Publications

2022

• Approximate Nash equilibria in large nonconvex aggregative games
  
  • Liu Kang
  • Oudjane Nadia
  • Wan Cheng
  Mathematics of Operations Research, INFORMS, 2022. This paper shows the existence of $\mathcal{O}(\frac{1}{n^\gamma})$-Nash equilibria in $n$-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players' actions, are lower semicontinuous in the former while $\gamma$-H\"{o}lder continuous in the latter. Neither the action sets nor the cost functions need to be convex. For an important class of sum-aggregative games, which includes congestion games with $\gamma$ equal to 1, a gradient-proximal algorithm is used to construct $\mathcal{O}(\frac{1}{n})$-Nash equilibria with at most $\mathcal{O}(n^3)$ iterations. These results are applied to a numerical example concerning the demand-side management of an electricity system. The asymptotic performance of the algorithm when $n$ tends to infinity is illustrated. (10.1287/moor.2022.1321)
  DOI : 10.1287/moor.2022.1321
• Asymptotic limit of the Landau-de Gennes model for liquid crystals around an inclusion
  
  • Stantejsky Dominik
  , 2022. Liquid crystals are a type of matter which share properties with both liquids and crystalline solids, i.e. the molecules of such materials can move but exhibit a positional and orientational order.One of the most remarkable characteristics is the formation of defect structures, in particular point and line singularities.In this work we use a version of the Landau-de Gennes model for nematic liquid crystals with an external magnetic field to describe the Saturn ring effect around an immersed particle.In an asymptotic regime where both point and line singularities occur, we derive an effective energy describing the formation and transition between different singularities.The first chapter deals with the physically relevant case of a spherical particle.After a rescaling of the physical energy, a limit energy in the sense of Gamma-convergence, stated on the particle surface, is derived.Studying the limit problem, we explain the transition between the dipole and Saturn ring configurations and the occurrence of a hysteresis phenomenon.In the second chapter we consider the general case of an arbitrary closed and sufficiently smooth particle.In contrast to spherical (or more general convex) particle, we obtain an additional term in the limit energy, showing quantitatively that the close-to-minimal energy is asymptotically concentrated on lines and surfaces nearby or on the particle.We also discuss regularity of minimizers and optimality conditions for the limit energy.The third chapter is dedicated to the numerical investigation of the limit energy and the development and implementation of adapted numerical methods.We verify the results of the first chapter for the sphere and then study the defect structures in the case of a peanut and croissant-like particle.
• Optimal first-order methods for convex functions with a quadratic upper bound
  
  • Goujaud Baptiste
  • Taylor Adrien
  • Dieuleveut Aymeric
  , 2022. We analyze worst-case convergence guarantees of first-order optimization methods over a function class extending that of smooth and convex functions. This class contains convex functions that admit a simple quadratic upper bound. Its study is motivated by its stability under minor perturbations. We provide a thorough analysis of first-order methods, including worst-case convergence guarantees for several algorithms, and demonstrate that some of them achieve the optimal worst-case guarantee over the class. We support our analysis by numerical validation of worst-case guarantees using performance estimation problems. A few observations can be drawn from this analysis, particularly regarding the optimality (resp. and adaptivity) of the heavy-ball method (resp. heavy-ball with line-search). Finally, we show how our analysis can be leveraged to obtain convergence guarantees over more complex classes of functions. Overall, this study brings insights on the choice of function classes over which standard first-order methods have working worst-case guarantees.
• Causal effect on a target population: a sensitivity analysis to handle missing covariates
  
