相关论文: Implicitizing rational hypersurfaces using approxi…

Chen, Sederberg, and Zheng introduced the notion of a $\mu$-basis for a rational ruled surface in Chen et al. (2001) and showed that its resultant is the implicit equation of the surface, if the parametrization is generically injective. We…

Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to evaluate the integral accurately at points on or near the…

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 propose a fast and accurate surface reconstruction algorithm for unorganized point clouds using an implicit representation. Recent learning methods are either single-object representations with small neural models that allow for high…

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…

Let $F(x_1,...,x_n)$ be a form of degree $d\geq 2$, which produces a geometrically irreducible hypersurface in $\mathbb{P}^{n-1}$. This paper is concerned with the number of rational points on F=0 which have height at most $B$. Whenever…

Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by several groups is to use this representation…

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

These are the substantially expanded notes of the lectures of JK at the summer school "Higher-Dimensional Geometry over Finite Fields" in G\"ottingen, June 2007. The first part gives an overview of the methods. The main new result is the…

Let $U\subseteq H^0(\mathcal{O}_{\mathbb{P}^1\times \mathbb{P}^1}(a,b))$ be a four-dimensional vector space and consider the rational map $\phi_U:\,\mathbb{P}^1\times \mathbb{P}^1 \dashrightarrow \mathbb{P}^3$ defined by its basis of…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…

Works on implicit regularization have studied gradient trajectories during the optimization process to explain why deep networks favor certain kinds of solutions over others. In deep linear networks, it has been shown that gradient descent…

There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that…

In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…

We consider an equation of multiple variables in which a partial derivative does not vanish at a point. The implicit function theorem provides a local existence and uniqueness of the function for the equation. In this paper, we propose an…

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…