Publications

2025

• PhysioBlocks: an Opensource Python Library for Simulating Block Diagrams of Dynamical Physiological Systems
  
  • Chapelle Dominique
  • Drieu Colin
  • Kimmig François
  , 2025. The PhysioBlocks Python library is designed to simulate the dynamics of physiological systems (in particular cardiovascular systems) represented by block diagrams, in order to provide built-in modularity. Accordingly, a system is represented by a network of modules (blocks) connected by nodes in which they share quantities (degrees of freedom) and exchange fluxes. The user can easily create a new network by combining existing blocks. At a more advanced level, new blocks can be defined. The library is distributed under the LGPL-3.0-only license, and the initial distribution focuses on providing building blocks associated with lumped-parameter models of the cardiovascular system.
• Irreversible thermalization vs reversible dynamics mediated by anomalous correlators: Wave turbulence theory and experiments in optical fibers
  
  • Torres Theo
  • Garnier J.
  • Zanaglia L.
  • Ferraro M.
  • Michel C.
  • Doya V.
  • Fatome J.
  • Kibler B.
  • Wabnitz S.
  • Picozzi Antonio
  • Millot G.
  , 2025. We theoretically and experimentally investigate spontaneous self-organization in a conservative (Hamiltonian) turbulent wave system, operating far from thermodynamic equilibrium. Our system is governed by two coherently coupled nonlinear Schrödinger equations, describing the polarization evolution of light in a dispersive nonlinear optical fiber. The analysis reveals the emergence of two fundamentally distinct turbulent regimes. In a first regime, the waves undergo a slow, irreversible thermalization process, which is accurately described by the wave turbulence kinetic equation and the associated H-theorem of entropy growth. In stark contrast with this expected irreversible process, we identify a second different regime, where strong phase-correlations spontaneously emerge, giving rise to a fast reversible oscillatory dynamics of the normal correlator and anomalous phase-correlator. Experimental observations confirm the occurrence of both irreversible thermalization and reversible dynamics mediated by the anomalous correlated fluctuations. (10.48550/arXiv.2512.17777)
  DOI : 10.48550/arXiv.2512.17777
• A High-order Multi-scale Finite Element Method (MsFEM) for solving Oseen problems in heterogeneous media
  
  • Balazi Loïc
  • Omnes Pascal
  , 2025. An enriched non-conforming Multi-scale Finite Element Method (MsFEM) to solve viscous incompressible flow problems in genuine heterogeneous or porous media was proposed in [Q. Feng, G. Allaire, and P. Omnes, Multiscale Model. Simul., 20(1):462–492, 2022] and further studied in [L. Balazi, G. Allaire, and P. Omnes, preprint \url{https://hal.science/hal-05198860}, 2025]. The main feature of this MsFEM is the consideration of high-order sets of weighting functions: for the velocity, they are polynomials of order $n$ on the faces and of order $n-1$ in the volume of the elements; for the pressure they are polynomials of order $n$ in the element volume. The present paper proposes to extend this method to the Oseen problem in heterogeneous porous media. Through numerical simulations, specially for the case $n=2$, we show that the developed MsFEM is able to deal with high Reynolds numbers.
• Optimal control under unknown intensity with Bayesian learning
  
  • Baradel Nicolas
  • Cormier Quentin
  , 2024. We consider an optimal control problem inspired by neuroscience, where the dynamics is driven by a Poisson process with a controlled stochastic intensity and an uncertain parameter. Given a prior distribution for the unknown parameter, we describe its evolution according to Bayes' rule. We reformulate the optimization problem using Girsanov's theorem and establish a dynamic programming principle. Finally, we characterize the value function as the unique viscosity solution to a finite-dimensional Hamilton-Jacobi-Bellman equation, which can be solved numerically.
• Efficient Monte-Carlo sampling of metastable systems using non-local collective variable updates
  
