pith. sign in

arxiv: 2606.01421 · v1 · pith:WW4NNW36new · submitted 2026-05-31 · 💻 cs.LG

Target localization, identification and sensing using latent symmetries

David Dukov , Malte R\"ontgen , Bryn Davies This is my paper

Pith reviewed 2026-06-28 17:23 UTC · model grok-4.3

classification 💻 cs.LG
keywords latent symmetriessensingscattererscapacitance matrixintruder localizationsymmetry breakingBayesian inferenceneural networks
0
0 comments X

The pith

Scatterer arrays with latent symmetries sense intruder position and radius by measuring symmetry breaking.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that an array of scatterers engineered to possess latent symmetries can act as a sensor for an added intruder scatterer. Using the capacitance matrix to model three-dimensional hybridization, the degree to which each latent symmetry is broken encodes the intruder's radius and position. Identification succeeds with a dictionary lookup, but Bayesian inference and a multi-layer perceptron yield better results when measurements contain noise. The work applies to three-dimensional open systems that cannot be reduced to sparse graphs, marking a new use of latent symmetries for sensing.

Core claim

An array of scatterers designed with latent symmetries functions as a sensor. An intruder scatterer breaks these symmetries, and the extent of each break, extracted from the capacitance matrix, identifies the intruder's radius and localizes its position. This identification remains possible in three-dimensional open systems and improves under measurement noise when Bayesian inference or a multi-layer perceptron replaces dictionary matching.

What carries the argument

Latent symmetries in the capacitance matrix of a scatterer array, whose breaking by an intruder encodes radius and position.

If this is right

  • The pattern of broken latent symmetries directly encodes the intruder's radius and position.
  • A dictionary of precomputed symmetry signatures suffices for identification when noise is absent.
  • Bayesian inference recovers radius and position more reliably than dictionary matching when measurement noise is present.
  • A multi-layer perceptron trained on symmetry signatures also outperforms dictionary matching under noise.
  • The method applies to three-dimensional open systems that cannot be approximated by sparse graphs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same symmetry-breaking analysis could be applied to other hybridization models beyond the capacitance matrix.
  • Sensor arrays could be designed once with fixed latent symmetries and then reused for multiple intruder types by changing only the inference step.
  • The approach suggests testing whether latent symmetries in other wave or diffusion systems yield comparable sensing capabilities.

Load-bearing premise

The capacitance matrix model correctly captures hybridization so that the pattern of symmetry breaking uniquely determines intruder radius and position even with added noise.

What would settle it

Compute or measure the capacitance matrix for a physical scatterer array containing an intruder of known radius at a known location, then test whether the observed symmetry-breaking degrees recover that radius and location within the claimed tolerance.

Figures

Figures reproduced from arXiv: 2606.01421 by Bryn Davies, David Dukov, Malte R\"ontgen.

