Ecological Psychology Executive Function as an ...

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Ecological Psychology Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/heco20

Executive Function as an Interaction-Dominant Process a

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Jason R. Anastas , Damian G. Kelty-Stephen & James A. Dixon

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Department of Psychology University of Connecticut b

Department of Psychology Grinnell College

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Center for the Ecological Study of Perception & Action, University of Connecticut Haskins Laboratories Published online: 28 Oct 2014.

To cite this article: Jason R. Anastas, Damian G. Kelty-Stephen & James A. Dixon (2014) Executive Function as an Interaction-Dominant Process, Ecological Psychology, 26:4, 262-282, DOI: 10.1080/10407413.2014.957985 To link to this article: http://dx.doi.org/10.1080/10407413.2014.957985

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Ecological Psychology, 26:262–282, 2014 Copyright © Taylor & Francis Group, LLC ISSN: 1040-7413 print/1532-6969 online DOI: 10.1080/10407413.2014.957985


Executive Function as an Interaction-Dominant Process Jason R. Anastas Department of Psychology University of Connecticut

Damian G. Kelty-Stephen Department of Psychology Grinnell College

James A. Dixon Department of Psychology University of Connecticut Center for the Ecological Study of Perception & Action University of Connecticut Haskins Laboratories

Traditional theories of psychology define the cognitive system as composed of insular, encapsulated components, controlled by a central executive. An alternative hypothesis suggests that cognitive control arises from the complex interaction among temporal scales of activity within the system. We examined the hand motions of preschool-age participants gathered during an executive-function task, card sorting, for evidence of multiplicative interactions across temporal scales. The time series of hand motions were submitted to iterated amplitude adjusted Fourier transformation (IAAFT), a surrogate data analysis technique that removes nonlinear, multiscale dependencies while preserving the linear structure of the time series. We found that removing multiscale effects via IAAFT led to a significant change in the width of the multifractal spectrum, an indicator of multiplicative interactions. The results suggest that cognitive control may arise from the interactions among temporal scales of activity within the system rather than as the result of a central executive. Correspondence should be addressed to Jason R. Anastas, University of Connecticut, 85 Lawler Road, West Hartford, CT 06117. E-mail: [email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline. com/heco.

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EXECUTIVE FUNCTION AS AN INTERACTION-DOMINANT PROCESS

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A central feature of the cognitive system is its ability to establish and maintain intentional, goal-directed action (Gibbs, 1999; Miller & Cohen, 2001; Pezzulo & Castelfranchi, 2009; Van Orden & Holden, 2002; Warren, 2006). The cognitive system monitors its progress toward goals and modifies itself in response to its ever-changing circumstances. This ability, sometimes called executive function, is a well-documented and ubiquitous aspect of human behavior (Anderson, 2002; Carlson, 2003; Munakata, Snyder, & Chatham, 2012; Rennie, Bull, & Diamond, 2004; Willoughby, Wirth, & Blair, 2012; Zelazo, Carter, Reznick, & Frye, 1997). Although the phenomena of executive function have been thoroughly catalogued (Davidson, Amso, Anderson, & Diamond, 2006), an explanation for its workings remains elusive (Harnad, 1990; Miyake et al., 2000; Phillips, 1998; Searle, 1990; Zelazo, Muller, Frye, & Marcovitch, 2003). It is important to note that how one seeks to explain executive function depends on some fundamental assumptions about how cognition works. In classical psychology, the cognitive system is presumed to be made up of a number of insular, encapsulated components, each responsible for a specific aspect of cognition (Newell, 1990). Examples of such components include working memory, spatial awareness, and motor control. On this account, the components of the cognitive system are linearly decomposable and function independently of one another (Shallice, 1988; Simon, 1962). The functioning of the cognitive system is described as the aggregate of each of these components; behavior is the sum of the activity of the parts (see Van Orden, Holden, & Turvey, 2003, for a discussion). If one accepts the architectural premise of independent components, then it follows that the coordination of these cognitive components requires explanation. Because of their independent, encapsulated nature, these components must somehow be made to work together in pursuit of the greater goals of the cognitive system. Even relatively simple cognitive tasks require the deployment of a variety of cognitive resources. For example, the simple act of flipping a light switch requires memory to recall which appliance is connected to the switch, spatial awareness to guide the hand to the switch, motor control to contort the hand in order to flip the switch, and perceptual awareness to recognize that the switch has been flipped and the light activated. Traditionally a master subsystem, the central executive, is posited to solve this problem. On this account, the central executive is responsible for the selection and maintenance of system goals (Baddeley, 2002; Denckla, 1994; Handley, Capon, Beveridge, Dennis, & Evans, 2004; Lezak, 1982; Pennington & Ozonoff, 1996; Zelazo, Craik, & Booth, 2004). It controls and coordinates the resources of the cognitive system. The other components of the cognitive system provide information to, and receive orders from, the central executive. In this way, the cognitive resources of the system are successfully coordinated in pursuit of system goals.