  • Schönle Christoph
  • Carbone Davide
  • Gabrié Marylou
  • Lelièvre Tony
  • Stoltz Gabriel
  , 2025. Monte-Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several works. Here, we generalize these approaches and explicitly spell out an algorithm for non-linear CVs and underdamped Langevin dynamics. We prove reversibility of the resulting scheme and demonstrate its performance on several numerical examples, observing a substantial performance increase compared to methods based on overdamped Langevin dynamics as considered previously. Advances in generative machine-learning-based proposal samplers now enable efficient sampling in CV spaces of intermediate dimensionality (tens to hundreds of variables), and our results extend their applicability toward more realistic molecular systems.
• Spatio-temporal equilibrium thermodynamics of guided optical waves at positive and negative temperatures
  
  • Zanaglia Lucas
  • Garnier Josselin
  • Michel Claire
  • Doya Valérie
  • Ferraro Mario
  • Wabnitz Stefan
  • Carusotto Iacopo
  • Picozzi Antonio
  , 2025. Optical thermalization has been recently studied theoretically and experimentally in the 2D spatial evolution of (quasi-)monochromatic light waves propagating in multimode fibers. In this work, we investigate the spatio-temporal equilibrium properties of incoherent multimode optical waves through the analysis of the (2+1)D Bose-Einstein thermal distribution and the corresponding classical Rayleigh-Jeans approximation. In the anomalous dispersion regime, the spatio-temporal equilibrium is characterized by positive temperatures. In this regime, we show that as the number of modes of the waveguide increases, the fundamental spatial mode becomes macroscopically populated, while its temporal spectrum undergoes significant narrowing, ultimately leading to complete (2+1)D spatio-temporal condensation in the thermodynamic limit. In the normal dispersion regime, the spatio-temporal equilibrium is characterized by negative temperature states that exhibit a hybrid character: the spatial equilibrium displays an inverted modal population, whereas the temporal spectrum remains peaked around the fundamental (carrier) optical frequency. In this regime, we predict that spatio-temporal light waves exhibit a phase transition to Bose-Einstein condensation at negative temperatures, which occurs by increasing the temperature above a negative critical value. Our work opens new avenues for future research, including the possibility for a dual spatio-temporal beam cleaning through full spatio-temporal light condensation, and lay the groundwork for the development of spatio-temporal optical thermodynamics. (10.48550/arXiv.2512.07784)
  DOI : 10.48550/arXiv.2512.07784
• Linear-quadratic optimal control for non-exchangeable mean-field SDEs and applications to systemic risk
  
  • de Crescenzo Anna
  • de Feo Filippo
  • Pham Huyên
  , 2025. We study the linear-quadratic control problem for a class of non-exchangeable mean-field systems, which model large populations of heterogeneous interacting agents. We explicitly characterize the optimal control in terms of a new infinite-dimensional system of Riccati equations, for which we establish existence and uniqueness. To illustrate our results, we apply this framework to a systemic risk model involving heterogeneous banks, demonstrating the impact of agent heterogeneity on optimal risk mitigation strategies.
• Estimation of extreme quantile from heavy tailed distributions with neural networks
  
  • Girard Stéphane
  • Allouche Michaël
  • Gobet Emmanuel
  , 2025. We propose new parameterizations for neural networks in order to estimate extreme risk measures, such as conditional tail moments or extreme quantiles, in heavy-tailed settings. The proposed neural network estimator is able to extrapolate in the distribution tails thanks to an extension of the usual extreme-value second-order condition to an arbitrary order. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail.
• Certificates for nonnegativity of multivariate integer polynomials under perturbations
  
  • Bender Matías R
  • Kozhasov Khazhgali
  • Tsigaridas Elias
  • Zhu Chaoping
  , 2025. We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their gradient ideals. We remove the two structural assumptions typically required by other approaches, namely that the polynomial attains its infimum and zero-dimensionality of the gradient ideal. Our approach combines a denominator-free stereographic transformation with a refined variant of the Hanzon–Jibetean perturbation scheme. The stereographic transformation preserves nonnegativity while making the polynomial coercive, with explicit bounds on the radius of positivity and on the nonzero critical values. Subsequently, we apply carefully constructed explicit perturbations that enforce zero-dimensionality of the gradient ideal without altering nonnegativity, allowing us to invoke recent algorithms to derive algebraic certificates or rational witness points. We present three algorithms implementing our framework and analyze their bit complexity in detail, which is single exponential with respect to the number of variables. A second contribution is a new explicit SOS perturbation scheme, which allows us to perturb any nonnegative polynomial in such a way that it can be written as a sum of squares (SOS). In contrast to Lasserre’s classical SOS approximation, which guaranties density but currently does not provide an effective control over the perturbation size, we only derive concrete perturbation bounds ensuring that a nonnegative polynomial enters the SOS cone.
• Duality between polyhedral approximation of value functions and optimal quantization of measures
  
