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  change with relatively broader constraints of task parameters . 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. One of the central and fundamental capacities of the typically developing human movement system is to extend a limb toward a target. Very much of movement coordination is the timely movement of one limb from one target to the next. So, it is no mistake that the In this low-stakes adaptation of the Fitts task, we hope to show five points of evidence about the relatively unconstrained use of vision for planning tactile interaction with a task environment over time. First, this simple task of making manual contact with targets in alternation depends on non-linear interactions over time across the body. Second, we know the first point because multiple parts of the body generate multifractal fluctuations during this task. Third, across progressively more cycles of alternation, stronger multifractal evidence of non-linearity at the hand predicts greater stability  in contact with targets. Fourth, again, across progressively more cycles of alternation, stronger multifractal evidence of non-linearity at the head supports use of visual information for making more stable contact with the targets – both the use of current visual information with eyes open and the use of past visual information after closing the eyes. Fifth and lastly, anticipating a loss of visual information stabilizes contacts with the targets, but this stabilizing effect of anticipation depends on the mixture multifractal evidence of non-linearity both at the head and the hand.A key aspect of movement coordination that the Fitts task epitomizes is hierarchical organization. The Fitts task requires a long run of movements through repeated cycles. The Fitts law relates movement times with a difficulty index defined as between-target distance divided by target width . So, theThis hierarchical form and the consonant fractal geometry have rich potential for supporting the movement system’s solution of vast challenges in movement coordination. The multifractal tensegrity hypothesis makes hierarchically organized interactions central to the explanation of dexterous behavior. Specifically, this perspective suggests that the interaction across scales is the hallmark of dexterity. It appeals to the physiological evidence that the human movement system embodies a balance between tensions and compressions across many nested scales, e.g., cellular, tissue, organ, synergy, and organism levels of analysis . OutsideThe multifractal tensegrity hypothesis takes a different view and makes multifractal geometry part of the central hypotheses about what drives motor coordination. It begins from the premise of expecting an interaction-driven architecture across all scales of the movement system, and it takes the expectation of multifractal structure as a logical prediction. According to this interaction-driven architecture, the aforementioned tension-compression balance reflects an architectural/morphological principle of “tensegrity.” The term “tensegrity” is a neologism short for “tensional integrity.” This tensional integrity certainly permits the distinction of anatomically distinct components. However, this tensional integrity entails that components hang together in a tightly-knit network relationship that allows local perturbations to spread globally. Thus, tensegrity allows global configuration to absorb and constrain minor local perturbation and to translate larger local perturbations into new global stabilities . A majorThe multifractal tensegrity hypothesis has shown early promise across a wide range of scientific programs. First, there has been broad evidence that human physiology exhibits multifractal fluctuations suggesting cascade-driven dynamics . Second,The present work aims to tailor empirical Fitts-task research to clarify specifically the relevance of the multifractal-tensegrity perspective. A general prediction that we hope to support is that the non-linear interactions across scale in the movement system support more accurate, more stable, and less variable achievement of the task. We use measured time series of movement variability and submit them to multifractal analysis to assess these non-linear interactions across scale. The idea that movement variability can promote greater stability might initially seem counterintuitive. However, it grows from the two sequential points: first, that movement variability is not equivalent to error and second, that movement variability might sooner afford ongoing exploration and corrections to ongoing sensory and kinesthetic information. That is, movement variability serves to enrich the movement-system’s relationships with the task environment. Hence, by enriching this relationship, more movement variability can stabilize performance . The prot-statistic: “multifractality of original series” minus “multifractality of surrogate series” divided by the standard error of surrogate multifractality. We