In topological graph theory, a graph-encoded map or gem is a method of encoding a cellular embedding of a graph using a different graph with four vertices per edge of the original graph. It is the topological analogue of runcination, a geometric operation on polyhedra. Graph-encoded maps were formulated and named by .Alternative and equivalent systems for representing cellular embeddings include signed rotation systems and ribbon graphs. The graph-encoded map for an embedded graph is another cubic graph together with a 3-edge-coloring of . Each edge of is expanded into exactly four vertices in , one for each choice of a side and endpoint of the edge. An edge in connects each such vertex to the vertex representing the opposite side and same endpoint of ; these edges are by convention colored red. Another edge in connects each vertex to the vertex representing the opposite endpoint and same side of ; these edges are by convention colored blue. An edge in of the third color, yellow, connects each vertex to the vertex representing another edge that meets at the same side and endpoint. An alternative description of is that it has a vertex for each flag of (a mutually incident triple of a vertex, edge, and face). If is a flag,then there is exactly one vertex , edge , and face such that , , and are also flags. The three colors of edges in represent each of these three types of flags that differ by one of their three elements. However, interpreting a graph-encoded map in this way requires more care. When the same face appears on both sides of an edge, as can happen for instance for a planar embedding of a tree, the two sides give rise to different gem vertices. And when the same vertex appears at both endpoints of a self-loop, the two ends of the edge again give rise to different gem vertices. In this way, each triple may be associated with up to four different vertices of the gem. Whenever a cubic graph can be 3-edge-colored so that the red-blue cycles of the coloring all have length four, the colored graph can be interpreted as a graph-encoded map, and represents an embedding of another graph .To recover and its embedding, interpret each 2-colored cycle of as the face of an embedding of onto a surface,contract each red--yellow cycle into a single vertex of , and replace each pair of parallel blue edges left by the contraction with a single edge of . The dual graph of a graph-encoded map may be obtained from the map by recoloring it so that the red edges of the gem become blue and the blue edges become red. (Wikipedia).
Graphing Equations By Plotting Points - Part 1
This video shows how to graph equations by plotting points. Part 1 of 2 http://www.mathispower4u.yolasite.com
From playlist Graphing Various Functions
From playlist 3d graphs
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
From playlist 3d graphs
From playlist 3d graphs
Graph Data Structure 1. Terminology and Representation (algorithms)
This is the first in a series of videos about the graph data structure. It mentions the applications of graphs, defines various terminology associated with graphs, and describes how a graph can be represented programmatically by means of adjacency lists or an adjacency matrix.
From playlist Data Structures
Graph Representation part 01 - Edge List
See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have described how we can represent and store a graph in computer's memory as vertex-list and edge-list. We have analyzed the time and space complexities
From playlist Data structures
Graph Neural Networks, Session 1: Introduction to Graphs
Examples of Graph representation of data Motivation for doing machine learning on Graphs
From playlist Graph Neural Networks (Hands-on)
PyG + SBERT: Heterogeneous Graphs Using SBERT SentenceTransformers for Node Classification SBERT 46
PyG w/ SBERT Sentence Transformers for Node Classification in heterogeneous Graphs, coded in PyG (PyTorch geometric) on a free COLAB NB. ML on GRAPHS. Graph-structured data such as social graphs, networks in cybersecurity, or molecular representations are our real-world scenarios which ge
From playlist SBERT: Python Code Sentence Transformers: a Bi-Encoder /Transformer model #sbert
CS224W: Machine Learning with Graphs | 2021 | Lecture 3.1 - Node Embeddings
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Cv1BEU Jure Leskovec Computer Science, PhD From previous lectures we see how we can use machine learning with feature engineering to make predictions on nodes, li
From playlist Stanford CS224W: Machine Learning with Graphs
Learn low-dim Embeddings that encode GRAPH structure (data) : "Representation Learning" /arXiv
Optimize your complex Graph Data before applying Neural Network predictions. Automatically learn to encode graph structure into low-dimensional embeddings, using techniques based on deep learning and nonlinear dimensionality reduction. An encoder-decoder perspective, random walk approach
From playlist Learn Graph Neural Networks: code, examples and theory
From causal inference to autoencoders, memorization & gene regulation - Caroline Uhler, MIT
Recent progress in genomics makes it possible to perform perturbation experiments at a very large scale. This motivates the development of a causal inference framework that is based on observational and interventional data. We characterize the causal relationships that are identifiable and
From playlist Statistics and computation
CS224W: Machine Learning with Graphs | 2021 | Lecture 9.2 - Designing the Most Powerful GNNs
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3nGksXo Jure Leskovec Computer Science, PhD In this lecture, we aim to design a maximally expressive GNN model. Our key insight is that a maximally expressive GNN
From playlist Stanford CS224W: Machine Learning with Graphs
Geometric Deep Learning II: Georg Gottwald
Machine Learning for the Working Mathematician: Week Six 31 March 2022 Georg Gottwald, Geometric Deep Learning II: Learning the Manifold Seminar series homepage (includes Zoom link): https://sites.google.com/view/mlwm-seminar-2022 Week Six part two lecture: https://youtu.be/q5gvsmF474k
From playlist Machine Learning for the Working Mathematician
Entropy-Based Bounds on Dimension Reduction in L_1 - Oded Regev
Oded Regev CNRS-ENS-Paris and Tel Aviv University November 28, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
SOURCE Boston 2008: All the Data That's Fit to Visualize
Speaker: Raffael Marty - Splunk With the ever-growing amount of data collected in IT environments, we need new methods and tools to deal with them. Event and Log Analysis is becoming one of the main tools for analysts to investigate and comprehend the state of their networks, hosts, appli
From playlist SOURCE Boston 2008
Node2vec : TensorFlow + KERAS code in live COLAB | Graph NN 2022
Real-time COLAB to learn Node2vec for Graph representation learning in KERAS implementation for learning low-dimensional embeddings of nodes in a graph, w/ neighborhood-preserving objective. Download your COLAB: https://colab.research.google.com/github/keras-team/keras-io/blob/master/exa
From playlist Word2Vec and Node2vec (pure TensorFlow 2.7 + KERAS)
Total Functions in the Polynomial Hierarchy - Robert Kleinberg
Computer Science/Discrete Mathematics Seminar I Topic: Total Functions in the Polynomial Hierarchy Speaker: Robert Kleinberg Affiliation: Cornell University Date: February 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Ex 1: Graph a Linear Equation Using a Table of Values
This video provides an example of graphing a line solved for y using a table of values. Complete Video List at http://www.mathispower4u.com Search by Topic at http://www.mathispower4u.wordpress.com
From playlist Graphing Linear Equations Using a Table of Values