  • Mehamdi Abdellah Bulaich
  • van Ackooij Wim
  • Brotcorne Luce
  • Gaubert Stéphane
  • Jacquet Quentin
  , 2025. Approximating a convex function by a polyhedral function that has a limited number of facets is a fundamental problem with applications in various fields, from mitigating the curse of dimensionality in optimal control to bi-level optimization. We establish a connection between this problem and the optimal quantization of a positive measure. Building on recent stability results in optimal transport, by Delalande and Mérigot, we deduce that the polyhedral approximation of a convex function is equivalent to the quantization of the Monge-Ampère measure of its Legendre-Fenchel dual. This duality motivates a simple greedy method for computing a parsimonious approximation of a polyhedral convex function, by clustering the vertices of a Newton polytope. We evaluate our algorithm on two applications: 1) A high-dimensional optimal control problem (quantum gate synthesis), leveraging McEneaney's max-plus-based curse-of-dimensionality attenuation method; 2) A bi-level optimization problem in electricity pricing. Numerical results demonstrate the efficiency of this approach.
• A generic framework to derive systems of conservation laws with source terms and its application to heat conduction in fluid flows: an alternative to the method of moments in kinetic theory of gases?
  
  • Haegeman Ward
  • Kokh Samuel
  • Massot Marc
  • Orlando Giuseppe
  ESAIM: Proceedings and Surveys, EDP Sciences, 2025, 78, pp.80-97. A generic framework to derive systems of conservation laws through the Stationary Action Principle is proposed. The equations are expressed in Eulerian coordinates while the variation of the action assumes an underlying Lagrangian description thus avoiding the need for any Lin constraint. The resulting models admit a supplementary conservation equation for the evolution of the Hamiltonian. We then use the newly developed framework to derive a hyperbolic model that includes heat conduction in the compressible fluid dynamics equations through the introduction of a new variable called the thermal impulse. The resulting model has already been obtained previously through the Stationary Action Principle but its derivation relied on several non-standard assumptions. Our new framework allows not only to lift these assumptions, but also to recover them as a consequence of the Stationary Action Principle. Finally, a comparison with a model including heat conduction derived through the kinetic theory of gases is conducted. (10.1051/proc/202578080)
  DOI : 10.1051/proc/202578080
• Continuity and approximability of competitive spectral radii
  
  • Akian Marianne
  • Gaubert Stéphane
  • Marchesini Loïc
  • Morris Ian
  , 2025. The competitive spectral radius extends the notion of joint spectral radius to the two-player case: two players alternatively select matrices in prescribed compact sets, resulting in an infinite matrix product; one player wishes to maximize the growth rate of this product, whereas the other player wishes to minimize it. We show that when the matrices represent linear operators preserving a cone and satisfying a "strict positivity" assumption, the competitive spectral radius depends continuously - and even in a Lipschitz-continuous way - on the matrix sets. Moreover, we show that the competive spectral radius can be approximated up to any accuracy. This relies on the solution of a discretized infinite dimensional non-linear eigenproblem. We illustrate the approach with an example of age-structured population dynamics.
• Variational inference for approximate objective priors using neural networks
  