Figure 1
Figure 1. Figure 1: The resonator geometry shown on the left is such that the capacitance matrix supports a latent symmetry at sites (resonators) 3 and 7. The plot shows the discrete values of the eigenvectors at the 10 sites, interpolated using polynomial splines for illustrative purposes. As a result of the latent symmetry, the eigen￾modes display a parity symmetry at those positions, demonstrated through the two red lines … view at source ↗
Figure 2
Figure 2. Figure 2: Examples of resonator arrays with latent and classical geometric symmetries. Plots (a) and (b) show arrays that are non-symmetric but have a pair of sites that are latently symmetric (these are sites 3 & 7 in (a) and sites 1 & 4 in (b)). Plots (c) and (d) show geometrically symmetric arrays which (trivially) have multiple pairs of latently symmetric sites. 3. Perturbations due to intruders. In this section… view at source ↗
Figure 3
Figure 3. Figure 3: Five spherical resonators of radius 0.1 positioned at the coordinates zi ∈ {−2, −1, 0, 1, 2} × {0} and an intruder Ω of variable radius at (3, 0). The symmetric pairs of the unperturbed system are {D1, D5} and {D2, D4}. Using the same reasoning as before, we find that the eigenvectors of this block matrix are vk ⊕ 0 and 0N ⊕ 1. The only difference is that the last eigenvalue is ˜α instead of 0. Similarly, … view at source ↗
Figure 4
Figure 4. Figure 4: Perturbations of system D by an intruder Ω of variable radius fixed at position (3, 0). The size of Ω of the intruder does not exceed that of the five resonators of the original system D. The plot on the right is in log-log scale. the coupling strength scales in proportion to the reciprocal of the distance between the two objects. The log-log plot on the right in [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Perturbations of system D by an intruder of variable radius sampled at 200 locations. In the bottom plot, the sample points S are chosen uniformly at random over the rectangular domain [0, 5] × [0, 3] and colour coded according to their proximity to the resonators D3, D4, D5 which are partially shown in black. The plots on top display the associated curves in rΩ for the functions F15 and F24 with respect t… view at source ↗
Figure 6
Figure 6. Figure 6: Perturbations of system D by an intruder of fixed radius but variable position. (a) the heatmap associated with the function F 0.1 15 are presented. (b) the heatmap associated with F 0.1 24 . The symmetric pair of resonators used for sensing is marked in red, and the remaining resonators in gray. The white annuli surrounding the resonators represent regions where an intruder cannot exist as it would overla… view at source ↗
Figure 7
Figure 7. Figure 7: Far-field behaviour of the functions F15 and F24. (a) a path along {x0} × [−10, 10] with x0 = 0.5 is simulated showing the asymptotic behaviour along the y-axis. (b) a path along [−20, 20] × {y0} with y0 = 0.5 is simulated to show the asymptotic behaviour along the x-axis. Secondly, we observe that as we move away from the resonators, the sensitivity decreases quickly, consistent with Proposition 3.3. We c… view at source ↗
Figure 8
Figure 8. Figure 8: Perturbations of system D by an intruder of fixed radius but variable position. In the top row, heatmaps associated with the functions F 0.06 15 and F 0.06 24 are presented. In the bottom row are the heatmaps associated with F 0.02 15 and F 0.02 24 . The symmetric pair of resonators used for sensing is marked in red, and the remaining resonators in gray. The white annuli surrounding the resonators represen… view at source ↗
Figure 9
Figure 9. Figure 9: Perturbations of a horseshoe system by an intruder of fixed radius but variable position. In the top row, heatmaps associated with intruder radius rΩ = 0.1 are presented, while in the bottom row, heatmaps associated with rΩ = 0.05 are presented. The symmetric pair of resonators used for sensing is marked in red, and the remaining resonators in gray. The setup is mirror symmetric with respect to the y = 0 l… view at source ↗
Figure 10
Figure 10. Figure 10: Perturbations of a resonator system by an intruder of variable radius sampled at 200 locations. The sample points S are chosen uniformly at random over a rectangular domain R, such that they don’t overlap with the resonators. (a) shows the horseshoe system, with R = [−4, 5.5]×[−5, 5]. The function F16 corresponds to the symmetric pair located at the tips of the horseshoe. (b) shows the asymmetric array fr… view at source ↗
Figure 11
