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[mxochicale]

Ref: Submission ID Dear Dr Xochicale, Your manuscript entitled "Nonlinear methods to quantify Movement Variability in Human-Humanoid Interaction Activities" has now been reviewed. Any reviewer comments on the suitability of your manuscript have been appended below. As a result, I regret to inform you that we cannot publish your manuscript in Scientific Reports. You will see that, while your work is of interest, substantive concerns were raised that suggest that your paper does not fulfil the publication requirements for Scientific Reports that is, that papers must be technically sound in method and analysis. Unfortunately, these reservations are sufficiently important to preclude publication of this study in Scientific Reports. Editor comments Unfortunately all reviewers struggle to find a significant novelty or generalizability of methods. However, they make detailed comments that will hopefully be useful. Thank you for the opportunity to consider your work. I am sorry that we cannot be more positive on this occasion and hope you will not be deterred from submitting future work to Scientific Reports. Kind regards, Anonimased Editorial Board Member Scientific Reports

Reviewer Comments:

Reviewer 1

This ms reports a single expt to determine the efficacy of several nonlinear dynamic (NLD) methods in the analysis of simple human-humanoid interactive movements. In particular there is an emphasis on the relative role and adequacy of RPs and RQAs to analyze timeseries. The conclusion is that RQA with Shannon Entropy is suitable to quantify activities. I see the paper as primarily a technical contribution on certain details of the appropriate use of NLD that have in general now been in use in the movement domain for 40 years or so. The motor control background and actual role to the study is very limited with serious omissions on previous NLD in motor control – no or little Beek, Haken, Kugler, Kelso, Turvey, Newell, Schoner among others. There are a substantial number of published movement RQA papers and Shannon entropy has been the backbone of information theory analysis of human movement – e.g., Fitts’ law (1954). An arm movement is the task but it comes across as just a vehicle for technical NLD analyses rather the other way around There are now many overview/review papers on stochastic and deterministic aspects of movement variability that also include to varying degrees treatment on the technical aspects of the application of methods. Indeed, motor control was early to the table on NLD. This does not mean that all the technical issues are closed but current work needs to be assessed in relation to that. Thus, in spite of the careful analysis and presentation through figures the novelty factor here and its breadth of contribution for motor control is not clear to me. To conclude as the authors do that RQA and Shannon entropy “are suitable” reflects the problem that I am raising. Surely, the field is beyond a determination of whether these methods are suitable? In summary, the paper in its current form provides little or no new twists for motor control and, moreover, it is not clear to me that it does for the technical aspects of the nonlinear measures. The paper raises the continuing embedding problem for the study question, nature of the data outcome and interpretation. and the specific implementation of NLD can influence interpretation, It almost seems that the authors are promoting the difficulty of broad based approaches to analysis given the individual nature of each data set and how this interacts with the analysis approach taken. There is no discussion of the likelihood given past motor control expts that mimicking /copying a movement pattern has different control regimens than a self-generated goal-seeking action. There is also a substantial active vs passive literature on movement control.

Reviewer 2

The manuscript entitled "Nonlinear methods to quantify Movement Variability in Human-Humanoid Interaction Activities" is an introduction to RQA for readers interested in human-machine interaction. I find the idea of analyzing human movement in the context of human-machine interaction interesting. The approach with RQA is also compelling. But these are the only positive things I can say about the manuscript. I think it cannot be published in its present form. The only way I can make sense of what's going on here is that the manuscript had been prepared initially for a very different kind of journal and then somehow made it to Sci Rep. A completely re-written version could be useful and interesting, and can give justice to the authors' ideas and hard work. My suggestion is to start from scratch and write the Intro and Discussion on human-humanoid interaction. Most of the current manuscript can be moved to a technical appendix to support the article. \newline

To get you started on a more theoretically grounded introduction to human-humanoid interaction, consider the following relevant literature. G. Dumas on the human dynamic clamp. Miyake on gait-cueing. Dotov and Froese on controlling dynamic systems. many other papers really. \newline

Major issues. \newline

• The manuscript is written as a tutorial on RQA. There are plenty of these tutorials out there, there's not much benefit in copy-pasting the equations in a new publication. Lookup Marwan's work, or Riley, Shockley, etc.. \newline

• There is no experiment strictly speaking, just some data was collected and then analyzed. \newline

• Consequently, there are no Results to report. We're just told to eyeball the figures that deal with how the analysis works, not really what we could learn about the task. Further analysis, as exploratory as it needs to be, could help you discover something interesting to report about the human-humanoid interaction, how it changes in response to a change in conditions. You need to find something useful that we can learn about human-humanoid interaction, not specifically about how RQA works, otherwise I don't see what's the point of publishing a bare tutorial. \newline

• There are serious issues with the writing style and grammar. Here are some examples from the abstract: \newline

Is it necessary for the first sentence to be that long? \newline Are you sure this applies to 'any given' motor task? \newline there are remain -> there remain \newline challenges on applying -> challenges to applying \newline To which twenty healthy ... not grammatical \newline an humanoid -> a humanoid \newline to found -> to find \newline I suppose you mean, we inspected the the RSSs and RPs for visual differences and analyzed statistically the RQAs. \newline ... quantify activities, sensors, window lengths, and smoothness? These categories are so unrelated, isn't it possible to focus on one or two? What smoothness? Why does it matter? \newline

• It is an unfortunately frequent mistake to state Takens' theorem without discussing how its application is constrained by assuming that the system in question is a smooth dynamic system with certain loose stationarity requirements (the manifold). A lot of the literature out there is hard to interpret because it doesn't make clear what exactly is the system that's being analyzed, assuming that RQA is a magic solution for all sorts of non-stationary signals. Since you've made the effort to write a tutorial-like manuscript, you might as well point the readers' attention to that problem.