  • Colnet Bénédicte
  • Josse Julie
  • Varoquaux Gaël
  • Scornet Erwan
  Journal of Causal Inference, De Gruyter, 2022, 10 (1), pp.372-414. Randomized Controlled Trials (RCTs) are often considered as the gold standard to conclude on the causal effect of a given intervention on an outcome, but they may lack of external validity when the population eligible to the RCT is substantially different from the target population. Having at hand a sample of the target population of interest allows to generalize the causal effect. Identifying this target population treatment effect needs covariates in both sets to capture all treatment effect modifiers that are shifted between the two sets. However such covariates are often not available in both sets. Standard estimators then use either weighting (IPSW), outcome modeling (G-formula), or combine the two in doubly robust approaches (AIPSW). In this paper, after completing existing proofs on the complete case consistency of those three estimators, we compute the expected bias induced by a missing covariate, assuming a Gaussian distribution and a semi-parametric linear model. This enables sensitivity analysis for each missing covariate pattern, giving the sign of the expected bias. We also show that there is no gain in imputing a partially-unobserved covariate. Finally we study the replacement of a missing covariate by a proxy. We illustrate all these results on simulations, as well as semi-synthetic benchmarks using data from the Tennessee Student/Teacher Achievement Ratio (STAR), and with a real-world example from critical care medicine. (10.1515/jci-2021-0059)
  DOI : 10.1515/jci-2021-0059
• Comparaison des lois conjointes et marginales par permutation des labels pour la régression et l’estimation de densité conditionnelle
  
  • Riu Benjamin
  , 2022. Cette thèse introduit de nouvelles techniques qui exploitent des permutations du vecteur des observations de la variable à expliquer pour améliorer les performances de généralisation dans la tâche de régression et transformer l’estimation de la fonction de densité conditionnelle en un problème de classification binaire. Des justifications théoriques et des benchmarks empiriques sur des jeux de données tabulaires sont proposés pour démontrer l’intérêt de ces techniques, en particulier lorsqu'elles sont combinées avec des réseaux de neurones profonds. La généralisation est un problème central en l'apprentissage machine. La plupart des modèles prédictifs nécessitent une calibration minutieuse des hyper-paramètres sur un échantillon de validation pour obtenir de bonnes performances de généralisation. Une nouvelle approche qui contourne cette difficulté est présentée. Elle est basée sur une nouvelle mesure du risque de généralisation qui quantifie directement la propension d'un modèle à sur-ajuster les données d’entraînement. Le critère associé, appelé MLR (Muddling Labels Regularization) est évalué sur le jeu de données d’entraînement et permet d’estimer la performance sur le jeu de données test. Pour cela, il utilise des permutations du vecteur des observations de la variable à expliquer pour quantifier la propension d'un modèle à mémoriser la part de bruit contenu dans les données. Pour transformer le critère MLR en une fonction de perte pour les réseaux de neurones profonds, l'opérateur Tikhonov est introduit. Il module la capacité de mémorisation d'un réseau de manière adaptative, différentiable et dépendante des données. En combinant la perte MLR et l'opérateur Tikhonov, on obtient la technique d’apprentissage AdaCap (ADAptative CAPacity control) qui optimise la capacité du réseau afin qu'il puisse apprendre les représentation abstraite de haut niveau correspondant au problème posé plutôt que de mémoriser le jeu de données d’entraînement. Le problème d’estimation de densité conditionnelle est également traité. Il est à la base de la majorité des tâches d'apprentissage machine, y compris l'apprentissage supervisé et non supervisé ainsi que les modèles génératifs. Une nouvelle méthode, MCD (Marginal Contrastive Discrimination) inspirée du noise contrastive learning est introduite. MCD reformule la tâche initiale en un problème d'apprentissage supervisé qui peut être résolu à l’aide d’un classifieur binaire. Des techniques de construction de jeux de données de contraste basées là encore sur des permutations du vecteur de la variable à expliquer sont également proposées. Elles permettent d’obtenir des jeux de données d’entraînement beaucoup plus grands que le jeu de données initial, et de tirer parti d'observations non-étiquetées et d’observations pour lesquelles on dispose de plusieurs réalisations.
• A multilevel fast-marching method
  