Figure 11. Figure 11: Perturbations of an asymmetric but latently symmetric system by an intruder of fixed radius but variable position. The heatmap on the left corresponds to an intruder of radius rΩ = 0.1, while the heatmap on the right corresponds to rΩ = 0.05. The symmetric pair of resonators used for sensing is marked in red, and the remaining resonators in gray. The distinguishable feature of these systems with latent sy… view at source ↗
Figure 12
Figure 12. Figure 12: Perturbations of a sparse system by an intruder of fixed radius but variable position. The heatmaps in the top row correspond to an intruder of radius rΩ = 0.1, while the heatmaps in the bottom row correspond to rΩ = 0.05. The resonator corresponding to Fpq is highlighted. Its pair is not shown, as we plot only half of the symmetric array here (the mirror symmetry is along the line x = 0). There is a reso… view at source ↗
Figure 13
Figure 13. Figure 13: On the left, a guess function of the form f(r; θ) = a exp(brc ) is fitted to the true model F15(r, 3, 0). After optimisation the optimal values for θ are a = 9.31 × 10−4 , b = 5.589, and c = 0.826. The error between the true model and the predictive model is plotted on the right, and it shows accuracy ranging between three to five significant figures. We can now construct a Gaussian Process Regression (GP… view at source ↗
Figure 14
Figure 14. Figure 14: Gaussian process regression model for the true function F15(rΩ, 3, 0). The process is fitted to 10 samples of multiplicative noise from a normal distribution with mean m = 1 and variance σ 2 = 0.04. After conditioning, the mean Gaussian process function is plotted in red, and a 95% confidence region is plotted around it in green. in [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison plots for the noisy guess function f(r; θopt)(1 + η) with η ∼ N (0, 0.04), and the Gaussian process regression model. On the left, a sample of the noisy guess function is plotted, as well as the mean function of the conditioned Gaussian process. On the right, the piecewise absolute errors for both models are shown. with multivaluedness and ill-conditioning, but we represent its preimage symboli… view at source ↗
Figure 16
Figure 16. Figure 16: Prediction of intruder’s position using a dictionary-based model. (a) uses just F15, (b) uses just F24 and (c) uses the combined function Fmin from (4.6). The true location is labeled with a white circle, while the predictions are given by green crosses. The intruder is of fixed radius rΩ = 0.06. Level sets are indicated by the white curves. which is equivalent to the mean absolute error (MAE) function, a… view at source ↗
Figure 17
Figure 17. Figure 17: Dictionary-based model applied to a noisy observation. Despite not being able to accurately use the deterministic dictionary-based model for prediction when measurement noise is involved, confidence regions can still be determined using the sensing functions F15 and F24 separately. The 95% confidence intervals are shown in green and pink, respectively. The resonators are shown in gray. 4.2.2. Multi-layer … view at source ↗
Figure 18
Figure 18. Figure 18: Training and testing losses during the tuning of hyperparameters of the multi-layer perceptron (MLP) model. Training loss is with respect to the training dataset, and the test loss is with respect to the validation dataset. Each epoch consists of a batch size of 30 data samples for both training and testing [PITH_FULL_IMAGE:figures/full_fig_p022_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Visualisation of several predictions by the multi-layer perceptron (MLP) and the dictionary￾based model (DM). The figure on the left shows predictions of samples with measurement noise σ = 0.05, and the figure on the right shows predictions of the same samples but with measurement noise σ = 0.1. The resonators are shown in gray. Fepq = log Fpq. Using Bayes’ rule, the posterior can be written as (4.8) p  … view at source ↗
Figure 20
Figure 20. Figure 20: Probability distributions for the Bayesian inference model with uniform prior. On the left, the joint posterior probability distribution for (x, y) is shown, and on the right are histograms representing the marginal distributions. The dashed black horizontal lines in the histograms correspond to the true coordinates. The mean prediction is taken over the uncorrelated part of the chains, while the probabil… view at source ↗
Figure 21
Figure 21. Figure 21: Probability distributions for the Bayesian inference model with standard Gaussian prior. On the left, the joint posterior probability distribution for (x, y) is shown, and on the right are histograms representing the marginal distributions. The dashed black horizontal lines in the histograms correspond to the true coordi￾nates. The mean prediction is taken over the uncorrelated part of the chains, while t… view at source ↗
read the original abstract

