-->PONE-D-25-41547-->-->THOI: An efficient and accessible library for computing higher-order interactions enhanced by batch-processing-->-->PLOS One

Dear Dr. BELLOLI,

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Academic Editor

PLOS One

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #1: Yes

Reviewer #2: Yes

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-->2. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: Yes

Reviewer #2: Yes

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-->3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: Yes

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-->4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: Yes

Reviewer #2: Yes

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-->5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: I found the present manuscript quite interesting, since it provides a very powerful tool to compute high-order interactions measures in complex systems, including the brain. The structure of paper is appropriate and figures are of great quality. Improvement in the performance of the proposed python library compared with other toolboxes in the literature is also very high. Therefore I recommend publication of the present manuscript

Reviewer #2: In this paper, Belloli et al. introduce a new toolbox for the efficient computation of higher-order information-theoretic measures. They not only evaluate its performance on simulated data, but also test it on multiple datasets, including human fMRI. This work represents a valuable contribution to the field, and I am highly supportive of its publication. I only have a few minor comments and questions that the authors may wish to address to improve the clarity of the narrative and the robustness of the paper.

1. Figure 2 (panels C–F) could be clearer. It took me some time to understand what these panels show, and I am still not entirely certain I interpreted them correctly. Does each line correspond to one of the 20 variables in the ground truth? For example, in panel E, does an interaction order of 40 mean that all blue variables contribute to minimizing \omega, while at an interaction order of 80 the variables shown in light red also contribute?

2. One aspect the authors could consider testing is the stability of these algorithms. If the algorithms were run multiple times, would they consistently identify the same subset that minimizes/maximizes \omega for a given interaction order?

3. In the analysis of the fMRI dataset, the authors could consider adding two panels to Figure 3 to show on the cortical surface which n-plets (brain regions) drive the statistically significant increases and decreases in \omega.

4. In the analysis of large databases of synthetic and real-world systems, the authors report correlations between features of the information-theoretic measures. How do the authors interpret the finding that several features (e.g., pro syn n-plets, order min \omega, and min \omega) are strongly anticorrelated across datasets?

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Reviewer #1: No

Reviewer #2: No

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THOI: An efficient and accessible library for computing higher-order interactions enhanced by batch-processing

PONE-D-25-41547R1

Dear Author,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Javed Iqbal, PhD

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #2: All comments have been addressed

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-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #2: Yes

**********

-->3. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #2: Yes

**********

-->4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #2: Yes

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-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #2: Yes

**********

-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #2: The authors carefully addressed all my comments, and I'm very happy to recommend this paper for publication.

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Reviewer #2: No

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