Multifractality in postural sway supports quiet eye training in aiming tasks: A study of golf putting

Multifractal perturbations to multiplicative cascades promote multifractal nonlinearity with asymmetric spectra

Biological and psychological processes have been conceptualized as emerging from intricate multiplicative interactions among component processes across various spatial and temporal scales. Among the statistical models employed to approximate these intricate nonlinear interactions across scales, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, several fundamental questions persist concerning the proper interpretations of multifractal evidence of nonlinear cross-scale interactivity. Does multifractal spectrum width depend on multiplicative interactions, constituent noise processes participating in those interactions, or both? We conducted numerical simulations of cascade time series featuring component noise processes characterizing a range of nonlinear temporal correlations: nonlinearly multifractal, linearly multifractal (obtained via the iterative amplitude adjusted wavelet transform of nonlinearly multifractal), phase-randomized linearity (obtained via the iterative amplitude adjustment Fourier transform of nonlinearly multifractal), and phase and amplitude randomized (obtained via shuffling of nonlinearly multifractal). Our findings show that the multiplicative interactions coordinate with the nonlinear temporal correlations of noise components to dictate emergent multifractal properties. Multiplicative cascades with stronger nonlinear temporal correlations make multifractal spectra more asymmetric with wider left sides. However, when considering multifractal spectral differences between the original and surrogate time series, even multiplicative cascades produce multifractality greater than in surrogate time series, even with linearized multifractal noise components. In contrast, additivity among component processes leads to a linear outcome. These findings provide a robust framework for generating multifractal expectations for biological and psychological models in which cascade dynamics flow from one part of an organism to another.

Postural control in gymnasts: anisotropic fractal scaling reveals proprioceptive reintegration in vestibular perturbation

Dexterous postural control subtly complements movement variability with sensory correlations at many scales. The expressive poise of gymnasts exemplifies this lyrical punctuation of release with constraint, from coarse grain to fine scales. Dexterous postural control upon a 2D support surface might collapse the variation of center of pressure (CoP) to a relatively 1D orientation-a direction often oriented towards the focal point of a visual task. Sensory corrections in dexterous postural control might manifest in temporal correlations, specifically as fractional Brownian motions whose differences are more and less correlated with fractional Gaussian noises (fGns) with progressively larger and smaller Hurst exponent H. Traditional empirical work examines this arrangement of lower-dimensional compression of CoP along two orthogonal axes, anteroposterior (AP) and mediolateral (ML). Eyes-open and face-forward orientations cultivate greater variability along AP than ML axes, and the orthogonal distribution of spatial variability has so far gone hand in hand with an orthogonal distribution of H, for example, larger in AP and lower in ML. However, perturbing the orientation of task focus might destabilize the postural synergy away from its 1D distribution and homogenize the temporal correlations across the 2D support surface, resulting in narrower angles between the directions of the largest and smallest H. We used oriented fractal scaling component analysis (OFSCA) to investigate whether sensory corrections in postural control might thus become suborthogonal. OFSCA models raw 2D CoP trajectory by decomposing it in all directions along the 2D support surface and fits the directions with the largest and smallest H. We studied a sample of gymnasts in eyes-open and face-forward quiet posture, and results from OFSCA confirm that such posture exhibits the classic orthogonal distribution of temporal correlations. Head-turning resulted in a simultaneous decrease in this angle Δθ, which promptly reversed once gymnasts reoriented their heads forward. However, when vision was absent, there was only a discernible negative trend in Δθ, indicating a shift in the angle's direction but not a statistically significant one. Thus, the narrowing of Δθ may signify an adaptive strategy in postural control. The swift recovery of Δθ upon returning to a forward-facing posture suggests that the temporary reduction is specific to head-turning and does not impose a lasting burden on postural control. Turning the head reduced the angle between these two orientations, facilitating the release of postural degrees of freedom towards a more uniform spread of the CoP across both dimensions of the support surface. The innovative aspect of this work is that it shows how fractality might serve as a control parameter of adaptive mechanisms of dexterous postural control.