Reviewer 3

This is an excellent methods paper that describes possible uses of several complex nonlinear dynamical systems analyses to time series data. Part of the goal of the paper is to highlight the potential uses of these methods to better understand motor variability patterns and their possible roles in diagnoses of nervous systems pathologies. The methods are well described, and their use well explained in the context of human-robot interactions using NAO, a well-known anthropomorphic robot with redundant degrees of freedom (DOF). In its current form however, the paper falls short of going beyond the narrow scope of serving as a methods paper. If this is what the authors intended, then the paper is better suited for a journal that more specifically deals with methods. Otherwise, if the authors are targeting a larger, more general audience, it will be important to broaden the scope of the paper and address some important issues with e.g., existing geometric models of redundant DOF that handle variability to diagnose and track treatment outcomes [1-3] with applications to robotics [4], other models of motor variability within a geometric framework [5, 6], that address pathologies of the nervous systems [7-9] and general literature on nonlinear dynamics approaches to issues with the nervous systems as they evolve across the lifespan [10-12] just to name a few. In its current form, the paper misses the opportunity to provide a link between motor control and disorders of the nervous systems, e.g., as they transition from neurodevelopmental to neurodegenerative, or as they differentiate between neuropsychiatric and neurological. It is possible to do so through motor variability [13]. Indeed, there are models of motor variability that do that already, but they are not discussed. Consequently, the reader cannot appreciate the relationships between embedding temporal dynamics parameters and capturing geometric and / or topological invariants in biorhythmic activities from the human nervous systems. Part of the missing information is the empirical ranges of parameters across different ages, as they shift across the human lifespan. Another aspect of the paper that misses an opportunity for further application of their results is that lack of characterization of the shared variability space between the human and the robot. What types of synergies self-emerge from the imitation/interaction and what time scales are necessary to make these interactions amenable to therapeutic use? Under what type of sampling resolution would it be possible to sense the robotic motions as an extension of the human motions, to make use of such interactions in more realistic mirroring ways. To that end, mirror systems may be something that the authors consider in their discussion of possible implications of the methods for therapeutic use. Given that these patterns of variations are bound to change from pathology to pathology, and differ in terms of amplitude vs. timing scales, how can one leverage these methods to characterize such interactions across ages and pathology types, e.g., autistic children vs. elderly with Parkinson’s disease vs. patients with neuropathy, etc. The ranges of variability change and the recruitment/release of DOF change as well. As such, the methods could be used to assess such differences, or to unveil commonalities across disorders and invariant aspects of the problem that transfer and generalize regardless of age or pathology type. These methods are known to the field, so there is no novelty element in their use. The novelty of the paper lies in their use with interactions between the humans and the robot. However, this aspect of the paper is not sufficiently developed to fully appreciate its potential. Twenty participants of a very homogeneous age 19.8 mean with 1.39 std are OK for a methods paper, but not so for a paper that has the potential to provide a broader scope of use. Likewise, the use of smoothing methods for data variability needs to be better justified, as there is physiologically relevant variability that tends to be smoothed out as noise and yet, in disorders of the nervous systems, bears the bulk of the information [14]. Which filters to use and how to preserve the original relevant information are open questions. In summary, this is an excellent methods paper to learn about a possible application of nonlinear dynamic systems approach to time series data from human motions during imitation of simple motions by a robot. It has the potential to add information about existing methods in the context of robot-human interactions. However, the authors are encouraged to expand their scope, better situate the paper in the extant literature of neuromotor control, particularly in relation to geometric models handling DOFs and methods that deal directly with motor variability in pathologies of the nervous systems.

Minor The authors are encouraged to have an English editor review the grammar and typos across the paper, including some figure descriptions e.g., page 7 describing “Due to space limitations and to have simple visualisation, we only present 10-sec (500 samples) window length time series for three participants (p01, p01 and p03) … (Figs 2C).” p01 is repeated

In the abstract, “While the analysis of movement of variability…” perhaps the authors mean “While the analysis of movement variability…”? “…performance evaluation, there are remain challenges on applying the most…” there remain challenges? etc., there are several awkward phrases throughout the paper, which is not written in the traditional formal of Nature papers either. References

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[mxochicale]

Dear Team at Scientific Reports Many thanks your reply and the valuable comments. Given the you took six months to made a decision from the submission on 30th of June 2021, I wonder if there is there a way that my work can be considered to be re submitted following the advice of the reviewers? Regards Miguel