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ANASTAS, KELTY-STEPHEN, DIXON

The top-left panel of Figure 1 shows a schematic example of the standard conception of cognition. The horizontal line represents system activity, whereas each box represents a component. A cognitive decision is made by the system. That decision is carried to the motor system and is then expressed in the form of an action. The system makes a further decision, which itself is relayed, and so forth. A fundamental property of this architecture is the insular nature of the functioning of the components. They affect one another only over established channels of communication; the internal operations of each component are insulated from neighboring components. Newell (1990), in his discussion of cognitive architectures, referred to this property as protection; mechanisms that “provided reliable internal barriers (fixed in hardware) to keep activity in one part of the system from affecting other parts of the system. The need for protection arose as soon as multiple tasks were performed in a computer” (p. 84). The architectural property of protection gives rise to a particular type of dynamics that runs on component-dominant interactions (Van Orden et al., 2003). An alternative explanation of executive function follows from the assertion that the cognitive system is an interaction-dominant system (Ihlen & Vereijken, 2010; Stephen, Dixon, & Isenhower, 2009; Van Orden et al., 2003). In interactiondominant systems, activity across the many functional aspects of the system is mutually dependent rather than being independent and encapsulated. For example, the activity of the system that supports perception would both affect, and be affected by, the activity supporting spatial awareness. On this account, components do not perform some set of computations and then deliver results to neighbors. Rather, the internal activity itself affects other processes directly. As a result, activity across many different temporal scales will interact in such a system. New cognitive structures, such as goal directedness, emerge from these multiscale interactions. Instead of behavior reflecting the sum of component functions, behavior under interaction-dominant dynamics reflects multiplicative (i.e., nonadditive) interactions across multiple scales. The top-right panel of Figure 1 shows a schematic example of an interactiondominant system. Instead of functioning in an insular way, activity at different temporal scales interacts, and various aspects of the system continually modify each other. The horizontal lines represent activity across different timescales, and the arrows represent the effect that activity at each scale has on the others. Activity at shorter scales begets activity at longer scales; activity at longer scales in turn constrains activity at shorter scales. The varying elements of the system do not just receive input from the other elements of the system; rather their internal operations are affected by other aspects of system activity. Perhaps not surprisingly, systems with such radically different architectural properties will generate behavior with different statistical structure given sufficiently fine-grained measurements. We posit that the variability in fluctuations of the body over time provide a window into cognitive changes in the child.

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FIGURE 1 The upper left panel shows a simplified diagram of a component-dominant system. Action is equivalent to the sum of the contributions of each of the components of the system. Each component receives input from the others, but its functioning is insular and protected from the activity of the other components. The upper right panel shows a simplified diagram of a complex, interaction-dominant system. Activity at the shorter scales changes activity at the longer scales, whereas activity at the longer scales constrains activity at the shorter scales. The bottom-left panel shows an example of a time series that is consistent with a component-dominant system. The lower right panel shows a sample time series that is consistent with an interaction-dominant system.


