How bipedalism shapes humans' actions with hand tools.

The task for an embodied cognitive understanding of humans' actions with tools is to elucidate how the human body, as a whole, supports the perception of affordances and dexterous action with objects in relation to other objects. Here, we focus on the relationship between humans' actions with handheld tools and bipedal posture. Posture plays a pivotal role in shaping animals' perception and action dynamics. While humans stand and locomote bipedally, other primates predominantly employ quadrupedal postures and locomotion, relying on both hands and feet to support the body. Drawing upon evidence from evolutionary biology, developmental psychology and performance studies, we elucidate the influence of bipedalism on our actions with objects and on our proficiency in using tools. We use the metaphor of cascades to capture the dynamic, nonlinear transformations in morphology and behaviour associated with posture and the use of tools across evolutionary and developmental timescales. Recent work illustrates the promise of multifractal cascade analysis to reveal nonlinear, cross-scale interactions across the entire body in real-time, supporting the perception of affordances for actions with tools. Cascade analysis enriches our comprehension of real-time performance and facilitates exploration of the relationships among whole-body coordination, individual development, and evolutionary processes.This article is part of the theme issue 'Minds in movement: embodied cognition in the age of artificial intelligence'.

Multi-scaling allometry in human development, mammalian morphology, and tree growth.

Various animal and plant species exhibit allometric relationships among their respective traits, wherein one trait undergoes expansion as a power-law function of another due to constraints acting on growth processes. For instance, the acknowledged consensus posits that tree height scales with the two-thirds power of stem diameter. In the context of human development, it is posited that body weight scales with the second power of height. This prevalent allometric relationship derives its nomenclature from fitting two variables linearly within a logarithmic framework, thus giving rise to the term "power-law relationship." Here, we challenge the conventional assumption that a singular power-law equation adequately encapsulates the allometric relationship between any two traits. We strategically leverage quantile regression analysis to demonstrate that the scaling exponent characterizing this power-law relationship is contingent upon the centile within these traits' distributions. This observation fundamentally underscores the proposition that individuals occupying disparate segments of the distribution may employ distinct growth strategies, as indicated by distinct power-law exponents. We introduce the innovative concept of "multi-scale allometry" to encapsulate this newfound insight. Through a comprehensive reevaluation of (i) the height-weight relationship within a cohort comprising 7, 863, 520 Japanese children aged 5-17 years for which the age, sex, height, and weight were recorded as part of a national study, (ii) the stem-diameter-height and crown-radius-height relationships within an expansive sample of 498, 838 georeferenced and taxonomically standardized records of individual trees spanning diverse geographical locations, and (iii) the brain-size-body-size relationship within an extensive dataset encompassing 1, 552 mammalian species, we resolutely substantiate the viability of multi-scale allometric analysis. This empirical substantiation advocates a paradigm shift from uni-scaling to multi-scaling allometric modeling, thereby affording greater prominence to the inherent growth processes that underlie the morphological diversity evident throughout the living world.

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.

Age- and height-dependent bias of underweight and overweight assessment standards for children and adolescents.

Background: Precision in evaluating underweight and overweight status among children and adolescents is paramount for averting health and developmental issues. Existing standards for these assessments have faced scrutiny regarding their validity. This study investigates the age and height dependencies within the international standards set by the International Obesity Task Force (IOTF), relying on body mass index (BMI), and contrasts them with Japanese standards utilizing the percentage of overweight (POW). Method: We scrutinized a comprehensive database comprising 7,863,520 children aged 5-17 years, sourced from the School Health Statistics Research initiative conducted by Japan's Ministry of Education, Culture, Sports, Science, and Technology. Employing the quantile regression method, we dissected the structure of weight-for-height distributions across different ages and sexes, quantifying the potentially biased assessments of underweight and overweight status by conventional criteria. Results: Applying IOFT criteria for underweight assessment revealed pronounced height dependence in males aged 11-13 and females aged 10-11. Notably, a discernible bias emerged, wherein children in the lower 25th percentile were classified as underweight five times more frequently than those in the upper 25th percentile. Similarly, the overweight assessment displayed robust height dependence in males aged 8-11 and females aged 7-10, with children in the lower 25th percentile for height deemed obese four or five times more frequently than their counterparts in the upper 25th percentile. Furthermore, using the Japanese POW criteria for assessment revealed significant age dependence in addition to considerably underestimating the percentage of underweight and overweight cases under the age of seven. However, the height dependence for the POW criterion was smaller than the BMI criterion, and the difference between height classes was less than 3-fold. Conclusion: Our findings underscore the intricacies of age-dependent changes in body composition during the growth process in children, emphasizing the absence of gold standards for assessing underweight and overweight. Careful judgment is crucial in cases of short or tall stature at the same age, surpassing sole reliance on conventional criteria results.

