Related papers: Computational procedures for weighted projective s…
A weighted projective stack is a stacky quotient $\mathscr P(\mathbf a)=(\mathbf A^n-\{0\})/\mathbb G_m$, where the action of $\mathbb G_m$ is with weights $\mathbf a\in\mathbb Z^n_{>0}$. Examples are: the compactified moduli stack of…
Suppose given an holomorphic and Hamiltonian action of a compact torus $T$ on a polarized Hodge manifold $M$. Assume that the action lifts to the quantizing line bundle, so that there is an induced unitary representation of $T$ on the…
In the last decade major steps towards an algorithmic treatment of orthogonal polynomials and special functions (OP & SF) have been made, notably Zeilberger's brilliant extension of Gosper's algorithm on algorithmic definite hypergeometric…
Let f be a generic polynomial mapping mapping from the plane to the plane. There are constructed quadratic forms whose signatures determine the number of positive and negative cusps of f.
Tame functions are a class of nonsmooth, nonconvex functions, which feature in a wide range of applications: functions encountered in the training of deep neural networks with all common activations, value functions of mixed-integer…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
We apply the geometric quantization method with real polarizations to the quantization of a symplectic torus. By quantizing with half-densities we canonically associate to the symplectic torus a projective Hilbert space and prove that the…
In this paper, we investigate the extent to which knowledge compilation can be used to improve inference from propositional weighted bases. We present a general notion of compilation of a weighted base that is parametrized by any…
This paper studies the problem of constructing polytopic representations of planar regions from depth camera readings. This problem is of great importance for terrain mapping in complicated environment and has great potentials in legged…
A classification technique for identifying focal mechanism type and fault plane orientation based on the polarity of P-wave "first motion" data is derived. A support vector machine is used to classify the polarity data in the space of…
We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose…
These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations.…
We consider the problem of computationally-efficient prediction from high dimensional and highly correlated predictors in challenging settings where accurate variable selection is effectively impossible. Direct application of penalization…
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to…
Large-scale numerical simulations of planetary interiors require dedicated visualization algorithms that are able to efficiently extract a large amount of information in an interactive and user-friendly way. Here we present a software…
Gaussian processes provide a flexible framework for spatial prediction, but their computational cost limits applicability to large-scale data with large sample size $n$. Predictive processes (PPs), a popular low-rank approximation, mitigate…
We study the enumerative geometry of orbits of multidimensional toric action on projective algebraic varieties and develop a new cyclic differential-graded operad, conjecturally governing the real version of the enumerative geometry of…
The purpose of this article is to develop foundational techniques from logarithmic geometry in order to define a functorial tropicalization map for fine and saturated logarithmic schemes in the case of constant coefficients. Our approach…
The theoretical models providing mathematical abstractions for several significant optimization problems in machine learning, combinatorial optimization, computer vision and statistical physics have intrinsic similarities. We propose a…
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…