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Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...
Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...
This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...
Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...
We review the main features and results of thermal leptogenesis within the type I seesaw mechanism, the minimal extension of the Standard Model explaining neutrino masses and mixing. After presenting the simplest approach, the vanilla scenario, we discuss ...
Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate func- tions based on random sampling according to a given probability measure. Recent work has shown th ...
Let W be a vector space over an algebraically closed field k. Let H be a quasisimple group of Lie type of characteristic p not equal char(k) acting irreducibly on W. Suppose also that G is a classical group with natural module W, chosen minimally with resp ...
Principal Component Analysis (PCA) has been widely used for manifold description and dimensionality reduction. Performance of PCA is however hampered when data exhibits nonlinear feature relations. In this work, we propose a new framework for manifold lear ...
This article approaches the incremental view maintenance problem from an algebraic perspective. The algebraic structure of a ring of databases is constructed and extended to form a powerful aggregate query calculus. The query calculus inherits the key prop ...
We investigate the problem of distributed sensors' failure detection in networks with a small number of defective sensors, whose measurements differ significantly from neighbouring sensor measurements. We build on the sparse nature of the binary sensor fai ...