Spatial variability and directional shifts in postural control in Parkinson's disease

Individuals with Parkinson's disease exhibit tremors, rigidity, and bradykinesia, disrupting normal movement variability and resulting in postural instability. This comprehensive study aimed to investigate the link between the temporal structure of postural sway variability and Parkinsonism by analyzing multiple datasets from young and older adults, including individuals with Parkinson's disease, across various task conditions. We used the Oriented Fractal Scaling Component Analysis (OFSCA), which identifies minimal and maximal long-range correlations within the center of pressure time series, allowing for detecting directional changes in postural sway variability. The objective was to uncover the primary directions along which individuals exerted control during the posture. The results, as anticipated, revealed that healthy adults predominantly exerted control along two orthogonal directions, closely aligned with the anteroposterior (AP) and mediolateral (ML) axes. In stark contrast, older adults and individuals with Parkinson's disease exhibited control along suborthogonal directions that notably diverged from the AP and ML axes. While older adults and those with Parkinson's disease demonstrated a similar reduction in the angle between these two control directions compared to healthy older adults, their reliance on this suborthogonal angle concerning endogenous fractal correlations exhibited significant differences from the healthy aging cohort. Importantly, individuals with Parkinson's disease did not manifest the sensitivity to destabilizing task settings observed in their healthy counterparts, affirming the distinction between Parkinson's disease and healthy aging.

Multifractal spectral features enhance classification of anomalous diffusion

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)2643-156410.1103/PhysRevResearch.5.023144], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising 10^{6} trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.

The effect of quiet eye training on golf putting performance in pressure situation

To explores the effect and mechanism of quiet eye training on the accuracy of golfers´ putts in pressure situations and provides methods and basis for targeted attention training and control. 22 young golfers in China golf team aged from 13 to 18 were randomly assigned to the experimental group (quiet eye training group) and the control group (technical guidance group) according to gender. Both groups of participants underwent two consecutive weeks of push training (3 sets per day, 20 golf putts per set, rest for 3 min between sets) separately in accordance with the guidance of a professional psychological research group and an expert coach. Eye tracking technology, biofeedback technology, and subjective evaluation methods were used to test and analyze the push process of the two groups of participants before and after training under pressure situations (Eye movement behaviors and the heart rate were recorded by ASL Mobile Eye-XG and NeXus-2 biofeedback, pressure and state anxiety were evaluated by self-rating pressure scale and S-AI. Golf putting performance was recorded by a research graduate assistant). A higher hit ratio as well as lower pressure and SAI level was founded in quiet eye training group in the pressure situation, the quiet eye movement time and total fixation time was longer than technical group. The quiet eye training group has a better putting performance. Quiet eye training can improve the golf putting performance in pressure situations. After quiet eye training, the state anxiety decreased, the quiet eye movement time and the total fixation time increased in pressure situations.

Temporal organization of stride-to-stride variations contradicts predictive models for sensorimotor control of footfalls during walking

Walking exhibits stride-to-stride variations. Given ongoing perturbations, these variations critically support continuous adaptations between the goal-directed organism and its surroundings. Here, we report that stride-to-stride variations during self-paced overground walking show cascade-like intermittency-stride intervals become uneven because stride intervals of different sizes interact and do not simply balance each other. Moreover, even when synchronizing footfalls with visual cues with variable timing of presentation, asynchrony in the timings of the cue and footfall shows cascade-like intermittency. This evidence conflicts with theories about the sensorimotor control of walking, according to which internal predictive models correct asynchrony in the timings of the cue and footfall from one stride to the next on crossing thresholds leading to the risk of falling. Hence, models of the sensorimotor control of walking must account for stride-to-stride variations beyond the constraints of threshold-dependent predictive internal models.

Impact of focus of attention on aiming performance in the first-person shooter videogame Aim Lab

Research examining the impact of Focus of Attention (FoA) has consistently demonstrated a benefit of adopting an external FoA over an internal FoA across a variety of sports and other domains. However, FoA research has yet to be applied within the rapidly growing world of competitive gaming. This study investigated whether an external FoA provided benefits over an internal FoA for aiming performance in First-Person Shooter (FPS) videogames, using the aim-training game Aim Lab. The study explored whether the level of participants' previous experience of FPS games impacted any effect, as few studies have investigated this directly. Participants with high (N = 20) and low (N = 17) FPS experience who had a minimum of 200 hours FPS experience were selected for the study. The participants were instructed before each set of ten trials to either attend to their wrist/arm movements (internal FoA) or to the target (external FoA). There was no significant main effect of FoA on performance and no significant interaction between FoA and experience. In contrast to findings in other studies, an external FoA provided no performance benefits over an internal FoA in the FPS game Aim Lab. We discuss methodological issues related to the measures used and suggest avenues for future research with a view to improving understanding of putative underlying mechanisms for FoA effects.

