Publications

2026

• Quantifying the impact of different forms of stress on fungal growth: an inference method based on high-resolution pictures of the mycelial network
  
  • Kuwata Lena
  • Chassereau Thibault
  • Chapeland-Leclerc Florence
  • David Pascal
  • Herbert Eric
  • Ruprich-Robert Gwenaël
  • Tomašević Milica
  • Véber Amandine
  Theoretical Population Biology, Elsevier, 2026, 172, pp.14-33. In a previous work, a complete methodology for monitoring the growth of a filamentous fungus was introduced, allowing the automated extraction of its graph structure and of its key statistics. In parallel, a stochastic growth-fragmentation model for the dynamics of such mycelial networks was introduced and studied. This simple model depends on three parameters: the elongation speed v of a single filament, the branching rate b_1 of a filament at its open end, and the per unit length rate b_2 at which a budding event happens and creates a new filament branching off from an existing one. Leaving aside the spatial structure of the mycelium and describing its structure essentially through the empirical measure of the lengths of its filament segments, the three parameters of the growth dynamics encoded in the model summarise the local balance between mass creation and regulation through non-linear mechanisms such as anastomosis or density-dependent growth modulation. In this work, we develop a generic statistical inference method based on the large-time behaviour of the stochastic model, and on the high-resolution pictures of the mycelial network obtained using the methodology for fungal growth monitoring, to reconstruct the effective growth parameters v, b_1 and b_2 from a single panorama of the filament network pictured after several hours of development and an empirical measurement of the exponential rate of increase of the number of branch points and apexes. We use this method to analyse the growth dynamics of Podospora anserina mycelia observed under standard conditions and when several forms of stress are applied, in order to quantify the effect of these stresses on the different mechanisms of fungal growth. By comparing the reconstructed effective parameters with the hyphal elongation speed and branching rates estimated from the much more complex dynamical tracking of individual filaments, we find that the effective branching rates we infer are in close agreement with the individual branching rates estimated from the dynamical tracking procedure. This suggests that, in this application at least, the effects of non-linear local regulation mechanisms on branching are well encoded by an effective Markovian rate during the exponential growth phase of the mycelium. By contrast, the effective elongation speed reconstructed with our model-based approach is approximately twice as low as the hyphal elongation speed estimated from the dynamical tracking procedure, a bias that may be explained by a mismatch between the definitions of ``elongation speed'' used in the two approaches. Nevertheless, our results show that the three parameters of our growth-fragmentation model, combined with experimental data that are now readily available, enable us to quantify different components of the exponential growth dynamics of an expanding mycelial network. (10.1016/j.tpb.2026.08.002)
  DOI : 10.1016/j.tpb.2026.08.002
• Bayesian model updating of operating wind turbine blades: A case study on the NREL 5-MW model
  
  • Delette Nina
  • Denimal Goy Enora
  • Pfister Jean-Lou
  • El Amri Mohamed Reda
  • Mevel Laurent
  , 2026. Structural Health Monitoring (SHM) is key to optimizing wind turbine maintenance, but data-driven methods struggle to locate and quantify damage on operational blades. This paper proposes a physics-based model updating framework dedicated to rotating blades. To bypass the limitations of classical Operational Modal Analysis (OMA) caused by blade rotation, we exploit the time-invariant Fourier harmonics of Floquet modes. A Bayesian framework is introduced to account for uncertainties, while a Gaussian Process surrogate model is deployed to reduce calculation costs. Validated on a simulated NREL 5MW turbine, the surrogate model drastically cuts computing time from four months to four hours. The method successfully localizes and quantifies the blade defect within a 10% precision margin, demonstrating that the overall accuracy is highly dependent on the surrogate model fidelity.
• Prediction of Glaze Ice Horns from Aerodynamic Degradation Through Logistic Regression
  
