Constructing an Evolutionary Tree and Path–Cycle Graph Evolution along It
Round 1
Reviewer 1 Report (New Reviewer)
This paper presents novel algorithms to solve the problem of constructing an evolutionary tree and the evolution of structures along it. The first algorithm outputs a tree with the minimum sum of the cost of embedding into it and the cost of embedding it into a given network. The second algorithm provides a minimum embedding of a tree into a network, taking into account incomplete linear sorting. The third algorithm reconstructs given structures on any two-star tree, while the fourth algorithm reduces the problem of DCJ reconstruction of given structures on any star to a logarithmic-length sequence of SAT problems. The paper includes explanatory illustrations, such as flowcharts, and numerical examples to help clarify the concepts.
Page 2, lines 54-56: What does this mean? Does this mean that the first problem involves creating a new tree that represents an "average" between a given tree and a given network? This is done by finding the tree that minimizes a given functional, which assigns a value to each possible tree of a fixed size. The goal is to find the tree that minimizes this value, which will be the best representation of the "average" between the two given structures. Please elaborate.
Page 2, lines 56-59: What does this mean? Does this mean that the second problem aims to explain how structures that are defined at the leaves of a tree evolve over time by continuing onto internal nodes of the tree? The continuation of these structures is determined by finding the arrangement that minimizes a given functional, which is defined for all possible arrangements along the tree. Essentially, the goal is to find the best possible way for the structures to evolve along the tree. Please elaborate.
Page 2, line 79: Please write “SAT (Boolean satisfiability problem)”.
Page 4, lines 146-148: Why so? Is your use of mathematical interpretations in embedding related to your inspiration from biological paradigms such as the evolution of genomes and genomic rearrangement?
Page 26, line 1003: Please write “SCJ (Single-Cut-or-Join)”. The SCJ distance is a measure of the evolutionary distance between two structures and is used to construct evolutionary trees and infer evolutionary relationships. The lower the SCJ distance between two structures, the more closely related they are thought to be in terms of their evolutionary history. Please elaborate.
Page 27, line 1010: Please write “DCJ (Double-Cut-and-Join)”.
Page 27, line 1025: Is “Double intermerging” the same as “DCJ (Double-Cut-and-Join)”?
Page 30, line 1161: Please explain the matching? Finding a subset of edges in a graph where no two edges share a common vertex.
Page 39: What are the concrete implications of your work? Please comment on that in the discussion.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report (New Reviewer)
The paper looks like a tutorial paper and novelty and research contribution is very minimal.
The problem description is not defined properly
Recent related literature is missing. For example, only each one article is cited in the years of 2022, 2021 and 2020.
Also many algorithms were existing for constructing an intermediate tree and the suggested algorithm is derived from the existing algorithm and it is not cited.
In most of the diagrams, authors mentioned as block diagram, but it is the flow chart.
Conclusion is also not properly arrived.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report (New Reviewer)
This manuscript Mathematics-1872620 proposed an exact cubic-time algorithm which outputs a tree with the minimum sum of the cost of an embedding into it and the cost of embedding it into a given network (theorem 1). The authors construct an algorithm that outputs a minimum embedding of a tree into a network taking into account incomplete linear sorting; the algorithm depends linearly on the number of nodes in the network and is exact if the sorting cost is not less than the sum of the duplication cost and the loss cost (theorem 2). The authors construct an exact approximately quadratic-time algorithm which, for arbitrary costs of SCJ operations, solves the problem of reconstruction of given structures on any two-star tree (theorem 3). The authors construct an exact algorithm which reduced the problem of DCJ reconstruction of given structures on any star to a logarithmic-length sequence of SAT problems, each of them being of approximately quadratic size (theorem 4). The theorems have rigorous and complete proofs of correctness and complexity of the algorithms, and are accompanied by numerical examples and numerous explanatory illustrations, including flowcharts. I feel the experiment results are sufficient. It was a pleasure reviewing this work and I can recommend it for publication in Signal Processing: Image Communication after a minor revision. I respectfully refer the authors to my comments below.
1. The English needs to be revised throughout. The authors should pay attention to the spelling and grammar throughout this work. I would only respectfully recommend that the authors perform this revision or seek the help of someone who can aid the authors.
2. (Section 1, General Introduction) The contribution of this work should be summed as several points in the last paragraph.
3. (Page 3, Section 1 General Introduction, Last paragraph) The reviewer suggests authors add a paragraph to describe the organization of this work, such as “The rest of this article is organized as follows. Section 2 …..”.