  • Akian Marianne
  • Gaubert Stéphane
  • Liu Shanqing
  , 2022. We introduce a new numerical method to approximate the solutions of a class of static Hamilton-Jacobi-Bellman equations arising from minimum time optimal control problems. We rely on several grid approximations, and look for the optimal trajectories by using the coarse grid approximations to reduce the search space for the optimal trajectories in fine grids. This may be thought of as an infinite dimensional version, for PDE, of the "highway hierarchy" method which has been developed to solve discrete shortest path problems. We obtain, for each level, an approximate value function on a sub-domain of the state space. We show that the sequence obtained in this way does converge to the viscosity solution of the HJB equation. Moreover, the number of arithmetic operations that we need to obtain an error of O(ε) is bounded by Õ(1/ε^(2d/(1+β)), to be compared with Õ(1/ε^(2d)) for ordinary grid-based methods. Here β ∈ (0, 1] depends on the "stiffness" of the value function around optimal trajectories, and the notation Õ ignores logarithmic factors. Under a regularity condition on the dynamics, we obtain a bound of Õ(1/ε^((1−β)d)) operations, for β < 1, and this bound becomes O(|log ε|) for β = 1. This allowed us to solve HJB PDE of eikonal type up to dimension 7.
• Tropical numerical methods for solving stochastic control problems
  
  • Akian Marianne
  • Chancelier Jean-Philippe
  • Pascal Luz
  • Tran Benoît
  , 2022. We consider Dynamic programming equations associated to discrete time stochastic control problems with continuous state space, which arise in particular from monotone time discretizations of Hamilton-Jacobi-Bellman equations. We develop and study several numerical algorithms for solving such equations, combining tropical numerical methods and stochastic dual dynamic programming methods. We also compare these algorithms with the point based methods for solving Partially Observable Markov Decision Processes (POMDP).
• Semi-relaxed Gromov-Wasserstein divergence for graphs classification
  
  • Vincent-Cuaz Cédric
  • Flamary Rémi
  • Corneli Marco
  • Vayer Titouan
  • Courty Nicolas
  , 2022. Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov- Wasserstein (GW) distance, based on Optimal Transport (OT), has been successful in providing meaningful comparison between such entities. GW operates on graphs, seen as probability measures over spaces depicted by their nodes connectivity relations. At the core of OT is the idea of mass conservation, which imposes a coupling between all the nodes from the two considered graphs. We argue in this paper that this property can be detrimental for tasks such as graph dictionary learning (DL), and we relax it by proposing a new semi-relaxed Gromov-Wasserstein divergence. The latter leads to immediate computational benefits and naturally induces a new graph DL method, shown to be relevant for unsupervised representation learning and classification of graphs
• A Patient-Specific Equivalent Dipole Model
  
  • Cardoso Gabriel
  • Robin Geneviève
  • Arrieula Andony
  • Potse Mark
  • Haïssaguerre Michel
  • Moulines Eric
  • Dubois Rémi
  , 2022. Sophisticated models for the electrocardiographic inverse problem are available, but their reliance on imaging data and large numbers of electrodes limit their use. Simple models such as the equivalent dipole model (EDM) therefore remain relevant. We developed a probabilistic approach to the equivalent unbounded uniform single dipole problem and developed a natural extension to the bounded nonuniform case that relies on a patientspecific statistical inference of the propagation mechanism between the location of the dipole and the electrode locations. The two models were tested on data simulated with a detailed heart-torso model with four different activation sequences and three different sets of tissue characteristics. We observed a throughout enhancement of the ability to reconstruct the ECG of the patient-specific model when compared to the uniform unbounded dipole model.
• An accelerated level-set method for inverse scattering problems
  
