Pith. sign in

REVIEW 3 major objections 6 minor 9 references

PRISM claims that a heteroscedastic Gaussian displacement field, learned by an implicit neural network, can describe population shape evolution and yield pointwise developmental-uncertainty maps in closed form through a Fisher-information i

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

PRISM learns a neural Gaussian field of shape displacements conditioned on age and uses Fisher information to estimate local temporal uncertainty, but the Cramér–Rao justification confuses latent age with an estimator.

T0 review reviewed 2026-08-03 challenge →

load-bearing objection The PRISM framework is useful and the experiments are thorough, but the central CR-bound argument for temporal uncertainty misapplies the bound to a latent variable and does not stand up as stated. the 3 major comments →

arxiv 2602.11467 v2 pith:5I6U52Q6 submitted 2026-02-12 cs.LG

PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling

Yining Jiao , Sreekalyani Bhamidi , Carlton Jude Zdanski , Julia S Kimbell , Andrew Prince , Cameron P Worden , Samuel Kirse , Christopher Rutter
show 3 more authors
Benjamin H Shields Jisan Mahmud Marc Niethammer
This is my paper
classification cs.LG
keywords implicit neural representationstatistical shape modelingFisher informationintrinsic timeheteroscedastic uncertaintypediatric airwayanomaly detectionCramér–Rao bound
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

PRISM is trying to establish that a single probabilistic implicit neural field can give a closed-form, spatially continuous estimate of how much a person's developmental stage varies at every point on the anatomy, conditioned on age. It models the displacement from a shared template as a heteroscedastic Gaussian with learned mean μ(p,t) and covariance Σ(p,t), then defines temporal uncertainty as the reciprocal Fisher information of the mean trajectory, 1/((∂μ/∂t)ᵀΣ⁻¹(∂μ/∂t)). A sympathetic reader would care because this turns the population distribution of shapes into a directly queryable uncertainty map, enabling intrinsic-age estimation, personalized growth prediction, and local anomaly detection without Monte Carlo sampling or per-patient optimization. The paper validates the idea on synthetic data with known ground truth and on pediatric airway CT scans, where the predicted bands align with observed variation.

Core claim

The central discovery is that the conditional distribution of a 3D displacement at any template point and age can be modeled as a Gaussian with network-predicted mean μ(p,t) and covariance Σ(p,t), and that the variance of a subject's latent developmental stage τ is then expressed, in closed form, as the reciprocal of the mean-trajectory Fisher information: σ²τ(p,t) ≈ 1/((∂μ/∂t)ᵀ Σ⁻¹ (∂μ/∂t)). The full Fisher information also contains a covariance-evolution term, but the paper argues that term measures how population diversity changes with time rather than how an individual localizes along the mean trajectory, so it is dropped. The result is a spatially heteroscedastic uncertainty field that

What carries the argument

The key object is the reciprocal Fisher information, σ²τ(p,t) = 1/((∂μ/∂t)ᵀ Σ⁻¹ (∂μ/∂t)), a closed-form, pointwise temporal-uncertainty measure obtained from derivatives of the learned mean with respect to time. It works by converting the heteroscedastic Gaussian likelihood into an estimation-theoretic bound on latent-time variance, and it is paired with an amortized inverse encoder g(p,d) that predicts intrinsic time from a local displacement in a single forward pass.

Load-bearing premise

The temporal-uncertainty formula only holds if a subject's latent developmental stage τ can be treated as an unbiased estimator of chronological age t that is a function of the observed displacement; the generative model does not enforce this, and when τ has its own variance the claimed bound can fail.

What would settle it

Simulate a dataset exactly from PRISM's generative assumption: draw τ|t ∼ N(t, γ²), then d|τ ∼ N(μ(τ), Σ(τ)); fit the model and compare the empirical variance of recovered τ at fixed t with 1/I. In the one-dimensional Gaussian case the bound predicts Var(τ|t) ≥ γ² + σ², but the generative truth is Var(τ|t) = γ², so the comparison will refute the bound unless τ is reconstructed deterministically from d.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Spatially continuous, resolution-independent uncertainty maps on anatomy become available without Monte Carlo resampling.
  • Per-point intrinsic time can be estimated in one forward pass of the inverse encoder, avoiding test-time optimization.
  • Personalized longitudinal prediction follows from assuming a subject's temporal z-score stays constant and propagating along the learned mean trajectory.
  • Anomaly detection can be localized by comparing each region's intrinsic time to the most developmentally advanced region within the same anatomy.

