Hypergraphs

Width of a hypergraph

In graph theory, there are two related properties of a hypergraph that are called its "width". Given a hypergraph H = (V, E), we say that a set K of edges pins another set F of edges if every edge in F intersects some edge in K. Then: * The width of H, denoted w(H), is the smallest size of a subset of E that pins E. * The matching width of H, denoted mw(H), is the maximum, over all matchings M in H, of the minimum size of a subset of E that pins M. Since E contains all matchings in E, for all H: w(H) ≥ mw(H). The width of a hypergraph is used in Hall-type theorems for hypergraphs. (Wikipedia).

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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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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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Calculus 2: Hyperbolic Functions (5 of 57) Finding Area Part 2

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the area bounded by a hyperbolic function. (Part 2) Next video in the series can be seen at: https://youtu.be/rSbrXt7hAQU

From playlist CALCULUS 2 CH 16 HYPERBOLIC FUNCTIONS

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Dimensions Chapter 5

Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Calculus 2: Hyperbolic Functions (4 of 57) Finding Area Part 1

Visit http://ilectureonline.com for more math and science lectures! In this video I will find the area bounded by a hyperbolic function. (Part 1) Next video in the series can be seen at: https://youtu.be/f1iRPnhR-mU

From playlist CALCULUS 2 CH 16 HYPERBOLIC FUNCTIONS

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Dimensions Chapter 1

Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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DSI | Hypergraphs and Topology for Data Science | By Emilie Purvine

Data scientists and applied mathematicians must grapple with complex data when analyzing complex systems. Analytical methods almost always represent phenomena as a much simpler level than the complex structure or dynamics inherent in systems, through either simpler measured or sampled data

From playlist DSI Virtual Seminar Series

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Emilie Purvine (3/3/23): Applied Topology for Discrete Structures

Discrete structures have a long history of use in applied mathematics. Graphs and hypergraphs provide models of social networks, biological systems, academic collaborations, and much more. Network science, and more recently hypernetwork science, have been used to great effect in analyzing

From playlist Vietoris-Rips Seminar

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Dimensions Chapter 2

Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Johnnie Gray: "Hyper-optimized tensor network contraction - simplifications, applications & appr..."

Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop I: Tensor Methods and their Applications in the Physical and Data Sciences "Hyper-optimized tensor network contraction - simplifications, applications and approximations" Johnnie Gray - California Ins

From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021

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Wolfram Physics Project: A Discussion with Fay Dowker

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From playlist Wolfram Physics Project Livestream Archive

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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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A Proof of the Kahn-Kalai Conjecture - Jinyoung Park

Computer Science/Discrete Mathematics Seminar I Topic: A Proof of the Kahn-Kalai Conjecture Speaker: Jinyoung Park Affiliation: Stanford University Date: May 16, 2022 Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and relate

From playlist Mathematics

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Dimensions Chapter 4

Chapter 4 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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A Tight Bound for Hypergraph Regularity - Guy Moshkovitz

Computer Science/Discrete Mathematics Seminar I Topic: A Tight Bound for Hypergraph Regularity Speaker: Guy Moshkovitz Affiliation: Harvard University Date: Febuary 27, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

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Raffaella Mulas - Spectral theory of hypergraphs

Hypergraphs are a generalization of graphs in which vertices are joined by edges of any size. In this talk, we generalize the graph normalized Laplace operators to the case of hypergraphs, and we discuss some properties of their spectra. We discuss the geometrical meaning of the largest an

From playlist Research Spotlight

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Emilie Purvine (5/2/21): Homology of Graphs and Hypergraphs

Graphs and hypergraphs are typically studied from a combinatorial perspective. A graph being a collection of vertices and pairwise relationships (edges) among the vertices, and a hypergraph capturing multi-way or groupwise relationships (hyperedges) among the vertices. But both of these ob

From playlist TDA: Tutte Institute & Western University - 2021

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Quasirandom Hypergraphs - Dhruv Mubayi

Dhruv Mubayi University of Illinois at Chicago March 4, 2013 Since the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs over 20 years ago, there has been a lot of effort by many researchers to extend the theory to hypergraphs. I will present some of this histo

From playlist Mathematics

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Wolfram Physics Project Launch

Stephen Wolfram publicly kicks off an ambitious new project to find the Fundamental Theory of Physics. Begins at 2:50 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: https://wolfr.am/physics Check out the announceme

From playlist Wolfram Physics Project Livestream Archive

Related pages

Graph theory | Clique (graph theory) | Independent set (graph theory) | Line graph of a hypergraph | Hall-type theorems for hypergraphs | Domination number | Matching in hypergraphs | Hypergraph