  • Baillie Nils
  • Van Biesbroeck Antoine
  • Gauchy Clément
  Computo, Société Française de Statistique, 2025. In Bayesian statistics, the choice of the prior can have an important influence on the posterior and the parameter estimation, especially when few data samples are available. To limit the added subjectivity from a priori information, one can use the framework of objective priors, more particularly, we focus on reference priors in this work. However, computing such priors is a difficult task in general. Hence, we consider cases where the reference prior simplifies to the Jeffreys prior. We develop in this paper a flexible algorithm based on variational inference which computes approximations of priors from a set of parametric distributions using neural networks. We also show that our algorithm can retrieve modified Jeffreys priors when constraints are specified in the optimization problem to ensure the solution is proper. We propose a simple method to recover a relevant approximation of the parametric posterior distribution using Markov Chain Monte Carlo (MCMC) methods even if the density function of the parametric prior is not known in general. Numerical experiments on several statistical models of increasing complexity are presented. We show the usefulness of this approach by recovering the target distribution. The performance of the algorithm is evaluated on both prior and posterior distributions, jointly using variational inference and MCMC sampling. (10.57750/76fh-t442)
  DOI : 10.57750/76fh-t442
• Equality of tropical rank and dimension for tropical linear series
  
  • Amini Omid
  • Gaubert Stéphane
  • Gierczak Lucas
  , 2024. The tropical rank of a semimodule of rational functions on a metric graph mirrors the concept of rank in linear algebra. Defined in terms of the maximal number of tropically independent elements within the semimodule, this quantity has remained elusive due to the challenges of computing it in practice. In this note, we establish that the tropical rank is, in fact, precisely equal to the topological dimension of the semimodule, one more than the dimension of the associated linear system of divisors. Moreover, we show that the equality of divisorial and tropical ranks in the definition of tropical linear series is equivalent to the pure dimensionality of the corresponding linear system. We conclude with several complementary results and questions on combinatorial, topological, and computability properties of the tropical rank.
• Quantitative rigidity of the Wasserstein contraction under convolution
  
  • Fathi Max
  • Goldman Michael
  • Tsodyks Daniel
  , 2025. <div><p>The aim of this paper is to investigate the contraction properties of p-Wasserstein distances with respect to convolution in Euclidean spaces both qualitatively and quantitatively. We connect this question to the question of uniform convexity of the Kantorovich functional on which there was substantial recent progress (mostly for p = 2 and partially for p &gt; 1). Motivated by this connection we extend these uniform convexity results to the case p = 1, which is of independent interest.</p></div>
• Preconditioned Langevin Dynamics with Score-based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems
  
  • Baldassari Lorenzo
  • Garnier Josselin
  • Sølna Knut
  • de Hoop Maarten V.
  , 2025. Designing algorithms for solving high-dimensional Bayesian inverse problems directly in infinite‑dimensional function spaces – where such problems are naturally formulated – is crucial to ensure stability and convergence as the discretization of the underlying problem is refined. In this paper, we contribute to this line of work by analyzing a widely used sampler for linear inverse problems: Langevin dynamics driven by score‑based generative models (SGMs) acting as priors, formulated directly in function space. Building on the theoretical framework for SGMs in Hilbert spaces, we give a rigorous definition of this sampler in the infinite-dimensional setting and derive, for the first time, error estimates that explicitly depend on the approximation error of the score. As a consequence, we obtain sufficient conditions for global convergence in Kullback–Leibler divergence on the underlying function space. Preventing numerical instabilities requires preconditioning of the Langevin algorithm and we prove the existence and form of an optimal preconditioner. The preconditioner depends on both the score error and the forward operator and guarantees a uniform convergence rate across all posterior modes. Our analysis applies to both Gaussian and a general class of non‑Gaussian priors. Finally, we present examples that illustrate and validate our theoretical findings.
• Efficient multi-fidelity Gaussian process regression for noisy outputs and non-nested experimental designs
  
  • Baillie Nils
  • Kerleguer Baptiste
  • Feau Cyril
  • Garnier Josselin
  , 2025. This paper presents a multi-fidelity Gaussian process surrogate modeling that generalizes the recursive formulation of the auto-regressive model when the high-fidelity and low-fidelity data sets are noisy and not necessarily nested. The estimation of high-fidelity parameters by the EM (expectation-maximization) algorithm is shown to be still possible in this context and a closed-form update formula is derived when the scaling factor is a parametric linear predictor function. This yields a decoupled optimization strategy for the parameter selection that is more efficient and scalable than the direct maximum likelihood maximization. The proposed approach is compared to other multi-fidelity models, and benchmarks for different application cases of increasing complexity are provided.
• A holographic non-uniqueness for the Helmholtz equation
  
