Non-linear Amplification of Variability Through Interaction Across Scales Supports Greater Accuracy in Manual Aiming: Evidence From a Multifractal Analysis With Comparisons to Linear Surrogates in the Fitts Task.
TL;DR: This work predicts that non-linear interactions across scales in hand movement series will produce variability that will actually stabilize aiming in the Fitts task, reducing standard deviation of target contacts and predicts the role of visual feedback in this case.
Abstract: Movement coordination depends on directing our limbs to the right place and in the right time. Movement science can study this central requirement in the Fitts task that asks participants to touch each of two targets in alternation, as accurately and as fast as they can. The Fitts task is an experimental attempt to focus on how the movement system balances its attention to speed and to accuracy. This balance in the Fitts task exhibits a hierarchical organization according to which finer details (e.g., kinematics of single sweeps from one target to the other) change with relatively broader constraints of task parameters (e.g., distance between targets and width of targets). The present work seeks to test the hypothesis that this hierarchical organization of movement coordination reflects a multifractal tensegrity in which non-linear interactions across scale support stability. We collected movement series data during a easy variant of the Fitts task to apply just such a multifractal analysis with surrogate comparison to allow clearer test of non-linear interactions across scale. Furthermore, we test the role of visual feedback both in potential and in fact, i.e., by manipulating both whether experimenters instructed participants that they might potentially have to close their eyes during the task and whether participants actually closed their eyes halfway through the task. We predict that (1) non-linear interactions across scales in hand movement series will produce variability that will actually stabilize aiming in the Fitts task, reducing standard deviation of target contacts; (2) non-linear interactions across scales in head sway will stabilize aiming following the actual closing eyes; and (3) non-linear interactions across scales in head sway and in hand movements will interact to support stabilizing effects of expectation about closing eyes. In sum, this work attempts to make the case that the multifractal-tensegrity hypothesis supports more accurate aiming behavior in the Fitts task.
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TL;DR: Signs of multifractality in the time series of fluctuations in Euclidean displacement in participants' center of pressure as they hefted weighted objects to perceive their heaviness and length suggest that multiplicative-cascade dynamics in posture play a role in prospective coordination during the engagement with objects and perception of their properties via effortful touch by the hand.
33 citations
TL;DR: The results suggest that the accuracy of perception via dynamic touch hinges on specific flowing patterns of multifractal fluctuations that people wear on their anatomical sleeves, which could support perception of object properties via dynamictouch.
Abstract: Research into haptic perception typically concentrates on mechanoreceptors and their supporting neuronal processes. This focus risks ignoring crucial aspects of active perception. For instance, bodily movements influence the information available to mechanoreceptors, entailing that movement facilitates haptic perception. Effortful manual wielding of an object prompts feedback loops at multiple spatio-temporal scales, rippling outwards from the wielding hand to the feet, maintaining an upright posture and interweaving to produce a nonlinear web of fluctuations throughout the body. Here, we investigated whether and how this bodywide nonlinearity engenders a flow of multifractal fluctuations that could support perception of object properties via dynamic touch. Blindfolded participants manually wielded weighted dowels and reported judgements of heaviness and length. Mechanical fluctuations on the anatomical sleeves (i.e. peripheries of the body), from hand to the upper body, as well as to the postural centre of pressure, showed evidence of multifractality arising from nonlinear temporal correlations across scales. The modelling of impulse-response functions obtained from vector autoregressive analysis revealed that distinct sets of pairwise exchanges of multifractal fluctuations entailed accuracy in heaviness and length judgements. These results suggest that the accuracy of perception via dynamic touch hinges on specific flowing patterns of multifractal fluctuations that people wear on their anatomical sleeves.
28 citations
TL;DR: It is suggested that vision stabilizes posture by reconfiguring the prestressed poise that prepares the body to interact with different spatial layouts, reflecting active postural adjustments.
14 citations
TL;DR: In this paper, the authors show that the balance of the standard deviation within stable bounds may depend on a tendency for temporal correlations to self-correct across time. And they interpret these findings as part of the growing evidence that multifractal nonlinearity is a modeling strategy that resonates strongly with ecological-psychological approaches to perception and action.
10 citations
TL;DR: Results showed that lower multifractality led to more accurate putts, and the perturbation of eye height led to less accuratePutts, particularly for QE-trained participants, and suggested that reduced multifractionality may act in a context-sensitive manner to restrain motoric degrees of freedom to achieve the task goal.
Abstract: The "quiet eye" (QE) approach to visually-guided aiming behavior invests fully in perceptual information9s potential to organize coordinated action. Sports psychologists refer to QE as the stillness of the eyes during aiming tasks and increasingly into self- and externally-paced tasks. Amidst the "noisy" fluctuations of the body, quiet eyes might leave fewer saccadic interruptions to the coupling between postural sway and optic flow. Postural sway exhibits fluctuations whose multifractal structure serves as a robust predictor of both visual and haptic perceptual responses. Postural sway generates optic flow centered on eye height. We predicted that perturbing the eye height by attaching wooden blocks below the feet would perturb the putting more so in QE-trained participants than in those trained technically. We also predicted that the efficacy of QE and responses to this perturbation would depend on multifractality in postural sway. Specifically, we predicted that less multifractality would predict more adaptive responses to the perturbation and higher putting accuracy. Results showed that lower multifractality led to more frequent successful putts, and the perturbation of eye height led to less frequent successful putts, particularly for QE-trained participants. Models of radial error (i.e., the distance between the final ball position and the hole) indicated that lower estimates of multifractality due to nonlinearity coincided with a more adaptive response to the perturbation. These results suggest that reduced multifractality may act in a context-sensitive manner to restrain motoric degrees of freedom to achieve the task goal.