will call this t-statistic tMF for short to abbreviate “t statistic for multifractal difference between original series and surrogate data.” The linear standard represented by the surrogate merely allows us to estimate multifractal structure as if there were no non-linear interactions. We aim to make the very specific prediction that standard deviation in target contacts in a Fitts task varies inversely with non-linearity tMF.The data-analysis change will be the use of multifractal analysis in concert with surrogate testing. Using multifractal analysis to quantify the strength of non-linear cross-scale interactions requires comparison with surrogate-data time series . We expet-statistic tMF comparing series multifractality to surrogate multifractality  in head sway  and even to give participants the expectation at the outset of potentially having to close their eyes. This change is to give force to speculation elsewhere about the role of visual feedback. Specifically, this manipulation would interrupt any visual information that might operate as an independent component exerting mechanistic effects producing non-fractal fluctuations e.g., . Howeveread sway . The pretMF at head and hand should moderate the effect of expectation in reducing aiming variability.Interactions across time scales should mean that visual information available shortly before closing eyes may persist longer in participants with greater multifractal non-linearity of head sway, and so although closing eyes should result in greater aiming variability, multifractal non-linearity of head sway may reduce aiming variability following the actual closing of eyes. Previous research into anticipation has already indicated relevance of multifractal evidence of non-linear interactions in supporting coordination of several events into an organized, anticipatory response under uncertainty ,b. HencetMF will have in stabilizing accuracy  in the Fitts tasks: (1) greater tMF in the hand predicting greater accuracy (lower standard deviation) in general, (2) greater tMF at the head predicting greater accuracy (lower standard deviation) following the closing of eyes, and (3) the interaction of greater tMF of hand and of head predicting greater aiming accuracy under the expectation of closing one’s eyes.The present work situated the Fitts task firmly in the foundation of multifractal tensegrity and tested whether the strength of multifractal signatures of non-linear cross-scale interactions actually support greater accuracy and so less aiming variability. We tested three hypothesized effects that multifractal-indicated non-linearity Twelve Grinnell College students participated in this experiment after providing informed consent according to the guidelines of the Grinnell College Institutional Review Board and in accordance with the Declaration of Helsinki. All participants were right-handed, had normal or corrected-to-normal vision, and exhibited no motor impairment. The motion-capture suits malfunctioned for the second half of one participant’s task, making the data for that one half of one participant’s data unusable. Data analysis included this participant’s first half of the task but excluded this participant’s second half.″ on each side) were glued to the desktop 10 inches (25.4 cm) away from one another and within comfortable arm’s reach. A Noitom Perception Neuron motion-capture suit recorded movements throughout the entire experiment and logged the data at 60 Hz using Noitom’s companion Axis Neuron software.Participants sat at a standard office desk. Two wooden blocks (1.5There was a 2 (Expectation) × 2 (Eyes-Closed in Block 2) × 2 (Block) mixed design. All participants completed two 10 min blocks of the task. Each participant was randomly assigned to either level of Expectation . Each participant was also randomly assigned to either level of Eyes Closed in Block 2 . Three participants appeared in each of the four between-groups crossings of Expectation with Eyes-Closed in Block 2.Experimenters helped participants put on the motion capture suit and then instructed them to sit at the desk and explained that the task would be to use the fingers of their dominant hand to touch the each of the blocks attached to the desk in alternation as fast and regularly as possible. Participants in one level of the Expectation independent variable heard the experimenter instruct them that they might have to close their eyes at some undetermined point during the task and to continue completing the fast, regular contact with the target. Participants in the other level of the Expectation independent variable heard no such instructions. All participants completed the task with their eyes open for the first 10 min block. After 10 min of the task, experimenters asked participants in one level of the Eyes-Closed independent variable to close their eyes for the remainder of the task, but experimenters made no such request to the participants in the other level of this independent variable, allowing them to continue