Fractal and multifractal descriptors restore ergodicity broken by non-Gaussianity in time series

Ergodicity breaking is a challenge for biological and psychological sciences. Ergodicity is a necessary condition for linear causal modeling. Long-range correlations and non-Gaussianity characterizing various biological and psychological measurements break ergodicity routinely, threatening our capacity for causal modeling. Long-range correlations (e.g., in fractional Gaussian noise, a.k.a. "pink noise") break ergodicity--in raw Gaussian series, as well as in some but not all standard descriptors of variability, i.e., in coefficient of variation (CV) and root mean square (RMS) but not standard deviation (SD) for longer series. The present work demonstrates that progressive increases in non-Gaussianity conspire with long-range correlations to break ergodicity in SD for all series lengths. Meanwhile, explicitly encoding the cascade dynamics that can generate temporally correlated non-Gaussian noise offers a way to restore ergodicity to our causal models. Specifically, fractal and multifractal properties encode both scale-invariant power-law correlations and their variety, respectively, both of which features index the underlying cascade parameters. Fractal and multifractal descriptors of long-range correlated non-Gaussian processes show no ergodicity breaking and hence, provide a more stable explanation for the long-range correlated non-Gaussian form of biological and psychological processes. Fractal and multifractal descriptors offer a path to restoring ergodicity to causal modeling in these fields.Comment: 33 pages, 11 figures. arXiv admin note: text overlap with arXiv:2202.0109

Multifractality, Interactivity, and the Adaptive Capacity of the Human Movement System: A Perspective for Advancing the Conceptual Basis of Neurologic Physical Therapy

Background and Purpose: Physical therapists seek to optimize movement as a means of reducing disability and improving health. The short-term effects of interventions designed to optimize movement ultimately are intended to be adapted for use across various future patterns of behavior, in potentially unpredictable ways, with varying frequency, and in the context of multiple tasks and environmental conditions. In this perspective article, we review and discuss the implications of recent evidence that optimal movement variability, which previously had been associated with adaptable motor behavior, contains a specific complex nonlinear feature known as “multifractality.” Summary of Key Points: Multifractal movement fluctuation patterns reflect robust physiologic interactivity occurring within the movement system across multiple time scales. Such patterns provide conceptual support for the idea that patterns of motor behavior occurring in the moment are inextricably linked in complex, physiologic ways to patterns of motor behavior occurring over much longer periods. The human movement system appears to be particularly tuned to multifractal fluctuation patterns and exhibits the ability to reorganize its output in response to external stimulation embedded with multifractal features. Recommendations for Clinical Practice: As a fundamental feature of human movement, multifractality opens new avenues for conceptualizing the link between physiologic interactivity and adaptive capacity. Preliminary evidence supporting the positive influence of multifractal rhythmic auditory stimulation on the gait patterns of individuals with Parkinson disease is used to illustrate how physical therapy interventions might be devised to specifically target the adaptive capacity of the human movement system. Video Abstract available for more insights from the authors (see Video, Supplemental Digital Content 1, https://links.lww.com/JNPT/A183)

Bringing the Nonlinearity of the Movement System to Gestural Theories of Language Use: Multifractal Structure of Spoken English Supports the Compensation for Coarticulation in Human Speech Perception

Coarticulation is the tendency for speech vocalization and articulation even at the phonemic level to change with context, and compensation for coarticulation (CfC) reflects the striking human ability to perceive phonemic stability despite this variability. A current controversy centers on whether CfC depends on contrast between formants of a speech-signal spectrogram—specifically, contrast between offset formants concluding context stimuli and onset formants opening the target sound—or on speech-sound variability specific to the coordinative movement of speech articulators (e.g., vocal folds, postural muscles, lips, tongues). This manuscript aims to encode that coordinative-movement context in terms of speech-signal multifractal structure and to determine whether speech's multifractal structure might explain the crucial gestural support for any proposed spectral contrast. We asked human participants to categorize individual target stimuli drawn from an 11-step [ga]-to-[da] continuum as either phonemes “GA” or “DA.” Three groups each heard a specific-type context stimulus preceding target stimuli: either real-speech [al] or [a], sine-wave tones at the third-formant offset frequency of either [al] or [aɹ], and either simulated-speech contexts [al] or [aɹ]. Here, simulating speech contexts involved randomizing the sequence of relatively homogeneous pitch periods within vowel-sound [a] of each [al] and [aɹ]. Crucially, simulated-speech contexts had the same offset and extremely similar vowel formants as and, to additional naïve participants, sounded identical to real-speech contexts. However, randomization distorted original speech-context multifractality, and effects of spectral contrast following speech only appeared after regression modeling of trial-by-trial “GA” judgments controlled for context-stimulus multifractality. Furthermore, simulated-speech contexts elicited faster responses (like tone contexts do) and weakened known biases in CfC, suggesting that spectral contrast depends on the nonlinear interactions across multiple scales that articulatory gestures express through the speech signal. Traditional mouse-tracking behaviors measured as participants moved their computer-mouse cursor to register their “GA”-or-“DA” decisions with mouse-clicks suggest that listening to speech leads the movement system to resonate with the multifractality of context stimuli. We interpret these results as shedding light on a new multifractal terrain upon which to found a better understanding in which movement systems play an important role in shaping how speech perception makes use of acoustic information