Where Pith is reading between the lines

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

  • The formula σ²τ ≈ 1/I is a Cramér–Rao lower bound, not an equality; comparing the predicted band to the empirical spread of inferred τ across subjects at a fixed age would show whether the approximation is conservative or optimistic in real data.
  • By discarding the covariance term IΣ, the uncertainty map reflects only how fast the mean shape changes; regions whose variability changes with age but whose mean is static would be reported as fully certain, which may miss a clinically relevant signal.
  • The single-covariate setup suggests a natural extension: for covariates such as age plus sex or height, replace the scalar Fisher information with a Fisher information matrix and a multivariate Cramér–Rao bound, and the same closed-form derivation should carry through.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. PRISM models the conditional distribution of 3D shape displacement d at template point p given covariate t as a heteroscedastic Gaussian N(μ(p,t),Σ(p,t)), with μ and Σ predicted by an MLP. An inverse encoder g maps (p,d) to an estimated intrinsic time τ̂. The paper's central theoretical claim is that the Fisher information of this Gaussian yields a closed-form local temporal uncertainty σ²_τ(p,t)≈1/I(p,t), interpreted as a Cramér–Rao lower bound on the population variance of the latent intrinsic time τ. Experiments on synthetic Starman(G/L), ANNY, and a pediatric airway dataset evaluate mean reconstruction, intrinsic-time estimation, personalized prediction, and OOD detection.

Significance. The paper targets a real gap: spatially resolved, covariate-conditioned uncertainty for statistical shape analysis. The framework is broad, the experiments are extensive, and the closed-form Gaussian Fisher information calculation in Appendix A.2 (Eqs. 68–69) is correct. The synthetic datasets with known ground-truth temporal uncertainty are a strength, as is the idea of an amortized inverse encoder. If the Cramér–Rao-based interpretation were valid, the contribution would be significant. However, the central theoretical step is not valid: the Cramér–Rao bound is applied to a latent variable rather than to an estimator, and the covariance term is discarded in a way that destroys the bound. The reported uncertainty quantities are therefore not the claimed population variances, and the clinical interpretability claims are unsupported. The empirical results may still be useful, but the paper's main contribution as stated does not hold.

