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Functional Renormalization Group Approach for Signal Detection
by Vincent Lahoche, Dine Ousmane Samary, Mohamed Tamaazousti
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Submission summary
| Authors (as registered SciPost users): | Dine Ousmane Samary |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202306_00023v3 (pdf) |
| Date submitted: | 2024-10-16 15:24 |
| Submitted by: | Ousmane Samary, Dine |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended self-consistent construction of the analogue effective field-theory framework for data, which can be viewed as a maximum entropy model. In particular, and exploiting universality arguments, we justify the ℤ2-symmetry of the classical action, and we stress the existence of a large-scale (local) regime and of a small-scale (nonlocal) regime. Secondly, and related to noise models, we observe the universal relation between phase transition and symmetry breaking in the vicinity of the detection threshold. Finally, we discuss the issue of defining the covariance matrix for tensorial-like data. Based on the cutting graph prescription, we note the superiority of definitions based on complete graphs of large size for data analysis.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We would like to thank the referee for making this comment on our manuscript. We have taken all comments into account. In fact, the version submitted was not the last one due to clumsiness. We have improved it and hope that the referee will be satisfied.
On the Behalf of all the authors
Dr Samary
List of changes
A1) We preferred to keep the original figure because, in our opinion, it makes
it easier to understand the other figures in the paper, particularly key figures such as Figures 10 and 16. Additionally, it visually illustrates the challenge posed by quasi-continuous spectra. We had also included the caricature figure
to further emphasize and illustrate this point. We hope the referee will not object to this choice. Please note that we have improved the readability of Figure 10 (previously Figure 14).
A2) We apologize for this oversight; indeed, there was an error in the file. The footnote has now been added on page 16 (footnote 9) and referenced again on page 41 (footnote 26).
B4) For some time, we have aimed to adapt the Blaizot-Mendes-Wschebor formalism to this problem, leveraging the fact that the exact 2-point function is known in the IR regime. However, certain subtleties in the construction mean that this work is still ongoing.
C1) We have added the requested comment in the revised version (page 35, in blue, at the end of the paragraph).
C2) We appreciate the referee’s remark and have incorporated it into the comment
which can now be found at the end of the introduction of the section 4. This time, it is included in blue, preceding the earlier remark.
C3) Once again, we apologize for the error in our previous submission. We have made slight improvements to the content of Remark 3, which is now placed on page 54, just above Figure 13. We believe this figure sufficiently addresses the referee’s question regarding the presence of a fixed point.
Finally, we checked the English throughout the manuscript and improved the sentences.