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Listed below, are sorted by year, the publications appearing in the HAL open archive.

2025

Uniswap v3: impermanent loss modeling and swap fees asymptotic analysis
- Echenim Mnacho
- Gobet Emmanuel
- Maurice Anne-Claire
, 2023. Automated Market Makers have emerged quite recently, and Uniswap is one of the most widely used platforms (it covers 60% of the total value locked on Ethereum blockchain at the time of writing this article). This protocol is challenging from a quantitative point of view, as it allows participants to choose where they wish to concentrate liquidity. There has been an increasing number of research papers on Uniswap v3 but often, these articles use heuristics or approximations that can be far from reality: for instance, the liquidity in the pool is sometimes assumed to be constant over time, which contradicts the mechanism of the protocol. The ob- jectives of this work are fourfold: first, to revisit Uniswap v3’s principles in detail (starting from the open source code) to build an unambiguous knowledge base. Second, to analyze the Im- permanent Loss of a liquidity provider by detailing its evolution, with no assumption on the swap trades or liquidity events that occur over the time period. Third, we introduce the notion of a liquidity curve. For each curve, we can construct a payoff at a given maturity, net of fees. Conversely, we show how any concave payoff can be synthetized by an initial liquidity curve and some tokens outside the pool; this paves the way for using Uniswap v3 to create options. Fourth, we analyze the asymptotic behavior of collected fees without any simplifying hypoth- esis (like a constant liquidity), under the mild assumption that the pool price coincides with a latent price (general Ito process) every time the latter changes by γ%. The asymptotic analysis is conducted as γ → 0. The value of the collected fees then coincides with an integral of call and put prices. Our derivations are supported by graphical illustrations and experiments.
On the entropy dissipation of systems of quadratures
- Pichard Teddy
- Laurent Frédérique
, 2025. <div>The method of moments in kinetic theory is a popular discretization technique with respect to the kinetic velocity variable. It can be seen as a non-linear Galerkin semi-discretization in velocity. Among these methods, the quadrature-based methods exploiting the theory of orthogonal polynomials are well suited for numerical purposes. However, two important properties of the original kinetic equation are lost during such approximations: the strong hyperbolicity, corresponding to transport phenomena, and the dissipation of entropy, corresponding to the trend of the solution towards an equilibrium. These two properties are closely related through symmetrization techniques. In this work, we aim to clarify the treatment of these two properties in the derivation of quadrature-based moment systems, and to prove H-theorems, namely dissipation of entropy and equilibrium representation, after such derivations. From this study, we develop of quadrature-based closures adapted to specific entropies. These closures are of two types, either with fixed quadrature points (or velocities), namely the discrete velocity methods (DVM), and with varying ones, namely the quadrature-based method of moments (QMOM). To adapt the closures to specific entropies, the number of quadrature points is increased compared to the number of moments, resulting in augmented systems (ADVM or AQMOM) with more unknowns than equations, and the additional parameters are constrained to match the entropy requirements. Similarly, the quadrature-based entropies are of two types, either those based on a symmetrization criterion on the flux vector, which are only intended to have an entropy, or those corresponding to a quadrature formula of the kinetic entropy, which are intended to reproduce the kinetic trend towards the equilibrium. At each step of these developments, based on the considered entropy, we provide definitions for the flux vectors, adapted relaxation operators (with common conservation properties), we compute the associated entropic variables, and highlight the corresponding symmetrization property of the flux and equilibria. Finally, we provide an entropy-dissipative discretization for such moment systems.</div>
Individual cell fate and population dynamics revealed by a mathematical model linking telomere length and replicative senescence
- Rat Anaïs
- Martinez Fernandez Veronica
- Doumic Marie
- Teixeira Maria Teresa
- Xu Zhou
Nature Communications, Nature Publishing Group, 2025, 16 (1), pp.1024. Progressive shortening of telomeres ultimately causes replicative senescence and is linked with aging and tumor suppression. Studying the intricate link between telomere shortening and senescence at the molecular level and its population-scale effects over time is challenging with current approaches but crucial for understanding behavior at the organ or tissue level. In this study, we developed a mathematical model for telomere shortening and the onset of replicative senescence using data from Saccharomyces cerevisiae without telomerase. Our model tracks individual cell states, their telomere length dynamics, and lifespan over time, revealing selection forces within a population. We discovered that both cell genealogy and global telomere length distribution are key to determine the population proliferation capacity. We also discovered that cell growth defects unrelated to telomeres also affect subsequent proliferation and may act as confounding variables in replicative senescence assays. Overall, while there is a deterministic limit for the shortest telomere length, the stochastic occurrence of non-terminal arrests drive cells into a totally different regime, which may promote genome instability and senescence escape. Our results offer a comprehensive framework for investigating the implications of telomere length on human diseases. (10.1101/2023.11.22.568287)
DOI : 10.1101/2023.11.22.568287
Humanity's Last Exam
- Phan Long
- Gatti Alice
- Han Ziwen
- Li Nathaniel
- Hu Josephina
- Zhang Hugh
- Shi Sean
- Choi Michael
- Agrawal Anish
- Chopra Arnav
- Khoja Adam
- Kim Ryan
- Hausenloy Jason
- Zhang Oliver
- Mazeika Mantas
- Anderson Daron
- Nguyen Tung
- Mahmood Mobeen
- Feng Fiona
- Feng Steven Y.