  • Audibert Lorenzo
  • Haddar Houssem
  • Liu Xiaoli
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2022, 15 (3), pp.1576-1600. We propose a rapid and robust iterative algorithm to solve inverse acoustic scattering problems formulated as a PDE constrained shape optimization problem. We use a level-set method to represent the obstacle geometry and propose a new scheme for updating the geometry based on an adaptation of accelerated gradient descent methods. The resulting algorithm aims at reducing the number of iterations and improving the accuracy of reconstructions. To cope with regularization issues, we propose a smoothing to the shape gradient using a single layer potential associated with ik where k is the wave number. Numerical experiments are given for several data types (full aperture, backscattering, phaseless, multiple frequencies) and show that our method outperforms a non accelerated approach in terms of convergence speed, accuracy and sensitivity to initial guesses. (10.1137/21M1457783)
  DOI : 10.1137/21M1457783
• Generalized adaptive partition-based method for two-stage stochastic linear programs : convergence and generalization
  
  • Forcier Maël
  • Leclère Vincent
  Operations Research Letters, Elsevier, 2022, 50 (5), pp.452-457. Adaptive Partition-based Methods (APM) are numerical methods to solve two-stage stochastic linear problems (2SLP). The core idea is to iteratively construct an adapted partition of the space of alea in order to aggregate scenarios while conserving the true value of the cost-to-go for the current first-stage control. Relying on the normal fan of the dual admissible set, we extend the classical and generalized APM method by i) extending the method to almost arbitrary 2SLP, ii) giving a necessary and sufficient condition for a partition to be adapted even for non-finite distribution, and iii) proving the convergence of the method. We give some additional insights by linking APM to the L-shaped algorithm. (10.1016/j.orl.2022.06.004)
  DOI : 10.1016/j.orl.2022.06.004
• Scaling limits of permutation classes with a finite specification: a dichotomy
  
  • Bassino Frédérique
  • Bouvel Mathilde
  • Féray Valentin
  • Gerin Lucas
  • Maazoun Mickaël
  • Pierrot Adeline
  Advances in Mathematics, Elsevier, 2022, 405, pp.108513. We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple permutations. Our goal is to study their limiting behavior in the sense of permutons.The limit depends on the structure of the specification restricted to families with the largest growth rate. When it is strongly connected, two cases occur. If the associated system of equations is linear, the limiting permuton is a deterministic X-shape. Otherwise, the limiting permuton is the Brownian separable permuton, a random object that already appeared as the limit of most substitution-closed permutation classes, among which the separable permutations. Moreover these results can be combined to study some non strongly connected cases. To prove our result, we use a characterization of the convergence of random permutons by the convergence of random subpermutations. Key steps are the combinatorial study, via substitution trees, of families of permutations with marked elements inducing a given pattern, and the singularity analysis of the corresponding generating functions. (10.1016/j.aim.2022.108513)
  DOI : 10.1016/j.aim.2022.108513
• A refined Weissman estimator for extreme quantiles
  
  • Allouche Michaël
  • El Methni Jonathan
  • Girard Stéphane
  , 2022. Weissman's extrapolation methodology for estimating extreme quantiles from heavy-tailed distributions is based on two estimators: an order statistic to estimate an intermediate quantile and an estimator of the tail-index. The common practice is to select the same intermediate sequence for both estimators. We show how an adapted choice of two different intermediate sequences leads to a reduction of the asymptotic bias associated with the resulting refined Weissman estimator. The asymptotic normality of the latter estimator is established and a data-driven method is introduced for the practical selection of the intermediate sequences. Our approach is compared to Weissman estimator and to six bias-reduced estimators of extreme quantiles in a large-scale simulation study. It appears that the refined Weissman estimator outperforms its competitors in a wide variety of situations, especially in challenging high-bias cases. Finally, an illustration of an actuarial real data set is provided.
• Finite Difference formulation of any lattice Boltzmann scheme
  