the task with eyes open. Participants completed the next 10 min of the task with either eyes open or eyes closed. There was no break between Block 1 and Block 2 except to recalibrate the machine.The motion-capture suit collected upper-body position information about head position and dominant-hand position.We computed multifractal analysis and surrogate testing on non-overlapping epochs of the continuous lateral position series for the dominant hand as it moved alternately from left to right. By “lateral position,” we mean the position of the hand relative to the midpoint between the targets, parallel to a line connecting the targets. As for the head movement series, we reduced the three-dimensional position series of the head to interpoint Euclidean-distance series indicating the Euclidean distance between each pair of consecutive 3-dimensional positions e.g., . WhereasIn a broad sense, newcomers to multifractal analysis might understand multifractality as a variability measure where we may not necessarily assume the homogeneity that makes a standard deviation so effective for quantifying variability. Linear modeling can use the linear autocorrelation  to model temporal sequence. However, non-linear time series may exhibit not just one autocorrelation but several – whether changing with time  or changing according to fluctuation size . Multifractal analysis covers a broad class of ways to query the variation of temporal sequence, and we apply it to both the original series and to surrogate series that have the same values and the same linear autocorrelation. The contrast of original-series multifractality and surrogate-series multifractality allows comparing the multifractal spectrum width in both cases and using the difference between them as a measure of non-linear interactions across time scale.We use the f as the relationships of average bin proportion and Shannon entropy (q-based variability with mass μ(q) generalizes single α and f estimates from earlier steps into continua α(q) and f(q). Multifractal analysis distinguishes temporally heterogeneous series from homogenous series by the amount of variety in α(q) and f(q) for all values of q yielding stable power-law relationships. The multifractal spectrum is the set of ordered pairs (α(q), f(q)), an often-asymmetric and inverted U-shaped relationship (q) and f(q) whenever log-scaled linear fits correlated at r of 0.995 for the log-scaled linear fit. We excluded values of q either (1) for which mass-weighted proportion and for which Shannon entropy were undefined  or (2) power-law fits for which r < 0.995. The final output of multifractal analysis here is the multifractal spectrum width wMF equal to the maximum estimated α(q) minus the minimum estimated α(q).First, CJ partitions (or “bins”) the series over sequences with lengths varying from four points to a fourth of series length /(Standard error of WMF of surrogate-data series). TMF indicates non-linear interactions across time scales in a standardized way that should generalize across series with differing histogram skew or linear autocorrelation.Multifractal-spectrum width varies with non-linear interactions across time scales but also with histogram skew or linear autocorrelation. Hence, evidence of non-linear interactions requires comparing multifractal-spectrum width for original series to multifractal-spectrum widths for a sample of  of the original fluctuation series. Any difference between original multifractal spectrum width and average surrogate multifractal-spectrum width must reflect a non-linearity – particularly if it falls outside of the 95% confidence interval, yielding a significant t statistic. Because the phase-randomized surrogates already include the autocorrelation over all time scales independently, this term “non-linearity” is specifically equivalent with the phrase “non-linear interactions across time scale.”These tMF(Hand) × tMF(Head), Closedeyes × (Number[Epoch] + Size[Epoch] + Expectation) × tMF(Head), Expectation × Number(Epoch) × WMF(Hand) × WMF(Head), Closedeyes × (Number[Epoch] + Size[Epoch] + Expectation) × (Mean[Head] + SD[Head]), and Number(Epoch) × Half.A single mixed-effect linear regression e.g.,  using R The first two sets of interactions tested the explicit hypotheses noted above. The second two sets of interactions controlled for simpler effects that a more skeptical point of view could want represented. We detail both in the next two subsections.tMF(Hand) × tMF(Head) and its component lower-order interactions and main effects tested whether the ongoing effect of expectation on SD(Aim) depended on epoch size as well as multifractal-indicated non-linearities in hand and head positions. In plainer language, this set of terms poses the questions: “Do non-linear interactions across time in the hand stabilize aiming? (Hypothesis 1) Does that support work with hand non-linearity to stabilize aiming under the anticipated threat of potentially losing visual information?” (Hypothesis 3).The first two sets of