1# Library to Find Best eBook for Read
Author : Danielle Rogers
Release : 2023
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Two Adventures in Spectral Graph Theory by : Danielle Rogers
Download or read book Two Adventures in Spectral Graph Theory written by Danielle Rogers. This book was released on 2023. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W. David Joyner
Release : 2017-12-28
Genre : Mathematics
Kind : eBook
Book Rating : 837/5 ( reviews)
Book Synopsis Adventures in Graph Theory by : W. David Joyner
Download or read book Adventures in Graph Theory written by W. David Joyner. This book was released on 2017-12-28. Available in PDF, EPUB and Kindle. Book excerpt: This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.
Author : William L. William L. Hamilton
Release : 2022-06-01
Genre : Computers
Kind : eBook
Book Rating : 886/5 ( reviews)
Book Synopsis Graph Representation Learning by : William L. William L. Hamilton
Download or read book Graph Representation Learning written by William L. William L. Hamilton. This book was released on 2022-06-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Xiaogang Liu
Release : 2015
Genre : Cayley graphs
Kind : eBook
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Book Synopsis Selected Topics in Spectral Graph Theory by : Xiaogang Liu
Download or read book Selected Topics in Spectral Graph Theory written by Xiaogang Liu. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yesim Demiroğlu Karabulut
Release : 2018
Genre :
Kind : eBook
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Book Synopsis Applications of Spectral Graph Theory to Some Classical Problems in Combinatorics and Number Theory by : Yesim Demiroğlu Karabulut
Download or read book Applications of Spectral Graph Theory to Some Classical Problems in Combinatorics and Number Theory written by Yesim Demiroğlu Karabulut. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: "In the first half of this thesis, we obtain sharp results for Waring's problem over general finite rings, by using a combination of Artin-Wedderburn theory and Hensel's lemma and building on new proofs of analogous results over finite fields that are achieved using spectral graph theory. We also prove an analogue of Sárközy's theorem for finite fields. In the second half of the thesis, we investigate the unit-graphs and the special unit-digraphs on matrix rings and we show that every n x n nonzero matrix over Fq can be written as a sum of two SLn-matrices when n > 1. We compute the eigenvalues of these graphs in terms of Kloosterman sums and study their spectral properties. We prove that if X is a subset of Mat2(Fq) with size [equation would not render] then X contains at least two distinct matrices whose difference has determinant for any [equation would not render]. Using this result we also prove a sum-product type result: if A,B,C;D[subset]Fq satisfy [equation would not render] as q[rightarrow][infinity], then (A-B)(C-D) equals all of F*q. In particular, if A is a subset of Fq with cardinality |A| > 3/2 q 3/4, then the subset (A - A)(A - A) equals all of Fq. We also recover some classical results, e.g. every element in any finite ring of odd order can be written as the sum of two units, and we also derive some character sum identities."--Page vii.