  • Novikov Roman
  • Sivkin Vladimir
  , 2025. We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in $\mathbb{R}^d$ , $d \geq 2$, outside the origin. We consider a sphere $S$ centered at the origin in $\mathbb{R}^d$ . We show that the radiation solution on $S$ is not uniquely determined by the intensity of the total solution on $S$. Extensions of this result to the case of other surfaces in place of $S$ are also mentioned. Our construction involves and develops technique of scattering on obstacles with Dirichlet boundary condition.
• Tight analyses of first-order methods with error feedback
  
  • Thomsen Daniel Berg
  • Taylor Adrien
  • Dieuleveut Aymeric
  , 2025. Communication between agents often constitutes a major computational bottleneck in distributed learning. One of the most common mitigation strategies is to compress the information exchanged, thereby reducing communication overhead. To counteract the degradation in convergence associated with compressed communication, error feedback schemes -- most notably $\mathrm{EF}$ and $\mathrm{EF}^{21}$ -- were introduced. In this work, we provide a tight analysis of both of these methods. Specifically, we find the Lyapunov function that yields the best possible convergence rate for each method -- with matching lower bounds. This principled approach yields sharp performance guarantees and enables a rigorous, apples-to-apples comparison between $\mathrm{EF}$, $\mathrm{EF}^{21}$, and compressed gradient descent. Our analysis is carried out in the simplified single-agent setting, which allows for clean theoretical insights and fair comparison of the underlying mechanisms. (10.48550/arXiv.2506.05271)
  DOI : 10.48550/arXiv.2506.05271
• Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs
  
  • Mazelet Sonia
  • Flamary Rémi
  • Thirion Bertrand
  , 2025. Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally expensive, which limits the scalability of these methods to large graphs. In this work, we present Unbalanced Learning of Optimal Transport (ULOT), a deep learning method that predicts optimal transport plans between two graphs. Our method is trained by minimizing the fused unbalanced Gromov-Wasserstein (FUGW) loss. We propose a novel neural architecture with cross-attention that is conditioned on the FUGW tradeoff hyperparameters. We evaluate ULOT on synthetic stochastic block model (SBM) graphs and on real cortical surface data obtained from fMRI. ULOT predicts transport plans with competitive loss up to two orders of magnitude faster than classical solvers. Furthermore, the predicted plan can be used as a warm start for classical solvers to accelerate their convergence. Finally, the predicted transport plan is fully differentiable with respect to the graph inputs and FUGW hyperparameters, enabling the optimization of functionals of the ULOT plan.<p>Preprint. Under review.</p>
• Graph Alignment via Birkhoff Relaxation
  
  • Varma Sushil Mahavir
  • Waldspurger Irène
  • Massoulié Laurent
  , 2025. We consider the graph alignment problem, wherein the objective is to find a vertex correspondence between two graphs that maximizes the edge overlap. The graph alignment problem is an instance of the quadratic assignment problem (QAP), known to be NP-hard in the worst case even to approximately solve. In this paper, we analyze Birkhoff relaxation, a tight convex relaxation of QAP, and present theoretical guarantees on its performance when the inputs follow the Gaussian Wigner Model. More specifically, the weighted adjacency matrices are correlated Gaussian Orthogonal Ensemble with correlation $\frac{1}{1+\sigma^2}$ .
• Thresholds for sensitive optimality and Blackwell optimality in stochastic games
  
  • Gaubert Stéphane
  • Grand-Clément Julien
  • Katz Ricardo D.
  , 2025. We investigate refinements of the mean-payoff criterion in two-player zero-sum perfect-information stochastic games. A strategy is Blackwell optimal if it is optimal in the discounted game for all discount factors sufficiently close to $1$. The notion of $d$-sensitive optimality interpolates between mean-payoff optimality (corresponding to the case $d=-1$) and Blackwell optimality ($d=+\infty$). The Blackwell threshold $α_{\sf Bw} \in [0,1[$ is the discount factor above which all optimal strategies in the discounted game are guaranteed to be Blackwell optimal. The $d$-sensitive threshold $α_{\sf d} \in [0,1[$ is defined analogously. Bounding $α_{\sf Bw}$ and $α_{\sf d}$ are fundamental problems in algorithmic game theory, since these thresholds control the complexity for computing Blackwell and $d$-sensitive optimal strategies, by reduction to discounted games which can be solved in $O\left((1-α)^{-1}\right)$ iterations. We provide the first bounds on the $d$-sensitive threshold $α_{\sf d}$ beyond the case $d=-1$, and we establish improved bounds for the Blackwell threshold $α_{\sf Bw}$. This is achieved by leveraging separation bounds on algebraic numbers, relying on Lagrange bounds and more advanced techniques based on Mahler measures and multiplicity theorems.
• The quest for the GRAph Level autoEncoder (GRALE)
  