- Zhao Haoran
- Yu Michael
- Gangal Varun
- Zou Chelsea
- Wang Zihan
- Wang Jessica P.
- Kumar Pawan
- Pokutnyi Oleksandr
- Gerbicz Robert
- Popov Serguei
- Levin John-Clark
- Kazakov Mstyslav
- Schmitt Johannes
- Galgon Geoff
- Sanchez Alvaro
- Lee Yongki
- Yeadon Will
- Sauers Scott
- Roth Marc
- Agu Chidozie
- Riis Søren
- Giska Fabian
- Utpala Saiteja
- Giboney Zachary
- Goshu Gashaw M.
- Xavier Joan of Arc
- Crowson Sarah-Jane
- Naiya Mohinder Maheshbhai
- Burns Noah
- Finke Lennart
- Cheng Zerui
- Park Hyunwoo
- Fournier-Facio Francesco
- Wydallis John
- Nandor Mark
- Singh Ankit
- Gehrunger Tim
- Cai Jiaqi
- Mccarty Ben
- Duclosel Darling
- Nam Jungbae
- Zampese Jennifer
- Hoerr Ryan G.
- Bacho Aras
- Loume Gautier Abou
- Galal Abdallah
- Cao Hangrui
- Garretson Alexis C
- Sileo Damien
- Ren Qiuyu
- Cojoc Doru
- Arkhipov Pavel
- Qazi Usman
- Li Lianghui
- Motwani Sumeet
- de Witt Christian Schroeder
- Taylor Edwin
- Veith Johannes
- Singer Eric
- Hartman Taylor D.
- Rissone Paolo
- Jin Jaehyeok
- Shi Jack Wei Lun
- Willcocks Chris G.
- Robinson Joshua
- Mikov Aleksandar
- Prabhu Ameya
- Tang Longke
- Alapont Xavier
- Uro Justine Leon
- Zhou Kevin
- Santos Emily de Oliveira
- Maksimov Andrey Pupasov
- Vendrow Edward
- Zenitani Kengo
- Guillod Julien
- Li Yuqi
- Vendrow Joshua
- Kuchkin Vladyslav
- Ze-An Ng
- Marion Pierre
- Efremov Denis
- Lynch Jayson
- Liang Kaiqu
- Gritsevskiy Andrew
- Martinez Dakotah
- Pageler Ben
- Crispino Nick
- Zvonkine Dimitri
- Fraga Natanael Wildner
- Soori Saeed
- Press Ori
- Tang Henry
- Salazar Julian
- Green Sean R.
- Brüssel Lina
- Twayana Moon
- Dieuleveut Aymeric
- Rogers T. Ryan
- Zhang Wenjin
- Li Bikun
- Yang Jinzhou
- Rao Arun
- Loiseau Gabriel
- Kalinin Mikhail
- Lukas Marco
- Manolescu Ciprian
- Mishra Subrata
- Kamdoum Ariel Ghislain Kemogne
- Kreiman Tobias
- Hogg Tad
- Jin Alvin
- Bosio Carlo
- Sun Gongbo
- Coppola Brian P
- Tarver Tim
- Heidinger Haline
- Sayous Rafael
- Ivanov Stefan
- Cavanagh Joseph M
- Shen Jiawei
- Imperial Joseph Marvin
- Schwaller Philippe
- Senthilkuma Shaipranesh
- Bran Andres M
- Dehghan Ali
- Algaba Andres
- Verbeken Brecht
- Noever David
- P V Ragavendran
- Schut Lisa
- Sucholutsky Ilia
- Zheltonozhskii Evgenii
- Lim Derek
- Stanley Richard
- Sivarajan Shankar
- Yang Tong
- Maar John
- Wykowski Julian
- Oller Martí
- Sandlin Jennifer
- Sahu Anmol
- Hu Yuzheng
- Fish Sara
- Heydari Nasser
- Apronti Archimedes
- Rawal Kaivalya
- Vilchis Tobias Garcia
- Zu Yuexuan
- Lackner Martin
- Koppel James
- Nguyen Jeremy
- Antonenko Daniil S.
