Homogeneous Ordered Graphs Metrically Homogeneous Graphs And Beyond
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| Author | : Gregory Cherlin |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2022-06-30 |
| Genre | : Mathematics |
| ISBN | : 1009229702 |
This is the first of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. In this volume, Cherlin develops a complete classification of homogeneous ordered graphs and provides a full proof. He then proposes a new family of metrically homogeneous graphs, a weakening of the usual homogeneity condition. A general classification conjecture is presented, together with general structure theory and applications to a general classification conjecture for such graphs. It also includes introductory chapters giving an overview of the results and methods of both volumes, and an appendix surveying recent developments in the area. An extensive accompanying bibliography of related literature, organized by topic, is available online.
| Author | : Gregory Cherlin |
| Publisher | : Cambridge University Press |
| Total Pages | : 289 |
| Release | : 2022-07-07 |
| Genre | : Mathematics |
| ISBN | : 1009229486 |
The second of two volumes presenting the state of the art in the classification of homogeneous structures and related problems in the intersection of model theory and combinatorics. It extends the results of the first volume to generalizations of graphs and tournaments with additional binary relations. An appendix explores open problems.
| Author | : Gregory L. Cherlin |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2022 |
| Genre | : Directed graphs |
| ISBN | : 9781009230186 |
These two volumes by Professor Cherlin present the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. In Volume I, the homogeneous ordered graphs are classified, a new family of metrically homogeneous graphs is constructed, and a general classification conjecture is presented, together with general structure theory and applications to a general classification conjecture for such graphs. Volume II continues the analysis into more general expansions of graphs or tournaments by an additional binary relation, called 3-multi-graphs or 3-multi-tournaments, applying and extending the results of Volume I, resulting in a detailed catalogue of such structures and a second classification conjecture. Appendices to both volumes explore recent developments and open questions.
| 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.
| Author | : Geoffrey Grimmett |
| Publisher | : Cambridge University Press |
| Total Pages | : 279 |
| Release | : 2018-01-25 |
| Genre | : Mathematics |
| ISBN | : 1108542999 |
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
| Author | : Alexander Kechris |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 419 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461241901 |
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
| Author | : Dragoš M. Cvetković |
| Publisher | : |
| Total Pages | : 374 |
| Release | : 1980 |
| Genre | : Mathematics |
| ISBN | : |
The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning fully justifying it to be treated as a theory in its own right.
| Author | : Caroline J. Klivans |
| Publisher | : CRC Press |
| Total Pages | : 296 |
| Release | : 2018-11-15 |
| Genre | : Computers |
| ISBN | : 135180099X |
The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and students will discover that this book provides a comprehensive background to approaching original sources. Features: Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM (Institute for Computational and Experimental Research in Mathematics). Before coming to Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics.
| Author | : Christian Rosendal |
| Publisher | : Cambridge University Press |
| Total Pages | : 309 |
| Release | : 2021-12-16 |
| Genre | : Mathematics |
| ISBN | : 110884247X |
Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
| Author | : Yizhou Sun |
| Publisher | : Morgan & Claypool Publishers |
| Total Pages | : 162 |
| Release | : 2012 |
| Genre | : Computers |
| ISBN | : 1608458806 |
Investigates the principles and methodologies of mining heterogeneous information networks. Departing from many existing network models that view interconnected data as homogeneous graphs or networks, the semi-structured heterogeneous information network model leverages the rich semantics of typed nodes and links in a network and uncovers surprisingly rich knowledge from the network.