  • Bellotti Thomas
  • Graille Benjamin
  • Massot Marc
  Numerische Mathematik, Springer Verlag, 2022. Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into a collision and a stream phase. This structure, despite the well-known advantages from a computational standpoint, is not suitable to construct a rigorous notion of consistency with respect to the target equations and to provide a precise notion of stability. In order to alleviate these shortages and introduce a rigorous framework, we demonstrate that any lattice Boltzmann scheme can be rewritten as a corresponding multi-step Finite Difference scheme on the conserved variables. This is achieved by devising a suitable formalism based on operators, commutative algebra and polynomials. Therefore, the notion of consistency of the corresponding Finite Difference scheme allows to invoke the Lax-Richtmyer theorem in the case of linear lattice Boltzmann schemes. Moreover, we show that the frequently-used von Neumann-like stability analysis for lattice Boltzmann schemes entirely corresponds to the von Neumann stability analysis of their Finite Difference counterpart. More generally, the usual tools for the analysis of Finite Difference schemes are now readily available to study lattice Boltzmann schemes. Their relevance is verified by means of numerical illustrations. (10.1007/s00211-022-01302-2)
  DOI : 10.1007/s00211-022-01302-2
• Interplay of Thermalization and Strong Disorder: Wave Turbulence Theory, Numerical Simulations, and Experiments in Multimode Optical Fibers
  
  • Berti Nicolas
  • Baudin Kilian
  • Fusaro Adrien
  • Millot Guy
  • Picozzi Antonio
  • Garnier Josselin
  Physical Review Letters, American Physical Society, 2022, 129 (6), pp.063901. We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schrödinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans distribution is driven by the nonlinearity. On the other hand, the structural disorder is responsible for a relaxation toward the homogeneous equilibrium distribution (particle equipartition), which thus inhibits thermalization (energy equipartition). On the basis of the wave turbulence theory, we derive a kinetic equation that accounts for the presence of strong disorder. The theory unveils the interplay of disorder and nonlinearity. It unexpectedly reveals that a nonequilibrium process of condensation and thermalization can take place in the regime where disorder effects dominate over nonlinear effects. We validate the theory by numerical simulations of the nonlinear Schrödinger equation and the derived kinetic equation, which are found in quantitative agreement without using any adjustable parameter. Experiments realized in multimode optical fibers with an applied external stress evidence the process of thermalization in the presence of strong disorder. (10.1103/PhysRevLett.129.063901)
  DOI : 10.1103/PhysRevLett.129.063901
• Multi-source Domain Adaptation via Weighted Joint Distributions Optimal Transport
  
  • Turrisi Rosanna
  • Flamary Rémi
  • Rakotomamonjy Alain
  • Pontil Massimiliano
  , 2022. The problem of domain adaptation on an unlabeled target dataset using knowledge from multiple labelled source datasets is becoming increasingly important. A key challenge is to design an approach that overcomes the covariate and target shift both among the sources, and between the source and target domains. In this paper, we address this problem from a new perspective: instead of looking for a latent representation invariant between source and target domains, we exploit the diversity of source distributions by tuning their weights to the target task at hand. Our method, named Weighted Joint Distribution Optimal Transport (WJDOT), aims at finding simultaneously an Optimal Transport-based alignment between the source and target distributions and a re-weighting of the sources distributions. We discuss the theoretical aspects of the method and propose a conceptually simple algorithm. Numerical experiments indicate that the proposed method achieves state-of-the-art performance on simulated and real-life datasets.
• Unbiasing and robustifying implied volatility calibration in a cryptocurrency market with large bid-ask spreads and missing quotes
  
  • Echenim Mnacho
  • Gobet Emmanuel
  • Maurice Anne-Claire
  , 2022.
• Quadratic second-order backward stochastic differential equation and numeric analysis for Sannikov's optimal contracting problem
  
