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).
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
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
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
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
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
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
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
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
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
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
Wolfram Physics Project: A Discussion with Fay Dowker
Fay Dowker joins Stephen Wolfram, Jonathan Gorard and Max Piskunov for a Wolfram Physics Project discussion. Begins at 1:47 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announc
From playlist Wolfram Physics Project Livestream Archive
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
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
Chapter 4 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
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
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
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
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
What is the area between the graphs of y = x^2 and y = 1 - x^2? - Week 12 - Lecture 6 - Mooculus
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From playlist Ohio State: Jim Fowler's Calculus One Lectures | CosmoLearning Mathematics
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