Multifractality Versus (Mono-) Fractality as Evidence of Nonlinear Interactions Across Timescales: Disentangling the Belief in Nonlinearity From the Diagnosis of Nonlinearity in Empirical Data

This article addresses the still popular but incorrect idea that monofractal (sometimes called “fractal” for short) structure might be a definitive signature of nonlinearity and, as a corollary, that monofractal analyses are nonlinear analyses. That this point (i.e., “fractal = nonlinear”) is incorrect remains novel to many readers. We suspect that unfamiliarity with autocorrelation has helped eclipse the linearity of fractal structure from more popular appreciation. In this article, in order to explain the linear nature of monofractality and its difference from multifractality, we present an introduction to the autocorrelation function and review short-lag memory, nonstationary motions, and the intermediary set of fractionally integrated processes that conventional fractal analyses quantify. Understanding from our own experiences how surprising the linearity of fractals is to accept, we attempt to make our points clear with as much graphic depiction as math. We hope to share our own experiences in struggling with this potentially strange-sounding idea that, really, monofractals are linear while at the same time contrasting them to multifractals that can indicate nonlinearity.     

Interdependence of Saccadic and Fixational Fluctuations

Recent research suggests that the different components of eye movements (fixations, saccades) are not strictly separate but are interdependent processes. This argument rests on observations that gaze-step sizes yield unimodal distributions and exhibit power-law scaling, indicative of interdependent processes coordinated across timescales. The studies that produced these findings, however, employed complex tasks (visual search, scene perception). Thus, the question is whether the observed interdependence is a fundamental property of eye movements or emerges in the interplay between cognitive processes and complex visual stimuli. In this study, we used a simple eye movement task where participants moved their eyes in a prescribed sequence at several different paces. We outlined diverging predictions for this task for independence versus interdependence of fixational and saccadic fluctuations and tested these predictions by assessing the spectral properties of eye movements. We found no clear peak in the power spectrum attributable exclusively to saccadic fluctuations. Furthermore, changing the pace of the eye movement sequence yielded a global shift in scaling relations evident in the power spectrum, not just a localized shift for saccadic fluctuations. These results support the conclusion that fixations and saccades are interdependent processes.     

Emotional reactivity and interoceptive sensitivity: Exploring the role of age

Psychonomic Bulletin & Review - Interoceptive sensitivity (IS) refers to the ability to accurately perceive visceral afferent information, and several prominent theories of emotions suggest...     

Lost in the Rhythm: Effects of Rhythm on Subsequent Interpersonal Coordination

Music is a natural human expression present in all cultures, but the functions it serves are still debated. Previous research indicates that rhythm, an essential feature of music, can enhance coordination of movement and increase social bonding. However, the prolonged effects of rhythm have not yet been investigated. In this study, pairs of participants were exposed to one of three kinds of auditory stimuli (rhythmic, arrhythmic, or white‐noise) and subsequently engaged in five trials of a joint‐action task demanding interpersonal coordination. We show that when compared with the other two stimuli, exposure to the rhythmic beat reduced the practice effect in task performance. Analysis of the behavioral data suggests that this reduction results from more temporally coupled motor movements over successive trials and that shared exposure to rhythm facilitates interpersonal motor coupling, which in this context serves to impede the attainment of necessary dynamic coordination. We propose that rhythm has the potential to enhance interpersonal motor coupling, which might serve as a mechanism behind its facilitation of positive social attitudes.     

Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) – A Method for Quantifying Correlation between Multivariate Time-Series

In this paper, Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) is introduced. It is an extension of Multidimensional Recurrence Quantification Analysis (MdRQA), which allows to quantify the (auto-)recurrence properties of a single multidimensional time-series. MdCRQA extends MdRQA to bi-variate cases to allow for the quantification of the co-evolution of two multidimensional time-series. Moreover, it is shown how a Diagonal Cross-Recurrence Profile (DCRP) can be computed from the MdCRQA output that allows to capture time-lagged coupling between two multidimensional time-series. The core concepts of these analyses are described, as well as practical aspects of their application. In the supplementary materials to this paper, implementations of MdCRQA and the DCRP as MatLab- and R-functions are provided.     

Typewriting Dynamics: What Distinguishes Simple From Complex Writing Tasks?

One of the main challenges of writing research has been its generative nature. As a production task, writing cannot be controlled as easily as other psychological laboratory tasks, such as reading. In this article, we present an analysis of 3 writing tasks, ranging from a simplified typing task to an ecological writing task. We show that multiple nonlinear metrics can be used to systematically characterize open, complex writing tasks. Moreover, we demonstrate that, when writing performance is quantified in such a way, a continuum of complexity can be identified on which increasingly complex writing performances can be placed.