Damian G. Kelty-Stephen

A Tutorial on Multifractality, Cascades, and Interactivity for Empirical Time Series in Ecological Science

Interactivity is a central theme of ecological psychology. According to Gibsonian views, behavior is the emergent property of interactions between organism and environment. Hence, an important challenge for ecological psychology has been to identify physical principles that provide an empirical window into interactivity. We suspect that multifractality, a concept from statistical physics, may be helpful in this regard, and we offer this article as a tutorial on multifractality with 2 main goals. First, we aim to describe multifractality with a series of simple, concrete, but progressively more elaborate examples that will incrementally elucidate the relationship between multifractality and interactivity. Second, we aim to describe a direct estimation method for computing the multifractal spectrum (e.g., Chhabra & Jensen, 1989), presenting it as an alternative that avoids the pitfalls of more popular methods and that may address more appropriately the measurements traditionally taken by ecological psychologists. In sum, this tutorial aims to unpack the theoretical background for an analytical method allowing rigorous test of interactivity in a variety of empirical settings.

Fractal Fluctuations in Quiet Standing Predict the Use of Mechanical Information for Haptic Perception

Movement science has traditionally understood high-dimensional fluctuations as either antithetical or irrelevant to low-dimensional control. However, fluctuations incident to changeful, sometimes unpredictable stimulation must somehow reshape low-dimensional aspects of control through perception. The movement system’s fluctuations may reflect cascade dynamics in which many-sized events interact nonlinearly across many scales. Cascades yield fractal fluctuations, and fractality of fluctuations may provide a window on the interactions across scale supporting perceptual processes. To test these ideas, we asked adult human participants to judge whole or partial length for unseen rods (with and without added masses). The participants’ only experience with the objects came from supporting them across their shoulders during quiet standing. First, the degree of fractal temporal correlations in trial-by-trial series of planar Euclidean displacements in center of pressure (COP) significantly improved prediction of subsequent trial-by-trial judgments, above and beyond prediction by traditional predictors of haptic perception and conventional measures of COP variability. Second, comparison with linear surrogate data indicated the presence of nonlinear interactions across scale in these time series. These results demonstrate that high-dimensional fluctuations may serve a crucial role in the cascade dynamics supporting apparently low-dimensional control strategies.

Bio-Inspired Design of Soft Robotic Assistive Devices: The Interface of Physics, Biology, and Behavior

Wearable assistive robotic devices are characterized by an interface, a meeting place of living tissue and mechanical forces, at which potential and kinetic energy are converted to one or the other form. Ecological scientists may make important contributions to the design of device interfaces because of a functional perspective on energy and information exchange. For ecological scientists, (a) behavioral forms are an assembly of whole functional systems from available parts, emerging in energy flows, and (b) nature explores for informationally based adaptive solutions to assemble behavioral forms by generating spontaneous patterns containing fluctuations. We present data from ongoing studies with infants that demonstrate how infants may explore for adaptive kicking solutions. Inspired by the ecological perspective and data from developing humans, ecological scientists may design interfaces to assist individuals with medical conditions that result in physical and/or mental impairment. We present one such device, what is called the “second skin,” to illustrate how a soft, prestressed material, worn on the skin surface, may be used synergistically with synthetic and biological muscles for assisting action. Our work on the second skin, thus far, suggests a set of ecologically inspired principles for design of wearable assistive robotic devices.

Stochastic Resonance Effects on Apnea, Bradycardia, and Oxygenation: A Randomized Controlled Trial

OBJECTIVE: To evaluate the effect of stochastic resonance (SR) stimulation on preterm infant oxygen desaturation, bradycardia, and apnea events. We hypothesized that SR stimulation will reduce these events. METHODS: This was a randomized crossover study conducted from April 2012 to July 2014. Eligible preterm infants were not receiving ventilation support and had at least 1 clinically documented apnea, bradycardia, and/or oxygen desaturation event. The 3 outcome variables were as follows: oxygen desaturation, bradycardia, and apnea events. Infants received up to two 3- or 4-hour intervention periods of 30-minute alternating intervals of SR stimulation and no SR stimulation. The first intervention period was randomly assigned to begin with SR stimulation either on or off, whereas the next intervention period automatically began with the opposite on/off state. We compared the SR stimulation “on” periods with the SR stimulation “off” periods with each infant serving as his or her own control. RESULTS: The sample consisted of 36 infants with a mean (±SD) gestational age of 30.5 ± 3 weeks and a birth weight of 1409 ± 450 g. SR stimulation decreased the number of apneic events by 50%. SR stimulation ameliorated every aspect of clinically significant oxygen desaturation events, with a 20% to 35% decrease in the number, duration, and intensity of oxygen desaturation events when SR stimulation was on. Also, SR stimulation produced a nearly 20% reduction in the intensity of bradycardia events. CONCLUSIONS: SR stimulation may be a noninvasive and nonpharmacologic treatment option for apnea, oxygen desaturation, and some aspects of bradycardia in premature infants.