- Chern Steffi
- Zhao Bingchen
- Arsene Pierrot
- Goldfarb Alan
- Ivanov Sergey
- Poświata Rafał
- Wang Chenguang
- Li Daofeng
- Crisostomi Donato
- Achilleos Andrea
- Myklebust Benjamin
- Sen Archan
- Perrella David
- Kaparov Nurdin
- Inlow Mark H
- Zang Allen
- Thornley Elliott
- Orel Daniil
- Poritski Vladislav
- Ben-David Shalev
- Berger Zachary
- Whitfill Parker
- Foster Michael
- Munro Daniel
- Ho Linh
- Hava Dan Bar
- Kuchkin Aleksey
- Lauff Robert
- Holmes David
- Sommerhage Frank
- Schneider Keith
- Kazibwe Zakayo
- Stambaugh Nate
- Singh Mukhwinder
- Magoulas Ilias
- Clarke Don
- Kim Dae Hyun
- Dias Felipe Meneguitti
- Elser Veit
- Agarwal Kanu Priya
- Vilchis Victor Efren Guadarrama
- Klose Immo
- Demian Christoph
- Anantheswaran Ujjwala
- Zweiger Adam
- Albani Guglielmo
- Li Jeffery
- Daans Nicolas
- Radionov Maksim
- Rozhoň Václav
- Ma Ziqiao
- Stump Christian
- Berkani Mohammed
- Platnick Jacob
- Nevirkovets Volodymyr
- Basler Luke
- Piccardo Marco
- Jeanplong Ferenc
- Cohen Niv
- Tkadlec Josef
- Rosu Paul
- Padlewski Piotr
- Barzowski Stanislaw
- Montgomery Kyle
- Menezes Aline
- Patel Arkil
- Wang Zixuan
- Tucker-Foltz Jamie
- Stade Jack
- Goertzen Tom
- Kazemi Fereshteh
- Milbauer Jeremiah
- Ambay John Arnold
- Shukla Abhishek
- Labrador Yan Carlos Leyva
- Givré Alan
- Wolff Hew
- Rossbach Vivien
- Aziz Muhammad Fayez
- Kaddar Younesse
- Chen Yanxu
- Zhang Robin
- Pan Jiayi
- Terpin Antonio
- Muennighoff Niklas
- Schoelkopf Hailey
- Zheng Eric
- Carmi Avishy
- Jones Adam
- Shah Jainam
- Brown Ethan D. L.
- Zhu Kelin
- Bartolo Max
- Wheeler Richard
- Ho Andrew
- Barkan Shaul
- Wang Jiaqi
- Stehberger Martin
- Kretov Egor
- Sridhar Kaustubh
- El-Wasif Zienab
- Zhang Anji
- Pyda Daniel
- Tam Joanna
- Cunningham David M.
- Goryachev Vladimir
- Patramanis Demosthenes
- Krause Michael
- Redenti Andrew
- Bugas Daniel
- Aldous David
- Lai Jesyin
- Coleman Shannon
- Bahaloo Mohsen
- Xu Jiangnan
- Lee Sangwon
- Zhao Sandy
- Tang Ning
- Cohen Michael K.
- Carroll Micah
- Paradise Orr
- Kirchner Jan Hendrik
- Steinerberger Stefan
- Ovchynnikov Maksym
- Matos Jason O.
- Shenoy Adithya
- Junior Benedito Alves de Oliveira
- Wang Michael
- Nie Yuzhou
- Giordano Paolo
- Petersen Philipp
- Sztyber-Betley Anna
- Shukla Priti
- Crozier Jonathan
- Pinto Antonella
- Verma Shreyas
- Joshi Prashant
- Yong Zheng-Xin
- Tee Allison
- Andréoletti Jérémy
- Weller Orion
- Singhal Raghav
- Zhang Gang
- Ivanov Alexander
- Khoury Seri
- Mostaghimi Hamid
- Thaman Kunvar
- Chen Qijia
- Khánh Tran Quoc
- Loader Jacob
- Cavalleri Stefano
- Szlyk Hannah
- Brown Zachary
- Roberts Jonathan
- Alley William
- Sun Kunyang
- Stendall Ryan
- Lamparth Max
- Reuel Anka
- Wang Ting
- Xu Hanmeng
- Raparthi Sreenivas Goud
- Hernández-Cámara Pablo
- Martin Freddie
- Malishev Dmitry
- Preu Thomas
- Korbak Tomek
- Abramovitch Marcus
- Williamson Dominic
- Chen Ziye
- Bálint Biró
- Bari M Saiful
- Kassani Peyman
- Wang Zihao
- Ansarinejad Behzad
- Goswami Laxman Prasad
- Sun Yewen
- Elgnainy Hossam
- Tordera Daniel
- Balabanian George
- Anderson Earth
- Kvistad Lynna
- Moyano Alejandro José
- Maheshwari Rajat
- Sakor Ahmad
- Eron Murat
- Mcalister Isaac C.
- Gimenez Javier
- Enyekwe Innocent
- O. Andrew Favre D.
- Shah Shailesh
- Zhou Xiaoxiang
- Kamalov Firuz
- Clark Ronald
- Abdoli Sherwin
- Santens Tim
- Meer Khalida
- Wang Harrison K
- Ramakrishnan Kalyan
- Chen Evan
- Tomasiello Alessandro
- de Luca G. Bruno
- Looi Shi-Zhuo
- Le Vinh-Kha
- Kolt Noam
- Mündler Niels
- Semler Avi
- Rodman Emma
- Drori Jacob
- Fossum Carl J
- Jagota Milind
- Pradeep Ronak
- Fan Honglu
- Shah Tej
- Eicher Jonathan
- Chen Michael
- Thaman Kushal
- Merrill William
- Harris Carter
- Gross Jason
- Gusev Ilya
- Sharma Asankhaya
- Agnihotri Shashank
- Zhelnov Pavel
- Usawasutsakorn Siranut
- Mofayezi Mohammadreza
- Bogdanov Sergei
- Piperski Alexander
- Carauleanu Marc
- Zhang David K.
- Ler Dylan
- Leventov Roman
- Soroko Ignat
- Jansen Thorben
- Lauer Pascal
- Duersch Joshua
- Taamazyan Vage
- Morak Wiktor
- Ma Wenjie
- Held William
- Huy Tran Đuc
- Xian Ruicheng
- Zebaze Armel Randy
- Mohamed Mohanad
- Leser Julian Noah
- Yuan Michelle X
- Yacar Laila
- Lengler Johannes
- Shahrtash Hossein
- Oliveira Edson
- Jackson Joseph W.
