About a non-standard interpolation problem

Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein algebra, using the Lagrange interpolation polynomial, plays a key role in the arguments

Challenge IEEE-ISBI/TCB : Application of Covariance matrices and wavelet marginals

This short memo aims at explaining our approach for the challenge IEEE-ISBI on Bone Texture Characterization. In this work, we focus on the use of covariance matrices and wavelet marginals in an SVM classifier.Comment: 9 pages, 4 Figues, 2 Tables, Challenge IEEE-ISBI : Bone Texture Characterizatio

One parameter regularizations of products of residue currents

We show that Coleff-Herrera type products of residue currents can be defined by analytic continuation of natural functions depending on one complex variable.Comment: 8 page

Segre numbers, a generalized King formula, and local intersections

Let $\mathcal J$ be an ideal sheaf on a reduced analytic space $X$ with zero set $Z$. We show that the Lelong numbers of the restrictions to $Z$ of certain generalized Monge-Amp\`ere products $(dd^c\log|f|^2)^k$, where $f$ is a tuple of generators of $\mathcal J$, coincide with the so-called Segre numbers of $\mathcal J$, introduced independently by Tworzewski and Gaffney-Gassler. More generally we show that these currents satisfy a generalization of the classical King formula that takes into account fixed and moving components of Vogel cycles associated with $\mathcal J$. A basic tool is a new calculus for products of positive currents of Bochner-Martinelli type. We also discuss connections to intersection theory