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Dear Mr. Xu:

I am writing to you in regards to manuscript which you submitted to IEEE Access.

In view of the criticisms of the reviewer(s) found at the bottom of this letter, your manuscript has not been recommended for publication in IEEE Access.

We do encourage you to revise and resubmit your article once you have addressed the concerns and criticisms of the reviewers.  I believe they have added good insight on how to further improve your article.  IEEE Access has a binary peer review process that does not allow revisions. Therefore, in order to uphold quality to IEEE standards, an article is rejected even if it requires minor edits.


Please revise your manuscript based on reviewers¡¯ feedback and resubmit; elaborate on your points and clarify with references, examples, data, etc. If you do not agree with the reviewers¡¯ views, then include your arguments in the updated manuscript. Also, note that if a reviewer suggested references, you should only add ones that will make your article better and more complete. Recommending references to specific publications is not appropriate for reviewers and you should report excessive cases to ieeeaccessEIC@ieee.org.

Please be advised that authors are only permitted to resubmit their article ONCE. If the updated manuscript is determined not to have addressed all of the previous reviewers¡¯ concerns, the article may be rejected and no further resubmissions will be allowed.

When resubmitting, please submit as a new manuscript and include the following 3 files:

1)        A document containing your response to reviewers from the previous peer review.  The ¡°response to reviewers¡± document (template attached) should have the following regarding each comment: a) Reviewer¡¯s concern, b) your response to the concern, c) your action to remedy the concern. The document should be uploaded with your manuscript files as a ¡°Supplemental File for Review.¡±
2)        Your updated manuscript with all your individual changes highlighted, including grammatical changes (e.g. preferably with the yellow highlight tool within the pdf file). This file should be uploaded with your manuscript files as a ¡°Supplemental File for Review¡±.
3)        A clean copy of the final manuscript (without highlighted changes) should be submitted as the ¡°Formatted (Double Column) Main File ¨C PDF Document Only.¡±

Finally, in your cover letter, please indicate if you would like us to assign your article to the same or different reviewers and we will do our best to accommodate your request.

We sincerely hope you will update your manuscript and resubmit soon. Please contact me if you have any questions.

Thank you for your interest in IEEE Access.




Reviewer(s)' Comments to Author:

Reviewer: 1

Recommendation: Accept (minor edits)

Comments:
Daer authors
kindly incorporated all changes and mention in comments

Additional Questions:
Does the paper contribute to the body of knowledge?: yes

Is the paper technically sound?: yes

Is the subject matter presented in a comprehensive manner?: yes

Are the references provided applicable and sufficient?: yes


Reviewer: 2

Recommendation: Accept (minor edits)

Comments:
I suggest to the authors to investigate the following points: a) The proposed solution does not take into account scoring features. The proposed model may be evolved in order to consider ranking expressions based on a similarity score. b) Adopting an inverted index data structure with conjunction (AND) operations of inverted lists could be used to implement Algorithm 2. You could investigate if this is a better approach regarding to retrieval performance.

Additional Questions:
Does the paper contribute to the body of knowledge?: Despite of presenting concluding experimental results and presenting related work discussion, the paper does not clearly present and discuss the main (relevant) difference of the proposed work (namely, contributions) regarding to previous work.

Is the paper technically sound?: The paper presents the modeling of the solution clearly discussing applied algorithms and data structures. Besides, the paper presents conducted experimental evaluation with preliminary interesting results.

Is the subject matter presented in a comprehensive manner?: Yes, it is. The paper is well organized: it presents the problem, the proposed and modeling of solution, and finally, an experimental evaluation. Regarding to visual layout aspects, the paper reading flow should be verified in order to make the reader to read entirely the left column before start reading the right column. For instance, look at page 4: because of the confusing layout, I read the section III.B before the section III.A.

Are the references provided applicable and sufficient?: Yes, they are. Most of the references are updated.


Reviewer: 3

Recommendation: Accept (minor edits)

Comments:


This paper presents a math retrieval method based on operator information which has higher retrieval efficiency and wider retrieval range. The reviewer assumes some improvements are still needed in this paper. Please see comment below:

Abstract
¡¤        There are some English usage problems which might confuse the readers.



Iv. Experimental results and analysis
¡¤        Viewing the experiment results in Table V, large number of similar expressions would be retrieved if the target expression is a simple expression. Should this be considered a shortcoming of the proposed method? It would be difficult to locate the exact position of the target expression.
¡¤        TABLE VII. The authors should also give the retrieval time comparison between the two methods.

Other problems:
¡¤        Please see the attached pdf file to revise some other errors.



Additional Questions:
Does the paper contribute to the body of knowledge?: Yes. The authors proposed a math retrieval method based on operator information which has higher retrieval efficiency and wider retrieval range. The proposed method shows excellent performance in retrieving complex-structure expressions.

Is the paper technically sound?: Yes. The FDS Analysis process, the skeleton storage process and mathematical expression matching algorithm are given in detail.

Is the subject matter presented in a comprehensive manner?: There are some English usage problems in the Abstract and Introduction part where some sentences are confusing. Please see the attached pdf file.

Are the references provided applicable and sufficient?: The reviewer assumes some references are unnecessary and should be substituted with more related ones.


Reviewer: 4

Recommendation: Reject (do not encourage resubmit)

Comments:
This paper proposes a retrieval method for mathematical formulas.
The problem that this paper tackles is comprehensively reviewed. The representation method is clearly described.

The paper seems to have the following three major defects:

1. Requirement of the retrieval:
The requirement which this paper tries to satisfy seems to be clear described. This requirement results in the usage of only operators. The authors should emphasize the kind of retrieval, which existing methods cannot support, and the proposed method supports.

2. Algorithm:
Algorithm 2, the retrieval algorithm, has the complexity of O(N), where N is the number of mathematical formulas. This is a kind of full search. The retrieval performance could not be tolerable for the large number of formulas. The retrieval algorithm often used has the complexity of O(log(N)). The binary search, a fundamental search method, is an example. The authors had better propose the retrieval method having the O(log(n)) complexity. A way is using index structures, B tree, or B+ tree for one dimensional data, or R tree, R* tree, or k-d tree for multi-dimensional data. These index structures bring the authors the O(log(N)) algorithm.

3. Performance evaluation:
The paper does not include the retrieval performance evaluation. The times in the retrieval should be measured by varying the number of formulas. The proposed algorithm should be compared with other methods including MIaS.

Additional Questions:
Does the paper contribute to the body of knowledge?: No.
No contribution could be found in the paper.

Is the paper technically sound?: No.
The retrieval method proposed does not have the technique enough to be accepted.
The representation method proposed is not clear.

Is the subject matter presented in a comprehensive manner?: Partially, no.
The subject treated is the retrieval of mathmatecal foumulas. The requirement of the retrieval is not clearly described. The retrieval, where the proposed method is required, is not clearly described.

Are the references provided applicable and sufficient?: Partially, no.
References for the representation of mathematical formulas are considered to be enough. References for the retrieval method and the access method including index structures are not included in the paper.
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