  • Sheng Bowen
  , 2022. This thesis works mainly on two subjects.The first part is about the wellposedness of quadratic second-order backward stochastic differential equation. After a summary of previous research results on the solutions of quadratic reflected backward SDE, i.e., wellposedness (existence and uniqueness), comparison principle, stability result, etc., we in this paper mainly consider the wellposedness of solutions for the corresponding second order backward SDE. Besides the quadratic growth, we also assume that the generator f is concave in z with linearly growing gradient. This leads to a new downcrossing inequality of the value function (also a f-supermartingale) V. Gaining the regularity of its right limit w.r.t. t we follow Soner, Touzi and Zhang to get the representation of solutions and implement the proof of wellposedness.The second part is about the Sannikov optimal contracting problem under defaultable output process. The contracting problem consists of a delegation scheme between two parties, the Agent in charge of the management of the output process, and the Principal who sets up the terms of a contract indexed on the performance of the output process so as to incite the Agent to best serve her objective. The contract requires the Agent approval at the initial time, and is then subject to the full commitment of both parties. The contract stipulates the termination time of the contract, a continuous payment until termination, and a lump sum payment at termination. Our main objective in this paper is to explore the effect of restricting the termination time of the contract to occur before the default of the contract. To this end, we propose a type of Galerkin neural network numerical approximation to investigate the behavior of the value function arised in the Principal's problem.
• NeuralNetwork-Quantile-Extrapolation
  
  • Allouche Michaël
  • Girard Stéphane
  • Gobet Emmanuel
  , 2022. We propose new parametrizations for neural networks in order to estimate extreme quantiles in both non-conditional and conditional heavy-tailed settings. All proposed neural network estimators feature a bias correction based on an extension of the usual second-order condition to an arbitrary order. The convergence rate of the uniform error between extreme log-quantiles and their neural network approximation is established. The finite sample performances of the non-conditional neural network estimator are compared to other 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. The source code is available at https://github.com/michael-allouche/ nn-quantile-extrapolation.git. Finally, the conditional neural network estimators are implemented to investigate the behavior of extreme rainfalls as functions of their geographical location in the southern part of France.
• Longest increasing paths with Lipschitz constraints
  
  • Basdevant Anne-Laure
  • Gerin Lucas
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2022, 58 (3). The Hammersley problem asks for the maximal number of points in a monotonous path through a Poisson point process. It is exactly solvable and notoriously known to belong to the KPZ universality class, with a cube-root scaling for the fluctuations. Here we introduce and analyze a variant in which we impose a Lipschitz condition on paths. Thanks to a coupling with the classical Hammersley problem we observe that this variant is also exactly solvable. It allows us to derive first and second orders asymptotics. It turns out that the cube-root scaling only holds for certain choices of the Lipschitz constants. (10.1214/21-AIHP1220)
  DOI : 10.1214/21-AIHP1220
• A R&D software platform for shape and topology optimization using body-fitted meshes
  
  • Danan David
  • Nardoni Chiara
  • Bordeu Felipe
  • Cortial Julien
  • Mang Chetra
  • Rey Christian
  • Allaire Grégoire
  • Lorang Xavier
  , 2022. Topology optimization is devoted to the optimal design of structures. It aims at finding the best material distribution inside a working domain while fulfilling mechanical, geometrical and manufacturing specifications. The need for lighter and efficient structural solutions has made topology optimization a vigorous research field in both academic and industrial structural engineering communities. This contribution focuses on PISCO, a Research and Development software platform for shape and topology optimization where the computational process is carried out in a level set framework combined with a body-fitted approach. The level set method relies on the classical sensitivity analysis from the shape optimization framework to compute a descent direction and advect the structural interface. In the present setting the level set method is coupled with a remeshing routine which enables the reconstruction of a body-fitted mesh at each step of the underlying optimization process. Since the structural interface is known explicitely at each step of the iterative procedure, the body-fitted approach simplifies the evaluation of the mechanical quantities of interest. PISCO is composed of several components including an algorithmic toolbox specialized in the treatment of level sets, a generic interface to finite element solvers, a toolbox handling mesh files in several classical formats, several algorithms for the resolution of constrained optimization problems, physical and geometrical optimization criteria and an advanced interface to the remeshing tool mmg3d. The components devoted to the physical analysis computations and the constrained optimization algorithms are implemented in a generic fashion in dedicated modules. The non-intrusiveness of the implementation is proved by the coupling with several external physical solvers. We rely on a gradient-flow numerical optimization algorithm to handle the balancing between the minimization of the objective and the non-violation of the constraints. Several industrial applications are presented to highlight the capabilities of the platform.
• High sensibility imaging of defects in elastic waveguides using near resonance frequencies
  
