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

We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be…

We explain how to compute top-dimensional intersections of psi-classes on moduli spaces of m-stable curves. On the moduli spaces of Deligne-Mumford stable pointed curves of genus one, these intersection numbers are determined by two…

We use the Serre-Godeaux varieties of finite groups, projective representation theory, the twisted Atiyah-Segal completion theorem, and our previous work on the topological period-index problem to compute the etale index of Brauer classes…

In this paper, a second-order accurate method was developed for calculating fluid flows in complex geometries. This method uses cut-Cartesian cell mesh in finite volume framework. Calculus is employed to relate fluxes and gradients along…

Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient…

A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…

There has been a great deal of recent interest in the development of spatial prediction algorithms for very large datasets and/or prediction domains. These methods have primarily been developed in the spatial statistics community, but there…

The differential cross-section for the reflection of light beams off rigid bodies obtained by the rotation of a generic derivable convex function is calculated. The calculation is developed using elementary notions of calculus and is…

The Macaulay2 package DecomposableSparseSystems implements methods for studying and numerically solving decomposable sparse polynomial systems. We describe the structure of decomposable sparse systems and explain how the methods in this…

This note introduces the $\texttt{LikelihoodGeometry}$ package for the computer algebra system $\textit{Macaulay2}$. This package gives tools to construct the likelihood correspondence of a discrete algebraic statistical model, a variety…

These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…

Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…

Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection…

Classical objects in computational geometry are defined by explicit relations. Several years ago the pioneering works of T. Asano, J. Matousek and T. Tokuyama introduced "implicit computational geometry", in which the geometric objects are…

The purpose of this paper is to develop an efficient computational model for Abelian categories of coherent sheaves over certain classes of varieties. These categories are naturally described as Serre quotient categories. Hence, our…

We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful…

Sparse representations using overcomplete dictionaries have proved to be a powerful tool in many signal processing applications such as denoising, super-resolution, inpainting, compression or classification. The sparsity of the…

In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…

Assuming the Tate conjecture and the computability of \'etale cohomology with finite coefficients, we give an algorithm that computes the N\'eron-Severi group of any smooth projective geometrically integral variety, and also the rank of the…

A random recursive cell splitting scheme of the $2$-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large…