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Previous work on the relationship between hand motions and cognition supports the notion that hand motions track closely with changes in cognitive functioning (Anastas, Stephen, & Dixon, 2011; Dale, Kehoe, & Spivey, 2007; Stephen & Dixon, 2011; Stephen et al., 2009). For example, Spivey, Grosjean, and Knoblich (2005) asked participants to click on different objects during a word identification task. Participants were asked to click on one of two pictures in response to a prerecorded voice prompt (e.g., when given a picture of a candle and a piece of candy, the voice prompt might say “candle,” which would instruct the participant to click that picture). In one condition, the two pictures were of objects that were phonologically similar (e.g., “candle” and “candy”). In the other, the two pictures were of objects that were phonologically dissimilar (e.g., “candle” and “jacket”). The xy coordinates of the mouse were sampled continuously throughout the task at 36 samples per second. Analysis of the trajectory of mouse movements showed a significant difference in the coordinates of the path to the picture in each pairing. When the two stimuli were phonologically dissimilar, participants on average took a faster, more direct route to the prompted picture. When the two stimuli were phonologically similar, participants took on average took a slower, slightly wider route to the correct picture, suggesting confusion over which picture to click on. It is important to note that the analysis of small-scale, densely sampled fluctuations in hand motions (in this case measured by mouse trajectory) revealed information about the participant’s cognitive processing (i.e., the degree of conflict between the competing stimuli). Thus, the statistical structure found in densely sampled measurement of behavior can provide insight into the type of processes which generated that behavior. In the next section, we review tools developed to address these issues.

INTERACTION-DOMINANT STATISTICAL PROPERTIES An empirical test of interactions across scales can be applied to the time series of cognitive performance. The key indicators of interactions across scales depend on the rich temporal structure embedded in such a series. The bottom-left panel of Figure 1 shows an example of a time series that is consistent with component-dominant dynamics (i.e., generated by a system like that shown in the upper left panel). More specifically, this time series has only linear effects and linear temporal correlations. In a sense, these properties of the behavioral time series are an expression of the independence of the system components. The bottom-right panel of Figure 1 shows an example of a time series consistent with interaction-dominant dynamics. As suggested by the upper right panel Figure 1, interactions across temporal scales create nonlinear effects and temporal correlations in the time series.



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Despite the apparent similarity of these time series, they have different statistical structure. Interactions across scales entail two important statistical relationships that may be tested empirically: (a) each single value in a time series is the confluence of factors at many different timescales, and (b) these factors at different timescales depend upon each other. In purely componential systems, the first condition is met by linear autocorrelation: each value of a time series is predictable, on average, from a sum of previous values at multiple time lags (i.e., autoregression). However, these different-lag effects are all independent from one another. Interactions across scales entail a multiplicative structure in which time series variation reflects dependence across sequence beyond what is expressible as the sum of autoregressive factors. Hence, a test of interactions across scales requires testing for temporal structure above and beyond what might be produced by linear autocorrelation. Recently, Ihlen and Vereijken (2010) showed how to employ multifractal analysis, in conjunction with a form surrogate data analysis, to differentiate between interaction-dominant and component-dominant dynamics in behavioral time series. Multifractal measures can reflect either multiplicative interactions across scales or additive cases of linear autocorrelation and non-Gaussian histograms. Ihlen and Vereijken used a technique called iterated amplitude adjusted Fourier transformation (IAAFT; Schreiber & Schmitz, 1996) to tease apart these different sources of multifractality. IAAFT generates linearized surrogate versions of original series by shuffling the original values while also preserving the linear, additive properties of the series (mean, variance, autocorrelation). Shuffling meanwhile removes any of the nonlinear, multiscale dependencies arising from multiplicative interactions across scales. Multifractality for a sample of IAAFT surrogates reflects the average contribution of the linear, additive features of a series. Significant differences of multifractal measures for the original series from those for the surrogates indicate a significant departure from linear, additive processes. If multifractal measures differ from what is expected for these linearized surrogates, then the original series reflects multiplicative interactions across scales (see Ihlen & Vereijken, 2010, for technical details).