  • Neves Carlos
  • Savoldi Ilaria
  • Congedo Pietro M
  • Denimal Goy Enora
  • Caccia Francesco
  • Guardone Alberto
  Journal of Aircraft, American Institute of Aeronautics and Astronautics, 2026, pp.1 - 19. In-flight, real-time ice detection enhances the pilot's airframe icing awareness during aircraft and unmanned aerial vehicle operations in adverse weather. The objective of this work is to develop a logistic regression-based binary and multi-class classifiers for ice class predictions to determine the onset of glaze ice horns on an airfoil using the degradation of aerodynamic performance during icing at mid-and low-Reynolds conditions. Multi-class classifiers divided the glaze ice horns class into incipient and developed. Cross-validation results yielded validation accuracies of 97% and 71% for ice horns onset detection accuracy. The high validation accuracy indicates that the instantaneous ice class can be inferred from the instantaneous aerodynamic performance. The glaze ice horns onset accuracy of the models was improved by 9% by overfitting the streamlined rime to glaze ice horns transition, and by using the aerodynamic performance time evolution as input. It was observed that a larger training batch reduced the glaze ice horns onset accuracy when using overfitting strategies. The trained models were used in virtual test cases showing that the improved multi-class classifier can anticipate the glaze ice horns onset by sensing a variance increment of the glaze ice horns probability. (10.2514/1.c038899)
  DOI : 10.2514/1.c038899
• Convergence analysis of moment-based approximations in kinetic theory
  
  • Pichard Teddy
  , 2026. As for Galerkin approximations, the method of moments consists in reducing the number of test functions in a variational approach to a finite number, then performing an approximation of the solution such that the resulting reduced problem is well-posed. It is commonly used in kinetic theory, relying on physical considerations, but few error estimates are available in the literature. This paper provides a functional framework adapted to study the convergence of these methods. Its use is illustrated for the convergence study of a vector of moments toward a kinetic distribution, pointwise, on a homogeneous time-dependent problem, and on a 1D-1V problem.
• Regularised double shuffle relations for planar Arborified Zeta Values
  
  • Catoire Pierre
  • Clavier Pierre J.
  • Fan Ku-Yu
  , 2026. We endow spaces of decorated planar rooted trees with new dendriform and tridendrifrom algebra structures and provide their combinatorial description. We then show that the planar counterparts of Arborified Zeta Values are algebra morphisms for these shuffle and quasi- shuffle products of planar rooted trees. We also prove an arborified version of Hoffman’s regularisation relation for Arborified Zeta Values. We conjecture that those give every rational relation between Arborified Zeta Values and show that this conjecture implies the regularised double shuffle conjecture for Multiple Zeta Values.
• Large deviations for mean field particle systems via analysis on spaces of measures
  
  • Pesce Valentin
  , 2026. This paper introduces a robust strategy to establish large deviation principles for mean field interacting particle systems in T d with vanishing noise. Viewed as a Freidlin-Wentzell type problem, our approach relies on recent techniques for partial differential equations (in short PDE) on the space of probability measures [5]. We first outline the proof strategy for the PDE approach to large deviations in a self-contained manner. As the number of particles goes to infinity, we then show that the transfer function of the system converges to the unique viscosity solution of a limiting Hamilton-Jacobi equation on the space of probability measures. Finally, we explicitly derive the rate function by formulating the solution of this limiting PDE as the value function of an optimal control problem.
• A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
  
  • Alfaro Matthieu
  • Chainais-Hillairet Claire
  • Nabet Flore
  Applied Mathematics Letters, Elsevier, 2026, 180, pp.109980. In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalities approach to prove the exponential decay of a relative entropy, and thus the convergence of the solution towards the stationary state selected by the total mass of the initial datum. (10.1016/j.aml.2026.109980)
  DOI : 10.1016/j.aml.2026.109980
• Surrogate-Based Strategies for Accelerated Bayesian Calibration of Computer Codes With Complete Maximum a Posteriori Estimation of Model Error
  
  • Kahol Omar
  • Le Maître Olivier
  • Congedo Pietro M
  • Denimal Goy Enora
  Journal of Mechanical Design, American Society of Mechanical Engineers, 2026, 148 (9). The calibration of a computer code is a process that reduces the uncertainty of model parameters by matching the code’s predictions to experimental observations of a quantity of interest. A more faithful representation of the global uncertainty is achieved by including a model error term, a discrepancy between the physical system and the computer code. The recently proposed complete maximum a posteriori (CMP) method is able to infer both a posterior distribution of the model parameters and a model error term, improving upon traditional frameworks. On the other hand, the CMP method relies on an optimization step which increases the cost of complex calibration problems. This article proposes a surrogate-based strategy to reduce the computational cost of the CMP method. First, we build a surrogate model of the model error’s hyperparameters using Gaussian processes. Second, we propose an iterative algorithm that builds a training set in regions of the parameter space that are more likely, reducing the overall cost of the algorithm and improving the accuracy of the surrogate. The proposed strategy is applied to four different examples, including a design problem in solid mechanics and a complex test case in fluid dynamics. The results show that the proposed strategy is able to accelerate the CMP method without losing accuracy, making it suitable for real-world applications. In an industrial application, we demonstrate a speed-up of almost 100 compared to the original CMP method. (10.1115/1.4071071)
  DOI : 10.1115/1.4071071
• Nonparametric hazard rate estimation with associated kernels and minimax bandwidth choice
  
