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Article
Peer-Review Record

Memory Constraints in Uncertainty Misestimation: A Computational Model of Working Memory and Environmental Change Detection

Mathematics 2025, 13(15), 2431; https://doi.org/10.3390/math13152431
by Li Xin Lim 1,*, Rei Akaishi 2 and Sébastien Hélie 3
Reviewer 2:
Reviewer 3: Anonymous
Mathematics 2025, 13(15), 2431; https://doi.org/10.3390/math13152431
Submission received: 1 May 2025 / Revised: 8 July 2025 / Accepted: 25 July 2025 / Published: 28 July 2025
(This article belongs to the Special Issue Mathematical and Computational Models of Cognition, 2nd Edition)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

>  the original text
R: reviewer

R:  
50 pages long submission is unusual. It looks like an extract from PhD dissertation to me. It looks like academic advisors (or reviewers) missed a few important details. If my educated guess is correct, more cuts in the text should be considered. 

R:
cognitive load is used 26 times in the submission
but no definition (or specification) such as in:
https://en.wikipedia.org/wiki/Cognitive_load
is provided.

R:
The reference to "bouned rationality" (see Wikipedia) is not present in the submission although the link to it may be the main achievement of this submission. Simon (https://en.wikipedia.org/wiki/Herbert_A._Simon) got a Nobel Prize for it but never provided any "proof". Your experimens may do it...

R: Fig. 1 does not follow any well-established methodology and computational science and mathematics. In particular, the outcome is unclear.  An activity diagram (see Wikipedia used for brainstorming, hence something that psychologists should be familiar with. The arrow/dot notation may be incorrect (the dot should be used with the arrowhead). 

R: Formula (2) looks suspicious and may be incorrectly assumed. No reasoning (or reference) why exponential growth takes place. I am not claiming that it is wrong but requesting that it is properly addressed.
This link: https://en.wikipedia.org/wiki/Task-invoked_pupillary_response has:
Task-invoked pupillary response (also known as the "Task-Evoked pupillary response") is a pupillary response caused by a cognitive load imposed on a human and as a result of the decrease in parasympathetic activity in the peripheral nervous system.[1] It is found to result in a linear increase in pupil dilation as the demand a task places on the working memory increases. Beatty evaluated task-invoked pupillary response in different tasks for short-term memory, language processing, reasoning, perception, sustained attention and selective attention and found that it fulfills Kahneman's three criteria for indicating processing load.[2][3] That is, it can reflect differences in processing load within a task, between different tasks and between individuals. It is used as an indicator of cognitive load levels in psychophysiology research.[2]
Please pay attention to: "linear increase".

R: there is no source for the above formula ([21] is suspected). The same comment is applicable to other formulas.

>  2.4 Model...
R: how is it representative for the general population?
p<0.1 is not a strong argument; p<0.05 can be regarded as "hardly sufficient".

R: the N-back test not explained.

R: The submission uses "paired" twice but does not go deep enough to explore the "pairwise comparisons method" for dealing with uncertainty. Adding a few references in the "future research subsection" in the Conclusions would enhance this submission:
https://doi.org/10.1016/j.ins.2023.119979
https://sciendo.com/article/10.1515/amcs-2016-0050

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a mathematical model and experiments to overcome limitation of working memory when analyzing the results of the reinforcement learning model. Overall, the work is very nice and it has a contribution. However, the paper is too long with too much detailed information. For example, the heading with four numbers such as 2.2.4.1, does not generally occur in the paper. I recommend the authors to make the paper shorter with the format of the journal for clear view of point and easier understanding for the readers. Additionally, the following point should be considered in the revised version.

- All overview part should be reduced or eliminated in the paper. It should be concentrated in the current problem.

- All parameters in the equations should be explained. For example, parameter k0, k1 in equation 2, urge in equation 7, and others. I also think that there are too many equations in the current paper and some of them are too general and can be explained by text, for example Eq. (1). Please remove or combine some of them.

- Numbers in axes of Figures 2, 4, 6, and 7 should be enlarged. The lines in Fig. 9 are too thin and should be thicker. Please check the numbers and text in other Figures again to make sure that they can be seen clearly.

- In the results part, comparison with previous studies should be included to make clearly the contribution of the current method.

- The discussion part in Section 4, and Section 5 are too long. They should be shortened, and some of them should be changed to the conclusion part.

- The conclusion part should include quantitative information about the accuracy of the current method and its limitations. It is better to show the novelty and contribution point-by-point.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors present an article where the issues regarding memory storage were discussed. Overall the article is good, the authors present an interesting introduction, present their model and an original approach to validate their model, based on human experiences. Many conditions were analyzed and the results are useful for artificial intelligence and neuroscience purposes. 

However, the results are not exactly new, they are based on the Dissertation Thesis and the content is publicly available at: https://hammer.purdue.edu/articles/thesis/The_interaction_of_working_memory_and_Uncertainty_mis_estimation_in_context-dependent_outcome_estimation/24549196

This fact does not invalidate the publication but it is important that the authors clarify if the content is not violating any institutional copyrights. 

Another issue that requires clarification is about the Ethical Committee approval of the research, considering that it contains experiments involving humans.  Is the research in compliance with the journal and the institutional policies regarding research involving  humans? 

Besides, there are some minor issues that need to be addressed.

  1. The manuscript is well written but there is a 'writing habit' through the manuscript where the equations are discussed before they are introduced. First the authors should describe the equation and just after that comment about their effects and consequences.
  2. When a equation is introduced it should be inside the phrase, and after that a comma or a dot. In this manuscript, usually a final dot is inserted before the equation, this should be fixed. 
  3. Most of the citations through the text are outdated, please update some references in the introduction to provide a better vision of the current state of the art related to the subject. 

Despite of the issues that I raised, I believe that if the two main issues are clarified in a satisfactory manner and the minor issues are fixed, the manuscript should be consider for publication. 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

It is a very useful publication. This line of research should be continued.

Using the pairwise comparisons method may greatly improve it.

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