Cascade-Driven Series with Narrower Multifractal Spectra Than Their Surrogates

Multifractal (or singularity) spectra widths w allow diagnosing cascade structure through comparing original seriesź widths wOrig to surrogate seriesź widths wSurr. However, interpretations of 0

Constraints are the solution, not the problem

Reichle and Reingold (2013) presented the hypothesis that parafoveal preview is a requirement for the average fixation during reading in order for lexical processing to control eye movements. Taking 240 ms as the customary fixation duration in reading a single word, they arrive at their conclusion by decomposing these 240 ms into stages of a strictly serial-processing model. This subtractive accounting finds the visual system coming up short so long as lexical processing is strictly foveal, that is, so long as lexical processing addresses only the word directly in front of the fovea during a fixation. Neurophysiological estimates of latencies in retinal transmission to the brain and in visual encoding leave little more than 60 ms for lexical processing and 90 ms for programming the next saccade. Reichle and Reingolds solution to this processing bottleneck is to propose that lexical processing of the next word usually begins parafoveally, that is, during the fixation of the current word. We question the generality of the solution that Reichle and Reingold (2013) offer. Rather the observation of comparatively short fixation durations may tie in with a wider range of findings on remarkably fast response times in which cognitive, neural, and physiological events unfolding at various time scales conspire to poise the human organism for a variety of stimuli and dramatically reduce the time needed to arrive at sensible response from stimulus onset (Wallot and Van Orden, 2012). We argue that the solution to the problem can be found by investigating the contextual constraints organizing cognitive activity.

Temporal correlations in postural sway moderate effects of stochastic resonance on postural stability

The present work documents reanalysis of previous research by Priplata and colleagues (Priplata et al., 2002) into the effects of subthreshold vibratory stimulation to the plantar surface of the foot on postural stability during quiet standing. In stochastic resonance, stimulating a nonlinear system with noise can promote system stability. Stochastic resonance has been proposed to have clinical applications as an intervention that might help to stabilize posture. Insoles designed to stimulate the plantar surface of the foot with uncorrelated white-noise fluctuations have been shown to reduce a number of standard measures of postural variability. An important remaining concern is that the efficacy of stochastic-resonance applications is subject to strong individual differences. Our reanalysis of data from Priplata et al.s original study provides evidence that effects of uncorrelated fluctuations in subthreshold vibratory stimulation are moderated by temporally correlated fluctuations in postural sway. We suggest how future development might capitalize on this finding to fine-tune existing stochastic-resonance applications to posture.

Expectations on Hierarchical Scales of Discourse: Multifractality Predicts Both Short- and Long-Range Effects of Violating Gender Expectations in Text Reading

Reader expectations form across hierarchical scales of discourse (e.g., from coarse to fine: genre, narrative, syntax). Cross-scale interactivity produces word reading times (RTs) with multifractal structure. After introducing multifractals, we test two hypotheses regarding their relevance to reader expectations: (1) multifractal evidence of cross-scale interactions from RTs preceding violation of expectations would interact with mean reading speed to predict RTs immediately after the expectation violation and (2) postsurprise RTs would exhibit stronger cross-scale interactions. Thirty-four adult participants read one of two 2,000-word stories that used gender stereotypes to suggest that an ambiguously named protagonist was male. However, the stories postponed gender information until word 1,000: male in one story and female in the other. For slower readers, cross-scale interactions accentuated postreveal slowing but also minimized subsequent pausing over 15 postreveal RTs. Surprise strengthened cross-scale interactions over all postsurprise RTs. These results suggest that multifractality may index anticipation across multiple scales of discourse.

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

ABSTRACT 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.

Self-trained perception need not be veridical: striking can exaggerate judgment by wielding and can transfer exaggeration to new stimuli

Previous literature on self-training dynamic touch suggested that haptic judgments of length following wielding might benefit from new information through participants’ own striking actions with the same stimuli. However, the conclusion that this self-training tended towards a veridical outcome of zero discrepancy between actual length and judged length was premature. In this replication, we allowed adult participants (n = 15) to strike on each trial and changed the stimuli in mid-experiment to determine whether striking helped participants build more accurate perceptions of length transferrable from one stimulus scale to another. We predicted that, if self-training led to better length judgments, the repeated striking would improve judgments and that, in turn, judgments following the switch of stimuli would show a good transfer of what participants had learned. On the other hand, self-training may simply exaggerate inertial properties of stimuli and may be sensitive to sudden changes in the scale of stimuli. Mixed-effect modeling of discrepancies show that striking only accentuated effects of inertial moment, producing exaggerated length judgments. Correlation between perceived length and actual length increased only for participants who experienced a switch in individual stimuli but not stimulus scale. We discuss the implications of these findings for any theoretical relationship between self-organization and veridicality.