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Eye movement dynamics and cognitive self-organization in typical and atypical development

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Abstract

This study analyzed distributions of Euclidean displacements in gaze (i.e. “gaze steps”) to evaluate the degree of componential cognitive constraints on audio-visual speech perception tasks. Children performing these tasks exhibited distributions of gaze steps that were closest to power-law or lognormal distributions, suggesting a multiplicatively interactive, flexible, self-organizing cognitive system rather than a component-dominant stipulated cognitive structure. Younger children and children diagnosed with an autism spectrum disorder (ASD) exhibited distributions that were closer to power-law than lognormal, indicating a reduced degree of self-organized structure. The relative goodness of lognormal fit was also a significant predictor of ASD, suggesting that this type of analysis may point towards a promising diagnostic tool. These results lend further support to an interaction-dominant framework that casts cognitive processing and development in terms of self-organization instead of fixed components and show that these analytical methods are sensitive to important developmental and neuropsychological differences.

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Notes

  1. This weak multiplicative distortion may be expressed in a couple of ways depending on how the distributions are instantiated. Exponential distributions can be generated by the sum of the squares of multiple independent normally distributed variables (i.e., the sum of independent components interacting with themselves, that is, accentuating their own contributions). Gamma distributions are generated by the sum of relatively few exponential distributions; exponential distributions are themselves specific cases of gamma distributions. Gamma distributions may also be generated by dividing the basic exponential distribution function by the gamma function, a continuous generalization of the factorial function (i.e., x!), itself a multiplicative transformation. As the number of added exponentials increases towards large limits (i.e., towards the limit of "very many random numbers" as noted in the main text), the gamma distribution converges towards the normal distribution. Alternatively, exponential distributions may be considered as the negative logarithm of uniform distributions in the range (0, 1). In this light, the sum of relatively few exponentials composing the gamma distribution is a logarithm of the product of relatively few uniformly distributed random variables. Because logarithm of repeated multiplication reduces to repeated addition of logarithms, the convergence of gamma distributions to normal distributions holds just the same. Although the values being added affect some aspects of the distribution, in the limit of very large sets of random variables or repeated additions, the distribution will converge to a normal distribution. Thus, in either the gamma or exponential case, no matter how multiplicativity appears in the generation of the distributions, it is quashed by repeated addition of very many random variables (whether those variables are exponential or squared normal). That is, skewed distributions following exponential or gamma form will collapse back towards normal distributions and thus reflect much stronger additive than multiplicative relationships among random variables. For this reason, we do not distinguish whether gamma or exponential distributions reflect greater or lesser multiplicativity: gamma distributions may be more multiplicative in general than in the limiting case of the exponential distribution if only because they involve dividing probabilities by values of the gamma function different from 1 (i.e., different from the multiplicative identity), but their convergence to normal distributions suggests that this multiplicativity is ultimately negligible in the largest limits.

  2. Lack of a characteristic scale refers statistically to the potential divergence of the second moment (i.e., variance). Practically, this point speaks to how confidently we can consider the observed sample to be representative of the yet unmeasured, unobserved behavior. Power-law distributions may not have a finite standard deviation, thus the observed bounds in a particular data set may provide no guarantee that the power-law distributed system will remain within those bounds. The summed behavior of a hierarchy of independent components at different scales may adequately approximate a particular observed power-law-distributed data set, but this system would be committed to the finite bounds of the proposed components. Thus, a multiplicative interdependent system (power-law distribution) and a hierarchy of additive components (multiple additive normal distributions) entail different predictions regarding future observed behavior, both at the lower and upper extremes of the distribution.

  3. The null effect of sex may be noteworthy because ASD disproportionately affects boys rather than girls.

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Acknowledgments

This research was supported by the Moss Rehabilitation Research Institute and National Institutes of Health grant R03DC007339 (J. Irwin, PI) to Haskins Laboratories. We thank Jessica Hafetz and James Dixon for their helpful suggestions.

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Authors and Affiliations

  1. Moss Rehabilitation Research Institute, 50 Township Line Rd., Elkins Park, PA, 19027, USA

    Daniel Mirman

  2. Haskins Laboratories, 300 George St., Suite 900, New Haven, CT, 06511, USA

    Julia R. Irwin

  3. Southern Connecticut State University, 501 Crescent St., New Haven, CT, 06515, USA

    Julia R. Irwin

  4. Wyss Institute for Biologically Inspired Engineering, 3 Blackfan Circle, Floor 5, Boston, MA, 02115, USA

    Damian G. Stephen

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Correspondence to Damian G. Stephen.

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Table 4 Full correlation matrix
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Mirman, D., Irwin, J.R. & Stephen, D.G. Eye movement dynamics and cognitive self-organization in typical and atypical development. Cogn Neurodyn 6, 61–73 (2012). https://doi.org/10.1007/s11571-011-9180-y

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