interactions tested the explicit hypotheses. Specifically, the higher-order interaction Expectation × Number(Epoch) × Size(Epoch) × tMF(Head) and its component lower-order interactions and main effects tested whether the ongoing effect of closed eyes on SD(Aim) depended on multifractal-indicated non-linearity in head position with moderation by expectation as well as by the size and number of epoch used to quantify standard deviation for SD(Aim). In plainer language, this set of terms poses the question: “Does the effect of closing one’s eyes on aiming variability depend on non-linear interactions across time at the head?” (Hypothesis 2).The higher-order interaction Closedeyes × [Number (Epoch) + Size(Epoch) + Expectation] × WMF(Hand) × WMF(Head) and its component lower-order interactions and main effects tested whether the ongoing effects of expectation on SD(Aim) for any epoch size dependent not on non-linearity but just multifractal-spectrum width. That is to say, they answer the following question: “Surrogate testing sounds difficult, and non-linear interactions across time scale sounds like splitting of computational hairs. Shouldn’t multifractal analysis be enough to explain the contribution of hand and head sway to aiming variability?”The remaining interactions provided control effects to address various more skeptical questions worth asking about SD(Aim). That is, these lower-order effects give the regression model due opportunity to control for the simpler explanation. They represent the possibility that comparison to surrogates and change with epoch size are each needless complications. Specifically, the higher-order interaction Expectation × Number(Epoch) × For that matter, from such a diligently skeptical point of view, we could doubt the usefulness of this multifractal mathematics at all. The next set of control terms offers a test representing this skeptical point of view. The higher-order-interaction Closedeyes × (Number[Epoch] + Size[Epoch] + Expectation) × (Mean[Head] + SD[Head]) and its component lower-order interactions and main effects tested whether any effect of closed eyes on SD(Aim) was sooner dependent on simpler descriptive statistics. That is to say, in plainer terms, “Shouldn’t aiming variability with eyes closed sooner depend on the average size and average variability of head sway? And shouldn’t these simpler statistics fewer algorithmic steps away from the raw data sooner show the relationships better with time, time span, and the threat of potentially losing visual information?”The last set of control effects described by the interaction Number(Epoch) × Half and its component main effects offers the model a way to articulate the simple effect of time. The plain-language question posed by these terms would be “Won’t fluctuations in hand and head also simply vary across continued time in the task regardless of potential or action loss of visual information?”We include three figures to depict example movements of the hand during 50 s portions of the Fitts task under each case. r = 0.7335. The regression-model predictions appear in The regression model returned a number of lower-order significant effects on SD(Aim), all of which appear in post hoc power analysis using bootstrapping to resample the dataset 1000 times found greater than 80% for all effects reported, as well as for 17 other predictors in the model that were non-significant. Hence, the repeated measures aspect of this design compensated for the small sample size. Raw data are available on request and online1.While it is regrettable that this preliminary experiment did not have more individual participants, the regression model met the heuristic benchmark of having more than 10 observations per predictor . FurtherThe absence of effects of multifractal-spectrum width on SD(Aim) suggesting indeed that multifractal analysis alone is insufficient to explain the contribution of hand and head sway to aiming variability. These null effects would on their own entail a failure to support hypotheses that multifractal analysis provides any insight into aiming variability in the Fitts task. However, the insufficiency of multifractal-spectrum width to predict aiming variability in the Fitts task is completely mute on the specific point of non-linear interactions across scales. As noted above, the better statistical signature of non-linear cross-scale interactions is the difference of multifractal-spectrum width between measured series and surrogate-data series. However, this use of surrogate data to estimate the non-linearity of cross-scale interactions appears to be carry significant weight in predicting variability in the Fitts task. And it appears to overshadow any such predictive weight for multifractal-spectrum width without surrogate comparison.MF(Hand) and tMF(Head). All of the following effects reviewed below appear schematized together in tMF(Hand) or of tMF(Head). To ease this task of interpreting these higher-order interactions, This section reviews the contributions of