相关论文: A method to compute Segre classes of subschemes of…

The CompHEP software package allows the evaluation of cross section and decays of elementary particles with a high level of automation. Arbitrary tree levelp rocesses can be calculated starting from the set of vertices prescribed by a given…

We introduce a Macaulay2 package for working with jet schemes. The main method constructs jets of ideals, polynomial rings and their quotients, ring homomorphisms, affine varieties, and (hyper)graphs. The package also includes additional…

Textures often show multiscale properties and hence multiscale techniques are considered useful for texture analysis. Scale-space theory as a biologically motivated approach may be used to construct multiscale textures. In this paper…

We demonstrate how some classical computations of divisor class groups can be obtained using the theory of rational coefficient Weil divisors and related results of Watanabe.

This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis, their properties depend on…

A fundamental property of Segre classes is their birational invariance. This invariance implies that the Segre class of a closed subscheme only depends on the integral closure of the defining ideal sheaf. In this paper, we show that,…

The classical Severi degree counts the number of algebraic curves of fixed genus and class passing through points in a surface. We express the Severi degrees of CP1 x CP1 as matrix elements of the exponential of a single operator M on Fock…

Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…

An algorithm is presented for the computation of the topology of a non-reduced space curve defined as the intersection of two implicit algebraic surfaces. It computes a Piecewise Linear Structure (PLS) isotopic to the original space curve.…

We explicitly compute examples of sheaves over the projectivization of the spectrum of the cohomology of sl_2. In particular, we compute \ker\Theta_M for every indecomposable M and we compute F_i(M) when M is an indecomposable Weyl module…

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

This article presents a new classification framework that can extract individual features per class. The scheme is based on a model of incoherent subspaces, each one associated to one class, and a model on how the elements in a class are…

Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…

We study locally Cohen-Macaulay curves of low degree in the Segre threefold with Picard number three and investigate the irreducible and connected components respectively of the Hilbert scheme of them. We also discuss the irreducibility of…

On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.

We obtain an explicit formula for the number of rational cuspidal curves of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed as an Euler…

In a given classification task, the accuracy of the learner is often hampered by finiteness of the training set, high-dimensionality of the feature space and severe overlap between classes. In the context of interpretable learners, with…

There is presented an algorithm for computing the topological degree for a large class of polynomial mappings. As an application there is given an effective algebraic formula for the intersection number of a polynomial immersion M --> R^2m,…

We present an improved algorithm for the computation of Zariski chambers on algebraic surfaces. The new algorithm significantly outperforms the so far available method and allows therefore to treat surfaces of high Picard number, where huge…

The choice of a homogeneous ideal in a polynomial ring defines a closed subscheme $Z$ in a projective space as well as an infinite sequence of cones over $Z$ in progressively higher dimension projective spaces. Recent work of Aluffi…