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.

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.

Older adults and individuals with Parkinson's disease control posture along suborthogonal directions that deviate from the traditional anteroposterior and mediolateral directions.

A rich and complex temporal structure of variability in postural sway characterizes healthy and adaptable postural control. However, neurodegenerative disorders such as Parkinson's disease, which often manifest as tremors, rigidity, and bradykinesia, disrupt this healthy variability. This study examined postural sway in young and older adults, including individuals with Parkinson's disease, under different upright standing conditions to investigate the potential connection between the temporal structure of variability in postural sway and Parkinsonism. A novel and innovative method called oriented fractal scaling component analysis was employed. This method involves decomposing the two-dimensional center of pressure (CoP) planar trajectories to pinpoint the directions associated with minimal and maximal temporal correlations in postural sway. As a result, it facilitates a comprehensive assessment of the directional characteristics within the temporal structure of sway variability. The results demonstrated that healthy young adults control posture along two orthogonal directions closely aligned with the traditional anatomical anteroposterior (AP) and mediolateral (ML) axes. In contrast, older adults and individuals with Parkinson's disease controlled posture along suborthogonal directions that significantly deviate from the AP and ML axes. These findings suggest that the altered temporal structure of sway variability is evident in individuals with Parkinson's disease and underlies postural deficits, surpassing what can be explained solely by the natural aging process.

NONAN GaitPrint: An IMU gait database of healthy young adults.

An ongoing thrust of research focused on human gait pertains to identifying individuals based on gait patterns. However, no existing gait database supports modeling efforts to assess gait patterns unique to individuals. Hence, we introduce the Nonlinear Analysis Core (NONAN) GaitPrint database containing whole body kinematics and foot placement during self-paced overground walking on a 200-meter looping indoor track. Noraxon Ultium MotionTM inertial measurement unit (IMU) sensors sampled the motion of 35 healthy young adults (19-35 years old; 18 men and 17 women; mean ± 1 s.d. age: 24.6 ± 2.7 years; height: 1.73 ± 0.78 m; body mass: 72.44 ± 15.04 kg) over 18 4-min trials across two days. Continuous variables include acceleration, velocity, position, and the acceleration, velocity, position, orientation, and rotational velocity of each corresponding body segment, and the angle of each respective joint. The discrete variables include an exhaustive set of gait parameters derived from the spatiotemporal dynamics of foot placement. We technically validate our data using continuous relative phase, Lyapunov exponent, and Hurst exponent-nonlinear metrics quantifying different aspects of healthy human gait.

Multifractality in stride-to-stride variations reveals that walking involves more movement tuning and adjusting than running.

Introduction: The seemingly periodic human gait exhibits stride-to-stride variations as it adapts to the changing task constraints. The optimal movement variability hypothesis (OMVH) states that healthy stride-to-stride variations exhibit "fractality"-a specific temporal structure in consecutive strides that are ordered, stable but also variable, and adaptable. Previous research has primarily focused on a single fractality measure, "monofractality." However, this measure can vary across time; strideto-stride variations can show "multifractality." Greater multifractality in stride-tostride variations would highlight the ability to tune and adjust movements more. Methods: We investigated monofractality and multifractality in a cohort of eight healthy adults during self-paced walking and running trials, both on a treadmill and overground. Footfall data were collected through force-sensitive sensors positioned on their heels and feet. We examined the effects of self-paced walking vs. running and treadmill vs. overground locomotion on the measure of monofractality, α-DFA, in addition to the multifractal spectrum width, W, and the asymmetry in the multifractal spectrum, WAsym, of stride interval time series. Results: While the α-DFA was larger than 0.50 for almost all conditions, α-DFA was higher in running and locomoting overground than walking and locomoting on a treadmill. Similarly, W was greater while locomoting overground than on a treadmill, but an opposite trend indicated that W was greater in walking than running. Larger WAsym values in the negative direction suggest that walking exhibits more variation in the persistence of shorter stride intervals than running. However, the ability to tune and adjust movements does not differ between treadmill and overground, although both exhibit more variation in the persistence of shorter stride intervals. Discussion: Hence, greater heterogeneity in shorter than longer stride intervals contributed to greater multifractality in walking compared to running, indicated by larger negative WAsym values. Our results highlight the need to incorporate multifractal methods to test the predictions of the OMVH.