INTERACTION DOMINANCE AND EXECUTIVE CONTROL Behavior during a task that strongly involves executive function should be well suited to distinguishing between component-dominant and interaction-dominant systems. Under the component-dominant hypothesis, we would expect strong contributions from the central executive, as it regulates the operations of the components. On this account, the central executive would require inputs from each component before issuing commands. The executive could only operate


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as quickly as the slowest component. Therefore, we would expect that the workings of the executive would be contained on one characteristic timescale (i.e., the timing of its effects on the system should be in a relatively narrow temporal range) that reflects the pacing of inputs from the task environment and components. Under the interaction-dominant hypothesis, the phenomenon of executive function is an emergent property that arises from system interactions. Thus, a task that requires executive function should clearly show evidence of the interactions that produce it. In this study, preschoolers were asked to perform a modified version of the Wisconsin Card Sort, a standard executive-function task in which they sorted cards according to a rule (Grant & Berg, 1948; McCrea, Mueller, & Parrila, 1999; McGrath, Scheldt, Hengtsberger, & Dark, 1997; Niemeier, Marwitz, Lesher, Walker, & Bushnik, 2007). Participants were not told the rule and thus had to induce it from feedback given by the experimenter. Further, the rule changed once during the task (full details are in the Methods section). We tracked the motion of each participant’s hand during the task, and the time series of motion data were examined for evidence of multiplicative interactions using IAAFT, providing a test of the component-dominant and interaction-dominant hypotheses.

METHODS Participants Seventeen preschoolers between the ages of 3 and 5 years old participated (M D 46:8 months of age, SD D 7:87 months). Participants were recruited from local preschools and the University of Connecticut child labs. Participants received no reward for participation. Both parental consent and child assent were obtained before participation. Materials Participants sorted cards from a specially prepared deck. On each card in the deck was a picture of a brightly colored animal wearing a piece of clothing. Two of these three characteristics (type of animal and color) corresponded to the two potential sorting dimensions. Each sorting dimension contained four levels. For color, the four levels were red, green, blue, and yellow. For type of animal, the four levels were cow, pig, lion, and wolf. Each card contained one level from each dimension. For example, one card had a picture of a red wolf wearing a hat, which represents one level from each of the dimensions. There was one card for each unique combination of the possible levels, making for a



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deck with 64 cards. Decks were preset before each run, where a run is a set of 30 consecutive card placements. Thus, the card order for each run was the same for all participants. The motion of each participant’s sorting hand was tracked for each run. Motion-tracking data were collected during sorting using a magnetic motioncapture device (Polhemus Fastrak, Polhemus Corporation, Colchester, VT, and 6–D Research System software, Skill Technologies, Inc., Phoenix, AZ). The position of the participant’s hand, relative to a static sensor attached to experimental surface, was sampled at 60 Hz. Participant hand motions were sampled in three dimensions, tracked on a Cartesian coordinate plane.

Procedure Participants were required to take cards from a facedown deck and place them into one of four piles, based on one of the previously described dimensions. Each pile contained a guide card, with each level of each rule represented once across the four guide cards. For example, one guide card contained a picture of a green lion wearing glasses. This was the only guide card to contain these three characteristics; participants would then place into this pile green cards or lion cards, depending on which rule was active (see Figure 2). After each card placement, the experimenter told the participant whether or not the card was correctly placed, according to whatever rule was active during that point in the run. Participants wore a cloth glove on their dominant hands during sorting; the motion tracker was attached to the glove using Velcro. Attaching the tracker this way allowed the participant to keep his or her hand free to grasp cards. Participants were told that the glove was a “magic glove” and needed to be worn in order to allow the card-sorting game to continue. Participants generally accepted this explanation for wearing the glove. Participants were asked to sort 30 cards per run. They received experimenter feedback as to whether or not each card was placed correctly, but participants were never told which rule to use for sorting. Consistent with the procedure used in the Wisconsin Card Sort, the rule was changed after 15 cards had been placed (the midpoint of the run). As with the initial rule, the participant was not informed that the rule had changed and was required to induce that a change had occurred through feedback. The rule was switched either from color to animal or vice versa. Participants were asked to complete up to five runs during the session. Many participants chose to opt out of the task after fewer than five runs. As a result, participants completed an average of three runs each. Only complete runs were analyzed, that is, runs in which 30 cards were placed by the participant.


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FIGURE 2 An example of the card-sorting task. Participants were presented with four guide cards (shown at the top of the figure). The guide cards each have a unique value of each of the two dimensions (i.e., animal, color). Participants were required to draw a card and place it into the correct guide pile as determined by the rule for that run. In the example, the sample card, a blue cow, would be placed into the second pile if the rule was “color” or the fourth pile if the rule was “animal.”

