Graph Theory: 05. Connected and Regular Graphs
We give the definition of a connected graph and give examples of connected and disconnected graphs. We also discuss the concepts of the neighbourhood of a vertex and the degree of a vertex. This allows us to define a regular graph, and we give some examples of these. --An introduction to
From playlist Graph Theory part-1
What is a Graph? | Graph Theory
What is a graph? A graph theory graph, in particular, is the subject of discussion today. In graph theory, a graph is an ordered pair consisting of a vertex set, then an edge set. Graphs are often represented as diagrams, with dots representing vertices, and lines representing edges. Each
From playlist Graph 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
Graph Theory: 04. Families of Graphs
This video describes some important families of graph in Graph Theory, including Complete Graphs, Bipartite Graphs, Paths and Cycles. --An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: https://www.youtube.com/watch?v=S1Zwhz-MhCs (Graph Theory: 02. Definit
From playlist Graph Theory part-1
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
Graph theory full course for Beginners
In mathematics, graph #theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A #graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction i
From playlist Graph Theory
Graph Theory: 02. Definition of a Graph
In this video we formally define what a graph is in Graph Theory and explain the concept with an example. In this introductory video, no previous knowledge of Graph Theory will be assumed. --An introduction to Graph Theory by Dr. Sarada Herke. This video is a remake of the "02. Definitio
From playlist Graph Theory part-1
Graph Theory FAQs: 01. More General Graph Definition
In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o
From playlist Graph Theory FAQs
What are Cycle Graphs? | Graph Theory, Graph Cycles, Cyclic Graphs
What are cycle graphs? We have talked before about graph cycles, which refers to a way of moving through a graph, but a cycle graph is slightly different. A cycle graph is what you would get if you took the vertices and edges of a graph cycle. We can think of cycle graphs as being path gra
From playlist Graph Theory
Tobias Moede - Coclass theory for nilpotent associative algebras
The coclass of a finite p-group of order p^n and class c is defined as n-c. Using coclass as the primary invariant in the investigation of finite p-groups turned out to be a very fruitful approach. Together with Bettina Eick, we have developed a coclass theory for nilpotent associative alg
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Christian Kuehn (7/25/22): Dynamical Systems for Deep Neural Networks
Abstract: In this talk, I am going to explain several approaches to explain the geometry and dynamics of neural networks. First, I will show, why neural networks should always be viewed within the framework of dynamical systems. Then I am going to show how to employ rigorous validated comp
From playlist Applied Geometry for Data Sciences 2022
Marian Mrozek (8/30/21): Combinatorial vs. Classical Dynamics: Recurrence
The study of combinatorial dynamical systems goes back to the seminal 1998 papers by Robin Forman. The main motivation to study combinatorial dynamics comes from data science. Combinatorial dynamics also provides very concise models of dynamical phenomena. Moreover, some topological invari
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Spectra of metric graphs and crystalline measures - Peter Sarnak
Members' Seminar Topic: Spectra of metric graphs and crystalline measures Speaker: Peter Sarnak Affiliation: Professor, School of Mathematics Date: February 10, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Rotations on graphs and fractional exponents in groups
A research talk I gave at Sogang University in Seoul on March 23, 2017. The first 10 minutes should be accessible to anybody. The talk audience was masters-level math graduate students. The work is based on "Generalizing the rotation interval to vertex maps on graphs", available here: htt
From playlist Research & conference talks
The Search for Randomness | Jean Bourgain
March 25, 2009 Jean Bourgain, IBM von Neumann Professor, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/bourgain Although the concept of randomness is ubiquitous, it turns out to be difficult to generate a truly random sequence of events
From playlist Mathematics
Oliver SCHNETZ - 2010-2020: a Decade of Quantum Computing
Supported by Dirk Kreimer, in 2010 I started analyzing and calculating high loop-order amplitudes in perturbative quantum field theory. The main tools were graphical functions, generalized single-valued hyperlogarithms (GSVHs), and the c_2-invariant. I will report on the progress that has
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Chris Godsil: Problems with continuous quantum walks
Continuous quantum walks are of great interest in quantum computing and, over the last decade, my group has been studying this topic intensively. As graph theorists, one of our main goals has been to get a better understanding of the relation between the properties of a walk and the proper
From playlist Combinatorics
Mateus Juda (7/29/20): Unsupervised features learning for sampled vector fields
Title: Unsupervised features learning for sampled vector fields Abstract: In this talk we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data to a graph structure and use tools designed for automatic, unsupervi
From playlist AATRN 2020
Dynamics of piecewise smooth maps (Lecture - 02) by Paul Glendinning
PROGRAM DYNAMICS OF COMPLEX SYSTEMS 2018 ORGANIZERS Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE: 16 June 2018 to 30 June 2018 VENUE: Ramanujan hall for Summer School held from 16 - 25 June, 2018; Madhava hall for W
From playlist Dynamics of Complex systems 2018
Graph Theory Talk: Graphs, Edges, Vertices, Adjacency Matrix and it's Eigenvalues
Graph Theory Stuff: Graphs, Edges, Vertices, Adjacency Matrix and it's Eigenvalues
From playlist Graph Theory