tMF(Hand). Instead, the regression model showed SD(Aim) increased with greater hand non-linearity and with continued time in the task . This positive relationship between multifractal non-linearity and SD(Aim) over time decreased for longer time spans , suggesting that stronger multifractal non-linearity at the hand predicted progressively less variable aiming behavior especially over longer time spans.As noted in the previous section, there were no main effects of tMF(Hand), there were no main effects of tMF(Head). Head non-linearity moderated the effect of actually closing eyes and losing visual information. Whereas closing eyes had produced a main effect of increasing SD(Aim), greater head non-linearity when closing eyes predicts a small but significant reduction in this increase . That is to say, head non-linearity initially stabilized aiming variability at the hand, suggesting that head non-linearity appears to support the persistence of past visual information. However, the next two significant effects show that, whatever head non-linearity can do to prolong the impact of past visual information during the closed-eyes half of the task, this effect is fleeting both in terms of how fast it vanishes over time and how small a time span we must use to estimate non-linearity to see the effect clearly. Small but positive interactions of this effect with continued time in the task  and longer time span for evaluating aiming behavior  both attenuate this stabilizing effect.Just as for tWe can summarize these effects of head non-linearity in the following ways. First, the participants’ awareness of potentially losing visual information seems to recruit head non-linearity – rather than hand non-linearity – as a stabilizing factor on aiming behavior . Second, irrespective of participant expectations, head non-linearity exerts an independent, additional stabilizing effect, reducing SD(Aim) perhaps by prolonging past visual information once participants actually close their eyes and lose current visual information. This evidence is thus precarious, with the first effect only marginally significant and the second effect significant but fleeting. As the next section shows, expectation remains necessary to knit the stabilizing effects of hand and head non-linearities together into a more reliable stabilizing effect on aiming variability.tMF(Hand) × tMF(Head). Over longer time in the task and over longer time spans, increases in both hand and head non-linearities predicted that SD(Aim) would increase . However, expectation significantly reversed this effect. Specifically, over longer time in the task and over longer time spans, the mere threat of potentially losing visual information along increases in both hand and head non-linearity predicted that SD(Aim) would decrease . That is to say that expectation changed the perceptual-motor impact of any relationship of non-linearity at the hand and at the head. The capacity of expectation to reduce aiming variability depends on multifractal non-linearity at both the head and the hand.There were only two significant interactions involving tMF(Hand) and of tMF(Head), i.e., model predicted change in SD(Aim) for the first and third quartiles of each tMF variable. In all cases, MF(Hand) and high tMF(Head) together (in solid lines) and low tMF(Hand) and low tMF(Head) together (in dashed lines). For simplicity’s sake, MF(Hand) and tMF(Head) predict greater variability in aiming. Without this expectation, less multifractal non-linearity appears to predict greater aiming stability  than multifractal non-linearity. Multifractal non-linearity seems to produce ever greater variability in aiming as we examine progressively longer epochs in the first half of the task, and the destabilizing aspect of multifractal non-linearity in the second half of the task is clearest in shorter epochs.The only benefit of more multifractal non-linearity without expectation is that it appeared to reduce aiming variability compared to less multifractal non-linearity immediately upon closing of eyes half way through the task. That is, in the left column of Across the board, multifractal non-linearity of hand and head becomes a stabilizing factor for participants expecting that they may potentially have to close their eyes. That is to say, the expectation of potentially losing visual information makes greater multifractal non-linearity a stabilizing factor for aiming and makes less multifractal non-linearity a destabilizing factor for aiming. The only instance in which multifractal non-linearity fails to serve stabilizing role in aiming behavior is roughly the last two thirds of the second half of the task when we consider epochs of 20 cycles. For all other cases, multifractal non-linearity does appear to interact with expectation to support more stable aiming, i.e., lower SD(Aim).As in the case without expectation, this pattern of results does predict an immediate benefit of multifractal non-linearity when participants close their eyes. The 20-cycle epochs shows