scholarly journals Bimonotone subdivisions of point configurations in the plane

2021 ◽  
Vol 12 (2) ◽  
pp. 125-138
Author(s):  
Elina Robeva ◽  
Melinda Sun
Keyword(s):  
Point Configurations

scholarly journals Conditional probabilities via line arrangements and point configurations

2021 ◽  
pp. 1-33
Author(s):  
Oliver Clarke ◽  
Fatemeh Mohammadi ◽  
Harshit J. Motwani
Keyword(s):  
Conditional Probabilities ◽  
Line Arrangements ◽  
Point Configurations

Effect of Point Configurations on Parameter Estimation Analysis of Circles

2021 ◽  
Vol 147 (3) ◽  
pp. 04021010
Author(s):  
Zhanfeng Song ◽  
Tao Fang ◽  
Paul Schonfeld ◽  
Jun Li
Keyword(s):  
Parameter Estimation ◽  
Point Configurations

scholarly journals Equations for point configurations to lie on a rational normal curve

2018 ◽  
Vol 340 ◽  
pp. 653-683
Author(s):  
Alessio Caminata ◽  
Noah Giansiracusa ◽  
Han-Bom Moon ◽  
Luca Schaffler
Keyword(s):  
Normal Curve ◽  
Point Configurations ◽  
Rational Normal Curve

scholarly journals 9-Point and 7-Point Configurations in 3-Space

1963 ◽  
Vol s3-13 (1) ◽  
pp. 384-384
Author(s):  
H. T. Croft
Keyword(s):  
Point Configurations

Einführung in eine anorganische Strukturchemie

1986 ◽  
Vol 175 (3-4) ◽  
Author(s):  
E. Hellner
Keyword(s):  
Three Dimensional ◽  
Standard Setting ◽  
Transformation Matrix ◽  
Two Dimensional ◽  
Coordination Polyhedra ◽  
Systematic Description ◽  
Point Configurations ◽  
Inorganic Structure

AbstractA systematic description and classification of inorganic structure types is proposed on the basis of homogeneous or heterogeneous point configurations (Bauverbände) described by invariant lattice complexes and coordination polyhedra; subscripts or matrices explain the transformation of the complexes in respect (M) to their standard setting; the value of the determinant of the transformation matrix defines the order of the complex. The Bauverbände (frameworks) may be described by three-dimensional networks or two-dimensional nets explicitely shown with structures types of the

scholarly journals Point configurations, phylogenetic trees, and dissimilarity vectors

2021 ◽  
Vol 118 (12) ◽  
pp. e2021244118
Author(s):  
Alessio Caminata ◽  
Noah Giansiracusa ◽  
Han-Bom Moon ◽  
Luca Schaffler
Keyword(s):  
Phylogenetic Trees ◽  
Geometric Interpretation ◽  
Explicit Characterization ◽  
Point Configurations ◽  
Definition Of ◽  
Tropical Basis ◽  
The Way

In 2004, Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.

scholarly journals Point configurations that are asymmetric yet balanced

2010 ◽  
Vol 138 (08) ◽  
pp. 2863-2863 ◽  
Author(s):  
Henry Cohn ◽  
Noam D. Elkies ◽  
Abhinav Kumar ◽  
Achill Schürmann
Keyword(s):  
Point Configurations

scholarly journals Heronian Friezes

2020 ◽  
Author(s):  
Sergey Fomin ◽  
Linus Setiabrata
Keyword(s):  
Computational Geometry ◽  
Euclidean Plane ◽  
Type A ◽  
Cluster Algebras ◽  
Algebraic Condition ◽  
Related Family ◽  
Point Configurations ◽  
Laurent Phenomenon ◽  
Geometric Origin ◽  
Propagation Rule

Abstract Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type $A$, we introduce and study Heronian friezes, the Euclidean analogues of Coxeter’s frieze patterns. We prove that a generic Heronian frieze possesses the glide symmetry (hence is periodic) and establish the appropriate version of the Laurent phenomenon. For a closely related family of Cayley–Menger friezes, we identify an algebraic condition of coherence, which all friezes of geometric origin satisfy. This yields an unambiguous propagation rule for coherent Cayley–Menger friezes, as well as the corresponding periodicity results.

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