Visualizing a Task Performer’s Gaze to Foster Observers’ Performance and Learning—a Systematic Literature Review on Eye Movement Modeling Examples

Eye movement modeling examples (EMMEs) are instructional videos (e.g., tutorials) that visualize another person’s gaze location while they demonstrate how to perform a task. This systematic literature review provides a detailed overview of studies on the effects of EMME to foster observers’ performance and learning and highlights their differences in EMME designs. Through a broad, systematic search on four relevant databases, we identified 72 EMME studies (78 experiments). First, we created an overview of the different study backgrounds. Studies most often taught tasks from the domains of sports/physical education, medicine, aviation, and STEM areas and had different rationales for displaying EMME. Next, we outlined how studies differed in terms of participant characteristics, task types, and the design of the EMME materials, which makes it hard to infer how these differences affect performance and learning. Third, we concluded that the vast majority of the experiments showed at least some positive effects of EMME during learning, on tests directly after learning, and tests after a delay. Finally, our results provide a first indication of which EMME characteristics may positively influence learning. Future research should start to more systematically examine the effects of specific EMME design choices for specific participant populations and task types.

Multifractal Nonlinearity Moderates Feedforward and Feedback Responses to Suprapostural Perturbations

An adaptive response to unexpected perturbations requires near-term and long-term adjustments over time. We used multifractal analysis to test how nonlinear interactions across timescales might support an adaptive response following an unpredictable perturbation. We reanalyzed torque data from 44 young and 24 older adults who performed a single-leg squat task challenged by an unexpected mechanical perturbation and a secondary visual-cognitive task. We report three findings: (a) multifractal nonlinearity interacted with pre-perturbation torque production and task error to presage greater pre-voluntary feedforward increases and greater voluntary reductions, respectively, in post-perturbation task error; (b) multifractal nonlinearity presaged relatively smaller task error than standard deviations of both pre-perturbation torques and pre-perturbation task error; and (c) increased task demand (e.g., age-related changes in dexterity and dual-task settings) led to multifractal nonlinearity presaging reduced task error. All these results were consistent with our expectations, except that a pre-perturbation knee torque-dependent increase in post-perturbation task error appeared later for older than for younger participants. This correlational multifractal modeling offered theoretical clarity on the possible roles of nonlinear interactions across timescales, moderating both feedforward and feedback processes, and presaging greater stability when the standard deviation is relatively large and task demands are strong. Thus, multifractal nonlinearity usefully describes movement variability even when paired with classical descriptors like the standard deviation. We discuss potential insights from these findings for understanding suprapostural dexterity and developing rehabilitative interventions.

Turing's cascade instability supports the coordination of the mind, brain, and behavior

Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor-that of the cascade. The time has come to confront Turing's cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing's cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.

Effects of Sleep Restriction on Self-Reported Putting Performance in Golf

In the present study, we aimed to explore the effects of sleep restriction (SR) on self-reported golf putting skills. Eleven collegiate golfers participated in a self-reported, counterbalanced experimental study under two conditions: (a) a SR condition in which sleep on the night prior to putting was restricted to 4-5 hours, and (b) a habitual normal sleep (NS) condition on the night before the putting test. Following each sleep condition, participants engaged in ten consecutive putting tests at 7 am, 11 am, and 3 pm. Participants reported their subjective sleepiness before each time frame, and their chronotype, defined as their individual circadian preference, was scored based on a morningness-eveningness questionnaire (MEQ). Participants restricted sleep to an average period of 267.6 minutes/night (SD = 51.2) in the SR condition and 426.2 (SD =38.0) minutes/night in the NS condition. A two-way analysis of variance revealed a significant main effect of the sleep condition on the lateral displacement of putts from the target (lateral misalignment) (p = 0.002). In addition, there was a significant main effect of time on distance from the target (distance misalignment) (p = 0.017), indicating less accuracy of putting in the SR condition. In the SR condition, the MEQ score was positively correlated with distance misalignment at 3 pm (ρ = 0.650, p = 0.030), suggesting that morningness types are susceptible to the effects of SR on putting performance. Our findings suggest that golfers should obtain sufficient sleep to optimize putting performance.

Perceiving and remembering speech depend on multifractal nonlinearity in movements producing and exploring speech

Speech perception and memory for speech require active engagement. Gestural theories have emphasized mainly the effect of speaker's movements on speech perception. They fail to address the effects of listener movement, focusing on communication as a boundary condition constraining movement among interlocutors. The present work attempts to break new ground by using multifractal geometry of physical movement as a common currency for supporting both sides of the speaker-listener dyads. Participants self-paced their listening to a narrative, after which they completed a test of memory querying their narrative comprehension and their ability to recognize words from the story. The multifractal evidence of nonlinear interactions across timescales predicted the fluency of speech perception. Self-pacing movements that enabled listeners to control the presentation of speech sounds constituted a rich exploratory process. The multifractal nonlinearity of this exploration supported several aspects of memory for the perceived spoken language. These findings extend the role of multifractal geometry in the speaker's movements to the narrative case of speech perception. In addition to posing novel basic research questions, these findings make a compelling case for calibrating multifractal structure in text-to-speech synthesizers for better perception and memory of speech.