Supportive consensus

A. Palomares; M. Rebollo; C. Carrascosa

doi:10.1371/journal.pone.0243215

Peer Review History

Original SubmissionJuly 8, 2020
24 Jul 2020 Decision Letter - Fei Chen, Editor PONE-D-20-21157 Supportive Consensus PLOS ONE Dear Dr. Palomares Chust, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. The associate editor received two consistent reviews. Both reviewers suggested that a major revision of the manuscript is needed before it can be accepted for publication. They also pointed out that the paper contains numerous grammatical mistakes and typos. Reviewer 1 suggested that the contribution of this paper should be highlighted. S/He also pointed out that the assumptions should be stated explicitly, and the convergence rate should be established. Reviewer 2 raised very specific comments regarding the presentation of the paper. Overall, I think this paper would be acceptable for publication if the above points are addressed convincingly, which would require a substantial revision. I therefore recommend major revision and re-review for this manuscript. Please submit your revised manuscript by Sep 07 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols We look forward to receiving your revised manuscript. Kind regards, Fei Chen Academic Editor PLOS ONE Journal Requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf 2. Please upload a copy of Figure ??, to which you refer in your text on page 16. If the figure is no longer to be included as part of the submission please remove all reference to it within the text. Additional Editor Comments (if provided): The associate editor received two consistent reviews. Both reviewers suggested that a major revision of the manuscript is needed before it can be accepted for publication. They also pointed out that the paper contains numerous grammatical mistakes and typos. Reviewer 1 suggested that the contribution of this paper should be highlighted. S/He also pointed out that the assumptions should be stated explicitly, and the convergence rate should be established. Reviewer 2 raised very specific comments regarding the presentation of the paper. Overall, I think this paper would be acceptable for publication if the above points are addressed convincingly, which would require a substantial revision. I therefore recommend major revision and re-review for this manuscript. [Note: HTML markup is below. Please do not edit.] 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 ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: No Reviewer #2: Yes ****** 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. Reviewer #1: Yes Reviewer #2: Yes ****** 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 ****** 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: This paper proposes multiple supportive consensus algorithms for multi-agent systems where each agent has a set constraint. Especially, the authors consider the case that there is no intersection among the set constraints of all the agents. The topic is interesting. However, it seems that this paper is not well-written. My comments are as follows. 1) There are many grammatical mistakes in this paper. For example, in page 1 line 2, it should be “to deal with” instead of “to dealing with”. In page 1 line 14, it should be “must obtain” instead of “must to obtain”. Please check the whole paper carefully to correct all the grammatical mistakes. 2) In page 3 line 80, the authors state the contributions of this paper in this paragraph. However, the introduction of the contributions is a little pale. I suggest presenting a more detailed introduction to the contributions here. For example, what algorithms do you propose? What are the differences between these proposed algorithms? How do you analyze the algorithms? How do you verify the effectiveness of the proposed algorithms? 3) The assumptions of the proposed algorithms should be stated clearly. For example, can the proposed algorithm work under directed graphs? Is the underlying graph required to be connected? Can the proposed algorithms work under arbitrary initial conditions? 4) The goals of these proposed algorithms should be stated clearly. Why do you need multiple algorithms to solve the same problem? What are the pros and cons of each algorithm? 5) Convergence properties of the proposed algorithms should be stated clearly. For example, what is the convergence rate? What are the exact convergent values? Reviewer #2: This paper presents an innovative kind of consensus, named as the Supportive Consensus. All the agents considered in this work may have their acceptable values bounded, and the classical consensus mean value is outside of the boundaries of some agents. For such case, the classical consensus is unable to give a solution while the Supportive Consensus protocol can. The idea of this work is novel, while the composition of the paper is terrible. (1) It is suggested that the body of each graph appear with its corresponding title such Figure 4, 5, and the others. (2) It is suggested that we call them table rather than figure for the Figures 1,2,3 in the current manuscript. (3) The definition of degree, which is used in line 117, is suggested to be provided in this work. Moreover, it is suggested that both the in-degree and the out-degree are provided. (4) The section number is left in line 179, “, as defined in Section .”. (5) The usage of ${{x}_{i}}(t)$ is not appropriate in lines 182, 184 and 186. As we know, ${{x}_{i}}(t)$ is the state of node $i$, and it is not the consensus value. (6) There are many redundant “=” in the equation below line 285. (7) The English should be improved since there are many grammatical problems such as “This paper presents a novel approach to dealing with…”(line 2), “, and we proof that if …”(line 22). There is no need to indent the beginning of some paragraphs such as the paragraphs on line 119 and line 124. ****** 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review?** For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No Reviewer #2: No [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. https://doi.org/10.1371/journal.pone.0243215.r001
