相关论文: Linear precision for parametric patches

In this paper, we establish a general setup for studying incidence-preserving motions of projective geometric configurations of points and lines via a "projective rigidity matrix". The spaces of infinitesimal motions of a point-line…

Let k be an imaginary quadratic number field (with class number 1). We describe a new, essentially linear-time algorithm, to list all isomorphism classes of cubic extensions L/k up to a bound X on the norm of the relative discriminant…

A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…

We study how to lift Markov bases and Gr\"obner bases along linear maps of lattices. We give a lifting algorithm that allows to compute such bases iteratively provided a certain associated semigroup is normal. Our main application is the…

When a projection of a symmetric or Hermitian matrix to the positive semidefinite cone is computed approximately (or to working precision on a computer), a natural question is to quantify its accuracy. A straightforward bound invoking…

We develop a constructive process which determines all extreme points of the unit ball of the space of $m$--linear forms, $m\geq1.$ Our method provides a full characterization of the geometry of that space through finitely many elementary…

We consider a class of cut-and-project sets $\Lambda = \Lambda_F \times \zahl$ in the plane. Let $L=\Lambda+w\real$, $w\in\real^2$, be a countable union of parallel lines. Then either (1) $L$ is a discrete family of lines, (2) $L$ is a…

Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of…

Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…

We study point-line configurations through the lens of projective geometry and matroid theory. Our focus is on their realisation spaces, where we introduce the concepts of liftable and quasi-liftable configurations, exploring cases in which…

We determine those maps between affine or projective spaces that are linear in the abstract sense of transforming collinear points into collinear points and whose restriction to any line is constant or injective. Our results are extensions…

In several applications, one must estimate a real-valued (symmetric) Toeplitz covariance matrix, typically shifted by the conjugated diagonal matrices of phase progression and phase "calibration" errors. Unlike the Hermitian Toeplitz…

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…

We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…

Man-made environments such as households, offices, or factory floors are typically composed of linear structures. Accordingly, polylines are a natural way to accurately represent their geometry. In this paper, we propose a novel…

This paper is devoted to the investigation of selected situations when the computation of projective (and other) equivalences of algebraic varieties can be efficiently solved with the help of finding projective equivalences of finite sets…

Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion.…

We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…

We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the…