  • Niclas Angèle
  • Bonnetier Eric
  • Seppecher L.
  • Vial Grégory
  , 2022. This work presents a new multi-frequency inversion method to image shape defects in slowly varying elastic waveguides. Contrary to previous works in this field, we choose to take advantage of the near resonance frequencies of the waveguide, where the elastic problem is known to be ill-conditioned. A phenomenon close to the tunnel effect in quantum mechanics can be observed at these frequencies, and locally resonant modes propagate in the waveguide. These modes are very sensitive to width variations, and measuring their amplitude enables reconstructing the local variations of the waveguide shape with very high sensibility. Given surface wavefield measurements for a range of near resonance frequencies, we provide a stable numerical reconstruction of the width of a slowly varying waveguide and illustrate it on defects like dilation or compression of a waveguide.
• How a moving passive observer can perceive its environment ? The Unruh effect revisited
  
  • Fink Mathias
  • Garnier Josselin
  , 2020, pp.102462. We consider a point-like observer that moves in a medium illuminated by noise sources with Lorentz-invariant spectrum. We show that the autocorrelation function of the signal recorded by the observer allows it to perceive its environment. More precisely, we consider an observer with constant acceleration (along a Rindler trajectory) and we exploit the recent work on the emergence of the Green's function from the cross correlation of signals transmitted by noise sources. First we recover the result that the signal recorded by the observer has a constant Wigner transform, i.e. a constant local spectrum, when the medium is homogeneous (this is the classical analogue of the Unruh effect). We complete that result by showing that the Rindler trajectory is the only straight-line trajectory that satisfies this property. We also show that, in the presence of an obstacle in the form of an infinite perfect mirror, the Wigner transform is perturbed when the observer comes into the neighborhood of the obstacle. The perturbation makes it possible for the observer to determine its position relative to the obstacle once the entire trajectory has been traversed. (10.1016/j.wavemoti.2019.102462)
  DOI : 10.1016/j.wavemoti.2019.102462
• A new modeling approach of myxococcus xanthus bacteria using polarity-based reversals
  
  • Bloch Hélène
  • Calvez Vincent
  • Gaudeul Benoît
  • Gouarin Loïc
  • Lefebvre-Lepot Aline
  • Mignot Tam
  • Romanos Michèle
  • Saulnier Jean-Baptiste
  , 2024. The aim of this paper is to model the collective behavior of Myxococcus xanthus bacteria to better understand the emerging patterns at the level of the colony. We use image analysis and data treatment on experimental data of Myxococcus xanthus bacteria as a starting point to build two models whose main novelty is the polarity-based reversals. The first model is based on contact dynamics approach and the second one follows a molecular dynamics approach. We compare the two cell-cell models and support each one with numerical simulations in 2D. The mathematical and biological aspects of each model are then discussed. (10.1051/proc/202477025)
  DOI : 10.1051/proc/202477025
• Adaptive Conformal Predictions for Time Series
  
  • Zaffran Margaux
  • Féron Olivier
  • Goude Yannig
  • Josse Julie
  • Dieuleveut Aymeric
  , 2022, 162. Uncertainty quantification of predictive models is crucial in decision-making problems. Conformal prediction is a general and theoretically sound answer. However, it requires exchangeable data, excluding time series. While recent works tackled this issue, we argue that Adaptive Conformal Inference (ACI, Gibbs and Candès, 2021), developed for distribution-shift time series, is a good procedure for time series with general dependency. We theoretically analyse the impact of the learning rate on its efficiency in the exchangeable and auto-regressive case. We propose a parameter-free method, AgACI, that adaptively builds upon ACI based on online expert aggregation. We lead extensive fair simulations against competing methods that advocate for ACI's use in time series. We conduct a real case study: electricity price forecasting. The proposed aggregation algorithm provides efficient prediction intervals for day-ahead forecasting. All the code and data to reproduce the experiments is made available.