Smoothness Harmonic: A Graph-Based Approach to Reveal Spatiotemporal Patterns of Cortical Dynamics in fMRI Data
Round 1
Reviewer 1 Report
This paper proposed smoothness harmonic as a metric to capture the slow-varying cortical dynamics in fMRI data. Experiments were conducted on a real fMRI dataset and the difference between children and adults has been given. In general, this paper is not well-written and hard to follow.
1. The mathematical expressions are not rigid enough. e.g., Line87-90 is very difficult to follow. The notations should be correctly given.
2. It is not clear on how to compute the smoothness harmonics from eq. 1-2
3. In figure 2, the calculation V_t V_{k=1} V_t^T does not hold considering the size of the matrices.
4. what unique conclusion can be drawn from the proposed metric?
It is very necessary to improve the quality of English expression and the quality of mathematical expressions.
Author Response
Please see the attachment for detailed notes to address the raised issues by reviewers. Many Thanks for reviewing our work.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Appraisal: I found the article quite interesting. The first sentence of the introduction should be corrected. Indeed, the BOLD – fMRI is only one of the possible techniques that allowed to collect information about the “in vivo” functioning of human brain. Since other techniques such as ASL as considered fMRI, the sentence is conceptually wrong. Please take a look at “Borogovac, A., & Asllani, I. (2012). Arterial Spin Labeling (ASL) fMRI: advantages, theoretical constrains, and experimental challenges in neurosciences. International journal of biomedical imaging, 2012, 818456. https://doi.org/10.1155/2012/818456”. Moreover, I do not understand in which manner the BOLD signal is unidimensional. The author cites a paper about the translational neuroimaging with fMRI. Please clarify this statement.
The author compared adult and children, using two datasets. This subsection in the introduction should be theoretically founded. Indeed, reading the introduction I asked to my self “Why?”, but the author only refer the theory of mind.
In the paragraph 2.1 I suggest that you need to introduce the concept of smoothness harmonics as a possible solution for the dynamic graphs, since static graph are able to reduce computational costs.
I did not find any info about MNI152nlin2009ascym. Can you add a reference to check this atlas?
In the table 1 you reported the values of classification analysis and I agree about the SVM in order to establish independent classification . For smoothness harmonics overall is 0.46 because the 2 groups are not similar. However, I advise to discuss it.
“This opens up opportunities for its appli- 185
cation in various aspects of neuroscientific discovery, including the extraction of different 186
smoothness harmonics that could be linked to various neuropsychiatric disorders, and the 187
provision of fast and online neuro-feedback in clinical settings. “ This sentence needs to be reformulated overall about the neuro-feedback in clinical settings. I do not agree with this part of the sentence.
Please, check the English.
Author Response
Many Thanks for reviewing our work. Please see the attachment for the detailed response to raised issues.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
1. The author's response on comment 3 is still not correct. According to the response, f^T U_{k=1} is a Tx1 vector, which can not multiply f, a N x T matrix.
2. The author added a discussion section and claimed its novelty by comparing with other metrics. Also, in the introduction, the author claims that the proposed metric is better than the other static metrics. To support the statement, the author should additionally present the result of the other metrics on the same dataset, and show whether the proposed metric can achieve more prominent result.
Author Response
Dear Reviewer,
Please see the attached detailed response letter below as the attachment.
Many Thanks.
Author Response File: 
Author Response.docx
Reviewer 2 Report
I found the manuscript improved as I've requested.
In the manuscript I found some typos, please correct.
Author Response
Dear Reviewer,
Thank you so much for the quick response.
In the latest version of the manuscript, we have corrected found typo errors for acceptance.
Many appreciations in advance.
Round 3
Reviewer 1 Report
The revised version of the equation on L117,page 5 is still not rigorous, please revise it. The element-wise multiplication cannot be worked between two matrices with different size.
The quality of English is can be improved.
Author Response
Dear Esteemed Reviewer,
Firstly, we would like to express our gratitude for the insightful comments provided by the reviewer, which have greatly contributed to making our mathematical expressions more rigorous and robust. We have witnessed a significant improvement in the quality of our manuscript from the first revision to the current version, largely thanks to the valuable feedback provided by the reviewer.
Secondly, we sincerely apologize for the inappropriate usage of mathematical notations in [Now in Line 119, Page 5], which may have caused confusion for both the reviewer and potential readers. In the revised manuscript, we have made changes to ensure that the matrix sizes align for element-wise multiplication between U_{k=1} and f by using the broadcastable notation. This adjustment ensures that the output matrix's shape (after element-wise multiplication) becomes [N, T], facilitating further computations involving dot products.
Lastly, we have improved the overall quality of the English language in this manuscript through proofreading and formatting to enhance its readability and increase its chances of acceptance.
