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Thanks to the authors for your efforts to improve the work. This version satisfied the reviewers successfully and can be accepted.
[# PeerJ Staff Note - this decision was reviewed and approved by Claudio Ardagna, a PeerJ Section Editor covering this Section #]
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I am pleased to acknowledge that the authors have diligently addressed and implemented all the comments I raised, significantly improving the content of this study. Hence, I confirm my approval for the manuscript to be accepted.
The authors have carefully revised the manuscript, and it can be accepted in current version.
The authors have carefully revised the manuscript, and it can be accepted in current version.
The authors have carefully revised the manuscript, and it can be accepted in current version.
The authors have carefully revised the manuscript, and it can be accepted in current version.
Please revise the paper according to the comments. Then it will be evaluate again.
**PeerJ Staff Note:** Please ensure that all review, editorial, and staff comments are addressed in a response letter and that any edits or clarifications mentioned in the letter are also inserted into the revised manuscript where appropriate.
**Language Note:** PeerJ staff have identified that the English language needs to be improved. When you prepare your next revision, please either (i) have a colleague who is proficient in English and familiar with the subject matter review your manuscript, or (ii) contact a professional editing service to review your manuscript. PeerJ can provide language editing services - you can contact us at copyediting@peerj.com for pricing (be sure to provide your manuscript number and title). – PeerJ Staff
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Your work outlines a groundbreaking method for reconstructing models based on direct causality topology from multivariate time series data. This work emphasizes the novelty of your approach in reconstructing models using direct causality topology and highlights how this method efficiently extracts the core topology and minimizes redundant information from multivariate time series data, without requiring prior domain knowledge. The paper is interesting and it may be useful for the readers of the journal. Here are some suggestions to refine your description:
1,the abstract may not highlight the significance of this work. Please consider rewrite or elaborate the abstract.
2,Sentence in line 195, “where X = {xt-l+1,··· ,xt-1,xt} and Y ={yt-l+1,··· ,yt-1,yt}”，what does the letter “l” represent in the expression of X and Y?
3,Sentence in line 230, “By conducting N-trial Monte Carlo simulations Kantz and Schreiber (2004), we compute the MIs, TEs, CMIs and CTEs for various surrogate time series, following (9), (7) and (11).” Double-check the number of mathematical expression.
4,Mention the necessity to double-check certain elements like figures and tables (e.g., Tables 3, 4, and 5) to ensure accuracy and consistency in your presentation.
5,Sentence in line 266, could you tell me the reason for “the initial states are X(0) = 0 and Y (0) = 0”?
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The paper introduces a novel method for reconstructing an equivalent underlying model using direct causality topology. This approach aims to extract the core topology and minimize redundant information from multivariate time series data without requiring prior domain knowledge. The following issues should be taken into consideration to improve the paper's quality further.
1. Can you tell me the reason for choosing ALGORITHMS in this work?
2. Some small errors should be double checked, for instance “the TEX→Y can be: expressed as:(line204).”
3. Update the literature review to include recent studies relevant to the topic. This would position the paper more solidly within the current research landscape.
4. Discuss potential applications of the research and future directions.
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