- Gonzalez Daniel Espinosa
- Zou Andy
- Chidambaram Muthu
- Manik Timothy
- Haffenden Hector
- Stander Dashiell
- Dasouqi Ali
- Shen Alexander
- Duc Emilien
- Golshani Bita
- Stap David
- Uzhou Mikalai
- Zhidkovskaya Alina Borisovna
- Lewark Lukas
- Vincze Mátyás
- Wehr Dustin
- Tang Colin
- Hossain Zaki
- Phillips Shaun
- Muzhen Jiang
- Ekström Fredrik
- Hammon Angela
- Patel Oam
- Remy Nicolas
- Farhidi Faraz
- Medley George
- Mohammadzadeh Forough
- Peñaflor Madellene
- Kassahun Haile
- Friedrich Alena
- Sparrow Claire
- Sakal Taom
- Dhamane Omkar
- Mirabadi Ali Khajegili
- Hallman Eric
- Battaglia Mike
- Maghsoudimehrabani Mohammad
- Hoang Hieu
- Amit Alon
- Hulbert Dave
- Pereira Roberto
- Weber Simon
- Mensah Stephen
- Andre Nathan
- Peristyy Anton
- Harjadi Chris
- Gupta Himanshu
- Malina Stephen
- Albanie Samuel
- Cai Will
- Mehkary Mustafa
- Reidegeld Frank
- Dick Anna-Katharina
- Friday Cary
- Sidhu Jasdeep
- Kim Wanyoung
- Costa Mariana
- Gurdogan Hubeyb
- Weber Brian
- Kumar Harsh
- Jiang Tong
- Agarwal Arunim
- Ceconello Chiara
- Vaz Warren S.
- Zhuang Chao
- Park Haon
- Tawfeek Andrew R.
- Aggarwal Daattavya
- Kirchhof Michael
- Dai Linjie
- Kim Evan
- Ferret Johan
- Wang Yuzhou
- Yan Minghao
- Burdzy Krzysztof
- Zhang Lixin
- Franca Antonio
- Pham Diana T.
- Loh Kang Yong
- Robinson Joshua
- Gul Shreen
- Chhablani Gunjan
- Du Zhehang
- Cosma Adrian
- White Colin
- Riblet Robin
- Saxena Prajvi
- Votava Jacob
- Vinnikov Vladimir
- Delaney Ethan
- Halasyamani Shiv
- Shahid Syed M.
- Mourrat Jean-Christophe
- Vetoshkin Lavr
- Bacho Renas
- Ginis Vincent
- Maksapetyan Aleksandr
- de la Rosa Florencia
- Li Xiuyu
- Malod Guillaume
- Lang Leon
- Laurendeau Julien
- Adesanya Fatimah
- Portier Julien
- Hollom Lawrence
- Souza Victor
- Zhou Yuchen Anna
- Yalın Yiğit
- Obikoya Gbenga Daniel
- Arnaboldi Luca
- Bigi Filippo
- Bacho Kaniuar
- Clavier Pierre
- Recchia Gabriel
- Popescu Mara
- Shulga Nikita
- Tanwie Ngefor Mildred
- Lux Thomas C. H.
- Rank Ben
- Ni Colin
- Yakimchyk Alesia
- Liu Huanxu
- Häggström Olle
- Verkama Emil
- Narayan Himanshu
- Gundlach Hans
- Brito-Santana Leonor
- Amaro Brian
- Vajipey Vivek
- Grover Rynaa
- Fan Yiyang
- Silva Gabriel Poesia Reis E
- Xin Linwei
- Kratish Yosi
- Łucki Jakub
- Li Wen-Ding
- Xu Justin
- Scaria Kevin Joseph
- Vargus Freddie
- Habibi Farzad
- Rodolà Emanuele
- Robins Jules
- Cheng Vincent
- Grabb Declan
- Bosio Ida
- Fruhauff Tony
- Akov Ido
- Lo Eve J. Y.
- Qi Hao
- Jiang Xi
- Segev Ben
- Fan Jingxuan
- Martinson Sarah
- Wang Erik Y.
- Hausknecht Kaylie
- Brenner Michael P.
- Mao Mao
- Jiang Yibo
- Zhang Xinyu
- Avagian David
- Scipio Eshawn Jessica
- Siddiqi Muhammad Rehan
- Ragoler Alon
- Tan Justin
- Patil Deepakkumar
- Plecnik Rebeka
- Kirtland Aaron
- Montecillo Roselynn Grace
- Durand Stephane
- Bodur Omer Faruk
- Adoul Zahra
- Zekry Mohamed
- Douville Guillaume
- Karakoc Ali
- Santos Tania C. B.
