Publications

2025

• Byzantine-Robust Gossip: Insights from a Dual Approach
  
  • Gaucher Renaud
  • Dieuleveut Aymeric
  • Hendrikx Hadrien
  , 2025. Distributed learning has many computational benefits but is vulnerable to attacks from a subset of devices transmitting incorrect information. This paper investigates Byzantine resilient algorithms in a decentralized setting, where devices communicate directly in a peer-to-peer manner within a communication network. We leverage the so-called dual approach for decentralized optimization and propose a Byzantine-robust algorithm. We provide convergence guarantees in the average consensus subcase, discuss the potential of the dual approach beyond this subcase, and re-interpret existing algorithms using the dual framework. Lastly, we experimentally show the soundness of our method.
• Long time behavior of a degenerate stochastic system modeling the response of a population face to environmental impacts
  
  • Collet Pierre
  • Ecotière Claire
  • Méléard Sylvie
  Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2025, 30 (none). We study the asymptotics of a two-dimensional stochastic differential system with a degenerate diffusion matrix. This system describes the dynamics of a population where individuals contribute to the degradation of their environment through two different behaviors. We exploit the almost one-dimensional form of the dynamical system to compute explicitly the Freidlin-Wentzell action functional. That allows to give conditions under which the small noise regime of the invariant measure is concentrated around the equilibrium of the dynamical system having the smallest diffusion coefficient. (10.1214/24-ECP650)
  DOI : 10.1214/24-ECP650
• ExceedGAN: Simulation above extreme thresholds using Generative Adversarial Networks
  
  • Allouche Michaël
  • Girard Stéphane
  • Gobet Emmanuel
  Extremes, Springer Verlag (Germany), 2025. This paper devises a novel neural-inspired approach for simulating multivariate extremes. Specifically, we propose a GAN-based generative model for sampling multivariate data exceeding large thresholds, giving rise to what we refer to as the ExceedGAN algorithm. Our approach is based on approximating marginal log-quantile functions using feedforward neural networks with eLU activation functions specifically introduced for bias correction. An error bound is provided {on the margins}, assuming a $J$th order condition from extreme value theory. The numerical experiments illustrate that ExceedGAN outperforms competitors, both on synthetic and real-world data sets.
• Crediting football players for creating dangerous actions in an unbiased way: the generation of threat (GoT) indices
  
  • Baouan Ali
  • Coustou Sebastien
  • Lacome Mathieu
  • Pulido Sergio
  • Rosenbaum Mathieu
  Journal of Quantitative Analysis in Sports, De Gruyter, 2025. We introduce an innovative methodology to identify football players at the origin of threatening actions in a team. In our framework, a threat is defined as entering the opposing team's danger area. We investigate the timing of threat events and ball touches of players, and capture their correlation using Hawkes processes. Our model-based approach allows us to evaluate a player's ability to create danger both directly and through interactions with teammates. We define a new index, called Generation of Threat (GoT), that measures in an unbiased way the contribution of a player to threat generation. For illustration, we present a detailed analysis of Chelsea's 2016-2017 season, with a standout performance from Eden Hazard. We are able to credit each player for his involvement in danger creation and determine the main circuits leading to threat. In the same spirit, we investigate the danger generation process of Stade Rennais in the 2021-2022 season. Furthermore, we establish a comprehensive ranking of Ligue 1 players based on their generated threat in the 2021-2022 season. Our analysis reveals surprising results, with players such as Jason Berthomier, Moses Simon and Frederic Guilbert among the top performers in the GoT rankings. We also present a ranking of Ligue 1 central defenders in terms of generation of threat and confirm the great performance of some center-back pairs, such as Nayef Aguerd and Warmed Omari.
• Partial regularity for optimal transport with $p$-cost away from fixed points
  
  • Goldman Michael
  • Koch Lukas
  Proceedings of the American Mathematical Society, American Mathematical Society, 2025. We consider maps $T$ solving the optimal transport problem with a cost $c(x-y)$ modeled on the $p$-cost. For Hölder continuous marginals, we prove a $C^{1,\alpha}$-partial regularity result for $T$ in the set $\{\lvert T(x)-x\rvert>0\}$.
• Signature volatility models: pricing and hedging with Fourier
  
  • Abi Jaber Eduardo
  • Gérard Louis-Amand
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2025, 16 (2). We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is remarkably universal, as it includes, but is not limited to, the celebrated Stein-Stein, Bergomi, and Heston models, together with some path-dependent variants. Second, we derive the joint characteristic functional of the log-price and integrated variance provided that some infinitedimensional extended tensor algebra valued Riccati equation admits a solution. This allows us to price and (quadratically) hedge certain European and path-dependent options using Fourier inversion techniques. We highlight the efficiency and accuracy of these Fourier techniques in a comprehensive numerical study. (10.1137/24M1636952)
  DOI : 10.1137/24M1636952
• Volume growth of Funk geometry and the flags of polytopes
  