major comments (3)
  1. [Sec. 4.3, Eq. (8); Appendix A.2.4] The proof of Eq. (8) assumes E_{p(d|p,t)}[τ]=t and differentiates to obtain E[τ U]=1. This is only valid if τ is a function of the observation d. In the paper's model, d is generated from τ (d|p,τ∼N(μ(p,τ),Σ(p,τ))), so τ is a latent random variable, not a statistic computed from d. The differentiation step in Eq. (72) is therefore unjustified. Concretely, in the hierarchical model d|τ∼N(τ,σ²), τ|t∼N(t,γ²), the marginal is d|t∼N(t,σ²+γ²), so I=1/(σ²+γ²) and Var(τ|t)=γ²<1/I, contradicting Eq. (8). The synthetic validations use noiseless, nearly monotone displacements where 1/Iμ approximately equals Var(τ|t), so they cannot detect this failure.
  2. [Sec. 4.3, Eqs. (9)–(11)] The full Fisher information of the Gaussian is Iμ+IΣ with IΣ≥0. The paper discards IΣ and redefines I(p,t):=Iμ. This is not a Cramér–Rao lower bound: the full-model bound is Var(τ)≥1/(Iμ+IΣ), which does not imply Var(τ)≥1/Iμ because 1/(Iμ+IΣ)≤1/Iμ. Orthogonality of mean and covariance in the Fisher–Rao metric justifies additivity of the two information terms, not omission of one term from the bound. Thus Eq. (11) at best defines a heuristic “temporal discriminability” measure; interpreting 1/Iμ as a lower bound on the population variance of intrinsic time is incorrect.
  3. [Sec. 4.2, Eq. (5); Sec. 5.2, Fig. 4] The inverse encoder g is trained on triplets (p,d,τ) with d=μ(p,τ) sampled from the learned forward model f. The clinical calibration plot in Fig. 4 checks whether observed points lie inside intervals derived from the same f. This is a self-consistency check between g and f, not validation against an independent ground truth. The paper acknowledges that no ground-truth intrinsic time exists for the airway dataset (Sec. 5.1.1), but the sentence “validating the calibration of our uncertainty estimates” (Sec. 5.2) overstates the evidence. Independent biological annotations or a held-out longitudinal cohort would be needed.
minor comments (6)
  1. [Sec. 4.4, Eq. (17)] The notation g(q,p) should be g(q,d_q) (or the point q's observed displacement); as written it suggests the encoder takes p as input.
  2. [Table 3] Table 3 reports only PRISM results; the claim that baselines cannot perform local time estimation should be stated in the main text, and the experimental protocol for baselines in this task should be described.
  3. [Sec. 4.4, Eq. (14)] Eq. (14) defines a global z-score using pointwise σ_τ(t0); clarify how the pointwise uncertainties are aggregated.
  4. [Appendix A.2.3, Eqs. (62)–(63)] The derivation of T3 uses symmetry of A and Σ; state this explicitly for readability.
  5. [Sec. 5.2 / Appendix B.6] Figure 7 is referenced in Sec. 5.2 but appears in Appendix B.6; add a cross-reference.
  6. [Abstract] The statement “The code will be open to public” should include a repository URL or a clear availability statement.

Circularity Check

1 steps flagged

Temporal-uncertainty claim rests on applying the Cramér–Rao bound to the latent variable τ as though it were an estimator computed from d; the proof's key identity assumes the very estimator interpretation that the generative model does not provide.

specific steps
  1. other [Sec. 4.3, Eq. (8); Appendix A.2.4, Step 2 (Eq. 72)]
    "We assume that the population-average intrinsic time equals the chronological time, i.e., Ep(d|p,t)[τ]=t ... Under this assumption, τ can be viewed as an unbiased estimator of t, and the Cramér–Rao inequality yields Var(τ|p,t)≥1/I(p,t) (Eq. 8). ... 1=∂tEp(d|p,t)[τ]=∫ τ·∂tp(d|p,t) dd=Ep(d|p,t)[τ·U] (A.2.4 Step 2)."

    Step 2's identity Ep[τU]=1 is exactly the statement that τ is an unbiased estimator computed from the observed d; it requires ∂t to pass through the d-integral with τ held fixed, i.e. τ is a statistic of d. But Sec. 3 defines τ as a latent variable ('intrinsic time τ, a latent variable representing true developmental progression'), with d generated from τ. For the marginal p(d|p,t), the latent τ is not a function of d, so Var(τ|p,t) is a generative-model input, not the variance of an estimator, and the CR bound does not constrain it. The proof thus assumes the estimator interpretation needed for the conclusion; the 'prediction' σ²_τ≈1/I is the variance of an estimator renamed as latent temporal uncertainty. Synthetic validation is noiseless with d=μ(p,τ), where 1/Iμ equals Var(τ|t) by the

full rationale

The closed-form Fisher information for a heteroscedastic Gaussian (Eq. 9) is a standard, correctly derived result and is not circular; the paper cites classical sources (Skovgaard, Nielsen, Amari) for it. The inverse encoder trained on forward-model-generated triplets is a standard amortized-inference construction, and since the synthetic test shapes are generated by an independent ground-truth process, that part is not circular on its own. No load-bearing self-citations were found: NAISR and ICON/GradICON are baselines or correspondence tools, not inputs to the claimed uncertainty theorem. The central circularity is in Sec. 4.3 / Appendix A.2.4: the Cramér–Rao bound is applied to the latent variable τ by reinterpreting it as an unbiased estimator of t. The proof's key step E[τU]=1 is valid only for a deterministic statistic of d, which contradicts the paper's own generative description where d is generated from τ. Consequently, Eq. (8) does not follow for the latent temporal variance, and Eq. (11) presents the inverse Fisher information as the latent uncertainty by definition of that reinterpretation rather than by derivation. This is a partial circularity: the mathematical machinery is independent, but the central 'prediction' of temporal uncertainty reduces to an assumed estimator property.

