Dominating Sets and Domination Number of Graphs | Graph Theory
A vertex is said to dominate itself and its neighbors. Then, a dominating set of a graph G is a vertex subset S of G such that every vertex in G is dominated by some vertex in S. This means every vertex in G-S is adjacent to some vertex in S. A dominating set of minimum cardinality is a mi
From playlist Graph Theory
Power Set of the Power Set of the Power Set of the Empty Set | Set Theory
The power set of the power set of the power set of the empty set, we'll go over how to find just that in today's set theory video lesson! We'll also go over the power set of the empty set, the power set of the power set of the empty set, and we'll se the power set of the power set of the p
From playlist Set Theory
Every Set is an Element of its Power Set | Set Theory
Every set is an element of its own power set. This is because the power set of a set S, P(S), contains all subsets of S. By definition, every set is a subset of itself, and thus by definition of the power set of S, it must contain S. This is even true for the always-fun empty set! We discu
From playlist Set Theory
What are Overlapping Sets? | Set Theory
What are overlapping sets? This is a relation between sets that I have not seen any YouTube videos on, so I figured I'd add this video explaining the term to the massive YouTube catalogue! In this video we define overlapping sets and give some examples. Two sets, A and B, are overlapping
From playlist Set Theory
Power set Subset Proof: Union of Power Sets is contained in the Power Set of the Union
Powerset Subset Proof: Union of Power Sets is contained in Powerset of Union If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer There are several w
From playlist Set Theory
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
Empty Set vs Set Containing Empty Set | Set Theory
What's the difference between the empty set and the set containing the empty set? We'll look at {} vs {{}} in today's set theory video lesson, discuss their cardinalities, and look at their power sets. As we'll see, the power set of the empty set is our friend { {} }! The river runs peacef
From playlist Set Theory
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
NP Completeness III - More Reductions - Lecutre 17
All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c
From playlist ArsDigita Algorithms by Shai Simonson
Definable equivariant retractions onto skeleta in (...) - M. Hils - Workshop 3 - CEB T1 2018
Martin Hils (Münster) / 28.03.2018 Definable equivariant retractions onto skeleta in non-archimedean geometry For a quasi-projective variety V over a non-archimedean valued field, Hrushovski and Loeser recently introduced a pro-definable space Vb, the stable completion of V , which is a
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Complement of Independent Set is Vertex Cover | Graph Theory
We prove the complement of an independent vertex set is a vertex cover. This makes for an easy direct proof once we recall our definitions. An independent vertex set is a set of vertices, no two of which are adjacent. A vertex cover is a set of vertices such that every edge has at least on
From playlist Graph Theory
13. Genetics 2 – Rules of Inheritance
MIT 7.016 Introductory Biology, Fall 2018 Instructor: Adam Martin View the complete course: https://ocw.mit.edu/7-016F18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63LmSVIVzy584-ZbjbJ-Y63 Professor Martin continues with genetics, discussing the laws of inheritance,
From playlist MIT 7.016 Introductory Biology, Fall 2018
AMMI 2022 Course "Geometric Deep Learning" - Seminar 1 (Physics-based GNNs) - Francesco Di Giovanni
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 Seminar 1 - Graph neural networks through the lens of multi-particle dynamics and gradient flows - Francesco Di Giovanni (Twitter) Slides: https://www.dropbox.com/s/
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
Virtual domination of 3-manifolds - Hongbin Sun
Hongbin Sun, UC Berkeley October 6, 2015 http://www.math.ias.edu/wgso3m/agenda 015-2016 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 academi
From playlist Workshop on Geometric Structures on 3-Manifolds
Henry Adams (3/3/15): The Vietoris Rips Complex of the Circle
Given a metric space X and a distance threshold r, the Vietoris-Rips simplicial complex has as its simplices the finite subsets of X of diameter less than r. A theorem of Jean-Claude Hausmann states that if X is a Riemannian manifold and r is sufficiently small, then the Vietoris-Rips comp
From playlist AATRN 2015
Hong Wang: The restriction problem and the polynomial method, Lecture 2
Stein’s restriction conjecture is about estimating functions with Fourier transform sup- ported on a hypersurface, for example, a sphere in Rn. These functions can be decomposed into a sum over wave packets supported on long thin tubes. Guth introduced the polynomial method in restriction
From playlist Harmonic Analysis and Analytic Number Theory
Paolo Boldi - Axioms for centrality: rank monotonicity for PageRank
https://indico.math.cnrs.fr/event/3475/attachments/2180/2562/Boldi_GomaxSlides.pdf
From playlist Google matrix: fundamentals, applications and beyond
Siddharth Pritam (8/10/22): Swap, Shift and Trim to Edge Collapse a Flag Filtration
Boissonnat and Pritam [SoCG'20] introduced an algorithm to reduce a filtration of flag (or clique) complexes, which can in particular speed up the computation of its persistent homology. They used so-called edge collapse to reduce the input flag filtration and their reduction method requir
From playlist AATRN 2022
What are Disjoint Sets? | Set Theory
What are disjoint sets? That is the topic of discussion in today's lesson! Two sets, A and B, are disjoint if and only if A intersect B is equal to the empty set. This means that two sets are disjoint if and only if they have no elements in common. This is the same as the two sets being "m
From playlist Set Theory