40 citations · 55 across the 14 of their papers we have counts for
18 papers
Algebraic Distance Optimization in Polyhedral Norms
Eliana Duarte, Nidhi Kaihnsa, Julia Lindberg +2
We consider the distance minimization problem to a real algebraic variety $X \subseteq \RR^n$ when the metric is induced by a polyhedral norm. Each point in the variety has a Voron…
-Equivariant Dimensionality Reduction on Stiefel Manifolds
Andrew Lee, Harlin Lee, Jose A. Perea +2
Many real-world datasets live on high-dimensional Stiefel and Grassmannian manifolds, and respectively, and benefit from projection onto l…
Critical Curvature of Algebraic Surfaces in Three-Space
Paul Breiding, Kristian Ranestad, Madeleine Weinstein
We study the curvature of a smooth algebraic surface of degree from the point of view of algebraic geometry. More precisely, we consider umbilical points…
On the structure of a poly- group
Madeline Weinstein
In this paper we study a certain class of polycyclic groups. We outline a method for constructing a poly- group by describing a process for selecting maps that ar…
Real Symmetric Matrices with Partitioned Eigenvalues
Madeleine Weinstein
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 distanc…
96120: The degree of the linear orbit of a cubic surface
Laura Brustenga i Moncusí, Sascha Timme, Madeleine Weinstein
The projective linear group \(\pgl(\comp,4)\) acts on cubic surfaces, considered as points of . We compute the degree of the -dimensional projecti…
Voronoi Cells in Metric Algebraic Geometry of Plane Curves
Madeline Brandt, Madeleine Weinstein
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 o…
The bottleneck degree of algebraic varieties
Sandra Di Rocco, David Eklund, Madeleine Weinstein
A bottleneck of a smooth algebraic variety is a pair of distinct points such that the Euclidean normal spaces at and contain the line…
Voronoi Cells of Varieties
Diego Cifuentes, Kristian Ranestad, Bernd Sturmfels +1
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 a…
Offset Hypersurfaces and Persistent Homology of Algebraic Varieties
Emil Horobet, Madeleine Weinstein
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 persisten…
Learning Algebraic Varieties from Samples
Paul Breiding, Sara Kalisnik Verovsek, Bernd Sturmfels +1
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 topolog…
Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions
Andrew Best, Karen Huan, Nathan McNew +4
Two well studied Ramsey-theoretic problems consider subsets of the natural numbers which either contain no three elements in arithmetic progression, or in geometric progression. We…
Invariance of the Sprague-Grundy Function for Variants of Wythoff's Game
Madeleine Weinstein
We prove three conjectures of Fraenkel and Ho regarding two classes of variants of Wythoff's game. The two classes of variants of Wythoff's game feature restrictions of the diagona…
Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers , with initial terms . Previo…
Benford Behavior of Generalized Zeckendorf Decompositions
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by and , every…
Geometric-progression-free sets over quadratic number fields
Andrew Best, Karen Huan, Nathan McNew +4
A problem of recent interest has been to study how large subsets of the natural numbers can be while avoiding 3-term geometric progressions. Building on recent progress on this pro…
Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers , with initial terms . We con…
Benford Behavior of Zeckendorf Decompositions
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers . A set $S \subset \…