- Shamseldeen Samir
- Karim Loukmane
- Liakhovitskaia Anna
- Resman Nate
- Farina Nicholas
- Gonzalez Juan Carlos
- Maayan Gabe
- Hoback Sarah
- Pena Rodrigo de Oliveira
- Sherman Glen
- Mariji Hodjat
- Pouriamanesh Rasoul
- Wu Wentao
- Demir Gözdenur
- Mendoza Sandra
- Alarab Ismail
- Cole Joshua
- Ferreira Danyelle
- Johnson Bryan
- Milliron Hsiaoyun
- Safdari Mohammad
- Dai Liangti
- Arthornthurasuk Siriphan
- Pronin Alexey
- Fan Jing
- Ramirez-Trinidad Angel
- Cartwright Ashley
- Pottmaier Daphiny
- Taheri Omid
- Outevsky David
- Stepanic Stanley
- Perry Samuel
- Askew Luke
- Rodríguez Raúl Adrián Huerta
- Dendane Abdelkader
- Ali Sam
- Lorena Ricardo
- Iyer Krishnamurthy
- Salauddin Sk Md
- Islam Murat
- Gonzalez Juan
- Ducey Josh
- Campbell Russell
- Somrak Maja
- Mavroudis Vasilios
- Vergo Eric
- Qin Juehang
- Borbás Benjámin
- Chu Eric
- Lindsey Jack
- Radhakrishnan Anil
- Jallon Antoine
- Mcinnis I. M. J.
- Hoover Alex
- Möller Sören
- Bian Song
- Lai John
- Patwardhan Tejal
- Yue Summer
- Wang Alexandr
- Hendrycks Dan
, 2025. Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 3,000 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.
Convergence and Error Estimates of A Semi-Lagrangian scheme for the Minimum Time Problem
- Akian Marianne
- Liu Shanqing
, 2024. We consider a semi-Lagrangian scheme for solving the minimum time problem, with a given target, and the associated eikonal type equation. We first use a discrete time deterministic optimal control problem interpretation of the time discretization scheme, and show that the discrete time value function is semiconcave under regularity assumptions on the dynamics and the boundary of target set. We establish a convergence rate of order $1$ in terms of time step based on this semiconcavity property. Then, we use a discrete time stochastic optimal control interpretation of the full discretization scheme, and we establish a convergence rate of order $1$ in terms of both time and spatial steps using certain interpolation operators, under further regularity assumptions. We extend our convergence results to problems with particular state constraints. We apply our results to analyze the convergence rate and computational complexity of the fast-marching method. We also consider the multi-level fast-marching method recently introduced by the authors.
Continuous-time modeling and bootstrap for chain ladder reserving
- Baradel Nicolas
, 2024. We revisit the famous Mack's model which gives an estimate for the mean square error of prediction of the chain ladder claims reserves. We introduce a stochastic dierential equation driven by a Brownian motion to model accumulated total claims amount for the chain ladder method. Within this continuous-time framework, we propose a bootstrap technique for estimating the distribution of claims reserves. It turns out that our approach leads to inherently capturing asymmetry and non-negativity, eliminating the necessity for additional assumptions. We conclude with a case study and comparative analysis against alternative methodologies based on Mack's model.
Small-scale interface dynamic modelling based on the geometric method of moments for a two-scale two-phase flow model with a disperse small scale
- Loison Arthur
- Pichard Teddy
- Kokh Samuel
- Massot Marc
Journal of Fluid Mechanics, Cambridge University Press (CUP), 2025, 1003 (A27), pp.1--42. In this contribution, we develop a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes as introduced by Loison et al. (2024). It relies on the stationary action principle and interface geometric variables. This contribution provides a novel method to derive small-scale models for the dynamics of the interface geometry. They are introduced here on a simplified case where all the scales and phases have the same velocity and that does not take into account large-scale capillary forces. The derivation tools yield a proper mathematical framework through hyperbolicity and signed entropy evolution. The formalism encompasses a hierarchy of small-scale reduced-order models based on a statistical description at a mesoscopic kinetic level and is naturally able to include the description of a disperse phase with polydispersity in size. This hierarchy includes both a cloud of spherical droplets and non-spherical droplets experiencing a dynamical behaviour through incompressible oscillations. The associated small-scale variables are moments of a number density function resulting from the geometric method of moments (GeoMOM). This method selects moments as small-scale geometric variables compatible with the structure and dynamics of the interface; they are defined independently of the flow topology and, therefore, this model allows the coupling of the two-scale flow with an inter-scale transfer. It is shown in particular that the resulting dynamics provides partial closures for the interface area density equation obtained from the averaging approach. (10.1017/jfm.2024.1200)
DOI : 10.1017/jfm.2024.1200
Brochette first-passage percolation
- Marivain Maxime
, 2025. We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point convergence theorem, identifying the time constant. In particular, we explore the case where the time constant vanishes and demonstrate the existence of a wide range of possible behaviours. Next, we prove a shape theorem, showing that the limiting shape is the $L^1$ diamond. Finally, we extend the analysis by proving a point-to-point convergence theorem in the setting where passage times are allowed to be infinite.
