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Dynamical mean field theory for models of confluent tissues and beyond
by Persia Jana Kamali, Pierfrancesco Urbani
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Submission summary
| Authors (as registered SciPost users): | Pierfrancesco Urbani |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2306.06420v3 (pdf) |
| Date accepted: | 2023-10-30 |
| Date submitted: | 2023-09-26 12:08 |
| Submitted by: | Urbani, Pierfrancesco |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider a recently proposed model to understand the rigidity transition in confluent tissues and we derive the dynamical mean field theory (DMFT) equations that describes several types of dynamics of the model in the thermodynamic limit: gradient descent, thermal Langevin noise and active drive. In particular we focus on gradient descent dynamics and we integrate numerically the corresponding DMFT equations. In this case we show that gradient descent is blind to the zero temperature replica symmetry breaking (RSB) transition point. This means that, even if the Gibbs measure in the zero temperature limit displays RSB, this algorithm is able to find its way to a zero energy configuration. We include a discussion on possible extensions of the DMFT derivation to study problems rooted in high-dimensional regression and optimization via the square loss function.
Author comments upon resubmission
we would like to resubmit our manuscript for publication in SciPost Physics.
We have provided a detailed response to the reports and revised accordingly the manuscript.
Yours sincerely,
The authors.
List of changes
We have detailed the list of changes in the responses to the reports.
Published as SciPost Phys. 15, 219 (2023)
Reports on this Submission
Report #1 by Anonymous (Referee 3) on 2023-10-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2306.06420v3, delivered 2023-10-10, doi: 10.21468/SciPost.Report.7924
Report
The authors included in Fig. 5 the location of the SAT/UNSAT transition and I think that this contribution significantly enhanced the paper.
Furthermore, the analysis of the timestep discretization is minimal but solid.
My main conceptual concerns are about the dimensionality issue which the authors acknowledge as an open problem; I find the sentence in the Perspectives section an honest remark.
I therefore think that the paper is now suitable for publication.