Fractality of Body Movements Predicts Perception of Affordances: Evidence From Stand-On-Ability Judgments About Slopes

We recorded head motion with one wireless marker attached to the back of the head during quiet stance as participants visually inspected a sloped ramp in order to perceive whether they might be able to stand on the surface. Participants responded with yes or no without attempting to stand on the ramp. As has been found in dynamic touch (Palatinus, Kelty-Stephen, Kinsella-Shaw, Carello, & Turvey, 2014), we hypothesized that multiscale fluctuation patterns in bodily movement during visual observation would predict perceptual judgments. Mixed-effects logistic regression predicted binary affordance judgments as a function of geographical slant angle, head-motion standar deviation, and multifractal spectrum width (Ihlen, 2012). Multifractal spectrum width was the strongest predictor of affordance judgments. Specifically, increased spectrum width predicted decreased odds of a yes answer. Interestingly, standard deviation was not a significant predictor, reinforcing our prediction that traditional measures of variability fail to account for what fractal measures of multiscale interactions can predict about information pickup in perception-action systems

Multifractality of Posture Modulates Multisensory Perception of Stand-On-Ability

By definition, perception is a multisensory process that unfolds in time as a complex sequence of exploratory activities of the organism. In such a system perception and action are integrated, and multiple energy arrays are available simultaneously. Perception of affordances interweaves sensory and motor activities into meaningful behavior given task constraints. The present contribution offers insight into the manner in which perception and action usher the organism through competent functional apprehension of its surroundings. We propose that the tensegrity structure of the body, manifested via multifractality of exploratory bodily movements informs perception of affordances. The affordance of stand-on-ability of ground surfaces served as the experimental paradigm. Observers viewed a surface set to a discrete angle and attempted to match it haptically with a continuously adjustable surface occluded by a curtain, or felt an occluded surface set to a discrete angle then matched it visually with a continuously adjustable visible surface. The complex intertwining of perception and action was demonstrated by the interactions of multifractality of postural sway with multiple energy arrays, responses, and changing geometric task demands

On the psychological origins of tool use

The ubiquity of tool use in human life has generated multiple lines of scientific and philosophical investigation to understand the development and expression of humans' engagement with tools and its relation to other dimensions of human experience. However, existing literature on tool use faces several epistemological challenges in which the same set of questions generate many different answers. At least four critical questions can be identified, which are intimately intertwined-(1) What constitutes tool use? (2) What psychological processes underlie tool use in humans and nonhuman animals? (3) Which of these psychological processes are exclusive to tool use? (4) Which psychological processes involved in tool use are exclusive to Homo sapiens? To help advance a multidisciplinary scientific understanding of tool use, six author groups representing different academic disciplines (e.g., anthropology, psychology, neuroscience) and different theoretical perspectives respond to each of these questions, and then point to the direction of future work on tool use. We find that while there are marked differences among the responses of the respective author groups to each question, there is a surprising degree of agreement about many essential concepts and questions. We believe that this interdisciplinary and intertheoretical discussion will foster a more comprehensive understanding of tool use than any one of these perspectives (or any one of these author groups) would (or could) on their own

Data from: Multifractal evidence of nonlinear interactions stabilizing posture for phasmids in windy conditions: a reanalysis of insect postural-sway data

The present work is a reanalysis of prior work documenting postural sway in phasmids (i.e., “stick insects”) [1]. The prior work pursued the possibility that postural sway was an evolutionary adaptation supporting motion camouflage to avoid the attention of predators. For instance, swaying along with leaves blown by the wind might reduce the likelihood of standing out to a predator. The present work addresses the alternative—but by no means conflicting and perhaps more explanatory—proposal that phasmid postural sway carries evidence of the tensegrity-like structures allowing postural stabilization under wind-like stimulation. Tensegrity structures are prestressed architectures embodying nonlinear interactions across scales of space and time that provide context-sensitive responses faster than neural tissue can support. Multifractal modeling of the postural-displacement series initially recorded in [1] offers a metric equally effective for quantifying complexity of phasmid postural sway under wind stimulation as for quantifying complexity of human postural sway [2-7]. Furthermore, multifractal modeling offers a means to demonstrate empirically the nonlinear interactions across space and time scales in body-wide coordination that tensegrity-based hypotheses predict. Specifically, multifractal modeling allows diagnosing the strength and direction of nonlinear interactions across time scale as the difference between multifractal estimates for the original postural-displacement series and for a sample of best-fitting linear models of the series. The reduction of postural sway directly following the application of wind stimulus appears as a significant decrease in the multifractal structure for original postural-displacement series as compared to best-fitting linear models of those series. This decrease indicates the capacity for nonlinear interactions across time scale to constrict variability, which is an aspect of nonlinear dynamics often overshadowed by the possibility that nonlinearity can produce more variability. This work offers the longer-range opportunity that multifractal modeling could provide a common language within which to coordinate behavioral sciences across a wide range of species