a dramatic decrease in aiming variability for high multifractal variability  that is only shallower when considering longer epochs. Hence, we see the same sharp, short, and fleeting decrease in SD(Aim) that we saw before without expectation  that we defined as “standard deviation of hand position relative to target position during target contact.” In answer to “Do non-linear interactions across time in hand stabilize aiming? (Hypothesis 1), we can now answer “Yes.” Greater multifractal non-linearity in the hand reduced aiming variability. This effect echoes older findings that the multifractal structure in hand fluctuations supports more accurate use of mechanical and visual information .These results replicate a previously known effect of head-sway non-linearity for supporting the use of visual information , confirmHead-sway non-linearity and hand non-linearity together moderated the effect of merely expecting potentially closing eyes. In answer to the question “Does that support work with hand non-linearity to stabilize aiming under the anticipated threat of potentially losing visual information?” (Hypothesis 3), we can now answer “Yes.” With or without prompting participants to actually close their eyes, expectation serves to diminish the reductive effect of hand non-linearity on aiming variability and to recruit head-sway non-linearity for reducing aiming variability instead. Multifractal non-linearity has its strongest stabilizing effect at the hand for longer epochs. Likewise, multifractal non-linearity at head and hand helps to translate expectation into stabilizing effects on aiming that become stronger for longer epochs.Head-sway fluctuations thus appear to carry double duty for reducing aiming variability, both in supporting the use of visual information and supporting the expectation that visual information might not be available later on. It its key to emphasize that expectation only showed interactions with head-sway alone and with both head-sway and hand. Regarding the interactions with head-sway alone, it is possible that this stabilizing effect of expectation involved a new or further use of visual information, i.e., expectation might engender more or different of the non-linear patterns of exploration of the optical array nesting the manual aiming task. Regarding the interactions with head-sway and hand fluctuations, it is also possible that expectation plays upon synergy-like relationships within the organism between head and hand.Candidate physiological explanations for these results could include localized tissues or specific subsystems. Certainly, heightened activity by sympathetic nervous system can increase change covariation among disparate physiological systems e.g., . ExpectaThe present results speak directly to a physiological explanation residing in geometrical forms embodied by the physiological mechanism of connective-tissue networks weaving muscle, bone, nervous system together through the fascia. It allows multifractal estimation of non-linear interactions across scale and charting out the field dynamics of how this non-linearity ebbs and flows across an organism’s spatial or temporal extend . Indeed,The connective-tissue networks ground perception and action upon a wider-than-neural set of physiological tissues. Evidence of tensegrity support for perception and action includes contextually-specific responses proceeding faster than neural transmission alone would support – variously called “ultrafast,” “mechanotransduction” , or, to distinguish from the slow reflex meandering across multiple synapses, “preflexes” . These uThese effects of multifractal-indicated non-linearity are not so exhaustive as to preclude effects of simpler statistics from head-sway. The method section’s detailing of the regression model notes that the inclusion of control effects allows us to ask the following: “Shouldn’t aiming variability with eyes closed sooner depend on the average size and average variability of head sway? And shouldn’t these simpler statistics fewer algorithmic steps away from the raw data sooner show the relationships better with time, time span, and the threat of potentially losing visual information?” Despite mean and standard deviation of head-sway registering significant main effects and interactions , none oft-statistics produce multifractal-based estimates of non-linear interactions across scale. For all of these effects of multifractal-indicated non-linearity, notably absent were any effects of multifractal-spectrum width itself. As noted in the method subsection detailing the regression model, our modeling included a full set of interactions between expectation, epoch size, epoch number, and – where other interactions included the surrogate-based t-statistic – multifractal-spectrum width. We offered the interactions to represent the following sentiment and curiosity: “Surrogate testing sounds difficult, and non-linear interactions across time scale sounds like splitting of computational hairs. Shouldn’t multifractal