Log-amplitude statistics of intermittent and non-Gaussian time series

Selective engagement of long-latency reflexes in postural control through wobble board training

Long-latency reflexes (LLRs) are critical precursors to intricate postural coordination of muscular adaptations that sustain equilibrium following abrupt disturbances. Both disturbances and adaptive responses reflect excursions of postural control from quiescent Gaussian stability under a narrow bell curve, excursions beyond Gaussianity unfolding at many timescales. LLRs slow with age, accentuating the risk of falls and undermining dexterity, particularly in settings with concurrent additional tasks. We investigated whether the wobble board could cultivate the engagement of LLRs selectively in healthy young participants executing a suprapostural Trail Making Task (TMT). A concurrent additional-task demand constituted visual precision predominantly along the anteroposterior (AP) axis and mechanical instability mainly along the mediolateral (ML) axis. We scrutinized planar center-of-pressure (CoP) trajectories to quantify postural non-Gaussianity across various temporal scales. Wobble board increased engagement of LLRs and decreased engagement of compensatory postural adjustments (CPAs), indicated by the peak in non-Gaussianity of CoP planar displacements over LLR-specific timescales (50-100 ms) and non-Gaussianity of CoP planar displacements progressively diminishing over CPA-specific timescales ([Formula: see text] ms). Engagement with TMT did not show any noticeable influence on non-Gaussian postural sway patterns. Despite aligning the unstable axis of the wobble board with participants' ML axis, thus rendering posture more unstable along the ML axis, the wobble board increased engagement of LLRs significantly more along the AP axis and reduced engagement of CPAs significantly more along the ML axis. These findings offer initial mechanistic insights into how wobble boards may bolster balance and potentially reduce the occurrence of falls by catalyzing the engagement of LLRs selectively.

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.

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.

Hypothetical control of postural sway

Quiet standing exhibits strongly intermittent variability that has inspired at least two interpretations. First, variability can be intermittent through the alternating engagement and disengagement of complementary control processes at distinct scales. A second and perhaps deeper way to interpret this intermittency is through the possibility that postural control depends on cascade-like interactions across many timescales at once, suggesting specific non-Gaussian distributional properties at different timescales. Multiscale probability density function (PDF) analysis shows that quiet standing on a stable surface exhibits a crossover from low, increasing non-Gaussianity (consistent with exponential distributions) at shorter timescales, reflecting inertial control, towards higher non-Gaussianity. Feedback-based control at medium to longer timescales yields a linear decrease that is characteristic of cascade dynamics. Destabilizing quiet standing with an unstable surface or closed eyes serves to attenuate inertial control and to elicit more of the feedback-based control over progressively shorter timescales. The result was to strengthen the appearance of the linear decay indicating cascade dynamics. Finally, both linear and nonlinear indices of postural sway also govern the relative strength of crossover or of linear decay, suggesting that tempering of non-Gaussianity across log-timescale is a function of both extrinsic constraints and endogenous postural control. These results provide new evidence that cascading interactions across longer timescales supporting postural corrections can even recruit shorter timescale processes with novel task constraints that can destabilize posture.

A Practical Guide to Analyzing Time-Varying Associations between Physical Activity and Affect Using Multilevel Modeling

There is growing interest in within-person associations of objectively measured physical and physiological variables with psychological states in daily life. Here we provide a practical guide with SAS code of multilevel modeling for analyzing physical activity data obtained by accelerometer and self-report data from intensive and repeated measures using ecological momentary assessments (EMA). We review previous applications of EMA in research and clinical settings and the analytical tools that are useful for EMA research. We exemplify the analyses of EMA data with cases on physical activity data and affect and discuss the future challenges in the field.

Covariation of depressive mood and spontaneous physical activity in major depressive disorder: toward continuous monitoring of depressive mood

The objective evaluation of depressive mood is considered to be useful for the diagnosis and treatment of depressive disorders. Thus, we investigated psychobehavioral correlates, particularly the statistical associations between momentary depressive mood and behavioral dynamics measured objectively, in patients with major depressive disorder (MDD) and healthy subjects. Patients with MDD ( n = 14) and healthy subjects ( n = 43) wore a watch-type computer device and rated their momentary symptoms using ecological momentary assessment. Spontaneous physical activity in daily life, referred to as locomotor activity, was also continuously measured by an activity monitor built into the device. A multilevel modeling approach was used to model the associations between changes in depressive mood scores and the local statistics of locomotor activity simultaneously measured. We further examined the cross validity of such associations across groups. The statistical model established indicated that worsening of the depressive mood was associated with the increased intermittency of locomotor activity, as characterized by a lower mean and higher skewness. The model was cross validated across groups, suggesting that the same psychobehavioral correlates are shared by both healthy subjects and patients, although the latter had significantly higher mean levels of depressive mood scores. Our findings suggest the presence of robust as well as common associations between momentary depressive mood and behavioral dynamics in healthy individuals and patients with depression, which may lead to the continuous monitoring of the pathogenic processes (from healthy states) and pathological states of MDD.

Log-amplitude statistics for Beck-Cohen superstatistics

As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ(2), inverse χ(2), and log-normal superstatistical distributions. Furthermore, we show that χ(2) and inverse χ(2) superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ(2) superstatistical distribution with degree 2.