4. (Section 1. General Introduction) The reviewer suggests authors don't list a lot of related tasks directly. It is better to select some representative and related literature or models to introduce with certain logic. For example, the latter model is an improvement on one aspect of the former model.
5. (Page 1, Section 1- General Introduction, the Paragraph I) The original statement is suggested to revised as “Tree graphs arise very widely, both in fundamental problems of discrete mathematics and in applied problems from very different subject areas. (such as: gmdl: toward precise head pose estimation via gaussian mixed distribution learning for students’ attention understanding;; mfdnet: collaborative poses perception and matrix fisher distribution for head pose estimation)”
6. The reviewer suggests authors add some formal descriptions of the proposed model (Proof of Theorem 1), such as loss functions and its optimization processing, so that the reader can better understand the process.
7. (Page 10, Figure 8) The reviewer suggests authors introduce clearly the block diagram of Figure 8 (in the body or in the picture description).
8. (Figures 9-11) Experimental pictures or tables should be described and the results should be analyzed in the picture description so that readers can clearly know the meaning without looking at the body.
9. (Page 4) Original statement is suggested to revised as “Evolution analysis is one of the most fundamental mathematical problems, having at the same time a broad practical importance [*]. (carm: confidence-aware recommender model via review representation learning and historical rating behavior in the online platforms;; anisotropic angle distribution learning for head pose estimation and attention understanding in human-computer interaction), (flexible ftir spectral imaging enhancement for industrial robot infrared vision sensing), (edmf: efficient deep matrix factorization with review feature learning for industrial recommender system).”.
10. The authors are suggested to add some experiments with the methods proposed in other literatures, then compare these results with yours, rather than just comparing the methods proposed by yourself on different models. At least four comparing methods on two public datasets.
11. Please add some experiment to discuss the advantage of Path-Cycle Graph Evolution.
12. Please add references published in Mathematics (this journal).
My overall impression of this manuscript is that it is in general well-organized. The work seems interesting and the technical contributions are solid. I would like to check the revised manuscript again.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report (New Reviewer)
Thank you for the updates.
Reviewer 2 Report (New Reviewer)
The revised manuscript is revised well as compared to the previous version. My comments are addressed well. Hence, I am recommending to accept this manuscript.
Reviewer 3 Report (New Reviewer)
The revised manuscript is improved compared to the former version. My previous comments are well addressed, and the presentation is improved significantly. The composition pattern and some other ideas are well elaborated, making them clearer. Overall, I tend to accept this manuscript.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
· I propose to define range of application of proposed approach. Tree graphs can be apply for classification problem and well-known methods for constructing graph trees, such as the ID3 algorithm, use attributes and their values to create nodes and edges in graphs. In alpha mapping (page 6 line 212) it is necessary add some nodes and its values, not for each classification problem it is possible.
· In graph transformation into pipe how nodes and edges should be interpreted?
· According to Figure 14, the edges can be joint, so how to interpret it?
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
I feel the study has some novelty like the case study, portion of the methodology, but it is not presented reasonably well.
I suggest the author be given a second chance to amend the article and add some paragraphs in the introduction, write a more appropriate literature review, methodology, results, and discussion. Bring along more proof, texts describing the results, analysis of the achieved results, and those published already. The paper, in its current form, is like a concise technical report with known techniques rather than an article for a scholarly international journal. I suggest the authors spend more time and prepare a better version. in this step i would request for major correction
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper aim at constructing an exact cubic-time algorithm, which outputs a tree with the minimum, sum 8 of the cost of an embedding into it and the cost of embedding it into a given network.
The main contributions and strengths of the manuscript the construction of a structure to that gives loaded directed graph consisting of paths (a path-cycle graph).
However, the authors did not follow the general rule of writing a manuscript.
1. However, the title of the manuscript is not appropriate/clear and should be well crafted. The title is do clear, hence the need to adjust it.
2. The abstract is not properly written also it does not contain and follow the format of a general abstract. See the author guideline of this journal
3. The manuscript is not well structured, has only 3 section.
4. The contains of the manuscript are not well cited. The first citation is on page 5 line 183. Do it mean all other ideas and concept before then were the authors?
5. The general organization of the manuscript is not in an accepted format. There is need for the author to study the journal author guideline and follow the format.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
author did not provide any respond to the reviewers and it is difficult to follow the corrections. so i will send back the paper for another revision.