Revision 1
9 Nov 2020 Author Response November 6, 2020 Fei Chen Academic Editor PLOS ONE Subject: Submission of revised paper PONE-D-20-21157, ’Supportive Consensus’. Dear Dr. Chen, Thank you for your e-mail dated 24th July 2020, enclosing the reviewers’ comments. We have carefully reviewed the comments and have revised the manuscript accordingly. Our responses are given in a point-by-point manner below. Changes to the document are shown in blue. We have rechecked the language, and the mistakes detected in the reading proof corrected. The paper’s contribution has been improved in a new section that explains the main results and the di.erences between the approaches we propose. Regarding the convergence analysis, we have included a new section that demonstrates the solution in a scenario with perfect information regarding the solution obtained by the algorithms. The convergence of those algorithms is ensured by the original work of Olfati–Saber and Murray, in which we base our proposal. As the algorithms match the requirements, stability is ensured. We have highlighted this fact in the paper too. The rest of the observations have been appropriately addressed, in our opinion. We hope the revised version is now suitable for publication and look forward to hearing from you in due course. Sincerely, Dr. Alberto Palomares . Associate Professor Universitat Politecnica de Valencia (Spain) Response to reviewer 1 Thank you for your review of our paper. We have answered each of your points below 1. There are many grammatical mistakes in this paper. For example, in page 1 line 2, it should be ”to deal with” instead of ”to dealing with”. In page 1 line 14, it should be ”must obtain” instead of ”must to obtain”. Please check the whole paper carefully to correct all the grammatical mistakes. We have rechecked the language. The mistakes indicated by the reviewer have been corrected, and some others detected in the reading proof. 2. In page 3 line 80, the authors state the contributions of this paper in this paragraph. However, the introduction of the contributions is a little pale. I suggest presenting a more detailed introduction to the contributions here. For example, what algorithms do you propose? What are the differences between these proposed algorithms? How do you analyze the algorithms? How do you verify the effectiveness of the proposed algorithms? We have included in the Scope section a broader explanation detailing the information required by the reviewer. In this part, we have described the algorithm, explain their differences in the approach to the supportive consensus problem, and the experiments to evaluate their performance and the quality of the solutions they reach. 3. The assumptions of the proposed algorithms should be stated clearly. For example, can the proposed algorithm work under directed graphs? Is the underlying graph required to be connected? Can the proposed algorithms work under arbitrary initial conditions? We have clarified these characteristics of the network in its definition. We assume that the consensus process runs over a non-directed, strongly connected network. Algorithms could be extended to the directed case but keeping the connection condition. ”Let G = {V, E} an undirected, strong connected graph with n nodes, V = {1, ..., n}, and e edges E . V × V , where (i, j) . E if there exists a link between nodes i and j.” Regarding the initial condition, the only consideration is that all the nodes must begin inside their ranges (see explanation after Eq. 21) We have remarked this fact. ”In general, assuming that the initial values of all agents (t=0) are within their bounds, the network globally always (t) has the capacity to compensate the total amount of values[. . . ]” 4. The goals of these proposed algorithms should be stated clearly. Why do you need multiple algorithms to solve the same problem? What are the pros and cons of each algorithm? We have added a paragraph at the beginning of the section ’Supportive Consensus Algorithms Proposal’ explaining the goals and the reasons for the different algorithms. 2 ’The algorithm that we have called SEA[. . . ]’ Furthermore, we have included a section ’Algorithm Summary’ summarizing the pros and cons of the proposed algorithms. 5. Convergence properties of the proposed algorithms should be stated clearly. For example, what is the convergence rate? What are the exact convergent values? We have included a new section that calculates the solution in a scenario with perfect information regarding the solution obtained by the algorithms. We have considered the centralized solution as the exact solution. The results obtained by the algorithms are approximations of this value. The convergence of the proposed algorithms is ensured by the original work of Olfati–Saber and Murray in which we base our proposal. As the algorithms match the requirements, stability is ensured. We have highlighted this fact in the paper, too, related to the sum conservation. ’As Algorithm conserves the sum of the initial values and fulfil the conditions of the Olfati–Saber consensus algorithm to converge,(Footnote: The convergence ...) we need to ensure that the Supportive Consensus function also conserves the sum. We check this condition in each one of the proposed algorithms.’ Response to reviewer 2 Thank you for your comments. Our answers to your points are as follow 1. It is suggested that the body of each graph appear with its corresponding title such Figure 4, 5, and the others. Following the submission rules of PLOS, figures have to be moved to the end of the paper and keep the captions in place. 2. It is suggested that we call them table rather than figure for the Figures 1,2,3 in the current manuscript. These figures contain both the table and the .figure, and as in the previous consideration. They appear at the end of the document. 3. The definition of degree, which is used in line 117, is suggested to be provided in this work. Moreover, it is suggested that both the in-degree and the out-degree are provided. We have included the definition of the degree of the network ” In graph theory, the degree of a node di is the number of edges that are incident to the node, and therefore \|Ni\| = di.”. As we assume a non-directed network, the definition of in-and out-degree are not necessary. 4. The section number is left in line 179, ”, as defined in Section .”. We have included the name of the section in the reference (Background) 5. The usage of xi(t) is not appropriate in lines 182, 184 and 186. As we know, xi(t) is the state of node i, and it is not the consensus value. We do not make any difference between the state of the node and its value and we use both as synonyms. The value xi(t) is the only information stored in the nodes. Its value is defined and bounded in equation 5. 6. There are many redundant ”=” in the equation below line 285. We have removed the equal signs at the end of each line of equation 5 7. The English should be improved since there are many grammatical problems such as ”This paper presents a novel approach to dealing with...” (line 2), ”, and we proof that if ...” (line 22). There is no need to indent the beginning of some paragraphs such as the paragraphs on line 119 and line 124. We have rechecked the language. The mistakes indicated by the reviewer have been corrected, and some others detected in the reading proof. Attachments Attachment Submitted filename: Response to Reviewers.pdf https://doi.org/10.1371/journal.pone.0243215.r002
18 Nov 2020 Decision Letter - Fei Chen, Editor Supportive Consensus PONE-D-20-21157R1 Dear Dr. Palomares Chust, 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. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Fei Chen Academic Editor PLOS ONE Additional Editor Comments (optional): The revised paper has been evaluated by the same reviewers. They both agreed that the paper is publishable, but also raised some minor comments. Please address them in the final version. Based on their comments, I am pleased to recommend it for publication. 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 #1: All comments have been addressed Reviewer #2: (No Response) ******** 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 #1: Yes Reviewer #2: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes 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. Reviewer #1: Yes Reviewer #2: Yes ****** 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 #1: Yes 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 #1: The authors have addressed all the comments that the reviewer raised. The reviewer's only concern is presented below. 1)In the background section, the authors stated "Let G = {V, E} an undirected, strong connected graph.....". However, it seems that the definition of "strongly connected" is only for directed graph. Please double check with the definition of "strongly connected". Reviewer #2: A new kind of algorithms called supportive consensus is presented in this work. Most of the suggestions from the reviewers have been settled in this round. (1) In the example for Algorithm 1, it is given that $R=\\{[6,10],[4,6],[2,5.2],[0,4]\\}$, which means that ${{x}_{A}}\\in [x_{A}^{INF},x_{A}^{SUP}]=[6,10]$. The solution of A is $x_A=5.4$, which is outside the scope of $[6,10]$. I think the authors should check the Algorithm 1 and its examples. (2) The title of Table 2 should be placed at the top of the table. (3) There are still some grammatical problems remained in this version of the manuscript. For example, “Let $G=\\{V,E\\}$ an undirected, strong connected graph” (line 134) should be “Let $G=\\{V,E\\}$ be an undirected, strong connected graph”. In line 204, “Lets call” should be “Let’s call”. ****** 7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review?** For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No Reviewer #2: No https://doi.org/10.1371/journal.pone.0243215.r003
Formally Accepted
1 Dec 2020 Acceptance Letter - Fei Chen, Editor PONE-D-20-21157R1 Supportive Consensus Dear Dr. Palomares: I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org. If we can help with anything else, please email us at plosone@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Dr. Fei Chen Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0243215.r004

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