Analysis An important marker of multiplicative interactions across scales is multifractality. Fractal temporal structure is the case in which fluctuations grow at a powerlaw relationship with time over all available timescales. It is called “fractal” because of the potentially “fractional” power-law exponents relating fluctuation statistics to time. Multifractal temporal structure entails that the rate of fluctuation in the system varies for different sizes of fluctuations. Because multiplicative interactions can produce multifractal structure, the presence of multifractality in a system may be partial evidence for the existence of interactions across scales of that system (Ihlen & Vereijken, 2010). Identifying multifractal structure in a time series is an important first step toward demonstrating that multiplicative interactions are present within a system. However, because non-Gaussian histograms and linear autocorrelation are capable of generating multifractal structure, further comparison is needed to diagnose multiplicative interactions across scale (Ihlen & Vereijken, 2010). If the original sequence of time series


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variation in cognitive performance arises from multiplicative interactions across scales, then the removal of original sequence and the preservation of the linear properties of the system should lead to a change in the degree of multifractality within the system. If the multifractal structure found within a system is unrelated to multiplicative interactions, then the removal of original sequence should have no effect on multifractality. Ihlen and Vereijken (2010) recommended using IAAFT to accomplish this comparison. Iterated Amplitude Adjusted Fourier Transformation (IAAFT) IAAFT generates a series of surrogates in which original sequence is destroyed, providing us with an appropriate set of time series to test the null hypothesis of multifractality due to skew or linear autocorrelation. First, we run a fast Fourier transform on the original series, producing both a phase spectrum and an amplitude spectrum. The traditional linear features of temporal structure are bound up in the amplitude spectrum, and information about actual sequence is bound up in the phase spectrum. To destroy sequence information and preserve linear autocorrelation, we ignore the original phase spectrum and preserve the original amplitude spectrum. Next, we randomly shuffle the values of the original time series and run a fast Fourier transform on the shuffled series. IAAFT takes the phase spectrum from the shuffled series and weaves it together with the amplitude spectrum of the original series. The inverse Fourier transform on this hybrid gives us a new surrogate series whose linear autocorrelation mimics that of the original series. However, the actual values of this inverse-Fourier series may not be the same as in the original. IAAFT does not simply replicate the amplitude spectrum; it also preserves the original series’ histogram. So, in the next step, we rank-order the values of the surrogate series, and we replace the rank-ordered surrogate values with the rankordered values of the original series. For instance, the highest, second-highest, and third-highest values in the surrogate series are replaced by the highest, second-highest, and third-highest values in the original series, respectively. This rank-order replacement populates the surrogate with the original values, but because the phase spectrum used to build this surrogate came from a randomly shuffled copy, the surrogate shares only two attributes with the original series: (a) the original series’ histogram and (b) the linear autocorrelation. Rank-ordered substitution of values obviously changes the profile of the inverse-Fourier series and so may slightly perturb the amplitude spectrum. For this reason, the IAAFT algorithm is iterated many hundred times to ensure that the surrogate’s linear autocorrelation is a good approximation of the original. In the current study, nine surrogates were generated for each of the original time series. The crucial relevance of IAAFT to present considerations lies in the shuffling. It is possible in a given time series that the observed multifractal structure is a


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consequence of distributional skew or linear autocorrelation of the series rather than the result of interactions across many different temporal scales. Shuffling the time series and weaving together the resulting phase spectrum with the original amplitude spectrum destroys the original sequence while preserving the linear autocorrelation. If the multifractal structure found in the series is due to the distributional or autocorrelational properties of the series, then we would expect that IAAFT would have no effect on the multifractal structure of the series; however, if that structure emerges as a result of interactions among temporal scales, then IAAFT would significantly alter the multifractal structure of the surrogates.

