In geometric graph theory, a convex embedding of a graph is an embedding of the graph into a Euclidean space, with its vertices represented as points and its edges as line segments, so that all of the vertices outside a specified subset belong to the convex hull of their neighbors. More precisely, if is a subset of the vertices of the graph, then a convex -embedding embeds the graph in such a way that every vertex either belongs to or is placed within the convex hull of its neighbors. A convex embedding into -dimensional Euclidean space is said to be in general position if every subset of its vertices spans a subspace of dimension . Convex embeddings were introduced by W. T. Tutte in 1963. Tutte showed that if the outer face of a planar graph is fixed to the shape of a given convex polygon in the plane, and the remaining vertices are placed by solving a system of linear equations describing the behavior of ideal springs on the edges of the graph, then the result will be a convex -embedding. More strongly, every face of an embedding constructed in this way will be a convex polygon, resulting in a convex drawing of the graph. Beyond planarity, convex embeddings gained interest from a 1988 result of Nati Linial, Lรกszlรณ Lovรกsz, and Avi Wigderson that a graph is k-vertex-connected if and only if it has a -dimensional convex -embedding in general position, for some of of its vertices, and that if it is k-vertex-connected then such an embedding can be constructed in polynomial time by choosing to be any subset of vertices, and solving Tutte's system of linear equations. One-dimensional convex embeddings (in general position), for a specified set of two vertices, are equivalent to bipolar orientations of the given graph. (Wikipedia).
What is the difference between convex and concave
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between convex and concave polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Determine if a polygon is concave or convex ex 2
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are four types of polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between concave and convex polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Geometry - Ch. 1: Basic Concepts (28 of 49) What are Convex and Concave Angles?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how to identify convex and concave polygons. Convex polygon: When extending any line segment (side) it does NOT cut through any of the other sides. Concave polygon: When extending any line seg
From playlist THE "WHAT IS" PLAYLIST
Symplectic embeddings from concave toric domains into convex ones - Dan Cristofaro-Gardiner
Dan Cristofaro-Gardiner Harvard University October 24, 2014 Embedded contact homology gives a sequence of obstructions to four-dimensional symplectic embeddings, called ECH capacities. These obstructions are known to be sharp in several interesting cases, for example for symplectic embedd
From playlist Mathematics
Examples related to Viterbo's conjectures - Michael Hutchings
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Examples related to Viterbo's conjectures Speaker: Michael Hutchings Affiliation: University of California, Berkeley Date: October 23, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Stein Structures: Existence and Flexibility - Kai Cieliebak
Kai Cieliebak Ludwig-Maximilians-Universitat, Munich, Germany March 2, 2012
From playlist Mathematics
Stein Structures: Existence and Flexibility - Kai Cieliebak
Kai Cieliebak Ludwig-Maximilians-Universitat, Munich, Germany March 1, 2012
From playlist Mathematics
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Beyond ECH capacities - Michael Hutchings
Michael Hutchings University of California, Berkeley October 24, 2014 ECH (embedded contact homology) capacities give obstructions to symplectically embedding one four-dimensional symplectic manifold with boundary into another. These obstructions are known to be sharp when the domain is a
From playlist Mathematics
Complex geometry of Teichmuller domains (Lecture 1) by Harish Seshadri
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - M.Musat
Magdalena Musat (University of Copenhagen) / 14.09.17 Title: Quantum correlations, tensor norms, and factorizable quantum channels Abstract: In joint work with Haagerup, we established in 2015 a reformulation of the Connes embedding problem in terms of an asymptotic property of quantum c
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Symplectic convexity? (an ongoing story...)
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Symplectic convexity? (an ongoing story...) Speaker: Jean Gutt Affiliation: University of Toulouse Date: October 21, 2022 What is the symplectic analogue of being convex? We shall present different ideas to
From playlist Mathematics
Amzi Jeffs (6/3/20): Convex sunflower theorems and neural codes
Title: Convex sunflower theorems and neural codes Abstract: In the 1970s neuroscientists O'Keefe and Dostrovsky made a groundbreaking experimental observation: neurons called "place cells" in a rat's hippocampus are active in a convex subset of the animal's environment, and thus encode a
From playlist AATRN 2020
Lattice formulas for rational SFT capacities of toric domains - Ben Wormleighton
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Lattice formulas for rational SFT capacities of toric domains Speaker: Ben Wormleighton Affiliation: Washington University Date: June 25, 2021 Siegel has recently defined โhigherโ symplectic capacities using ration
From playlist Mathematics
Angle and Segment Bisector Constructions
I give you the steps and demonstrations on how to construct a perpendicular bisector of a segment and an angle bisector with a compass and a straight edge. Find free review test, useful notes and more at http://www.mathplane.com If you'd like to make a donation to support my efforts look f
From playlist Geometry