We show that an array of scatterers which has been designed to have latent ("hidden") symmetries can be used as a sensor. We use the capacitance matrix as a canonical model for three-dimensional hybridisation and study how the introduction of an "intruder'' scatterer breaks the latent symmetries. By analysing the degree to which each symmetry is broken, we identify the radius of the intruder and localize its position. This can be achieved using a dictionary-based approach, however Bayesian inference or an artificial neural network (multi-layer perceptron) perform better in the presence of measurement noise. To our knowledge, this is the first time latent symmetries have been exploited successfully for sensing problems. It is also the first time latent symmetries have been observed in a three-dimensional open system that cannot be approximated by a sparse graph.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that arrays of scatterers engineered with latent symmetries can function as sensors. Using the capacitance matrix to model 3D hybridization, the introduction of an intruder scatterer breaks these symmetries; the degree of breaking encodes the intruder's radius and position. Identification is performed via dictionary matching, with Bayesian inference and multi-layer perceptrons shown to outperform the dictionary approach under measurement noise. The work asserts novelty as the first exploitation of latent symmetries for sensing and the first observation of such symmetries in a 3D open system not reducible to a sparse graph.

Significance. If the capacitance-matrix results transfer to physical hardware, the approach could enable new symmetry-based sensing modalities that leverage hidden symmetries rather than explicit geometric features. The comparative evaluation of dictionary, Bayesian, and neural-network recovery methods under noise provides a concrete demonstration of robustness. The absence of free parameters in the symmetry-breaking analysis and the explicit handling of an open 3D system are strengths that would strengthen the contribution if the model is validated.

major comments (1)
  1. [Modeling section / abstract statement on capacitance matrix] The central claim that symmetry-breaking signatures uniquely encode intruder radius and position (even under noise) rests on the capacitance matrix faithfully representing hybridization. No comparison is provided to full-wave Maxwell solvers that include radiation, retardation, or non-quasistatic effects; if these alter the observed breaking degrees beyond the noise levels used for the Bayesian/NN classifiers, the identifiability result does not transfer. This is load-bearing for both the sensing performance claims and the novelty assertion regarding 3D open systems.
minor comments (2)
  1. [Abstract] The abstract states performance advantages for Bayesian inference and MLPs but supplies no quantitative metrics (e.g., localization error, radius classification accuracy, noise levels tested). These should be added with explicit tables or figures.
  2. [Introduction / methods] Notation for the latent symmetries and the breaking metric is introduced without a clear definition or reference to prior work on latent symmetries; a short dedicated subsection would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting an important modeling consideration. We address the major comment below.

read point-by-point responses

  1. Referee: [Modeling section / abstract statement on capacitance matrix] The central claim that symmetry-breaking signatures uniquely encode intruder radius and position (even under noise) rests on the capacitance matrix faithfully representing hybridization. No comparison is provided to full-wave Maxwell solvers that include radiation, retardation, or non-quasistatic effects; if these alter the observed breaking degrees beyond the noise levels used for the Bayesian/NN classifiers, the identifiability result does not transfer. This is load-bearing for both the sensing performance claims and the novelty assertion regarding 3D open systems.

    Authors: The capacitance matrix is a standard and widely accepted quasistatic model for electrostatic hybridization between conducting scatterers, as established in the literature on metamaterials and electrostatic sensing. Our results demonstrate that latent symmetries and their breaking are well-defined mathematical properties of this matrix, enabling unique encoding of intruder parameters (radius and position) within the model, including under the noise levels considered for the Bayesian and neural-network methods. The novelty claims refer specifically to the first exploitation of latent symmetries for sensing and their observation in a 3D open system that cannot be reduced to a sparse graph, both within this canonical modeling framework. We agree that direct numerical comparison to full-wave Maxwell solvers would be valuable to assess the impact of radiation, retardation, and non-quasistatic effects on the symmetry-breaking signatures. In the revised manuscript we will add a dedicated discussion subsection clarifying the scope and limitations of the quasistatic approximation (including the frequency and size regimes where it remains accurate) and identifying full-wave validation as an important direction for future experimental work. This revision will make the load-bearing assumptions explicit without changing the core identifiability results obtained inside the model. revision: partial

Circularity Check

0 steps flagged

No significant circularity; modeling and inference steps are independent

full rationale

The paper adopts the capacitance matrix as a canonical model for hybridization, introduces an intruder to break latent symmetries, and quantifies the breaking degrees to feed into standard identification methods (dictionary lookup, Bayesian inference, MLP). These steps do not reduce to self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. The central claim rests on physical modeling of symmetry breaking rather than any equation or result that is constructed from the sensing output itself. No uniqueness theorems or ansatzes are smuggled via self-citation chains, and the approach is presented as an application of existing symmetry concepts to a new sensing task. This is the expected self-contained outcome for a modeling-plus-inference paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, invented entities, or detailed axioms beyond the stated modeling choice.