Chhabra and Jensen Method Once we have obtained a set of shuffled series for each of the originals, we must determine whether or not the shuffling has affected the degree of multifractality within the series. We used a method developed by Chhabra and Jensen (1989) to determine the multifractal spectrum of the original time series and all of the surrogate time series. The Chhabra and Jensen method has long been used for determining the multifractal spectrum of a time series (Muñoz-Diosdado, GuzmánVargas, Ramírez-Rojas, Del Río-Correa, & Angulo-Brown, 2005; Stephen & Dixon, 2011; Wang, Ning, & Chen, 2003). It takes as input a response series of fluctuations and produces as output a series of values that estimate the rate of change of these fluctuations, denoted by a, across a wide variety of fluctuation sizes, denoted by q. This array of values is called a multifractal spectrum and represents the rate of change of fluctuations in the series, ranging from very small fluctuations (i.e., more negative q) to very large ones (i.e., more positive q). We ran each of the original and surrogate time series through the Chhabra and Jensen method, producing a multifractal spectrum for each series. The multifractal spectrum width of each series—that is, simply the ˛ of our lowest q subtracted from the highest provides a standard measure of the degree of multifractality. A large multifractal spectrum width indicates a series with a wide range of variability; a small multifractal spectrum width indicates a system with little difference. Each surrogate used the same range of q values as the original series. Figure 3 shows a typical multifractal spectrum for an original time series compared with the surrogates generated for that series. If the IAAFT procedure leads to a significant change in multifractal spectrum width in the surrogates, we can safely conclude that multiplicative interactions are present in the system and are driving the creation of the multifractal structure that we have found. If there is no significant difference in spectrum width between the original series and the surrogates, then we can conclude that any multifractal structure found in the time series is due to its distributional properties rather than a result of multiplicative interactions.



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FIGURE 3 A set of sample multifractal spectra. The inner lines represent the spectra for the surrogates; the outermost line represents the spectrum for the original series from which the surrogates were generated. The decrease in multifractal width is caused by the shuffling from IAAFT.

RESULTS Each participant’s runs were divided into two parts, based on when the rule switch occurred. Prior to the switch, participants sorted an average of 12.04 cards correctly out of 15 total placements .SD D 3:88/. After the switch, participants sorted an average of 8.5 cards correctly out of 15 .SD D 4:21/. Participants took roughly the same amount of time to place 15 cards both before .M D 133:50 s,


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SD D 51:85/ and after .M D 135:20; SD D 48:90/ the rule switch. Time series lengths were also roughly the same before (M D 8,010 points, SD D 3,111) and after (M D 8,112 points, SD D 2,934) the rule switch. Time series both before and after the rule switch were of length comparable to past behavioral time series on which fractal analyses were performed (Gurses & Celik, 2013; Kelty-Stephen & Dixon, 2013). Because we were interested in rule switch effects, we split the time series gathered during each sort at the point where the rule switch had occurred; this provided us with two time series for each run. From each original motion series, we created a time series of displacements for each run separately by calculating Euclidean distances between adjacent measurements. Figure 4 shows a sample displacement time series for a preswitch run. We used the displacement series to generate nine surrogates for each of these runs and compared the displacement series with their created surrogates for gathered both before and after the rule switch. We then ran an independent samples t test, where one of the groups

FIGURE 4 A sample displacement time series of participant hand motions, collected during a prerule switch run.



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contained all of the spectral widths for the original runs and one contained all of the spectral widths for the surrogates. First, we compared the widths of the preswitch original runs with the preswitch surrogates. The mean width .M D 1:471; SD D :373/ for the original series was significantly greater than the mean width .M D 1:093; SD D :448/ of the surrogate series, t.498/ D 5:73; p < :0001 (see Figure 5). Next, we looked at the postrule switch runs; the mean width .M D 1:483, SD D :376/ for the original series was significantly greater than the mean width .M D 1:133; SD D :519/ of the surrogate series, t.498/ D 4:63; p < :0001 (see Figure 6). We predicted that both pre- and postswitch sorting would rely on interactiondominant architecture and that there would be no difference in spectral widths before and after the rule switch. In order to test this prediction, we ran a factorial analysis of variance (ANOVA) comparing pre- and postswitch runs as one factor. We found no significant effect for the rule switch, F.1; 996/ D 1:525; p > :05.

FIGURE 5 Comparison between the mean multifractal spectrum widths of the originals (blue bar) versus the surrogates (red bar) for preswitch runs. Error bars represent 1 standard error of the mean.


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FIGURE 6 Comparison between the mean multifractal spectrum widths of the originals (blue bar) versus the surrogates (red bar) for postswitch runs. Error bars represent 1 standard error of the mean.