Kernel density estimation for stationary random fields with values in a finite-dimensional Riemannian manifold
- Nefzi Wiem
- Yao Anne-Françoise
- KHARDANI Salah
, 2025. <div><p>This paper investigates some asymptotic properties of the kernel spatial density estimation for stationary α-mixing process on a finite-dimensional Riemannian manifold without boundary. The results extend beyond the classical independently and identically distributed (i.i.d.) data, focusing on the case where the manifold is known and extending the classical theory to random fields.</p></div>
Nonparametric Regression on Riemannian manifold under α-Mixing process
- Nefzi Wiem
- Yao Anne-Françoise
- KHARDANI Salah
, 2025. <div><p>The main focus of our paper is to investigate the behavior of the kernel estimator for the regression function between a real-valued random variable Y and a random variable X, where X takes values in a Riemannian submanifold. The estimator is adapted from the article of Pelletier (2006). Additionally, we study data that adheres to the α-mixing condition, which imposes valuable constraints on the dependence structure of the observations. Specifically, we provide the rate of convergence in mean square error, enabling us to assess the precision and efficiency of the estimator.</p></div>
Derivation of a 4-moment model for electron transport in Hall thrusters from a gyrokinetic model
- Tazakkati Zoubaïr
- Laguna Alejandro Alvarez
- Massot Marc
- Pichard Teddy
, 2025. <div><p>We model the motion of a population of electrons in a strong electromagnetic field undergoing elastic electron/electron collisions. This regime is derived from a dimensional analysis of the electron confinement in Hall-effect thrusters. The electrons exhibit a very high cyclotron frequency and a E × B-drift, modelled by stiff PDEs at the mesoscopic scale. We obtain a gyrokinetic model in which the fastest oscillations of the system are filtered out by averaging the rotation of the electrons around the magnetic field lines. The model is derived in the strong electromagnetic field limit. Based on this gyrokinetic model, we then develop a 10-moment model. The averaging operation performed at the kinetic scale leads to symmetry properties that allow to reduce the 10-moment model to a 4-moment model.</p></div>
Méthodes d'assimilation de données pour des simulations lagrangiennes
- Duvillard Marius
, 2025. Cette thèse porte sur le développement de méthodes d'assimilation de données pour les simulations lagrangiennes basées sur une discrétisation particulaire, avec des applications pour la simulation en mécanique des fluides. Nous étudions des situations où un ensemble de simulations et des observations à des temps discrets sont utilisés sont pour corriger l'estimation de l'état du système. Dans ce contexte, la procédure de mise à jour de la discrétisation particulaire à partir des observations disponibles constitue une problématique centrale.Dans un premier temps, nous adaptons le filtre de Kalman d'ensemble pour corriger les champs en modifiant uniquement les intensités des particules de la discrétisation. Les positions des particules restent alors inchangées ou sont régénérées sur une grille régulière, conduisant à deux méthodes distinctes.Ensuite, nous présentons une approche variationnelle d'ensemble pour corriger les positions des particules. Nous montrons que cette approche peut être combinée avec les premiers filtres pour corriger séquentiellement les positions et les intensités. Nous évaluons ces différentes méthodes sur des applications en dynamique des fluides incompressibles discrétisées par des méthodes de vortex, et nous analysons l'efficacité des filtres sur des problèmes d'advection où l'erreur de position peut être importante.
A stochastic algorithm for deterministic multistage optimization problems
- Akian Marianne
- Chancelier Jean-Philippe
- Tran Benoît
Annals of Operations Research, Springer Verlag, 2025, 345, pp.1-38. Several attempt to dampen the curse of dimensionnality problem of the Dynamic Programming approach for solving multistage optimization problems have been investigated. One popular way to address this issue is the Stochastic Dual Dynamic Programming method (SDDP) introduced by Perreira and Pinto in 1991 for Markov Decision Processes.Assuming that the value function is convex (for a minimization problem), one builds a non-decreasing sequence of lower (or outer) convex approximations of the value function. Those convex approximations are constructed as a supremum of affine cuts. On continuous time deterministic optimal control problems, assuming that the value function is semiconvex, Zheng Qu, inspired by the work of McEneaney, introduced in 2013 a stochastic max-plus scheme that builds upper (or inner) non-increasing approximations of the value function. In this note, we build a common framework for both the SDDP and a discrete time version of Zheng Qu's algorithm to solve deterministic multistage optimization problems. Our algorithm generates monotone approximations of the value functions as a pointwise supremum, or infimum, of basic (affine or quadratic for example) functions which are randomly selected. We give sufficient conditions on the way basic functions are selected in order to ensure almost sure convergence of the approximations to the value function on a set of interest. (10.1007/s10479-024-06153-8)
DOI : 10.1007/s10479-024-06153-8
Refined Analysis of Federated Averaging's Bias and Federated Richardson-Romberg Extrapolation
- Mangold Paul
- Durmus Alain
- Dieuleveut Aymeric
- Samsonov Sergey
- Moulines Eric
, 2025. In this paper, we present a novel analysis of FedAvg with constant step size, relying on the Markov property of the underlying process. We demonstrate that the global iterates of the algorithm converge to a stationary distribution and analyze its resulting bias and variance relative to the problem's solution. We provide a first-order bias expansion in both homogeneous and heterogeneous settings. Interestingly, this bias decomposes into two distinct components: one that depends solely on stochastic gradient noise and another on client heterogeneity. Finally, we introduce a new algorithm based on the Richardson-Romberg extrapolation technique to mitigate this bias.
Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration
- Abi Jaber Eduardo
- Bruneau Soukaïna
- de Carvalho Nathan
- Sotnikov Dimitri
- Tur Laurent
, 2025. In energy markets, joint historical and implied calibration is of paramount importance for practitioners yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from the option market. We address this crucial problem with a parsimonious multiplicative multi-factor Heath-Jarrow-Morton (HJM) model for forward curves, combined with a stochastic volatility factor coming from the Lifted Heston model. We develop a sequential fast calibration procedure leveraging the Kemna-Vorst approximation of futures contracts: (i) historical correlations and the Variance Swap (VS) volatility term structure are captured through Level, Slope, and Curvature factors, (ii) the VS volatility term structure can then be corrected for a perfect match via a fixed-point algorithm, (iii) implied volatility smiles are calibrated using Fourier-based techniques. Our model displays remarkable joint historical and implied calibration fits -to both German power and TTF gas marketsand enables realistic interpolation within the implied volatility hypercube.
Wavelet-Based Multiscale Flow For Realistic Image Deformation in the Large Diffeomorphic Deformation Model Framework
- Gaudfernau Fleur
- Blondiaux Eléonore
- Allassonnière Stéphanie
- Le Pennec Erwan
Journal of Mathematical Imaging and Vision, Springer Verlag, 2025, 67 (2), pp.10. Estimating accurate high-dimensional transformations remains very challenging, especially in a clinical setting. In this paper, we introduce a multiscale parameterization of deformations to enhance registration and atlas estimation in the Large Deformation Diffeomorphic Metric Mapping framework. Using the Haar wavelet transform, a multiscale representation of the initial velocity fields is computed to optimize transformations in a coarse-to-fine fashion. This additional layer of spatial regularization does not modify the underlying model of deformations. As such, it preserves the original kernel Hilbert space structure of the velocity fields, enabling the algorithm to perform efficient gradient descent. Numerical experiments on several datasets, including abnormal fetal brain images, show that compared to the original algorithm, the coarse-to-fine strategy reaches higher performance and yields template images that preserve important details while avoiding unrealistic features. This highly versatile strategy can easily be applied to other mathematical frameworks for almost no additional computational cost. (10.1007/s10851-024-01219-5)
DOI : 10.1007/s10851-024-01219-5
Surface Waves in Randomly Perturbed Discrete Models
- Garnier Josselin
- Sharma Basant Lal
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2025, 23 (1), pp.158-186. (10.1137/24M165510X)
DOI : 10.1137/24M165510X
Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2 -distance
- Gentiloni-Silveri Marta
- Ocello Antonio
, 2025. Score-based Generative Models (SGMs) aim to sample from a target distribution by learning score functions using samples perturbed by Gaussian noise. Existing convergence bounds for SGMs in the W2-distance rely on stringent assumptions about the data distribution. In this work, we present a novel framework for analyzing W2-convergence in SGMs, significantly relaxing traditional assumptions such as log-concavity and score regularity. Leveraging the regularization properties of the Ornstein-Uhlenbeck (OU) process, we show that weak log-concavity of the data distribution evolves into log-concavity over time. This transition is rigorously quantified through a PDE-based analysis of the Hamilton-Jacobi-Bellman equation governing the log-density of the forward process. Moreover, we establish that the drift of the time-reversed OU process alternates between contractive and noncontractive regimes, reflecting the dynamics of concavity. Our approach circumvents the need for stringent regularity conditions on the score function and its estimators, relying instead on milder, more practical assumptions. We demonstrate the wide applicability of this framework through explicit computations on Gaussian mixture models, illustrating its versatility and potential for broader classes of data distributions.
Polynomial approximations in a generalized Nyman–Beurling criterion
- Alouges François
- Darses Sébastien
- Hillion Erwan
, 2023, pp.767 - 785. The Nyman-Beurling criterion, equivalent to the Riemann hypothesis, is an approximation problem in the space of square integrable functions on $(0,\infty)$, involving dilations of the fractional part function by factors $\theta_k\in(0,1)$, $k\ge1$. Randomizing the $\theta_k$ generates new structures and criteria. One of them is a sufficient condition that splits into (i) showing that the indicator function can be approximated by convolution with the fractional part, (ii) a control on the coefficients of the approximation. This self-contained paper aims at identifying functions for which (i) holds unconditionally, by means of polynomial approximations. This yields in passing a short probabilistic proof of a known consequence of Wiener's Tauberian theorem. In order to tackle (ii) in the future, we give some expressions of the scalar products. New and remarkable structures arise for the Gram matrix, in particular moment matrices for a suitable weight that may be the squared $\Xi$-function for instance. (10.5802/jtnb.1227)
DOI : 10.5802/jtnb.1227
An exterior optimal transport problem
- Candau-Tilh Jules
- Goldman Michael
- Merlet Benoît
Calculus of Variations and Partial Differential Equations, Springer Verlag, 2025, 64 (2), pp.45. This paper deals with a variant of the optimal transportation problem. Given f ∈ L 1 (R d , [0, 1]) and a cost function c ∈ C(R d × R d) of the form c(x, y) = k(y − x), we minimise ∫ c dγ among transport plans γ whose first marginal is f and whose second marginal is not prescribed but constrained to be smaller than 1 − f. Denoting by Υ(f) the infimum of this problem, we then consider the maximisation problem sup{Υ(f) : ∫ f = m} where m > 0 is given. We prove that maximisers exist under general assumptions on k, and that for k radial, increasing and coercive these maximisers are the characteristic functions of the balls of volume m. (10.1007/s00526-024-02900-8)