axioms (1)
  • domain assumption The capacitance matrix serves as a canonical model for three-dimensional hybridisation
    Invoked in the abstract as the basis for studying symmetry breaking.

pith-pipeline@v0.9.1-grok · 5661 in / 1284 out tokens · 34729 ms · 2026-06-28T17:23:23.003482+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

39 extracted references · 19 canonical work pages · 1 internal anchor

  1. [1]

    Ammari, B

    H. Ammari, B. Davies, and E. O. Hiltunen , Functional analytic methods for discrete approximations of subwavelength resonator systems , Pure Appl. Anal., 6 (2024), pp. 873--939

    2024

  2. [2]

    Ammari, B

    H. Ammari, B. Davies, E. O. Hiltunen, H. Lee, and S. Yu , High-order exceptional points and enhanced sensing in subwavelength resonator arrays , Studies in Applied Mathematics, 146 (2021), pp. 440--462

    2021

  3. [3]

    Ammari, B

    H. Ammari, B. Davies, E. O. Hiltunen, and S. Yu , Topologically protected edge modes in one-dimensional chains of subwavelength resonators , J. Math. Pures Appl., 144 (2020), pp. 17--49

    2020

  4. [4]

    T. Bai, A. L. Teckentrup, and K. C. Zygalakis , Gaussian processes for B ayesian inverse problems associated with linear partial differential equations , Stat. Comput., 34 (2024), p. 139

    2024

  5. [5]

    P. A. Brand \ a o , Latent symmetry in a minimal non- Hermitian trimer , Mar. 2026, https://doi.org/10.48550/arXiv.2603.15768, https://arxiv.org/abs/2603.15768

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2603.15768 2026

  6. [6]

    Bunimovich, D

    L. Bunimovich, D. Smith, and B. Webb , Finding hidden structures, hierarchies, and cores in networks via isospectral reduction. , Applied Mathematics & Nonlinear Sciences, 4 (2019)

    2019

  7. [7]

    Cao and J

    J. Cao and J. Nick , Exceptional point enhanced small particle detection in systems of subwavelength resonators , arXiv preprint arXiv:2505.01646, (2025)

    arXiv 2025

  8. [8]

    A. Chan, G. Coutinho, W. Drazen, O. Eisenberg, C. Godsil, M. Kempton, G. Lippner, C. Tamon, and H. Zhan , Fundamentals of fractional revival in graphs , Linear Algebra Its Appl., 655 (2022), pp. 129--158, https://doi.org/10.1016/j.laa.2022.09.010

    work page doi:10.1016/j.laa.2022.09.010 2022

  9. [9]

    D. Chen, M. Davies, M. J. Ehrhardt, C.-B. Schönlieb, F. Sherry, and J. Tachella , Imaging with equivariant deep learning: From unrolled network design to fully unsupervised learning , IEEE Signal Processing Magazine, 40 (2023), pp. 134--147, https://doi.org/10.1109/MSP.2022.3205430

    work page doi:10.1109/msp.2022.3205430 2023

  10. [10]

    X. Chen, Z. Wei, L. Maokun, P. Rocca, et al. , A review of deep learning approaches for inverse scattering problems , Prog. Electromag. Res., 167 (2020), pp. 67--81

    2020

  11. [11]

    Cui, R.-Y

    X. Cui, R.-Y. Zhang, X. Wang, W. Wang, G. Ma, and C. T. Chan , Experimental Realization of Stable Exceptional Chains Protected by Non-Hermitian Latent Symmetries Unique to Mechanical Systems , Phys. Rev. Lett., 131 (2023), p. 237201, https://doi.org/10.1103/PhysRevLett.131.237201

    work page doi:10.1103/physrevlett.131.237201 2023

  12. [12]

    Datchev and H

    K. Datchev and H. Hezari , Inverse problems in spectral geometry , Inverse problems and applications: inside out. II, 60 (2011), pp. 455--485

    2011

  13. [13]