We also tested the interaction between preswitch/postswitch sorting and surrogate/nonsurrogate runs to determine whether or not the significant differences in spectrum widths described earlier were affected by whether or not a run was captured before or after the rule switch. This interaction was not significant, F.1; 196/ D :073.

DISCUSSION We found that the mean spectral width of the original time series was significantly greater than the surrogates generated by IAAFT. This held true both before the rule switch and after it. When IAAFT destroyed the original sequence within the series, the degree of multifractality within the surrogates was significantly decreased. This would suggest that the multifractal structure found during performance on an executive function task was generated by multiplicative interactions across different temporal scales.



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In classical theories of psychology, the cognitive system is assumed to be component dominant; that is, the cognitive system is made up of a number of insular, encapsulated components. In order to explain how these components are coordinated in spite of their independence from one another, one must endow the system with a master subsystem, usually called the central executive. The central executive monitors and controls the other components in the system. To the degree that a task requires strong contributions from the central executive, the interactions within the system should be dominated by the temporal scale on which the executive operates. To appreciate this more fully, consider that the central executive must wait for input from all relevant sources (e.g., the environment and system components) before sending the next set of orders. Thus, the slowest process relevant to a particular goal or subgoal will determine the pace at which the central executive operates (i.e., delivers the next set of instructions). Further, between-component effects should be diminished because the central executive is monitoring and controlling the deployment of each component. In sum, as the central executive increases control, the interactions in the system should become increasingly dominated by a characteristic timescale (that of the executive) and within-system effects should be increasingly linear because they run through the executive. The central point here is that executive-function tasks should, under the component-dominant hypothesis, produce behavior that is characterized by complex but linear effects. An alternative account is that executive function is an emergent, macroscale property of the cognitive system. Interactions across multiple timescales continually give rise to cognitive structure that is stable because of its dynamic organization rather than its static nature. This organization allows the system to adapt to its changing environmental circumstances. Under this hypothesis, tasks that require executive function should strongly invoke the across-scale interactions necessary to create stable cognitive structure. Consistent with this idea, the IAAFT analysis shows that destroying the sequence changes the width of the multifractal spectrum. Thus, this study suggests that executive function is an emergent phenomenon that is the product of interactions across many temporal scales in the cognitive system. The hypothesis that executive function might emerge from the underlying substrate of multifractal fluctuations is strongly consistent with recent work on haptic perception. The systematic time variability of fractal fluctuations at the hand (Stephen, Arzamarski, & Michaels, 2010), at the foot (Stephen & Hajnal, 2011), and at the torso (Palatinus, Dixon, & Kelty-Stephen, 2013) have all shown multifractality to support the deployment of information search for haptic judgments. Interestingly, this work on haptic perception has also revealed specific effects of multifractality on high-level properties typically attributed to executive function, such as use of feedback, memory for feedback, and transfer of training. This patterning of the information search thus appears to be gener-


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ically multifractal irrespective of disparities between anatomical components and appears to reflect rather the interaction of multiply-sized fluctuations. The relatively wide multifractal spectra in this case of children having to induce the proper sorting rule aligns with previous evidence of relatively wide multifractal spectra in adults’ sorting-hand fluctuations under the same task constraint of having to induce the rule (Stephen, Anastas, & Dixon, 2012). Furthermore, it reflects the same sort of widening of the multifractal spectrum found in cases of haptic perception when experimental instructions enlist selective attention, another ability attributed to executive function, wherein participants must delve into a diversely structured task environment and translate only a small portion of the stimulus into a judgment (Palatinus, Kelty-Stephen, KinsellaShaw, Carello, & Turvey, in press). Participants having to induce a rule under no instruction except for feedback must “focus in” on various subsets, probing details rather than overall structure. In this way, the cognitive system may spread apart the temporal structure of its fluctuations to take a more nuanced posture with regard to the information it must glean from the task environment. Implications for Research on Executive Function We believe that the present results, along with the current body of research on the topic, suggest further exploration into the way in which across-scale interactions can lead to the successful deployment of executive function. Having demonstrated that executive function may be an interaction-dominant process, the next step is to attempt to quantify these interactions. Research in this vein should focus on establishing the relationship between changes in multifractal structure and changes in cognitive performance. For example, which scales are most active during an executive-function task? How does each scale affect each of the others? Addressing these questions will help us understand how those interactions impact the performance we see at the behavioral level. We recognize that componentdominance is an assumption, perhaps even an implicit assumption, of many researchers interested in executive function as a key developmental (or individual difference) dimension. As with many assumptions, the implications for how one conducts research, models results, and constructs theory are profound but largely unrecognized. For example, from a traditional component-dominant perspective executive function is a property of the individual, much like a trait, rather than the soft-assembled product of the individual’s history and task conditions. Such a conception naturally leads to research programs that look for variations in internal structures to explain differences among individuals (e.g., Yuan & Naftali, 2014) because the statistical regularity of executive function must be due to something stable that an individual possesses. Likewise, variations across executive-function tasks, within an individual, are attributed to task properties