  • Breuil Luce
  • Kaakai Sarah
  , 2026. <div><p>In this paper, we introduce a general theoretical framework for nonparametric hazard rate estimation using associated kernels, whose shapes depend on the point of estimation. Within this framework, we establish rigorous asymptotic results, including a second-order expansion of the MISE, and a central limit theorem for the proposed estimator. We also prove a new oracle-type inequality for both local and global adaptive bandwidth selection, extending the Goldenshluger–Lepski method to the context of associated kernels. Our results propose a systematic way to construct and analyze new associated kernels. Finally, we show that the general framework applies to the Gamma kernel, and we provide several examples of applications on simulated data and experimental data for the study of aging. </p></div>
• Recurrence and capacity of stable branching random walks
  
  • Aurillard Antoine
  , 2026. We study the linear growth rate of the range of size-conditioned Branching Random Walks (BRW) when the offspring distribution µ is critical and attracted to an α-stable law. This is done via the infinite invariant BRW introduced by Le Gall &amp; Lin and a new criterion which relates this growth rate of the range to a notion of dimension of the underlying tree in a general way. Then, in the transient case (that is, when the range does grow linearly), we extend the notion of branching capacity to this α-stable case. We show that it is still related to the asymptotic probability that a BRW (or its infinite version) reaches a distant set in Z d , and we estimate the α-stable branching capacity of balls.
• A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms
  
  • Orlando Giuseppe
  • Haegeman Ward
  • Pelanti Marica
  • Massot Marc
  Computers and Fluids, Elsevier, 2026, 317, pp.107193. We present a robust computational framework for the numerical solution of a hyperbolic 6-equation single-velocity two-phase system. The system's main interest is that, when combined with instantaneous mechanical relaxation, it recovers the solution of the 5-equation model of Kapila. Several numerical methods based on this strategy have been developed over the years. However, neither the 5- nor 6-equation model admits a complete set of jump conditions because they involve non-conservative products. Different discretizations of these terms in the 6-equation model exist. The precise impact of these discretizations on the numerical solutions of the 5-equation model, in particular for shocks, is still an open question to which this work provides new insights. We consider the phasic total energies as prognostic variables to naturally enforce discrete conservation of total energy and compare the accuracy and robustness of different discretizations for the hyperbolic operator. Namely, we discuss the construction of an HLLC approximate Riemann solver in relation to jump conditions. We then compare an HLLC wave-propagation scheme which includes the non-conservative terms, with Rusanov and HLLC solvers for the conservative part in combination with suitable approaches for the non-conservative terms. We show that some approaches for the discretization of non-conservative terms fit within the framework of path-conservative schemes for hyperbolic problems. We then analyze the use of various numerical strategies on several relevant test cases, showing both the impact of the theoretical shortcomings of the models as well as the importance of the choice of a robust framework for the global numerical strategy. (10.1016/j.compfluid.2026.107193)
  DOI : 10.1016/j.compfluid.2026.107193
• Reinforcement Learning for Solving Multimodal Functions with CMA-ES
  
  • Oedingen Marc
  • Girardin Oskar
  • Hansen Nikolaus
  • Chotard Alexandre
  , 2026, 16989, pp.136-151. In this paper, we investigate dynamic meta-parameter control for the covariance matrix adaptation evolution strategy (CMA-ES) through deep reinforcement learning (DRL). We formalize the online adaptation of meta-parameters as a Markov decision process (MDP), where each iteration corresponds to one decision step. Based on this formalization, we integrate a controller designed with proximal policy optimization (PPO) into CMA-ES that adapts the learning rates of the mean and the damping parameter of cumulative step-size adaptation (CSA) during the optimization run. Importantly, the controller preserves all known invariance properties of CMA-ES. We train the PPO model only on the Rastrigin function. The learned controller enables CMA-ES with default population size to solve a variety of multimodal functions: on the Rastrigin function, the PPO-CMA-ES is four times faster than IPOP-CMA-ES, and it is also highly competitive on a variety of other multimodal functions, while maintaining reasonable performance on unimodal functions. (10.1007/978-3-032-36217-9_9)
  DOI : 10.1007/978-3-032-36217-9_9
• Frequency sorting in graded dispersive resonator arrays via volume-interaction matrices
  
