Geometric graphs | Hyperbolic geometry | Network theory

Hyperbolic geometric graph

A hyperbolic geometric graph (HGG) or hyperbolic geometric network (HGN) is a special type of spatial network where (1) latent coordinates of nodes are sprinkled according to a probability density function into ahyperbolic space of constant negative curvature and (2) an edge between two nodes is present if they are close according to a function of the metric (typically either a Heaviside step function resulting in deterministic connections between vertices closer than a certain threshold distance, or a decaying function of hyperbolic distance yielding the connection probability). A HGG generalizes a random geometric graph (RGG) whose embedding space is Euclidean. (Wikipedia).

Hyperbolic geometric graph
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Hyperbola 3D Animation | Objective conic hyperbola | Digital Learning

Hyperbola 3D Animation In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other an

From playlist Maths Topics

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Hyperbolic Geometry is Projective Relativistic Geometry (full lecture)

This is the full lecture of a seminar on a new way of thinking about Hyperbolic Geometry, basically viewing it as relativistic geometry projectivized, that I gave a few years ago at UNSW. We discuss three dimensional relativistic space and its quadratic/bilinear form, particularly the uppe

From playlist MathSeminars

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What are Hyperbolas? | Ch 1, Hyperbolic Trigonometry

This is the first chapter in a series about hyperbolas from first principles, reimagining trigonometry using hyperbolas instead of circles. This first chapter defines hyperbolas and hyperbolic relationships and sets some foreshadowings for later chapters This is my completed submission t

From playlist Summer of Math Exposition 2 videos

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Algebra Ch 40: Hyperbolas (1 of 10) What is a Hyperbola?

Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn a hyperbola is a graph that result from meeting the following conditions: 1) |d1-d2|=constant (same number) 2) the grap

From playlist THE "HOW TO" PLAYLIST

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Introduction to Hyperbolic Functions

This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Differentiation of Hyperbolic Functions

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Ex 1: Conic Section - Graph a Hyperbola with Center at the Origin (Horizontal)

This video provides an example of how to graph and find the major components of a hyperbola given the standard equation of the hyperbola. The hyperbola has a horizontal transverse axis. Site: http:/mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Graphing and Writing Equations of Hyperbolas

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What is the definition of a hyperbola

Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ

From playlist The Hyperbola in Conic Sections

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Minerva Lectures 2012 - Ian Agol Talk 2: The virtual Haken conjecture & geometric group theory

Talk two of the second Minerva lecture series, by Prof. Ian Agol on October 23rd, 2012 at the Mathematics Department, Princeton University. More information available at: http://www.math.princeton.edu/events/seminars/minerva-lectures/minerva-lecture-ii-virtual-haken-conjecture-what-geomet

From playlist Minerva Lectures - Ian Agol

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Emily Stark: Action rigidity for free products of hyperbolic manifold groups

CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 22, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM

From playlist Virtual Conference

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What is the definition of a hyperbola

Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ

From playlist The Hyperbola in Conic Sections

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Jessica Purcell - Lecture 2 - Fully augmented links and circle packings

Jessica Purcell, Monash University Title: Fully augmented links and circle packings Fully augmented links form a family of hyperbolic links that are a playground for hands-on hyperbolic geometry. In the first part of the talk, I’ll define the links and show how to determine their hyperboli

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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Martin Boundaries of Random Walks on Relatively Hyperbolic Groups by Debanjan Nandi

PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis

From playlist Ergodic Theory and Dynamical Systems 2022

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The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b

Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine

From playlist Universal Hyperbolic Geometry

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Large Genus Asymptotics in Flat Surfaces and Hyperbolic Geodesics - Amol Aggarwal

Mathematical Physics Seminar Topic: Large Genus Asymptotics in Flat Surfaces and Hyperbolic Geodesics Speaker: Amol Aggarwal Affiliation: Visiting Professor, School of Mathematics Date: March 30, 2022 In this talk we will describe the behaviors of flat surfaces and geodesics on hyperboli

From playlist Mathematics

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Aspirality and separability for surface subgroups in 3-manifold group - Yi Liu

Yi Liu, Caltech October 8, 2015 http://www.math.ias.edu/wgso3m/agenda 2015-2016 Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic year a

From playlist Workshop on Geometric Structures on 3-Manifolds

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Marcos Kiwi: Random hyperbolic graphs

Abstract: Random hyperbolic graphs (RHG) were proposed rather recently (2010) as a model of real-world networks. Informally speaking, they are like random geometric graphs where the underlying metric space has negative curvature (i.e., is hyperbolic). In contrast to other models of complex

From playlist Probability and Statistics

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When invariants are equivalent - Jean Pierre Mutanguha

Short Talks by Postdoctoral Members Topic: When invariants are equivalent Speaker: Jean Pierre Mutanguha Affiliation: Member, School of Mathematics Date: September 28, 2021

From playlist Mathematics

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Danny Calegari: Big Mapping Class Groups - lecture 1

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h

From playlist Topology

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Examples of non-positively curved groups II - Kim Ruane

Women and Mathematics Title: Examples of non-positively curved groups II Speaker: Kim Ruane Affiliation: Tufts University Date: May 24, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

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How to determine the parts of a hyperbola and then sketch the graph

Learn how to graph hyperbolas. To graph a hyperbola from the equation, we first express the equation in the standard form, that is in the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola. Next, we identify

From playlist The Hyperbola in Conic Sections

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Hyperboloid model | Poincaré disk model | Graph (discrete mathematics) | Inverse transform sampling | Probability density function | Constant curvature | Hyperbolic law of cosines | Hyperbolic space | Set (mathematics) | Closed-form expression | Depletion force | Probability distribution | Limiting case (mathematics) | Euclidean space | Constant function | Graph partition | Degree distribution | Cardinality | Gaussian curvature | Heaviside step function | Random geometric graph | Spatial network