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(i.e., the degree to which the task requires executive function). This parsing of executive function into a small number of causally efficacious units is a direct consequence of the component-dominant assumption. Indeed, given component dominance as a starting point, it is difficult to imagine how else the system could work. The crucial departure of the interaction-focused approach from more traditional approaches to cognitive performance has mostly to do with the possibility that the real-time engagement of a cognitive function, such as executive function, might arise from a different architecture. We note that interaction dominance does not deny the existence of the many phenomena of cognitive science. Rather, we are committed to exploring how these phenomena come into existence. The interaction dominance of executive function suggests that the emergence of new skills and capacities to induce, apply, inhibit, or transfer rules depends on interactions across scales. This suggests that the embodiment of cognition includes more than just the coarse-scaled gestures that already stand in for some linguistic meaning (e.g., more than the shaking or nodding one’s head for “no” or “yes,” respectively). Fluctuations across a wide range of scales, many of which have no obvious interpretation to an observer, are involved in self-regulating the cognitive system. We propose that the measurable fluctuations at all scales reflect the reshuffling of energy distributions that might be ambient through the environment, internal to the organism, or spreading messily across boundaries that typically delineate them (e.g., Lewontin, 1982). Empirically testing such a proposal would emphasize the nesting of temporal and spatial scales as a prior principle to any of the many scale-dependent factors dedicated to this or that corner of the cognitive patchwork. The strength of nesting, whether in terms of monofractal or multifractal measures, has already shown itself to be an important variable in presaging the appearance of a new cognitive structure (Dixon, Holden, Mirman, & Stephen, 2012). Multifractal measures have the key advantage of spreading the fractal properties of a cascading system out along a continuum of “fluctuation size,” permitting us to begin to dig into the shape and directionality of the cascade. For instance, we can ask whether observable cognitive structure reflects “bottom-up” cascades or “topdown” cascades simply by examining the interplay of fractal scaling for many different intervals of the multifractal spectrum (Dixon & Kelty-Stephen, 2012). Hence, we can even fit these cascade-directed inquiries into the same parlance of cognitive psychologists keen to admit that large events can filter down to affect the relatively smaller events they contain as in “top-down processing” and that small events can percolate upward or be amplified to form large events as in “bottom-up processing.” We can examine ostensibly the “same” task-fulfilling behaviors such as card sorting under different instructions and find significantly different relationships between the events of different size (Stephen, Anastas, et al., 2012).


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We can also inquire as to how cascade processes might spread across the body to understand how the perceiving-acting system learns to sample its ambient energy in novel contexts, even in cases when the organism is not old enough to simply verbalize her strategies (e.g., Stephen, Hsu, et al., 2012). These early options have so far borne tangible fruit for psychological investigation, and we also find promising the success of cascade-based multifractal formalisms, in geophysical domains, for classifying, comparing, and predicting phenomena that other approaches have only found too unruly, turbulent, and capricious to allow effective modeling (Schertzer & Lovejoy, 2004). We might identify the types and geometries of cascades that give rise to individual differences in abilities and responses to task constraints, and phrasing the explanation in these cascadebased terms might allow us to discover generic physical principles that promote executive function across many phyla or many materials without needing to cherry-pick only those systems apparently endowed with the proper internal, cognitive components (Stephen & Van Orden, 2012; Turvey & Carello, 2012).

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