  • Alexopoulos Konstantinos
  , 2026. We study graded arrays of highly dispersive subwavelength resonators through their volume-potential matrix reduction. The reduction gives a finite-dimensional nonlinear resonance problem whose diagonal entries encode the local dispersive response and whose off-diagonal entries encode volume-mediated coupling between distinct resonators. We show that monotone material grading turns this matrix into an analytically controllable frequency sorter. When graded detuning dominates coupling in the reduced characteristic matrix, the characteristic vectors localize near individual resonators; under an explicit half-lattice-site localization condition, this localization becomes a monotone frequency-position map. We also prove a constructive inverse-design statement: prescribed monotone target frequencies can be realized by choosing the local dispersive parameters, with robustness under sufficiently small grading errors. Numerical experiments, whose parameters and algorithms are recorded in an appendix, illustrate localized resonances, designed frequency-position maps, disorder stability, spacing dependence, and a resolved physical Lippmann-Schwinger validation beyond the leading logarithmic quadrature model.
• A two-point phase recovering with spherical wave reference
  
  • Novikov Roman
  • Sivkin Vladimir
  , 2026. We consider a reference wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region. We give two-point formulas for approximate phase recovering of the radiation solution from the intensity of the total solution for the case of spherical reference wave. We show that these formulas can be used, in particular, for approximate phase recovering from holographic data on a single plane. By these formulas, we continue previous studies with plane wave reference.
• Optimal filtering in closed manifolds- a deterministic perspective
  
  • Le Ruz Gaël
  • Moireau Philippe
  , 2026. In this paper, we adopt an optimal control viewpoint to formulate a rigorous deterministic filtering theory when the dynamics and the observations are defined on manifolds. Therefore, our result extends the Mortensen observer to closed manifolds, namely a compact manifold without boundary, in both continuous and discrete time, where the second ultimately yields a convergent time discretization of the first. The resulting observer requires the computation of the viscosity solution of a Hamilton-Jacobi-Bellman equation on the state manifold, which we illustrate on the sphere.
• dd-RCMA-ES: CMA-ES with Projection-Based Restricted Covariance Matrix Adaptation for High-Dimensional Problems
  
  • Akimoto Youhei
  • Hansen Nikolaus
  ACM Transactions on Evolutionary Learning and Optimization, ACM, 2026. This paper addresses the computational challenges of the covariance matrix adaptation evolution strategy (CMA-ES) in high-dimensional optimization of an objective function \(f:\mathbb{R}^{n}\to\mathbb{R}\) where \(n\gg 100\) , particularly for problems exhibiting sparse-sensitivity structures where only a small number of directions are highly sensitive. To overcome the bottleneck associated with the covariance matrix, we propose a novel restricted covariance matrix model, reducing storage requirements from quadratic to linear in \(n\) . An efficient adaptation mechanism for this model is introduced, with linear time complexity per iteration, providing a substantial improvement over the standard CMA-ES. We also present two-point step-size adaptation (TPA) as an alternative to the cumulative step-size adaptation (CSA), particularly suitable for high-dimensional optimization. In contrast to CSA, TPA is not negatively affected by ineffective subspaces, prevalent in higher dimensions where non-relevant design variables may be introduced. The proposed algorithm, dd-RCMA-ES, determines its hyper-parameters based on the problem dimension \(n\) and the model complexity \(k\) , thereby maintaining the out-of-the-box usability of the standard CMA-ES, while offering the flexibility to upper bound the model complexity if desired. Experimental evaluations across 18 test problems in dimensions varying from 80 to 10240 demonstrate the efficiency of dd-RCMA-ES in terms of the number of function calls required to achieve a given target precision. In comparison with other CMA-ES variants, the dd-RCMA-ES excels on problems with sparse structures that comprise a small number of both, highly sensitive and insensitive directions. (10.1145/3840285)
  DOI : 10.1145/3840285
• A simple rigorous integrator for semilinear parabolic PDEs
  