Multifractal foundations of biomarker discovery for heart disease and stroke.

Any reliable biomarker has to be specific, generalizable, and reproducible across individuals and contexts. The exact values of such a biomarker must represent similar health states in different individuals and at different times within the same individual to result in the minimum possible false-positive and false-negative rates. The application of standard cut-off points and risk scores across populations hinges upon the assumption of such generalizability. Such generalizability, in turn, hinges upon this condition that the phenomenon investigated by current statistical methods is ergodic, i.e., its statistical measures converge over individuals and time within the finite limit of observations. However, emerging evidence indicates that biological processes abound with nonergodicity, threatening this generalizability. Here, we present a solution for how to make generalizable inferences by deriving ergodic descriptions of nonergodic phenomena. For this aim, we proposed capturing the origin of ergodicity-breaking in many biological processes: cascade dynamics. To assess our hypotheses, we embraced the challenge of identifying reliable biomarkers for heart disease and stroke, which, despite being the leading cause of death worldwide and decades of research, lacks reliable biomarkers and risk stratification tools. We showed that raw R-R interval data and its common descriptors based on mean and variance are nonergodic and non-specific. On the other hand, the cascade-dynamical descriptors, the Hurst exponent encoding linear temporal correlations, and multifractal nonlinearity encoding nonlinear interactions across scales described the nonergodic heart rate variability more ergodically and were specific. This study inaugurates applying the critical concept of ergodicity in discovering and applying digital biomarkers of health and disease.

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.

Reproducible biomarkers: Leveraging nonlinear descriptors in the face of non-ergodicity.

Any reliable biomarker has to be specific, generalizable, and reproducible across individuals and contexts. The exact values of such a biomarker must represent similar health states in different individuals and at different times within the same individual to result in the minimum possible false-positive and false-negative rates. The application of standard cut-off points and risk scores across populations hinges upon the assumption of such generalizability. Such generalizability, in turn, hinges upon this condition that the phenomenon investigated by current statistical methods is ergodic, i.e., its statistical measures converge over individuals and time within the finite limit of observations. However, emerging evidence indicates that biological processes abound with non-ergodicity, threatening this generalizability. Here, we present a solution for how to make generalizable inferences by deriving ergodic descriptions of non-ergodic phenomena. For this aim, we proposed capturing the origin of ergodicity-breaking in many biological processes: cascade dynamics. To assess our hypotheses, we embraced the challenge of identifying reliable biomarkers for heart disease and stroke, which, despite being the leading cause of death worldwide and decades of research, lacks reliable biomarkers and risk stratification tools. We showed that raw R-R interval data and its common descriptors based on mean and variance are non-ergodic and non-specific. On the other hand, the cascade-dynamical descriptors, the Hurst exponent encoding linear temporal correlations, and multifractal nonlinearity encoding nonlinear interactions across scales described the non-ergodic heart rate variability ergodically and were specific. This study inaugurates applying the critical concept of ergodicity in discovering and applying digital biomarkers of health and disease.

Investigating and acquiring motor expertise using virtual reality.

After just months of simulated training, on January 19, 2019 a 23-year-old E-sports pro-gamer, Enzo Bonito, took to the racetrack and beat Lucas di Grassi, a Formula E and ex-Formula 1 driver with decades of real-world racing experience. This event raised the possibility that practicing in virtual reality can be surprisingly effective for acquiring motor expertise in real-world tasks. Here, we evaluate the potential of virtual reality to serve as a space for training to expert levels in highly complex real-world tasks in time windows much shorter than those required in the real world and at much lower financial cost without the hazards of the real world. We also discuss how VR can also serve as an experimental platform for exploring the science of expertise more generally.

Walking speed and dual task input modality impact performance on a self-paced treadmill.