  • Faifman Dmitry
  • Vernicos Constantin
  • Walsh Cormac
  Geometry and Topology, Mathematical Sciences Publishers, 2025, 29 (7), pp.3773-3811. We consider the Holmes-Thompson volume of balls in the Funk geometry on the interior of a convex domain. We conjecture that for a fixed radius, this volume is minimized when the domain is a simplex and the ball is centered at the barycenter, or in the centrally-symmetric case, when the domain is a Hanner polytope. This interpolates between Mahler's conjecture and Kalai's flag conjecture. We verify this conjecture for unconditional domains. For polytopal Funk geometries, we study the asymptotics of the volume of balls of large radius, and compute the two highest-order terms. The highest depends only on the combinatorics, namely on the number of flags. The second highest depends also on the geometry, and thus serves as a geometric analogue of the centro-affine area for polytopes. We then show that for any polytope, the second highest coefficient is minimized by a unique choice of center point, extending the notion of Santaló point. Finally, we show that, in dimension two, this coefficient, with respect to the minimal center point, is uniquely maximized by affine images of the regular polygon. (10.2140/gt.2025.29.3773)
  DOI : 10.2140/gt.2025.29.3773
• Learning homogenized hyperelastic behavior for topology optimization of lattice structures
  
  • Ribeiro Nogueira Breno
  • Allaire Grégoire
  , 2025. (10.5281/zenodo.14900138)
  DOI : 10.5281/zenodo.14900138
• Finite elements for Wasserstein $W_p$ gradient flows
  
  • Cancès Clément
  • Matthes Daniel
  • Nabet Flore
  • Rott Eva-Maria
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2025, 59 (3), pp.1565-1600. Wasserstein $\bbW_p$ gradient flows for nonlinear integral functionals of the density yield degenerate parabolic equations involving diffusion operators of $q$-Laplacian type, with $q$ being $p$'s conjugate exponent. We propose a finite element scheme building on conformal $\mathbb{P}_1$ Lagrange elements with mass lumping and a backward Euler time discretization strategy. Our scheme preserves mass and positivity while energy decays in time. Building on the theory of gradient flows in metric spaces, we further prove convergence towards a weak solution of the PDE that satisfies the energy dissipation equality. The analytical results are illustrated by numerical simulations. (10.1051/m2an/2025035)
  DOI : 10.1051/m2an/2025035
• A holographic uniqueness theorem for the two-dimensional Helmholtz equation
  
  • Nair Arjun
  • Novikov Roman
  The Journal of Geometric Analysis, Springer, 2025, 35 (4), pp.123. We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in $\mathbb R^2$. We consider a straight line in this region, such that the direction of propagation of the plane wave is not parallel to this line. We show that the radiation solution in the exterior region is uniquely determined by the intensity of the total solution on an interval of this line. In particular, this result solves one of the old mathematical questions of holography in its two-dimensional setting. Our proofs also contribute to the theory of the Karp expansion of radiation solutions in two dimensions. (10.1007/s12220-025-01949-x)
  DOI : 10.1007/s12220-025-01949-x
• Objective assessment of cardiac function using patient-specific biophysical modeling based on cardiovascular MRI combined with catheterization
  
  • Gusseva Maria
  • Castellanos Daniel Alexander
  • Veeram Reddy Surendranath
  • Hussain Tarique
  • Chapelle Dominique
  • Chabiniok Radomír
  AJP - Heart and Circulatory Physiology, American Physiological Society, 2025, 329 (5), pp.H118-H1191. Synthesizing multi-modality data, such as cardiovascular magnetic resonance imaging (MRI) combined with catheterization, into a single framework is challenging. Different acquisition systems are subjected to different measurement errors. Coupling clinical data with biomechanical models can assist in clinical data processing (e.g., model-based filtering of measurement noise) and quantify myocardial mechanics via metrics not readily available in the data, such as myocardial contractility. In this work we use a biomechanical modeling with the aim 1) to quantitatively compare model- and data-derived signals, and 2) to explore the potential of model-derived myocardial contractility and distal resistance of the circulation (Rd) to robustly quantify cardiovascular physiology. We used 51 ventricular catheterization pressure and cine MRI volume datasets from patients with single-ventricle physiology and left and right ventricles of patients with repaired tetralogy of Fallot. Ventricular time-varying elastance (TVE) metrics and linear regression were used to quantify the relationship between the maximum value of TVE (Emax) and maximum time derivative of ventricular pressure (max(dP/dt)) in data- and model-derived pressure and volume signals at p<0.05. Pearson’s correlations were used to compare model-derived contractility and data-derived Emax and max(dP/dt), and model-derived Rd and data-derived vascular resistance. All data and model-derived linear regressions were significant (p<0.05). Model-derived max(dP/dt) vs. data-derived Emax produced higher R2 than data-derived max(dP/dt) vs. data-derived Emax. Correlations demonstrated significant relationships between most data- and model-derived metrics. This work revealed the clinical value of biomechanical modeling to assist in clinical data processing by providing high-quality pressure and volume signals, and to quantify cardiovascular pathophysiology. (10.1152/ajpheart.00232.2025)
  DOI : 10.1152/ajpheart.00232.2025