  • Berg Jan Bouwe van Den
  • Breden Maxime
  , 2026. Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results is usually not guaranteed. We propose a new method for the rigorous integration of parabolic PDEs, i.e., the derivation of rigorous and explicit error bounds between the numerically obtained approximate solution and the exact one, which is then proven to exist over the entire time interval considered. These guaranteed error bounds are obtained a posteriori, using a fixed point reformulation based on a piece-wise in time constant approximation of the linearization around the numerical solution. Our setup leads to relatively simple-to-understand estimates, which has several advantages. Most critically, it allows us to optimize various aspects of the proof, and in particular to provide an adaptive time-stepping strategy. In case the solution converges to a stable hyperbolic equilibrium, we are also able to prove this convergence, applying our rigorous integrator with a final, infinitely long timestep. We showcase the ability of our method to rigorously integrate over relatively long time intervals, and to capture non-trivial dynamics, via examples on the Swift--Hohenberg equation, the Ohta--Kawasaki equation and the Kuramoto--Sivashinsky equation. We expect that the simplicity and efficiency of the approach will enable generalization to a wide variety of other parabolic PDEs, as well as applications to boundary value problems.
• A 3D-shell model of left atrial electromechanics
  
  • Ruz Oscar
  • Brito-Pacheco Carlos
  • Vidrascu Marina
  • Chapelle Dominique
  • Fernández Miguel Angel
  Biomechanics and Modeling in Mechanobiology, Springer Verlag, 2026. The thin-walled nature of the atrial myocardium can lead to artificial stiffening when full 3D electromechanical models are discretized using standard finite elements. In this work, we propose an electromechanical model of the left atrium based on a 3D-shell formulation that overcomes these limitations. The model incorporates both passive and active components of atrial tissue mechanics, while atrioventricular interaction is described by the coupling with a 0D electromechanical model of the left ventricle. The proposed approach is assessed under physiological and pathological conditions and systematically compared with the standard full 3D formulation. The results demonstrate the superior robustness and computational efficiency of the proposed 3D-shell electromechanical model. (10.1007/s10237-026-02117-y)
  DOI : 10.1007/s10237-026-02117-y
• Diffusion-based Annealed Boltzmann Generators : benefits, pitfalls and hopes
  
  • Grenioux Louis
  • Noble Maxence
  Transactions on Machine Learning Research, [Amherst Massachusetts]: OpenReview.net, 2022, 2026. Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics. Boltzmann Generators (BGs) tackle it by combining a generative model with a Monte Carlo (MC) correction step to obtain asymptotically unbiased samples from an unnormalized target. Most current BGs use classic MC mechanisms such as importance sampling, which both require tractable likelihoods from the backbone model and scale poorly in high-dimensional, multi-modal targets. We study BGs built on annealed Monte Carlo (aMC), which is designed to overcome these limitations by bridging a simple reference to the target through a sequence of intermediate densities. Diffusion models (DMs) are powerful generative models and have already been incorporated into aMC-based recalibration schemes via the diffusion-induced density path, making them appealing backbones for aMC-BGs. We provide an empirical meta-analysis of DM-based aMC-BGs on controlled multi-modal Gaussian mixtures (varying mode separation, number of modes, and dimension), explicitly disentangling inference effects from learning effects by comparing (i) a perfectly learned DM and (ii) a DM trained from data. Even with a perfect DM, standard integrations using only first-order stochastic denoising kernels fail systematically, whereas second-order denoising kernels can substantially improve performance when covariance information is available. We further propose a deterministic aMC integration based on first-order transport maps derived from DMs, which outperforms the stochastic first-order variant at higher computational cost. Finally, in the learned-DM setting, all DM-aMC variants struggle to produce accurate BGs; we trace the main bottleneck to inaccurate DM log-density estimation.
• From Hyper Roughness to Jumps as H → -1/2
  
  • Abi Jaber Eduardo
  • Attal Elie
  • Rosenbaum Mathieu
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2026, 36 (4), pp.3635-3660. We investigate the weak limit of the hyper-rough square-root process as the Hurst index H goes to -1/2 . This limit corresponds to the fractional kernel $t ^{H-1/2}$ losing integrability at zero. We establish the joint convergence of the couple (X, M) , where X is the hyper-rough process and M the associated martingale, to a fully correlated inverse Gaussian Lévy jump process. This unveils the existence of a continuum between hyper-rough continuous models and jump processes, as a function of the Hurst index. Since we prove a convergence of continuous to discontinuous processes, the usual Skorokhod J1 topology is not suitable for our problem. Instead, we obtain the weak convergence in the Skorokhod M1 topology for X and in the non-Skorokhod S topology for M .
• Strong law of large numbers and condition for supercritical branching processes
  
