Functions and Graphs

Functions and Graphs
Author: I. M. Gelfand
Publisher: Courier Corporation
Total Pages: 116
Release: 2002-01-01
Genre: Mathematics
ISBN: 0486425649

This volume presents students with problems and exercises designed to illuminate the properties of functions and graphs. The 1st part of the book employs simple functions to analyze the fundamental methods of constructing graphs. The 2nd half deals with more complicated and refined questions concerning linear functions, quadratic trinomials, linear fractional functions, power functions, and rational functions. 1969 edition.

Graph Representation Learning

Graph Representation Learning
Author: William L. William L. Hamilton
Publisher: Springer Nature
Total Pages: 141
Release: 2022-06-01
Genre: Computers
ISBN: 3031015886

Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

Graphs and Geometry

Graphs and Geometry
Author: László Lovász
Publisher: American Mathematical Soc.
Total Pages: 444
Release: 2019-08-28
Genre: Geometry
ISBN: 1470450879

Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical meaning and applications in proofs and algorithms. This book surveys a number of such connections between graph theory and geometry: among others, rubber band representations, coin representations, orthogonal representations, and discrete analytic functions. Applications are given in information theory, statistical physics, graph algorithms and quantum physics. The book is based on courses and lectures that the author has given over the last few decades and offers readers with some knowledge of graph theory, linear algebra, and probability a thorough introduction to this exciting new area with a large collection of illuminating examples and exercises.

Charts, Tables and Graphs

Charts, Tables and Graphs
Author: Michael Priestley
Publisher: Teaching Resources
Total Pages: 64
Release: 2005
Genre: Education
ISBN: 9780439517751

Each page includes an attention-grabbing graph, chart, or table with questions to help kids read and interpret the data. Includes bar and line graphs, circle graphs, schedules, pictographs, and lots more. A perfect way to build on kids' interests and prepare them for standardized tests.

Introduction to Quantum Graphs

Introduction to Quantum Graphs
Author: Gregory Berkolaiko
Publisher: American Mathematical Soc.
Total Pages: 291
Release: 2013
Genre: Mathematics
ISBN: 0821892118

A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

Graphs and Charts Activity Book

Graphs and Charts Activity Book
Author: Darran Stobbart
Publisher: Maths Activity Books
Total Pages: 0
Release: 2020-03-03
Genre:
ISBN: 9781474960472

Discover all kinds of graphs and charts and how to use them in this entertaining activity book. The activities encourage children to collect and analyse data, from tallying the number of animals spotted on safari, to displaying types of weather on a bar chart and sorting animals into a Venn diagram. Quizzes after each section let children test what they've learned.

Knowledge Graphs

Knowledge Graphs
Author: Aidan Hogan
Publisher: Morgan & Claypool Publishers
Total Pages: 257
Release: 2021-11-08
Genre: Computers
ISBN: 1636392369

This book provides a comprehensive and accessible introduction to knowledge graphs, which have recently garnered notable attention from both industry and academia. Knowledge graphs are founded on the principle of applying a graph-based abstraction to data, and are now broadly deployed in scenarios that require integrating and extracting value from multiple, diverse sources of data at large scale. The book defines knowledge graphs and provides a high-level overview of how they are used. It presents and contrasts popular graph models that are commonly used to represent data as graphs, and the languages by which they can be queried before describing how the resulting data graph can be enhanced with notions of schema, identity, and context. The book discusses how ontologies and rules can be used to encode knowledge as well as how inductive techniques—based on statistics, graph analytics, machine learning, etc.—can be used to encode and extract knowledge. It covers techniques for the creation, enrichment, assessment, and refinement of knowledge graphs and surveys recent open and enterprise knowledge graphs and the industries or applications within which they have been most widely adopted. The book closes by discussing the current limitations and future directions along which knowledge graphs are likely to evolve. This book is aimed at students, researchers, and practitioners who wish to learn more about knowledge graphs and how they facilitate extracting value from diverse data at large scale. To make the book accessible for newcomers, running examples and graphical notation are used throughout. Formal definitions and extensive references are also provided for those who opt to delve more deeply into specific topics.

Understanding Charts and Graphs

Understanding Charts and Graphs
Author: Christine Taylor-Butler
Publisher: C. Press/F. Watts Trade
Total Pages: 0
Release: 2012
Genre: Mathematical statistics
ISBN: 9780531262405

Guides students through the basics of using charts and graphs they will be exposed to in math.

Introduction to Random Graphs

Introduction to Random Graphs
Author: Alan Frieze
Publisher: Cambridge University Press
Total Pages: 483
Release: 2016
Genre: Mathematics
ISBN: 1107118506

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Making Graphs

Making Graphs
Author: Bridget Heos
Publisher: Math World
Total Pages: 0
Release: 2015-08
Genre: Juvenile Nonfiction
ISBN: 9781622432356

A class is learning a lesson on making graphs and interpreting data, and the class clown, Logan, has some off-the-wall answers to his classmates' surveys.