DOI : 10.1007/s00526-024-02900-8
Optimisation of space-time periodic eigenvalues
- Bogosel Beniamin
- Mazari Idriss
- Nadin Grégoire
, 2025. <div><p>The goal of this paper is to provide a qualitative analysis of the optimisation of space-time periodic principal eigenvalues. Namely, considering a fixed time horizon T and the d-dimensional torus T d , let, for any m ∈ L ∞ ((0, T ) × T d ), λ(m) be the principal eigenvalue of the operator ∂t -∆ -m endowed with (time-space) periodic boundary conditions. The main question we set out to answer is the following: how to choose m so as to minimise λ(m)? This question stems from population dynamics. We prove that in several cases it is always beneficial to rearrange m with respect to time in a symmetric way, which is the first comparison result for the rearrangement in time of parabolic equations. Furthermore, we investigate the validity (or lack thereof) of Talenti inequalities for the rearrangement in time of parabolic equations. The numerical simulations which illustrate our results were obtained by developing a framework within which it is possible to optimise criteria with respect to functions having a prescribed rearrangement (or distribution function).</p></div>
Kinetic theory and moment models of electrons in a reactive weakly-ionized non-equilibrium plasma
- Laguna Alejandro Alvarez
- Pichard Teddy
Kinetic and Related Models, AIMS, 2025. <div><p>We study the electrons in a multi-component weakly-ionized plasma with an external electric field under conditions that are far from thermodynamic equilibrium, representative of a gas discharge plasma. Our starting point is the generalized Boltzmann equation with elastic, inelastic and reactive collisions. We perform a dimensional analysis of the equation and an asymptotic analysis of the collision operators for small electron-to-atom mass ratios and small ionization levels. The dimensional analysis leads to a diffusive scaling for the electron transport. We perform a Hilbert expansion of the electron distribution function that, in the asymptotic limit, results in a reduced model characterized by a spherically symmetric distribution function in the velocity space with a small anisotropic perturbation. We show that the spherical-harmonics expansion model, widely used in low-temperature plasmas, is a particular case of our approach. We approximate the solution of our kinetic model with a truncated moment hierarchy. Finally, we study the moment problem for a particular case: a Langevin collision (equivalent to Maxwell molecules) for the electron-gas elastic collisions. The resulting Stieltjes moment problem leads to an advection-diffusion-reaction system of equations that is approximated with two different closures: the quadrature method of moments and a Hermitian moment closure. A special focus is given along the derivations and approximations to the notion of entropy dissipation.</p></div> (10.3934/krm.2025007)
DOI : 10.3934/krm.2025007
Macroscopic limit from a structured population model to the Kirkpatrick-Barton model
- Raoul Gaël
Bulletin des Sciences Mathématiques, Elsevier, 2025, 205, pp.103697. We consider an ecology model in which the population is structured by a spatial variable and a phenotypic trait. The model combines a parabolic operator on the spatial variable with a kinetic operator on the trait variable. We prove the existence of solutions to that model, and show that these solutions are unique. The kinetic operator present in the model, that represents the effect of sexual reproductions, satisfies a Tanaka-type inequality: it implies a contraction of the Wasserstein distance in the space of phenotypic traits. We combine this contraction argument with parabolic estimates controlling the spatial regularity of solutions to prove the convergence of the population size and the mean phenotypic trait to solutions of the Kirkpatrick-Barton model, which is a well-established model in evolutionary ecology. Specifically, at high reproductive rates, we provide explicit convergence estimates for the moments of solutions of the kinetic model. (10.48550/arXiv.1706.04094)
DOI : 10.48550/arXiv.1706.04094
From Stochastic Zakharov System to Multiplicative Stochastic Nonlinear Schrödinger Equation
- Barrué Grégoire
- de Bouard Anne
- Debussche Arnaud
Stochastics and Partial Differential Equations: Analysis and Computations, Springer US, 2025, pp.1-40. We study the convergence of a Zakharov system driven by a time white noise, colored in space, to a multiplicative stochastic nonlinear Schrödinger equation, as the ion-sound speed tends to infinity. In the absence of noise, the conservation of energy gives bounds on the solutions, but this evolution becomes singular in the presence of the noise. To overcome this difficulty, we show that the problem may be recasted in the diffusion-approximation framework, and make use of the perturbed test-function method. We also obtain convergence in probability. The result is limited to dimension one, to avoid too much technicalities. As a prerequisite, we prove the existence and uniqueness of regular solutions of the stochastic Zakharov system.
Solving inverse source wave problem from Carleman estimates to observer design
- Boulakia Muriel
- de Buhan Maya
- Delaunay Tiphaine
- Imperiale Sébastien
- Moireau Philippe
Mathematical Control and Related Fields, AIMS, 2025. In this work, we are interested by the identification in a wave equation of a space dependent source term multiplied by a known time and space dependent function, from internal velocity or field measurements. The first part of the work consists in proving stability inequalities associated with this inverse problem from adapted Carleman estimates. Then, we present a sequential reconstruction strategy which is proved to be equivalent to the minimization of a cost functional with Tikhonov regularization. Based on the obtained stability estimates, the reconstruction error is evaluated with respect to the noise intensity. Finally, the proposed method is illustrated with numerical simulations, both in the case of regular source terms and of piecewise constant source terms. (10.3934/mcrf.2025007)
DOI : 10.3934/mcrf.2025007

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