Multifractal characterization of nystagmus eye movements.

In this work, we investigate the multifractal properties of eye movement dynamics of children with infantile nystagmus, particularly the fluctuations of its velocity. The eye movements of three children and one adult with infantile nystagmus were evaluated in a simple task in comparison with 28 children with no ocular pathologies. Four indices emerge from the analysis: the classical Hurst exponent, the singularity strength corresponding to the maximum of the singularity spectrum, the asymmetry of the singularity spectrum, and the multifractal strength, each of which characterizes a particular aspect of eye movement dynamics. Our findings indicate that, when compared to children with no ocular pathologies, patients with infantile nystagmus present lower values of all indices. Except for the multifractal strength, the difference in the remaining indices is statistically significant. To test whether the characterization of patients with infantile nystagmus in terms of multifractality indices allows them to be distinguished from children without ocular pathologies, we performed an unsupervised clustering analysis and classified the subjects using supervised clustering techniques. The results indicate that these indices do, indeed, distinctively characterize the eye movements of patients with infantile nystagmus.

Modelling the eye movements of dyslexic children during reading as a continuous time random walk.

The study of eye movements during reading is considered a valuable tool for understanding the underlying cognitive processes and for its ability to detect alterations that could be associated with neurocognitive deficiencies or visual conditions. During reading, the gaze moves from one position to the next on the text performing a saccade-fixation sequence. This dynamics resembles processes usually described as continuous time random walk, where the jumps are the saccadic movements and waiting times are the duration of fixations. The time between jumps (intersaccadic time) consists of stochastic waiting time and flight time, which is a function of the jump length (the amplitude of the saccade). This motivates the present proposal of a model of eye movements during reading in the framework of the intermittent random walk but considering the time between jumps as a combined stochastic-deterministic process. The parameters used in this model were obtained from records of eye movements of children with dyslexia and typically developed for children performing a reading task. The jump lengths arise from the characteristics of the selected text. The time required for the flights was obtained based on a previously proposed model. Synthetic signals were generated and compared with actual eye movement signals in a complexity-entropy plane.

Information-theoretic characterization of eye-tracking signals with relation to cognitive tasks.

Eye tracking is being increasingly used as a more powerful diagnosis instrument when compared with traditional pen-and-paper tests in psychopedagogy and psychology. This technology may significantly improve neurocognitive assessments in gathering indirect latent information about the subjects' performance. However, the meaning and implications of these data are far from being fully understood. In this work, we present a comprehensive study of eye tracking time series in terms of statistical complexity measures. We registered the eye tracking movements of several subjects solving the two parts of the commonly applied Trail Making Test (TMT-A and TMT-B) and studied their Shannon entropy, disequilibrium, statistical complexity, and Fisher information with respect to three different probability distributions. The results show that these quantifiers reveal information about different features of the gaze depending on the distribution considered. As a meaningful result, we found that Fisher information in the position distribution reflects the difficulties encountered by the subject when solving the task. Such a characterization may be of interest to understand the underlying cognitive tasks performed by the subjects, and, additionally, it can serve as a source of valuable parameters to quantitatively assess how and why the subjects budget their attention, providing psychologists and psychopedagogues with more refined neuropsychological evaluation features and tools.

Models for saccadic motion and postsaccadic oscillations.

In a recent letter [S. Bouzat et al., Phys. Rev. Lett. 120, 178101 (2018)10.1103/PhysRevLett.120.178101], a mathematical model for eyeball and pupil motion was developed allowing for the understanding of the postsaccadic oscillations (PSO) as inertial effects. The model assumes that the inner part of the iris, which defines the pupil, moves driven by inertial forces induced by the eyeball rotation, in addition to viscous and elastic forces. Among other achievements, the model correctly reproduces eye-tracking experiments concerning PSO profiles and their dependence on the saccade size. In this paper we propose various extensions of the mentioned model, we provide analytical solutions, and we perform an exhaustive analysis of the dynamics. In particular, we consider a more general time dependence for the eyeball velocity enabling the description of saccades with vanishing initial acceleration. Moreover, we give the analytical solution in terms of hypergeometric functions for the constant parameter version of the model and we provide particular expressions for some cases of interest. We also introduce a new version of the model with inhomogeneous viscosity that can improve the fitting of the experimental results. Our analysis of the solutions explores the dependence of the PSO profiles on the system parameters for varying saccade sizes. We show that the PSO emerge in critical-like ways when parameters such as the elasticity of the iris, the global eyeball velocity, or the saccade size vary. Moreover, we find that the PSO profiles with the first overshoot smaller than the second one, which are usually observed in experiments, can be associated to parameter regions close to criticality.