Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript presents a novel dynamic filtering algorithm named BUNCH for identifying hierarchically structured persistent entities in interactive particle systems (IPS) and introduces a quantitative metric, "lifeness." The research is highly original and interdisciplinary, bridging statistical physics, machine learning, and complex systems theory.  However, the manuscript's current impact is hampered by key issues concerning the ​​clarity of the methodological description, the rigor of the experimental validation, and the fluency of the language.​​  

1. The description of the BUNCH algorithm's core workflow is not precise or intuitive enough. Although pseudocode is provided, the textual descriptions of key steps are too general, making it difficult for readers to fully understand the algorithm's internal mechanism.
2.  The paper claims that BUNCH is superior to parameterized methods but provides no quantitative comparison with any existing hierarchical clustering algorithms on the same dataset.
3. The manuscript contains grammatical errors, spelling mistakes, and awkward expressions, which adversely affect the reading experience.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

 

This manuscript introduces BUNCH, a hierarchical filtering algorithm designed to identify persistent entities in interactive particle systems (IPS) by fitting dynamical trajectories to a tree structure based on hierarchical mixtures of Gaussian clusters (HMGC). The work operationalizes "lifeness" as a scalar product of entity complexity and lifespan, with simulations suggesting associations between lifeness and long-range interactions. The study demonstrates technical effort in algorithm development and numerical experiments, but the presentation lacks clarity in methodological details and novelty justification. I think the paper could be published with revisions, especially the revision about the presitation of figures and tables, I provide comments to enhance the paper's rigor and impact.

 

1. The methodological description of BUNCH (Sections 3.1–3.3) lacks sufficient detail for reproducibility. For instance, the pseudocode in Section 3.2 omits key steps like the "ellipticalKmeans" implementation or convergence criteria. Expanding this with algorithmic complexities (e.g., time/space costs) and parameter choices (e.g., the learning rate α) would aid replication.
2. Figure 2-6 is rather blurry; both the formulas and the tables are presented as images. This needs to be improved. The formulas should be input using the normal formula input method (such as MathType), and the tables should be presented in text form rather than as screenshots.
3. The definition and interpretation of "lifeness" remain abstract. While Section 2.4 introduces it mathematically, its practical relevance to real-world systems (e.g., biological or physical entities) is underexplored. May it is helpful to add a discussion on how lifeness metrics could be validated or applied beyond synthetic IPS would strengthen the work's applicability.

 

And also, there are some minor detail comments​

1. Abstract, line 10: The phrase "lifeness of an entity as a scalar" is vague; specify whether it is dimensionless or has units (e.g., nats × time) to avoid ambiguity.
2. Section 2.2, line 52: The HMGC model description uses undefined symbols (e.g., μ, Σ, φ); include a table or appendix listing all mathematical notation for clarity.
3. Section 3.2, pseudocode line 296: "ellipticalKmeans(l)" may not elaborated; reference a standard algorithm or provide equations for the E- and M-steps mentioned in Section 3.1.
4. Figure 2 caption: The description "Each gray ellipse represents one live cluster" maybe insufficient; specify how ellipse attributes (e.g., thickness) map to hierarchy levels and cluster properties.
5. Section 4.1, line 419: The term "suprisal" may used without definition; briefly define it (e.g., as negative log-evidence) upon first occurrence to aid readers unfamiliar with information theory.
6. Equation in Section 4, line 397: The force equation uses χ_ij seems without clarifying its symmetry; note whether it is symmetric or skew-symmetric to align with Section 5.1's discussion.
7. Section 6, line 552: The conclusion overgeneralizes by stating BUNCH "enables hierarchically assessing properties" without noting limitations (e.g., scalability to large particle counts).

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

İn this paper, a new dynamical filtering algorithm was proposed in researching the 2 D problems. The study is important and the paper is well designed and written. The conclusions draw from the research are generally convincing. Before the final publication, there’re still some problems which need to be addressed.

1) The reference list of this paper should be improved. Most of the articles were published 10 or 20 years ago. Does this mean that related research in recent years has rarely been reported? İf not, please give some introduction of the related research in recent years.

2) The format throughout the whole paper should be carefull revised. For example, the equations should be added with serial number, the lines and curves in the figures should be expressed clearly and introduced, as well as the tables. The present form is difficult to read in some areas.

3) In this paper, the feasibility of the proposed method was demonstrated by simulating multiple interactive particle systems. In my opnion, the superiority of the proposed model should be expressed more clearly, can some quantitative evaluation been provided with the selected parameters if possible?

4) The novetly of the whole paper is unclear in some degrees. Generally speaking, the novetly of the proposed algorithm is usually expressed by comparing the results obtained from this algorithm and some other method. Can this work been done?

5）The conclusion part should be revised carefully or rewritten. The tense of this part and the whole paper should be possitive.

6) The author declared that longer interaction range is associated with more lifeness in a subcritical range. İn my opnion, the conclusion is insufficient based on the obtained work and should be checked through further more work, even the author himself also said ‘preliminary’.

7) The titles of some figures and table are too long and wordy, please make corresponding modification for more brief expression.

8) According to the research method proposed in this paper, BUNCH performs a bottom-up sweep where cluster features and the identity of their children are estimated in a hybrid Bayesian and maximum likelihood fashion. As everyone knows, the maximum likelihood fashion usually reult in obvious conservative estimation. Will this affect the feasible of the algorithm?

 

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript has been revised, with significant improvements in scientific originality, clarity of methodological description, and language quality, reaching an acceptable standard. Although there remains room for enhancement in the rigor of experimental validation, this limitation is acceptable given the proof-of-concept nature of the study and the high degree of algorithmic originality.
Suggestions for Further Revisions:​
1）If possible, it is recommended to add a section comparing and discussing the output of BUNCH with one or two representative hierarchical clustering algorithms on the same simulated data. Even a qualitative comparison would significantly strengthen the persuasiveness of the paper.
2）In the discussion section, a more in-depth exploration of the limitations of the BUNCH algorithm and potential directions for future improvement would be beneficial.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Thanks for the revision work provided by the author. Now the quality of the paper has been improved obviously. İn my opinion, it can be accepted for publication.

Author Response

Many thanks for your review.