Axiom & Free-Parameter Ledger

4 free parameters · 8 axioms · 1 invented entities

The central claim rests on Gaussianity of the displacement field, the correctness of the template-registration pseudo-labels, a specific (and apparently flawed) use of the Cramér–Rao bound, and the decision to discard the covariance Fisher-information term. These are not standard axioms; they are modeling choices that the paper does not independently justify.

free parameters (4)
  • Neural network weights of forward model f (μ and Σ heads) = learned via NLL minimization
    Central quantities μ(p,t), Σ(p,t) are outputs of an MLP; all downstream Fisher information and intrinsic-time estimates are functions of these fitted weights.
  • Neural network weights of inverse encoder g = learned via L1 regression on synthetic pairs (p, μ(p,τ), τ)
    Intrinsic time estimates and OOD scores depend entirely on this trained encoder.
  • Per-subject registration latent codes z_fwd, z_bwd ∈ R^1024 = learned per training shape
    The displacement pseudo-labels d=Φ_bwd(p)-p fed to PRISM come from a registration model whose per-subject codes are fitted; errors propagate to PRISM.
  • Loss weights λ_sdf=3000, λ_norm=100, λ_eik=50, λ_icon=λ_grad=100, λ_L1=λ_NLL=1, Twarm=10 = as listed in Sec. 4.3 and A.1
    Hand-chosen; no sensitivity analysis is provided.
axioms (8)
  • standard math Closed-form Fisher information of a multivariate normal: I = μ_tᵀΣ⁻¹μ_t + ½tr((Σ⁻¹Σ_t)²)
    Used in Eq. (9) and derived in Appendix A.2; cited to Skovgaard (1984) and Nielsen (2023).
  • standard math Isserlis' theorem for fourth moments of a centered Gaussian
    Used in Appendix A.2.2 to compute E[Q²].
  • ad hoc to paper Cramér–Rao inequality applies to the variance of the latent variable τ under the assumption E[τ]=t
    This is the flawed step. The proof treats τ as an unbiased estimator of t, but τ is a latent variable, not a statistic of d; the bound is not valid generally (Sec. 4.3 Eq. 8, Appendix A.2.4).
  • domain assumption Population-average intrinsic time equals chronological time: E_{p(d|p,t)}[τ]=t
    Stated in Sec. 4.3; plausible for population trajectories but unverifiable on clinical data.
  • domain assumption Every observed shape is represented as displacement from a shared template with point correspondence established by a separately trained invertible registration model
    PRISM is trained on pseudo-displacements from this registration (Appendix A.1); errors in correspondence become errors in μ, Σ, and Fisher information.
  • domain assumption p(d|p,t) is exactly a heteroscedastic Gaussian field with covariance parameterized by the network
    Eq. (2); the closed-form FI formula depends on Gaussianity, and the paper does not test normality of residuals.
  • ad hoc to paper Only the mean term Iμ of the Fisher information is retained; the covariance term IΣ is dropped as orthogonal and irrelevant to temporal localization
    Sec. 4.3 Eqs. (9)-(11). Since total information is Iμ+IΣ, using 1/Iμ is not the CR lower bound; this choice is not flagged as an approximation in the main text.
  • domain assumption In personalized prediction, the subject's temporal z-score zτ remains constant over the forecast interval
    Eqs. (14)-(15); no longitudinal validation of this stationarity.
invented entities (1)
  • Latent intrinsic time τ (developmental stage) no independent evidence
    purpose: Represents true biological maturation distinct from chronological age; used to define temporal uncertainty p(τ|p,t), to estimate developmental age from local shape, and to derive the OOD score.
    No direct biological measurement is provided for real subjects; synthetic datasets define τ by construction, and clinical validation is indirect (chronological age as surrogate, qualitative alignment). It is a useful latent construct but not an independently verified entity.

