10 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Institut national de recherche en sciences et technologies du numériqueFR7 papers
- Centre Inria d'Université Côte d'AzurFR4 papers
- Centre National de la Recherche ScientifiqueFR3 papers
- Sorbonne UniversitéFR3 papers
- Université Côte d'AzurFR3 papers
- Athena Research and Innovation Center In Information Communication & Knowledge TechnologiesGR2 papers
- Laboratoire Jean-Alexandre DieudonnéFR2 papers
- National and Kapodistrian University of AthensGR2 papers
- OURAGAN: Outils de Résolution Algébriques pour la Géométrie et ses ApplicationsFR2 papers
- Centre for Arctic Gas Hydrate, Environment and ClimateNO1 paper
- Centro de Investigação em Matemática e AplicaçõesPT1 paper
- Communauté d'universités et d'établissements Université Côte d'AzurFR1 paper
14 papers
On Łojasiewicz Inequalities and the Effective Putinar's Positivstellensatz
Lorenzo Baldi, Bernard Mourrain, Adam Parusinski
The representation of positive polynomials on a semi-algebraic set in terms of sums of squares is a central question in real algebraic geometry, which the Positivstellensatz answer…
Influence of lung physical properties on its flow--volume curves using a detailed multi-scale mathematical model of the lung
Riccardo Di Dio, Michaël Brunengo, Benjamin Mauroy
We develop a mathematical model of the lung that can estimate independently the air flows and pressures in the upper bronchi. It accounts for the lung multi-scale properties and fo…
Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description
Evelyne Hubert, Tobias Metzlaff, Cordian Riener
The Weyl group of a crystallographic root system has a nonlinear action on the compact torus. The orbit space of this action is a compact basic semi-algebraic set. We present a pol…
Tensor decomposition for learning Gaussian mixtures from moments
Rima Khouja, Pierre-Alexandre Mattei, Bernard Mourrain
In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gauss…
Computing real radicals by moment optimization
Lorenzo Baldi, Bernard Mourrain
We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of, which is based on convex moment optimization. A truncated positive generi…
Efficient Sampling from Feasible Sets of SDPs and Volume Approximation
Apostolos Chalkis, Ioannis Emiris, Vissarion Fisikopoulos +2
We present algorithmic, complexity, and implementation results on the problem of sampling points from a spectrahedron, that is the feasible region of a semidefinite program. Our ma…
Computing minimal Gorenstein covers
Juan Elias, Roser Homs, Bernard Mourrain
We analyze and present an effective solution to the minimal Gorenstein cover problem: given a local Artin k-algebra , compute an Artin Gorenstein -alg…
On the maximal number of real embeddings of minimally rigid graphs in , and
Evangelos Bartzos, Ioannis Z. Emiris, Jan Legerský +1
Rigidity theory studies the properties of graphs that can have rigid embeddings in a euclidean space or on a sphere and which in addition satisfy certain edge length…
Skew-Symmetric Tensor Decomposition
Enrique Arrondo, Alessandra Bernardi, Pedro Macias Marques +1
We introduce the ``skew apolarity lemma'' and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in { with $d\leq…
Sparse polynomial interpolation: sparse recovery, super resolution, or Prony?
Cédric Josz, Jean-Bernard Lasserre, Bernard Mourrain
We show that the sparse polynomial interpolation problem reduces to a discrete super-resolution problem on the -dimensional torus. Therefore the semidefinite programming approac…
Rational invariants of even ternary forms under the orthogonal group
Paul Görlach, Evelyne Hubert, Théo Papadopoulo
In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group on the space $\mathbb{R}[x,y,z]_{2…
Fast algorithm for border bases of Artinian Gorenstein algebras
Bernard Mourrain
Given a multi-index sequence , we present a new efficient algorithm to compute generators of the linear recurrence relations between the terms of . We transform this prob…
Structured low rank decomposition of multivariate Hankel matrices
Jouhayna Harmouch, Houssam Khalil, Bernard Mourrain
We study the decomposition of a multivariate Hankel matrix H\_ as a sum of Hankel matrices of small rank in correlation with the decomposition of its symbol as a sum of poly…
Waring-like decompositions of polynomials - 1
Maria Virginia Catalisano, Luca Chiantini, Anthony V. Geramita +1
Let be a homogeneous form of degree in variables. A Waring decomposition of is a way to express as a sum of powers of linear forms. In this paper we co…