    Davies and L

    B. Davies and L. Herren , Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors , Proc. R. Soc. A, 478 (2022), p. 20210765

    2022

  14. [14]

    R. A. Diaz and W. J. Herrera , The positivity and other properties of the matrix of capacitance: Physical and mathematical implications , Journal of Electrostatics, 69 (2011), pp. 587--595

    2011

  15. [15]

    L. Eek, M. R \"o ntgen, A. Moustaj, and C. Morais Smith , Higher-order topology protected by latent crystalline symmetries , SciPost Physics, 18 (2025), p. 061, https://doi.org/10.21468/SciPostPhys.18.2.061

    work page doi:10.21468/scipostphys.18.2.061 2025

  16. [16]

    Godsil and J

    C. Godsil and J. Smith , Strongly cospectral vertices , Australasian Journal of Combinatorics, 88 (2024), pp. 1--21

    2024

  17. [17]

    Q.-H. Guo, Y. Zhang, X.-H. Wan, and L.-Y. Zheng , Observation of chiral edge state pairs in an acoustic trimer waveguide , Appl. Phys. Lett., 126 (2025), p. 133102, https://doi.org/10.1063/5.0256334

    work page doi:10.1063/5.0256334 2025

  18. [18]

    W. D. Heiss , The physics of exceptional points , Jouranl of Physics A, 45 (2012), p. 444016

    2012

  19. [19]

    Himmel, M

    J. Himmel, M. Ehrhardt, M. Heinrich, M. R \"o ntgen, A. Szameit, and T. A. W. Wolterink , Eigenmodes of Latent-Symmetric Quantum Photonic Networks , ACS Photonics, (2025), https://doi.org/10.1021/acsphotonics.5c01082

    work page doi:10.1021/acsphotonics.5c01082 2025

  20. [20]

    Himmel, M

    J. Himmel, M. Ehrhardt, M. Heinrich, S. Weidemann, T. A. W. Wolterink, M. R \"o ntgen, P. Schmelcher, and A. Szameit , State transfer in latent-symmetric networks , eLight, 6 (2026), p. 3, https://doi.org/10.1186/s43593-025-00114-9

    work page doi:10.1186/s43593-025-00114-9 2026

  21. [21]

    S. N. Kempkes, P. Capiod, S. Ismaili, J. Mulkens, L. Eek, I. Swart, and C. Morais Smith , Compact localized boundary states in a quasi- 1D electronic diamond-necklace chain , Quantum Front, 2 (2023), p. 1, https://doi.org/10.1007/s44214-023-00026-0

    work page doi:10.1007/s44214-023-00026-0 2023

  22. [22]

    Kempton, J

    M. Kempton, J. Sinkovic, D. Smith, and B. Webb , Characterizing cospectral vertices via isospectral reduction , Linear Algebra Its Appl., 594 (2020), pp. 226--248, https://doi.org/10.1016/j.laa.2020.02.020

    work page doi:10.1016/j.laa.2020.02.020 2020

  23. [23]

    D. P. Kingma and J. Ba , Adam: A method for stochastic optimization , in International Conference on Learning Representations (ICLR), 2015

    2015

  24. [24]

    J.-R. Lin, S. Wang, H. Li, and Z.-W. Zuo , Topological Anderson insulators by latent symmetry , Phys. Rev. B, 113 (2026), p. 094201, https://doi.org/10.1103/6cf5-jsg3

    work page doi:10.1103/6cf5-jsg3 2026

  25. [25]

    J. C. Maxwell , A Treatise on Electricity and Magnetism , vol. 1, Clarendon Press, 1873

  26. [26]

    Nayak , Multivariable constrained nonlinear optimization , in Fundamentals of Optimization Techniques with Algorithms, S

    S. Nayak , Multivariable constrained nonlinear optimization , in Fundamentals of Optimization Techniques with Algorithms, S. Nayak, ed., Academic Press, 2020, pp. 135--170, https://doi.org/https://doi.org/10.1016/B978-0-12-821126-7.00005-X, https://www.sciencedirect.com/science/article/pii/B978012821126700005X

    work page doi:10.1016/b978-0-12-821126-7.00005-x 2020

  27. [27]

