[REVIEW]: Interplay between Chaos and Stochasticity in Celestial Mechanics

[whedon]

Submitting author: !--author-handle-->@matteoettam09<!--end-author-handle-- (Matteo Manzi) Repository: https://github.com/matteoettam09/FTLE.jl Branch with paper.md (empty if default branch): Version: Editor: !--editor-->@carstenbauer<!--end-editor-- Reviewers: @dawbarton, @Datseris Archive: Pending

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Review checklist for @dawbarton

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• [x] As the reviewer I confirm that I have read the JuliaCon conflict of interest policy and that there are no conflicts of interest for me to review this work.

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General checks

• [x] Repository: Is the source code for this software available at the repository url?
• [x] License: Does the repository contain a plain-text LICENSE file with the contents of an OSI approved software license?
• [x] Authorship: Has the submitting author (@matteoettam09) made major contributions to the software? Does the full list of paper authors seem appropriate and complete?

Functionality

• [ ] Installation: Does installation proceed as outlined in the documentation?
• [ ] Functionality: Have the functional claims of the software been confirmed?
• [ ] Performance: If there are any performance claims of the software, have they been confirmed? (If there are no claims, please check off this item.)

Documentation

• [ ] A statement of need: Do the authors clearly state what problems the software is designed to solve and who the target audience is?
• [ ] Installation instructions: Is there a clearly-stated list of dependencies? Ideally these should be handled with an automated package management solution.
• [ ] Example usage: Do the authors include examples of how to use the software (ideally to solve real-world analysis problems).
• [ ] Functionality documentation: Is the core functionality of the software documented to a satisfactory level (e.g., API method documentation)?
• [ ] Automated tests: Are there automated tests or manual steps described so that the function of the software can be verified?
• [ ] Community guidelines: Are there clear guidelines for third parties wishing to 1) Contribute to the software 2) Report issues or problems with the software 3) Seek support

Paper format

• [ ] Authors: Does the paper.tex file include a list of authors with their affiliations?
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• [ ] Page limit: Is the page limit for extended abstracts respected by the submitted document?

Content

• [ ] Context: is the scientific context motivating the work correctly presented?

• [ ] Methodology: is the approach taken in the work justified, presented with enough details and reference to reproduce it?

• [ ] Results: are the results presented and compared to approaches with similar goals?

  Review checklist for @Datseris

  Conflict of interest

• [x] As the reviewer I confirm that I have read the JuliaCon conflict of interest policy and that there are no conflicts of interest for me to review this work.

Code of Conduct

• [x] I confirm that I read and will adhere to the JuliaCon code of conduct.

General checks

• [x] Repository: Is the source code for this software available at the repository url?
• [x] License: Does the repository contain a plain-text LICENSE file with the contents of an OSI approved software license?
• [x] Authorship: Has the submitting author (@matteoettam09) made major contributions to the software? Does the full list of paper authors seem appropriate and complete?

Functionality

• [ ] Installation: Does installation proceed as outlined in the documentation?
• [ ] Functionality: Have the functional claims of the software been confirmed?
• [ ] Performance: If there are any performance claims of the software, have they been confirmed? (If there are no claims, please check off this item.)

Documentation

• [ ] A statement of need: Do the authors clearly state what problems the software is designed to solve and who the target audience is?
• [ ] Installation instructions: Is there a clearly-stated list of dependencies? Ideally these should be handled with an automated package management solution.
• [ ] Example usage: Do the authors include examples of how to use the software (ideally to solve real-world analysis problems).
• [ ] Functionality documentation: Is the core functionality of the software documented to a satisfactory level (e.g., API method documentation)?
• [ ] Automated tests: Are there automated tests or manual steps described so that the function of the software can be verified?
• [ ] Community guidelines: Are there clear guidelines for third parties wishing to 1) Contribute to the software 2) Report issues or problems with the software 3) Seek support

Paper format

• [x] Authors: Does the paper.tex file include a list of authors with their affiliations?
• [x] A statement of need: Do the authors clearly state what problems the software is designed to solve and who the target audience is?
• [x] References: Do all archival references that should have a DOI list one (e.g., papers, datasets, software)?
• [x] Page limit: Is the page limit for extended abstracts respected by the submitted document?

Content

• [x] Context: is the scientific context motivating the work correctly presented?
• [ ] Methodology: is the approach taken in the work justified, presented with enough details and reference to reproduce it?
• [ ] Results: are the results presented and compared to approaches with similar goals?

[whedon]

Hello human, I'm @whedon, a robot that can help you with some common editorial tasks. @dawbarton, @Datseris it looks like you're currently assigned to review this paper :tada:.

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[carstenbauer]

@whedon generate pdf

[whedon]

Failed to discover a Statement of need section in paper

[whedon]

Wordcount for paper.tex is 858

[whedon]

:point_right::page_facing_up: Download article proof :page_facing_up: View article proof on GitHub :page_facing_up: :point_left:

[whedon]

Software report (experimental):

github.com/AlDanial/cloc v 1.88  T=0.08 s (279.6 files/s, 139678.4 lines/s)
-------------------------------------------------------------------------------
Language                     files          blank        comment           code
-------------------------------------------------------------------------------
SVG                              1              0              0           7144
TeX                              8            246            188           2399
Julia                           10            183            178            529
Ruby                             1              8              4             45
Markdown                         1             17              0             29
YAML                             1              0              0             22
-------------------------------------------------------------------------------
SUM:                            22            454            370          10168
-------------------------------------------------------------------------------

