12 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Institut de Recherche Mathématique AvancéeFR147 papers
- Université de StrasbourgFR9 papers
- Institut national de recherche en sciences et technologies du numériqueFR8 papers
- Laboratoire Jacques-Louis LionsFR8 papers
- Centre National de la Recherche ScientifiqueFR7 papers
- Laboratoire Analyse, Géométrie et ApplicationsFR6 papers
- Laboratoire de Mathématiques Jean LerayFR5 papers
- Université de LorraineFR5 papers
- Université Paris CitéFR5 papers
- Institut Élie Cartan de LorraineFR4 papers
- Laboratoire de Mathématiques d'OrsayFR4 papers
- Laboratoire de Mathématiques Raphaël SalemFR4 papers
262 papers
A weak invariance principle for triangular arrays of independent random variables in some Besov spaces
Davide Giraudo, Sadillo Sharipov
We establish a Donsker-Prokhorov invariance principle in some Besov spaces. Specifically, we show that polygonal line processes associated with partial sum processes of a triangula…
Radon Measure Representations for Infinite-Width Neural Networks with Singular Activations
Mathias Dus
The theoretical foundation of infinite-width shallow neural networks relies heavily on continuous integral representations and Barron spaces. Recently, harmonic analysis-specifical…
On the construction of geographical maps: Lagrange, Chebyshev, Darboux and Milnor
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos
Lagrange, Chebyshev, and Darboux, in 1779, 1856, and 1911, respectively, wrote articles all bearing the same title, \emph{On the Construction of Geographical Maps}. In 1969, Milnor…
Convergence-Symmetric Metric Spaces
Ismail Saglam, Ken'Ichi Ohshika, Athanase Papadopoulos +1
We study some basic properties of spaces which satisfy the usual axioms of a metric space but without the symmetry axiom. We realised that such a study is needed in view of the rel…
Generalizing Lusztig's total positivity II : geometric properties
Olivier Guichard, Anna Wienhard
Positive structures in Lie groups with respect to a subset of the set of positive roots provide a generalization of Lusztig's total positivity in split real Lie groups to the s…
Functional central limit theorems for -statistics of beta-mixing data
Davide Giraudo
We investigate the convergence of partial sum processes based on a strictly stationary -mixing sequence of random variables. The convergence in the space of continuous function…
Polytopes and posets associated to preorders
Frédéric Chapoton, Christos A. Athanasiadis
Preorder polytopes, defined from preorders on finite sets, are introduced and studied from a lattice point enumeration point of view. They naturally generalize arbor polytopes, rec…
The combinatorial structure of the unit tangent spheres and cotangent spheres of Teichm{ü}ller space with Thurston's Finsler metric
Ken'Ichi Ohshika, Athanase Papadopoulos
We prove several new results on the combinatorial structures of the unit spheres of the norms induced by Thurston's metric on the tangent and cotangent spaces of the Teichm{ü}ller…
Integrals of general geometric random variables on the moduli space of hyperbolic surfaces
Victor Le Guilloux
In this article we provide an integration formula enabling us to integrate random variables defined on the moduli space of hyperbolic surfaces which involve the lengths of closed g…
Chern classes of Laughlin bundles on the quasihole moduli space
Florent Dupont, Semyon Klevtsov
We study fractional quantum Hall states with quasihole excitations, on Riemann surfaces of arbitrary genus. For configurations with quasiholes we construct a vector bundle abov…
Spherical trigonometry before the modern era:The treatise of Nasir al-Din al-Tusi
Athanase Papadopoulos
This is an overview of Nasir al-Din al-Tusi's Treatise of the quadrilateral, an invaluable 13th century document on spherical geometry which was translated into French in 1891. The…
Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization
Mathias Dus
We present a geometric framework for Reinforcement Learning (RL) that views policies as maps into the Wasserstein space of action probabilities. First, we define a Riemannian struc…
Simulation Based Inference of a Simple Neural Network Structure
Pierre Charitat, Ségolen Geffray, Christophe Pouzat
Neurophysiologists are nowadays able to record from a large number of extracellular electrodes and to extract, from the raw data, the sequences of action potentials or spikes gener…
Probabilistic Weyl Law for Twisted Toeplitz Matrices with Rough Symbols
Lucas Noël
In this article, we study the convergence of the empirical spectral measure of twisted Toeplitz matrices subject to small random perturbations. We show that the empirical spectral…
Notes on angles and solid angles, in relation with Euler's memoir De mensura angulorum solidorum
Stelios Negrepontis, Athanase Papadopoulos
We provide some historical context to the study of solid angles carried out by Euler in his memoir \emph{De mensura angulorum solidorum} (On the measure of solid angles). We extend…
Johann Heinrich Lambert's memoir "Theorie der Parallellinien": A review with commentary
Athanase Papadopoulos, Guillaume Théret
We review the memoir \emph{heorie der Parallellinien} by Johann Heinrich Lambert, written in 1766. Lambert, a victim of the prejudices of his time, conceived this memoir as an atte…
Wide-Surface Furnace for In Situ X-Ray Diffraction of Combinatorial Samples using a High-Throughput Approach
Giulio Cordaro, Juande Sirvent, Cristian Mocuta +7
The combinatorial approach applied to functional oxides has enabled the production of material libraries that formally contain infinite compositions. A complete ternary diagram can…
Simone Weil, Andr{é} Weil, Bourbaki and Pythagorean mathematics
Athanase Papadopoulos
Simone Weil is one of the most prominent 20th century French philosophers. She is the sister of Andr{é} Weil, the renowned mathematician, the father of modern algebraic geometry an…
Grassmannian Geometry and Global Convergence of Variable Projection for Neural Networks
Mathias Dus
Training deep neural networks and Physics-Informed Neural Networks (PINNs) often leads to ill-conditioned and stiff optimization problems. A key structural feature of these models…
On the Lambert conformal conical projection and the general map of the Russian Empire
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos +1
The problem of drawing geographical maps is the one of mapping a subset of the sphere, representing a country or some other region on the surface of the Earth, into the Euclidean p…
Galilei and Huygens: Music and science
Athanase Papadopoulos
Vincenzo Galilei and Constantijn Huygens were both humanists and eminent musicians, the former from the late Renaissance and the latter from the early Modern era. Their respective…
Andr{é} and Simone Weil: Mathematics, social activism and Indian culture
Athanase Papadopoulos, Susumu Tanabé
This is an essay on the relation of Andr{é} and Simone Weil with Indian culture and Sanskrit literature, especially the Bhagavad G{ī}t{ā}, a Hindu scripture which they knew well, w…
Euler's work on spherical geometry: An overview with comments
Athanase Papadopoulos, Vladimir Turaev
We review Euler's work on spherical geometry. After an introduction concerning the general place that trigonometric formulae occupy in geometry, we start by the two memoirs of Eule…
Sharpness for monotone absorbing Interacting Particle Systems
Jean Bérard, Barbara Dembin, Laure Marêché
We prove a sharpness result for the dynamics of finite-range Interacting Particle Systems (IPS) on , which generalizes to a whole class of IPS the sharpness result…