analysis be enough to explain the contribution of hand and head sway to aiming variability?” Our model has entirely failed to find any support for this notion. Other variants of the Fitts task with greater difficulty may change this result, but for our present purposes, we meant only to test whether non-linearity was important for a very simple case of goal-directed behavior. Simple tasks elicit non-linearly complex behaviors, which point we do not see as a shortcoming or challenge to interpretation but rather as a signature of how pervasive non-linear interactions across scale can be.Multifractality appears worthless in this study except insofar as surrogate testing and resulting Pervasiveness has been a key theme of earlier fractality-inspired discourse e.g., . Here, wThe present work sought to revisit a foundational task in movement science. Previous work applying fractal methodology to the Fitts task has focused on changes in fractal scaling in the movement-time or movement-amplitude series. In more difficult variants of the Fitts task, greater speed or greater accuracy leads to stronger evidence of fractal scaling in movement-time series or in movement-amplitude series, respectively . On the This work still observes position variability in aiming per cycle  as a key dependent measure. However, whereas movement-time and movement-amplitude series unfold at the same cycle-by-cycle scale of analysis, the present approach of analyzing fluctuations in the movement series per time sample drops below that cycle scale of analysis in order to investigate what more continuous structure may support the coarser cycle-by-cycle performance. Furthermore, in answer to the claims that temporal structure follows from visual feedback , this stThe present research found that aiming variability in the Fitts task, i.e., the standard deviation of positions of the hand during target contact, was predictable from non-linear interactions across scales at the hand and the head. Crucially, this appeal directly to non-linear interactions across scales follows directly from the facts that aiming variability was not sooner – or to any degree – predictable from the multifractal-spectrum width alone and that the better predictors of aiming variability were t-statistics expressing the difference of the original series from linear surrogates. It is important to note that any monofractal results are indistinguishable from the structure expressed in linear surrogates . Hence, The present research further found that the effect of non-linear interactions across scale differed according to different part of the participating movement system. Non-linear interactions across time scale associated with wider multifractal spectra at the hand reduced aiming variability in the Fitts task. Non-linear interactions across time scale associated with wider multifractal spectra at the head reduced aiming variability immediately following closing of the eyes, suggesting that effects of visual feedback depend on the head-sway of the participating movement system. Hence, contrary to In short, aiming in the Fitts task is a full-bodied task that relies on non-linear interactions that span the body no less than the time scales of expectations and explicit instructions. The current work is the latest supporting the notion of motor coordination as a process developing through interactions across multiple scales e.g., . This noThe datasets generated for this study are available on request to the corresponding author.CB contributed to the experimental design, collected all human subjects’ data, and contributed to the data analysis as well as the composition of the manuscript. NC and JZ contributed to the data analysis and the composition of the manuscript. DK-S contributed to the experimental design, data collection, and composition of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Advances in wavefront-shaping methods and computational power have recently allowed for a novel approach to high-resolution imaging, utilizing deterministic light propagation through optically complex media and, of particular importance for this work, multimode optical fibers (MMFs)7. We report a compact and highly optimized approach for minimally invasive in vivo brain imaging applications. The volume of tissue lesion was reduced by more than 100-fold, while preserving diffraction-limited imaging performance utilizing wavefront control of light propagation through a single 50-μm-core MMF. Here, we demonstrated high-resolution fluorescence imaging of subcellular neuronal structures, dendrites and synaptic specializations, in deep-brain regions of living mice, as well as monitored stimulus-driven functional Ca2+ responses. These results represent a major breakthrough in the compromise between high-resolution imaging and tissue damage, heralding new possibilities for deep-brain imaging in vivo.Achieving intravital optical imaging with diffraction-limited spatial resolution of deep-brain structures represents an important step toward the