38 citations
- Institut de Mathématiques de Jussieu-Paris Rive GaucheFR44 papers
- Sorbonne UniversitéFR33 papers
- Université Paris CitéFR19 papers
- Centre National de la Recherche ScientifiqueFR12 papers
- Institut national de recherche en sciences et technologies du numériqueFR12 papers
- National and Kapodistrian University of AthensGR5 papers
- Institut FourierFR4 papers
- LIP6FR4 papers
- Université Pierre-et-Marie-CurieFR4 papers
- City University of Hong KongHK3 papers
- Geometric (India)IN3 papers
- Technische Universität BerlinDE3 papers
55 papers
Solving parametric polynomial systems using Generic Rational Univariate Representation
Florent Corniquel
In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the…
Certificates for nonnegativity of multivariate integer polynomials under perturbations
Matías R Bender, Khazhgali Kozhasov, Elias Tsigaridas +1
We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their…
Self-adjoint extensions of singular Sturm-Liouville operators on graphs and Weyl's law
Elisha Falbel
We study self-adjoint extensions of a second order differential operator of Sturm-Liouville type on a graph. We relate self-adjointness of the operator to the existence of non-comp…
Minima and Critical Points of the Bethe Free Energy Are Invariant Under Deformation Retractions of Factor Graphs
Grégoire Sergeant-Perthuis, Léo Boitel
In graphical models, factor graphs, and more generally energy-based models, the interactions between variables are encoded by a graph, a hypergraph, or, in the most general case, a…
Geometric families of multiple elliptic Gamma functions and arithmetic applications, I
Pierre L. L. Morain
This is the first paper in a series where we study arithmetic applications of the multiple elliptic Gamma functions originated from mathematical physics. The main purpose of this p…
Positive Univariate Polynomials: SOS certificates, algorithms, bit complexity, and T-systems
Matías Bender, Philipp Di Dio, Elias Tsigaridas
We consider certificates of positivity for univariate polynomials with rational coefficients that are positive over (an interval of)~. Such certificates take the form o…