The Mongue-Elkan method is a general text string comparison method based on an internal character-based similarity measure (e.g. edit distance) combined with a token level (i.e. word level) similarity measure. We propose a generalization of this method based on the notion of the generalized arithmetic mean instead of the simple average used in the expression to calculate the Monge-Elkan method....

We characterize complete intersections in terms of local differential geometry. Let X ⊂ CPn+a be a variety. We first localize the problem; we give a criterion for X to be a complete intersection that is testable at any smooth point of X. We rephrase the criterion in the language of projective differential geometry and derive a sufficient condition for X to be a complete intersection that is com...

laboratoire d’informatique Gaspard-Monge ESIEE Doctor of Philosophy Image processing algorithms for the visualization of interventional devices in X-ray fluoroscopy.

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

Parabolic Monge-Ampère equations are divided into contact inequivalent classes, for each of which a normal form is given. Two of these are new in the C category.

We show that the uniform estimate in the Calabi-Yau theorem easily follows from the local stability of the complex Monge-Ampère equation.

This paper establishes Hölder estimates of Du and Lp estimates of D2u for solutions u to the parabolic Monge-Ampère equation −Aut + ( det D2u)1/n = f .

We present a proof of strict g-convexity in 2D for solutions generated Jacobian equations with g-Monge–Ampère measure bounded away from 0. Subsequently this implies $$C^1$$ differentiability the case above. Our follows one given by Trudinger and Wang Monge–Ampère case. Thus, like theirs, our argument is local yields quantitative estimate on g-convexity. As result new even optimal transport case...

We discuss the Siciak-Zaharjuta extremal function of a real convex body in Cn, a solution of the homogeneous complex Monge-Ampère equation on the exterior of the convex body. We determine several conditions under which a foliation by holomorphic curves can be found in the complement of the convex body along which the extremal function is harmonic. We study a variational problem for holomorphic ...

The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in H. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].