reviewed 2026-08-03 · how reviews work

0 comments
Cite this review

Pith. "Pith review of PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling." pith.science (2026). https://pith.science/paper/5I6U52Q6

@misc{pith2026260211467,
  author       = {Pith},
  title        = {Pith review of: PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5I6U52Q6}},
  note         = {Machine review of arXiv:2602.11467}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Understanding how anatomical shapes evolve in response to developmental covariates - and quantifying their spatially varying uncertainties - is critical in healthcare research. Existing approaches typically rely on global time-warping formulations that ignore spatially heterogeneous dynamics. We introduce PRISM, a novel framework that bridges implicit neural representations with uncertainty-aware statistical shape analysis. PRISM models the conditional distribution of shapes given covariates, providing spatially continuous estimates of both the population mean and covariate-dependent uncertainty at arbitrary locations. A key theoretical contribution is a closed-form Fisher Information metric that enables efficient, analytically tractable local temporal uncertainty quantification via automatic differentiation. Experiments on three synthetic datasets and one clinical dataset demonstrate PRISM's strong performance across diverse tasks - from modeling shape evolution to personalized shape prediction and anomaly detection - within a unified framework, while providing interpretable and clinically meaningful uncertainty estimates.

Figures

Figures reproduced from arXiv: 2602.11467 by Andrew Prince, Benjamin H Shields, Cameron P Worden, Carlton Jude Zdanski, Christopher Rutter, Jisan Mahmud, Julia S Kimbell, Marc Niethammer, Samuel Kirse, Sreekalyani Bhamidi, Yining Jiao.

Figure 1
Figure 1. Figure 1: Overview of the PRISM framework. (a) illustrates the population distribution of developmental stages (e.g., physiological ages) at a fixed covariate (e.g., chronological age), indicating that individuals can be developmentally delayed, expected, or fast. (b) visualizes the probabilistic shape deformation trajectory p(d | p, t), differentiating between variations in developmental progression (indicated by b… view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative validation of uncertainty estimation on the simulated Starman datasets. (a) Results on the Starman(G) dataset and (b) results on the Starman(L) dataset. The plot compares the uncertainty estimates from PRISM at different locations with the ground truth. The blue shaded regions represent the ground truth distribution of the conditional distribution p(τ | p, t), while the red shaded regions show … view at source ↗
Figure 4
Figure 4. Figure 4: Spatially-varying uncertainty quantification across anatomical landmarks in pediatric airways. Each subplot displays the relationship between chronological age t (x-axis) and the predicted intrinsic developmental age τˆ = g(p, d) (y-axis) at a specific anatomical landmark, where g(·) is the learned inverse encoder. Landmarks progress from the nose tip (top-left) to the carina (bottom￾right). The shaded reg… view at source ↗
Figure 5
Figure 5. Figure 5: Starman dataset generation. Left: Template shape with four control points governing arm and leg deformations. Middle: Shape evolution across physical time t ∈ [0, 1]. Right: Temporal uncertainty functions στ (t) for Starman(L), where arms (red) exhibit early growth and legs (blue) exhibit late growth. A.2.5. GEOMETRIC INTERPRETATION OF THE FISHER INFORMATION The additive structure of the Fisher Information… view at source ↗
Figure 6
Figure 6. Figure 6: Preprocessing pipeline for pediatric airway shape analysis. (a) Raw airway geometries are straightened using a rotation￾minimizing frame to remove extrinsic pose variations while preserving intrinsic shape characteristics. (b) An invertible neural network learns bidirectional deformations between each target shape and a common template, with inverse consistency regularization ensuring geometric coherence. … view at source ↗
Figure 7
Figure 7. Figure 7: Probabilistic reconstruction of longitudinal pediatric airway development. This visualization demonstrates PRISM’s capacity to represent real-world clinical data. The columns correspond to increasing ages from left to right. (Row 1) Mean Trajectory: The predicted mean shape evolution (µ(t)), capturing the central trend of anatomical growth. (Rows 2 & 3) Uncertainty Bounds: The shapes generated at the upper… view at source ↗