  • Krzakala Paul
  • Melo Gabriel
  • Laclau Charlotte
  • d'Alché-Buc Florence
  • Flamary Rémi
  , 2025. Although graph-based learning has attracted a lot of attention, graph representation learning is still a challenging task whose resolution may impact key application fields such as chemistry or biology. To this end, we introduce GRALE, a novel graph autoencoder that encodes and decodes graphs of varying sizes into a shared embedding space. GRALE is trained using an Optimal Transport-inspired loss that compares the original and reconstructed graphs and leverages a differentiable node matching module, which is trained jointly with the encoder and decoder. The proposed attention-based architecture relies on Evoformer, the core component of AlphaFold, which we extend to support both graph encoding and decoding. We show, in numerical experiments on simulated and molecular data, that GRALE enables a highly general form of pre-training, applicable to a wide range of downstream tasks, from classification and regression to more complex tasks such as graph interpolation, editing, matching, and prediction.
• Design of experiments based on a low fidelity model for seismic fragility curves estimation
  
  • Van Biesbroeck Antoine
  • Gauchy Clément
  • Feau Cyril
  • Garnier Josselin
  ESAIM: Proceedings and Surveys, EDP Sciences, 2025, 79, pp.96-109. Seismic fragility curves are key quantities of interest for Seismic Probabilistic Risk Assessment studies. They express the probability of failure of a mechanical structure of interest conditional to a scalar value derived from the ground motion signal coined Intensity Measure. In the literature, Bayesian approaches have emerged to enable their estimation within the difficult context of limited data availability. Yet, the log-normal modeling over which most of them are based requires the use of computationally expensive Markov chain Monte Carlo methods for providing Bayesian estimators. In this work, we propose an efficient modeling for the estimation of fragility curves in the Bayesian context, based on a low fidelity model of the structure’s response to the ground motion signal and an objective prior. The analytical expression of our modeling allows fast generation of estimates. Also, the representative bias arisen by the modeling choice is handled with a judicious design of experiments methodology. Finally, our method is evaluated on a real case study, and the results highlight its efficiency and its ability to robustly overcome any bias when coupled with the design of experiments we propose. (10.1051/proc/202579096)
  DOI : 10.1051/proc/202579096
• The Nullstellensatz and Positivstellensatz for Sparse Tropical Polynomial Systems
  
  • Akian Marianne
  • Béreau Antoine
  • Gaubert Stéphane
  Foundations of Computational Mathematics, Springer Verlag, 2025. Grigoriev and Podolskii (2018) have established a tropical analogue of the effective Nullstellensatz, showing that a system of tropical polynomial equations is solvable if and only if a linearized system obtained from a truncated Macaulay matrix is solvable. They provided an upper bound of the minimal admissible truncation degree, as a function of the degrees of the tropical polynomials. We establish a tropical Nullstellensatz adapted to sparse tropical polynomial systems. Our approach is inspired by a construction of Canny-Emiris (1993), refined by Sturmfels (1994). This leads to an improved bound of the truncation degree, which coincides with the classical Macaulay degree in the case of n + 1 equations in n unknowns. We also establish a tropical Positivstellensatz, allowing one to decide the inclusion of tropical basic semialgebraic sets. This allows one to reduce decision problems for tropical semi-algebraic sets to the solution of systems of tropical linear equalities and inequalities. (10.1007/s10208-025-09708-8)
  DOI : 10.1007/s10208-025-09708-8