Interference between a walking task (target speeds on a self-paced treadmill) and dual visual and tactile-visual response time task was investigated. Ambulatory dual-task scenarios reveal how attention is divided between walking and additional tasks, but the impact of walking speed and dual-task modality on gait characteristics and dual-task performance is unclear. The purpose of this study was to evaluate the effect of visual and tactile-visual dual-task on gait performance. Participants (n=15) targeted four speeds (0.5, 1.0, 1.3, and 1.5 m/s) on a self-paced treadmill with a visual speed indicator (a green region centered at the target speed). Participants completed the same speed profile on the treadmill without (Self-Paced) and with a response time dual task (Self-Paced with Dual Task) requiring finger-tap responses to go/no-go cues. Six gait characteristics were calculated: proportion of time in the desired speed green region (GTP), speed ratio (ratio of mean to target speed), time to green region after target speed change (NRT), normalized stride width (NSW), normalized stride length (NSL), and stride time (ST). Both stride length and width were normalized by participant leg length. Lower GTP and greater speed ratio at slower speeds during dual tasking indicate speed-dependent changes in gait characteristics. Changes in NSL and ST were more affected by speed than dual task. These findings support that when speed is a parameter that is tracked, participants do not universally decrease speed in the presence of a dual task. These findings can support the decisions made when designing new wearable technologies that support navigation, communication, and mobility.

Better than DFA? A Bayesian Method for Estimating the Hurst Exponent in Behavioral Sciences.

Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical technique used to evaluate the strength of long-range correlations in empirical time series in terms of the Hurst exponent, H. Specifically, DFA quantifies the linear regression slope in log-log coordinates representing the relationship between the time series' variability and the number of timescales over which this variability is computed. We compared the performance of two methods of fractal analysis-the current gold standard, DFA, and a Bayesian method that is not currently well-known in behavioral sciences: the Hurst-Kolmogorov (HK) method-in estimating the Hurst exponent of synthetic and empirical time series. Simulations demonstrate that the HK method consistently outperforms DFA in three important ways. The HK method: (i) accurately assesses long-range correlations when the measurement time series is short, (ii) shows minimal dispersion about the central tendency, and (iii) yields a point estimate that does not depend on the length of the measurement time series or its underlying Hurst exponent. Comparing the two methods using empirical time series from multiple settings further supports these findings. We conclude that applying DFA to synthetic time series and empirical time series during brief trials is unreliable and encourage the systematic application of the HK method to assess the Hurst exponent of empirical time series in behavioral sciences.

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.

Leveraging a virtual alley with continuously varying width modulates step width variability during self-paced treadmill walking.

Increased fall risk in older adults and clinical populations is linked with increased amount and altered temporal structure of step width variability. One approach to rehabilitation seeks to reduce fall risk in older adults by reducing the amount of step width variability and restoring the temporal structure characteristic of healthy young adults. The success of such a program depends on our ability to modulate step width variability effectively. To this end, we investigated how manipulation of the visual walking space in a virtual environment could modulate the amount and temporal structure of step width variability. Nine healthy adults performed self-paced treadmill walking in a virtual alley in a fixed-width Control condition (1.91 m) and two conditions in which the alley's width oscillated sinusoidally at 0.03 Hz: between 0.38 and 1.14 m and 0.38-2.67 m in Narrow and Wide conditions, respectively. The step width time series from each condition was evaluated using: (i) the standard deviation to identify changes in the amount of variability and (ii) the fractal scaling exponent estimated using detrended fluctuation analysis (DFA) to identify changes in the temporal structure of variability in terms of persistence in fluctuations. The Wide condition neither affected the standard deviation nor the fractal scaling exponent of step width time series. The Narrow condition did not affect the standard deviation of step width time series compared to the Control condition but significantly increased its fractal scaling exponent compared to the Control and Wide conditions, suggestive of more persistent fluctuations characteristic of a healthy gait. These results show that virtual reality based rehabilitative intervention can modulate step width variability to potentially reduce fall risk in older adults and clinical populations.

Multifractal test for nonlinearity of interactions across scales in time series.

The creativity and emergence of biological and psychological behavior tend to be nonlinear, and correspondingly, biological and psychological measures contain degrees of irregularity. The linear model might fail to reduce these measurements to a sum of independent random factors (yielding a stable mean for the measurement), implying nonlinear changes over time. The present work reviews some of the concepts implicated in nonlinear changes over time and details the mathematical steps involved in their identification. It introduces multifractality as a mathematical framework helpful in determining whether and to what degree the measured series exhibits nonlinear changes over time. These mathematical steps include multifractal analysis and surrogate data production for resolving when multifractality entails nonlinear changes over time. Ultimately, when measurements fail to fit the structures of the traditional linear model, multifractal modeling allows for making those nonlinear excursions explicit, that is, to come up with a quantitative estimate of how strongly events may interact across timescales. This estimate may serve some interests as merely a potentially statistically significant indicator of independence failing to hold, but we suspect that this estimate might serve more generally as a predictor of perceptuomotor or cognitive performance.

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.