Statistical information for the repository '9f658cf947335d2ff50f888e' was
gathered on 2023/01/09.
The following historical commit information, by author, was found:

Author                     Commits    Insertions      Deletions    % of changes
mmanzi95                         1            57              0          100.00

Below are the number of rows from each author that have survived and are still
intact in the current revision:

Author                     Rows      Stability          Age       % in comments
mmanzi95                     57          100.0          0.0                7.02

[whedon]

Reference check summary (note 'MISSING' DOIs are suggestions that need verification):

OK DOIs

- 10.2139/ssrn.4041723 is OK
- 10.1016/0370-1573(79)90023-1 is OK
- 10.1007/978-3-540-85146-2 is OK
- 10.1017/9781108768900 is OK
- 10.1142/S0218127416300366 is OK
- 10.1142/S0218127416300366 is OK
- 10.1007/978-94-009-7793-8_19 is OK

MISSING DOIs

- None

INVALID DOIs

- None

[whedon]

:point_right::page_facing_up: Download article proof :page_facing_up: View article proof on GitHub :page_facing_up: :point_left:

[whedon]

:wave: @Datseris, please update us on how your review is going (this is an automated reminder).

[whedon]

:wave: @dawbarton, please update us on how your review is going (this is an automated reminder).

[Datseris]

Hello, I'd like to submit my review. At the moment, I think this paper needs major revisions, according to the comments:

• The software repository does not have documentation. According to my checklist, such a documentation is necessary. I can't tick of many checks without a documentation. I'd recommend the authors to go through the checklist I have to tick-off as a reviewier, and ensure the things that are demanded there exists on the repository, including installation instructions, examples, etc. Once a documentation is in place, I will go through installation and running to also tick the remaining boxes that are about the source code.
• The paper is rather short, however it treats topics that are not really straight forward. The definition of chaos for stochastic systems is a rather involved topic and, since the authors here seem to provide such a definition, they need to be clear about what it means and why one should use this over other alternatives. Specifically:
  • This is the first time I hear about the "Cauchy-Green strain tensor", and I have not seen it before used to compute Lyapunov exponents. The construct has to be related to the established Λ matrix of Oseledets or some other established construct. (Oseledets matrix: https://en.wikipedia.org/wiki/Lyapunov_exponent#Definition_of_the_Lyapunov_spectrum )
  • What does it mean to compute the derivative of x with respect to x0 in Equation 3? By the very definition of deterministic chaos, such a function does not exist in the analytic sense. How do the authors compute this derivative in practice? Generally speaking, at the moment it is unclear to me how the authors actually compute the things they compute. I should be able to figure out how they do this without having to look at the source code.
  • Is this derivative valid in the context of stochastic equations? In which sense? If the authors have not checked for that in the analytic sense, then they should be clear that they simply apply the same numerical algorithm in some timeseries X irrespectively of the origins, i.e., without considering whether the derivative exists.
  • Assuming we apply this function to a deterministic system, is it different from the existing function local_growth_rates that exists in DynamicalSystems.jl and provides finite time lyapunov exponents? If it is different, how?
  • Are there alternative ways to compute Lyapunov exponents for stochastic systems? If yes, the authors should compare to the alternative ways.
• Most plots in the paper do not have colorbars even though they are colormaps. This needs to be fixed.

[dawbarton]

Just to add to Datseris' review -

• Not only are there no installation instructions, there doesn't really seem to be any software either. The repository is not set up as a package and the src folder appears to only contain demos. The method described just seems to be the lines

  Delta = transpose(dzt_dz0)*dzt_dz0
  eig_val = eigen(Delta).values
  FTLE[j, i] = 1/T * log(sqrt(maximum(eig_val)))

As it stands, I'm not sure why this should be published.

[carstenbauer]

Hey @matteoettam09, please take a look at the reviews by @Datseris and @dawbarton. They've both expressed that a major revision of the paper / the repository is necessary. It would be great if you could comment on the raised criticism and could decide whether you want to move forward with this.

[matteoettam09]

Hello @carstenbauer, @Datseris, @dawbarton.

Sorry, for the late feedback.

In order:

• we underestimated the requirements, from a software development point of view, for the short paper requirements.
• Cauchy-Green strain tensor: there is a vast literature in fluid dynamics (e.g., http://georgehaller.com/publications/index.html) and celestial mechanics (e.g., https://dart.polimi.it/publications/) making use of this tensor for chaotic motion evaluation using numerical propagation, It's just a matter of nomenclature: the state transition matrix is the Y matrix in the wikipedia page, and instead of the 1/2 we have a squared root in the logarithm. Also, as we are interested only in the maximum eigenvalue of the spectrum to evaluate chaotic behaviour, we perform the eigendecomposition before.
• As to if the limit is defined for stochastic differential equations and the comparison with existing ways of computing the Lypaunov spectrum for sde, we didn't discuss that, given the two pages limit.
• About the computation, we integrate numerically the variational equations of the dynamical systems (which we can derive analytically), so nothing qualitatively different from the original ode/sde.
• So yes, this derivative is valid in the context of stochastic equations, as the stochastic process is not a function of the initial condition, only the state-dependent volatility.

We currently don't have the time resources to move forward with this, sorry, hopefully someone reading this thread read the work, its pain points and push it forward.

[carstenbauer]

Alright, I'm closing for the reasons above. In any case, thanks @Datseris @dawbarton for your reviews!

[lucaferranti]

@editorialbot reject

[editorialbot]

Paper rejected.