Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Weinstein, Madeleine"'
Many real-world datasets live on high-dimensional Stiefel and Grassmannian manifolds, $V_k(\mathbb{R}^N)$ and $Gr(k, \mathbb{R}^N)$ respectively, and benefit from projection onto lower-dimensional Stiefel (respectively, Grassmannian) manifolds. In th
Externí odkaz:
http://arxiv.org/abs/2309.10775
We study the curvature of a smooth algebraic surface $X\subset \mathbb R^3$ of degree $d$ from the point of view of algebraic geometry. More precisely, we consider umbilical points and points of critical curvature. We prove that the number of complex
Externí odkaz:
http://arxiv.org/abs/2206.09130
Autor:
Weinstein, Madeleine
We study the real algebraic variety of real symmetric matrices with eigenvalue multiplicities determined by a partition. We present formulas for the dimension and Euclidean distance degree. We give a parametrization by rational functions. For small m
Externí odkaz:
http://arxiv.org/abs/2008.08554
The projective linear group \(\pgl(\comp,4)\) acts on cubic surfaces, considered as points of $\mathbb{P}_{\mathbb{C}}^{19}$. We compute the degree of the $15$-dimensional projective variety given by the Zariski closure of the orbit of a general cubi
Externí odkaz:
http://arxiv.org/abs/1909.06620
Autor:
Brandt, Madeline, Weinstein, Madeleine
Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells obtained from point samples of the curve. We use this result to study m
Externí odkaz:
http://arxiv.org/abs/1906.11337
A bottleneck of a smooth algebraic variety $X \subset \mathbb{C}^n$ is a pair of distinct points $(x,y) \in X$ such that the Euclidean normal spaces at $x$ and $y$ contain the line spanned by $x$ and $y$. The narrowness of bottlenecks is a fundamenta
Externí odkaz:
http://arxiv.org/abs/1904.04502
Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. We compute the algebraic boundaries of these Voronoi cells.
Externí odkaz:
http://arxiv.org/abs/1811.08395
Autor:
Horobet, Emil, Weinstein, Madeleine
In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persistent homology. Moreover, we connect persistent homology and algebraic opt
Externí odkaz:
http://arxiv.org/abs/1803.07281
Publikováno v:
Revista Matem\'atica Complutense (2018)
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining polynomials.
Externí odkaz:
http://arxiv.org/abs/1802.09436
Publikováno v:
In Journal of Symbolic Computation March-April 2022 109:351-366