goal of understanding the mammalian central nervous system Beyond this limit, scattering and optical aberrations introduced by the heterogenous refractive index distribution within brain tissue prohibit observing subcortical structures (even in mice), many of which are implicated in important neuronal processes such as memory formation and gating of sensory and motor information, as well as neurological diseases4. The importance of visualizing these brain regions has precipitated the development of diverse optical strategies, including the removal of overlying cortical structures8 and insertion of fiber bundles9 and graded index (GRIN) lenses11. Unfortunately, these approaches create substantial mechanical lesions of the tissue, precipitating neuropathological responses that include inflammation and gliosis12 and possibly ultimately compromising the physiology of neuronal networks and behavior of the animal14. Here, we adopted an endoscopic approach utilizing multimode optical fibers (MMFs). The principles behind the MMF imaging method are detailed in the Supplementary Methods7. The optical geometry was optimized to provide the functional stability and mobility necessary for use in vivo  high-resolution imaging of brain tissue can achieve micrometer resolution up to penetration depths of ~1 mmivo Fig. . Integra7 enabled the acquisition of the full transformation matrix of a 50-μm-core MMF in <4 min. Imaging can be performed immediately after the TM acquisition, and the calibration did not change in time, provided that the fiber was not deformed and that its position relative to the rest of the optical system was not changed (Supplementary Note The source unit of the system distributes laser light (488 nm) into two single-mode optical fibers, one to deliver the excitation signal to the LC-SLM and the other to provide a reference signal during calibration. The main optical arm, comprising the LC-SLM, MMF probe, relay optics, and a fluorescence detection unit, was designed to be compact and is embedded within a robust caged framework housed on a three-dimensional micro-positioning stage to facilitate alignment during calibration as well as navigation of the MMF probe into the brain tissue (Supplementary Methods). Finally, the calibration arm, used only during TM acquisition, relays the MMF probe output signal to a camera, where it interferes with the reference beam. The implementation of a GPU-accelerated toolbox for LC-SLM control17 because these can be easily confused with synaptic structures. This is a particular concern where high-resolution images are collected from sparsely labeled samples over a small area, as it is frequently the case in neurobiology19. Furthermore, previous implementations of the MMF imaging system have failed at achieving sufficient spatial resolution for the visualization of dendritic spines and exclusively reported images of soma20. Our results offer robust validation of the MMF approach for the acquisition of fluorescent images in living tissue. A limitation is that the field-of-view currently corresponds to the core diameter of the MMF (50 μm); if necessary, a wider field-of-view can be achieved using an MMF with a larger core diameter (105 μm) while maintaining the spatial resolution , and could be incorporated into our geometry.While structural imaging is a valuable technique, we sought to assess whether fiber-based dynamic imaging can also be achieved. Our system detected changes in fluorescence elicited in a neuron loaded with the Caivo Fig. . In its 25 and potential future advances in minimally invasive imaging in vivo in a multitude of organs. Future developments will now aim to achieve the scanning speeds necessary for dynamic imaging over wider areas, enabling neuronal population activity to be monitored and a critical step toward brain imaging in freely moving animals (Supplementary Note 26. More suitable for fluorescence imaging would be to exploit the intrinsic optical sectioning offered by two-photon microscopy, which has been demonstrated through a step-index MMF27. Finally, super-resolution imaging could be achieved by implementing a STED configuration because, unlike structured illumination or localization microscopy, the spectrally broad fluorescence would not have to be imaged through the MMF—i.e., the control of two monochromatic illumination beams would be sufficient28.In summary, we have achieved structural and functional in vivo fluorescent imaging of neurons within deep-brain structures of mice that we believe to be the least invasive, deep-brain, high-resolution approach reported to date. This method provides a route to achieving high-resolution optical access to deep-brain subcellular processes in living and ultimately in freely behaving animals, one of the most unique and appealing possibilities of MMF imaging systems, with minimal disruption to the associated circuitry. This study also prominently demonstrates the applications of wavefront-shaping microscopy in biomedical researchSupplementary material