man-Woman and Gypsy-Girl pictures that slowly change from one prototype to the other as one progresses along the series. These have been used previously to demonstrate hysteresis of category judgments on ambiguous figures; the Man Woman series has been both modelled as a problem in neural network theory and mapped onto part of a cusp catastrophe surface. It. is shown that the transition process is complicated with a zone of uncertainty and prevalence of bimodality in many of the pairwise similarity judgments. The dynamics are interpreted in terms of transitions between two saddle-node attractors that are themselves not a discrete pair but have some overlap in their composition.

Forcing function effects on nonlinear trajectories: identifying very local brain dynamics.

Effects of imposing a sinusoidal acoustic and visual forcing function at various frequencies onto an EEG process are examined in terms of various indices of the nonlinear dynamics. Conjoint use of four methods of data analysis; Lyapunov exponents, the entropic analogue of the Schwarzian derivative, surrogate distributions, and higher-order kernel analyses in the time domain, is illustrated. Local epochs with unstable dynamics are identifed on very short series.