    S. J. D. Prince , Understanding Deep Learning , MIT Press, 2023

    2023

  28. [28]

    M. C. Rechtsman , Optical sensing gets exceptional , Nature, 548 (2017), pp. 161--162

    2017

  29. [29]

    R \"o ntgen, X

    M. R \"o ntgen, X. Chen, W. Gao, M. Pyzh, P. Schmelcher, V. Pagneux, V. Achilleos, and A. Coutant , Topological states protected by hidden symmetry , Phys. Rev. B, 110 (2024), p. 035106, https://doi.org/10.1103/PhysRevB.110.035106

    work page doi:10.1103/physrevb.110.035106 2024

  30. [30]

    R \"o ntgen, C

    M. R \"o ntgen, C. V. Morfonios, P. Schmelcher, and V. Pagneux , Hidden symmetries in acoustic wave systems , Phys. Rev. Lett., 130 (2023), p. 077201, https://doi.org/10.1103/PhysRevLett.130.077201

    work page doi:10.1103/physrevlett.130.077201 2023

  31. [31]

    R \"o ntgen, C

    M. R \"o ntgen, C. V. Morfonios, P. Schmelcher, and V. Pagneux , Hidden symmetries in acoustic wave systems , Physical Review Letters, 130:077201 (2023)

    2023

  32. [32]

    R \"o ntgen, M

    M. R \"o ntgen, M. Pyzh, C. V. Morfonios, N. E. Palaiodimopoulos, F. K. Diakonos, and P. Schmelcher , Latent symmetry induced degeneracies , Phys. Rev. Lett., 126 (2021), p. 180601, https://doi.org/10.1103/PhysRevLett.126.180601

    work page doi:10.1103/physrevlett.126.180601 2021

  33. [33]

    R \"o ntgen, M

    M. R \"o ntgen, M. Pyzh, C. V. Morfonios, and P. Schmelcher , On symmetries of a matrix and its isospectral reduction , May 2021, https://doi.org/10.48550/arXiv.2105.12579, https://arxiv.org/abs/2105.12579

    work page doi:10.48550/arxiv.2105.12579 2021

  34. [34]

    R \"o ntgen, O

    M. R \"o ntgen, O. Richoux, G. Theocharis, C. V. Morfonios, P. Schmelcher, P. del Hougne , and V. Achilleos , Equireflectionality and customized unbalanced coherent perfect absorption in asymmetric waveguide networks , Phys. Rev. Appl., 20 (2023), p. 044082, https://doi.org/10.1103/PhysRevApplied.20.044082

    work page doi:10.1103/physrevapplied.20.044082 2023

  35. [35]

    Smith and B

    D. Smith and B. Webb , Hidden symmetries in real and theoretical networks , Physica A, 514 (2019), pp. 855--867

    2019

  36. [36]

    J. Sol, M. R \"o ntgen, and P. del Hougne , Covert Scattering Control in Metamaterials with Non-Locally Encoded Hidden Symmetry , Advanced Materials, 36 (2024), p. 2303891, https://doi.org/10.1002/adma.202303891

    work page doi:10.1002/adma.202303891 2024

  37. [37]

    C.-L. Sung, W. Wang, F. Cakoni, I. Harris, and Y. Hung , Functional-input G aussian processes with applications to inverse scattering problems , Stat. Sinica, 34 (2024), pp. 1883--1902

    2024

  38. [38]

    Vollmer, S

    F. Vollmer, S. Arnold, and D. Keng , Single virus detection from the reactive shift of a whispering-gallery mode , Proc. Natl. Acad. Sci. USA, 105 (2008), pp. 20701--20704

    2008

  39. [39]

    Zheng, Y.-F

    L.-Y. Zheng, Y.-F. Li, J. Zhang, and Y. Huang , Robust topological edge states induced by latent mirror symmetry , Phys. Rev. B, 108 (2023), p. L220303, https://doi.org/10.1103/PhysRevB.108.L220303

    work page doi:10.1103/physrevb.108.l220303 2023