  • Bansaye Vincent
  • Berah Tresnia
  • Cloez Bertrand
  Probability Theory and Related Fields, Springer Verlag, 2026, pp.38 p.. We consider branching processes for structured populations: each individual is characterised by a type or trait which belongs to a general measurable state space. We focus on the supercritical recurrent case, where the population may survive and grow and the trait distribution converges to a probability measure. The branching process is then expected to be driven by the positive triplet of first eigenvalue problem of the first moment semigroup. Under the assumption of convergence of the renormalized semigroup in weighted total variation norm, we prove strong convergence of the renormalized empirical measure and non-degeneracy of the limit of the martingale. Convergence is obtained under an LlogL condition which provides a Kesten-Stigum result in infinite dimension and relaxes the uniform convergence of the first moment semigroup in the work of Asmussen and Hering in 1976. The techniques of proof combine families of martingales and contraction properties and the truncation procedure of Asmussen and Hering. These results unify part of the literature and capture new situations, as illustrated by absorbed branching diffusion, the house of cards model and some growth-fragmentation processes. (10.1007/s00440-026-01524-7)
  DOI : 10.1007/s00440-026-01524-7
• Deciphering the Replication-Division Coordination in E. coli: A Unified Mathematical framework for Systematic Model Comparison
  
  • Perrin Alexandre
  • Doumic Marie
  • El Karoui Meriem
  • Méléard Sylvie
  , 2025. Despite extensive research, the quantitative principles that govern the coordination between DNA replication and cell division in bacteria remain debated. Multiple theoretical models have been proposed, some postulating that a single regulatory process is sufficient to ensure replication–division coordination, while others argue that two concurrent processes are required for robust control. In this work, we develop a unifying mathematical framework within which models can be consistently formulated, qualitatively analysed and quantitatively compared. This framework also allows us to propose a new double-process model. Through theoretical analysis, we establish the necessary and sufficient conditions under which single-process models can reproduce physiological cell behaviours. Beyond the correlation-based analyses extensively used to date, we further demonstrate within a comprehensive statistical framework that double-process models more accurately recapitulate experimental data across all growth conditions. Specifically, the new model we propose robustly captures the replication-division coordination in every growth regime, thereby providing a foundation for future mechanistic studies. (10.1101/2025.07.25.666816)
  DOI : 10.1101/2025.07.25.666816
• PhysioBlocks: A Python Library for Graph-Based Nodal Simulation of Dynamical Physiological Systems
  
  • Chapelle Dominique
  • Drieu Colin
  • Kimmig François
  , 2026. The PhysioBlocks Python library is designed to simulate the dynamics of physiological systems (in particular cardiovascular systems) represented by graphs of connected components - as e.g.for electrical circuits - 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 global time-discrete system of equations is automatically assembled by using a Modified Nodal Analysis type of approach. 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.
• Asymptotics of a two-species particle system associated to the doubly parabolic Keller-Segel equation in the plane
  
  • Fournier Nicolas
  • Tomasevic Milica
  , 2026. We consider the two-species particle system introduced by Stevens [22] related to the doubly parabolic Keller-Segel equation. It consists of N cells and of a varying number of chemoattractant particles. Cells diffuse in the plane and follow the (mollified) empirical gradient of concentration of chemoattractant. Chemoattractant particles are produced by cells at some constant rate, diffuse and disappear at some constant rate. We show that when the sensitivity of cells to the chemoattractant is small enough, under some rather weak condition on the family of mollifiers, this system approximates the parabolic-parabolic Keller-Segel equation as N → ∞. We also prove that when N is fixed and when the production rate of chemoattractant particles tends to infinity, this system approximates the (non-Markovian) one-species system introduced in [25] and further studied in [12].
• On the simulation of extreme events with neural networks
  
  • Allouche Michaël
  • Girard Stéphane
  • Gobet Emmanuel
  , 2026. This article aims at investigating the use of generative methods based on neural networks to simulate extreme events. Although very popular, these methods are mainly invoked in empirical works. Therefore, providing theoretical guidelines for using such models in extreme values context is of primal importance. To this end, we propose an overview of most recent generative methods dedicated to extremes, giving some theoretical and practical tips on their tail behaviour thanks to both extreme-value and copula tools.