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

9 extracted references · 3 linked inside Pith

  1. [2]

    (67) A.2.3

    = tr (AΣ)2 = tr (Σ−1Σt)2 .(62) Evaluation ofT 3.By a similar index manipulation (using symmetry ofAandΣ): T3 = X i,j,k,l AijAklΣilΣjk = tr (AΣ)2 =T 2.(63) 17 Combining the terms.We obtain: E[Q2] =T 1 +T 2 +T 3 = (E[Q])2 + 2tr (Σ−1Σt)2 .(64) Therefore, the variance ofQis: Var(Q) =E[Q 2]−(E[Q]) 2 = 2tr (Σ−1Σt)2 .(65) Back toU quadratic.SinceU quadratic = 1 ...

    1984

  2. [3]

    doi: 10.1007/s10994-021-05946-3

    ISSN 1573-0565. doi: 10.1007/s10994-021-05946-3. URL http://dx.doi. org/10.1007/s10994-021-05946-3. Isserlis, L. On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables.Biometrika, 12(1/2):134–139,

    doi:10.1007/s10994-021-05946-3

  3. [4]

    The closed-form Fisher Information for multivariate normal distributions is a classical result (Skovgaard, 1984; Nielsen, 2023)

    The derivations follow standard techniques from estimation theory (Cram´er, 1999; Rao et al., 1945), information geometry (Amari, 2016), and matrix calculus (Petersen et al., 2008). The closed-form Fisher Information for multivariate normal distributions is a classical result (Skovgaard, 1984; Nielsen, 2023). 14 A.2.1. SCOREFUNCTIONDERIVATION We begin wit...

    1999

  4. [9]

    The segmentation model was trained on 68 manually annotated CT-segmentation pairs

    to generate an initial prediction, which then guides a second full-resolution UNet for refined segmentation. The segmentation model was trained on 68 manually annotated CT-segmentation pairs. Centerline Extraction.Following (Hong et al., 2013), we extract the airway centerline by solving Laplace’s equation within the segmented volume. The centerline is de...

    2013

  5. [1975]

    As shown in Fig

    constructed along the extracted airway centerline. As shown in Fig. 6(a), this RMF maps the curved airway into a cylinder-like representation where the z-axis corresponds to airway depth and the xy-plane captures cross-sectional variations. SDF Sampling.Following (Park et al., 2019; Sitzmann et al., 2020), we compute signed distance function (SDF) samples...

    2019

  6. [2016]

    URL https://arxiv.org/abs/1606.06650. 12 A. Theory and Methods Table 6.Summary of notation. Symbol Description Data & Geometry NNumber of shape observations Yi Thei-th observed shape TReference template shape Ω⊂R 3 Canonical domain pTemplate coordinate dDisplacement vector yTarget position (y=p+d) ϕi Displacement field for subjecti Time Variables tChronol...

    Pith/arXiv arXiv 2021

  7. [2021]

    doi: 10.1016/j.inffus.2021.05.008

    ISSN 1566-2535. doi: 10.1016/j.inffus.2021.05.008. URL http://dx. doi.org/10.1016/j.inffus.2021.05.008. Amari, S.-i.Information geometry and its applications, volume

    doi:10.1016/j.inffus.2021.05.008 2021

  8. [2024]

    Jungo, A

    URL https://arxiv.org/abs/2303.09234. Jungo, A. and Reyes, M. Assessing reliability and chal- lenges of uncertainty estimations for medical image seg- mentation. InInternational Conference on Medical Im- age Computing and Computer-Assisted Intervention, pp. 48–56. Springer,

    Pith/arXiv arXiv

  9. [2025]

    URL https://arxiv.org/abs/2511.03589. Cole, T. J., Donaldson, M. D., and Ben-Shlomo, Y . Sitar—a useful instrument for growth curve analysis.International journal of epidemiology, 39(6):1558–1566,

    Pith/arXiv arXiv

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.