10 citations
Cites background from "Non-linear Amplification of Variabi..."
...…the case of nonvisual judgments of length and heaviness of manually-wielded objects (Mangalam & Kelty-Stephen, 2020) but also in visuomotor tasks (Bell et al., 2019; Booth et al., 2018) and in response to perturbations, such as those due to prismatic goggles in a visual aiming task (Carver et…...
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...In a Fitts task, greater multifractality tMF in hand and head movements predicted less stable contact with the targets, but it became a predictor of more stable contact when participants had the diffuse warning that they might be asked to close their eyes and continue the task (Bell et al., 2019)....
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...Multifractal nonlinearity, tMF, in postural sway predicts perceptual responses as well, not just in the case of nonvisual judgments of length and heaviness of manually-wielded objects (Mangalam & Kelty-Stephen, 2020) but also in visuomotor tasks (Bell et al., 2019; Booth et al., 2018) and in response to perturbations, such as those due to prismatic goggles in a visual aiming task (Carver et al....
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TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Abstract: In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.
65,425 citations
"Non-linear Amplification of Variabi..." refers background in this paper
...It estimates exponents α and f as the relationships of average bin proportion and Shannon entropy (Shannon, 1948; Figure 1; right panel), respectively, with bin size....
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TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
Abstract: It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
9,015 citations
"Non-linear Amplification of Variabi..." refers background in this paper
...The current work is the latest supporting the notion of motor coordination as a process developing through interactions across multiple scales (e.g., Turing, 1952; Gottlieb, 2007; Molenaar, 2008)....
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01 Jan 2003TL;DR: In this paper, a framework for investigating change over time is presented, where the multilevel model for change is introduced and a framework is presented for investigating event occurrence over time.
Abstract: PART I 1. A framework for investigating change over time 2. Exploring Longitudinal Data on Change 3. Introducing the multilevel model for change 4. Doing data analysis with the multilevel mode for change 5. Treating TIME more flexibly 6. Modelling discontinuous and nonlinear change 7. Examining the multilevel model's error covariance structure 8. Modelling change using covariance structure analysis PART II 9. A Framework for Investigating Event Occurrence 10. Describing discrete-time event occurrence data 11. Fitting basic Discrete-Time Hazard Models 12. Extending the Discrete-Time Hazard Model 13. Describing Continuous-Time Event Occurrence Data 14. Fitting Cox Regression Models 15. Extending the Cox Regression Model
8,435 citations
TL;DR: In this article, an easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities are discussed, which are particularly needed for binary, ordinal, and time-to-event outcomes.
Abstract: Multivariable regression models are powerful tools that are used frequently in studies of clinical outcomes. These models can use a mixture of categorical and continuous variables and can handle partially observed (censored) responses. However, uncritical application of modelling techniques can result in models that poorly fit the dataset at hand, or, even more likely, inaccurately predict outcomes on new subjects. One must know how to measure qualities of a model's fit in order to avoid poorly fitted or overfitted models. Measurement of predictive accuracy can be difficult for survival time data in the presence of censoring. We discuss an easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities. Both types of predictive accuracy should be unbiasedly validated using bootstrapping or cross-validation, before using predictions in a new data series. We discuss some of the hazards of poorly fitted and overfitted regression models and present one modelling strategy that avoids many of the problems discussed. The methods described are applicable to all regression models, but are particularly needed for binary, ordinal, and time-to-event outcomes. Methods are illustrated with a survival analysis in prostate cancer using Cox regression.
7,879 citations
TL;DR: The motor system in the present case is defined as including the visual and proprioceptive feedback loops that permit S to monitor his own activity, and the information capacity of the motor system is specified by its ability to produce consistently one class of movement from among several alternative movement classes.
Abstract: Information theory has recently been employed to specify more precisely than has hitherto been possible man's capacity in certain sensory, perceptual, and perceptual-motor functions (5, 10, 13, 15, 17, 18). The experiments reported in the present paper extend the theory to the human motor system. The applicability of only the basic concepts, amount of information, noise, channel capacity, and rate of information transmission, will be examined at this time. General familiarity with these concepts as formulated by recent writers (4, 11,20, 22) is assumed. Strictly speaking, we cannot study man's motor system at the behavioral level in isolation from its associated sensory mechanisms. We can only analyze the behavior of the entire receptor-neural-effector system. However, by asking 51 to make rapid and uniform responses that have been highly overlearned, and by holding all relevant stimulus conditions constant with the exception of those resulting from 5"s own movements, we can create an experimental situation in which it is reasonable to assume that performance is limited primarily by the capacity of the motor system. The motor system in the present case is defined as including the visual and proprioceptive feedback loops that permit S to monitor his own activity. The information capacity of the motor system is specified by its ability to produce consistently one class of movement from among several alternative movement classes. The greater the number of alternative classes, the greater is the information capacity of a particular type of response. Since measurable aspects of motor responses, such as their force, direction, and amplitude, are continuous variables, their information capacity is limited only by the amount of statistical variability, or noise, that is characteristic of repeated efforts to produce the same response. The information capacity of the motor Editor's Note. This article is a reprint of an original work published in 1954 in the Journal of Experimental Psychology, 47, 381391.
7,599 citations
"Non-linear Amplification of Variabi..." refers background or methods in this paper
...So, it is no mistake that the Fitts (1954) task remains a central paradigm of movement-science research: the Fitts task asks participants to make contact with one of two targets in alternation, swiftly and accurately, and in so doing, it epitomizes the challenge of movement coordination....
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...The Fitts law relates movement times with a difficulty index defined as between-target distance divided by target width (Fitts, 1954)....
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