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Author : George Michael Foust
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.:/5 (49 download)
Download or read book Hyper-graph Designs written by George Michael Foust and published by . This book was released on 1998 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mario Gionfriddo
Publisher : Nova Science Publishers
ISBN 13 : 9781633219113
Total Pages : 0 pages
Book Rating : 4.2/5 (191 download)
Download or read book Hypergraphs and Designs written by Mario Gionfriddo and published by Nova Science Publishers. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial designs represent an important area of contemporary discrete mathematics closely related to such fields as finite geometries, regular graphs and multigraphs, factorisations of graphs, linear algebra, number theory, finite fields, group and quasigroup theory, Latin squares, and matroids. It has a history of more than 150 years when it started as a collection of unrelated problems. Nowadays the field is a well-developed theory with deep mathematical results and a wide range of applications in coding theory, cryptography, computer science, and other areas. In the most general setting, a combinatorial design consists of a ground set of elements and a collection of subsets of these elements satisfying some specific restrictions; the latter are often expressed in the language of graphs. On the other side, hypergraph theory is a relatively new field which started in early 60s of the last century as a generalization of graph theory. A hypergraph consists of a ground set of elements and a collection of subsets of these elements without any specific restrictions. In this sense the concept of hypergraph is more general than the concept of combinatorial design. While it started as a generalization of graph theory, hypergraph theory soon became a separate subject because many new properties have been discovered that miss or degenerate in graphs. Compared to graph theory, the language of hypergraphs not only allows us to formulate and solve more general problems, it also helps us to understand and solve several graph theory problems by simplifying and unifying many previously unrelated concepts. The main feature of this book is applying the hypergraph approach to the theory of combinatorial designs. An alternative title of it could be "Combinatorial designs as hypergraphs". There is no analogue to this book on the market. Its primary audience is researchers and graduate students taking courses in design theory, combinatorial geometry, finite geometry, discrete mathematics, graph theory, combinatorics, cryptography, information and coding theory, and similar areas. The aim of this book is to show the connection and mutual benefit between hypergraph theory and design theory. It does not intend to give a survey of all important results or methods in any of these subjects.
Author : Vitaly Ivanovich Voloshin
Publisher : American Mathematical Soc.
ISBN 13 : 0821828126
Total Pages : 199 pages
Book Rating : 4.8/5 (218 download)
Download or read book Coloring Mixed Hypergraphs: Theory, Algorithms and Applications written by Vitaly Ivanovich Voloshin and published by American Mathematical Soc.. This book was released on 2002 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications. Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory ofcolorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and the maximum number of colors. This feature pervades the theory, methods, algorithms, and applications of mixed hypergraph coloring. The book has broad appeal. It will be of interest to bothpure and applied mathematicians, particularly those in the areas of discrete mathematics, combinatorial optimization, operations research, computer science, software engineering, molecular biology, and related businesses and industries. It also makes a nice supplementary text for courses in graph theory and discrete mathematics. This is especially useful for students in combinatorics and optimization. Since the area is new, students will have the chance at this stage to obtain results that maybecome classic in the future.
Author : Stefan Glock
Publisher : American Mathematical Society
ISBN 13 : 1470460246
Total Pages : 144 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Existence of Designs via Iterative Absorption: Hypergraph $F$-Designs for Arbitrary $F$ written by Stefan Glock and published by American Mathematical Society. This book was released on 2023-04-07 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author : Alain Bretto
Publisher : Springer Science & Business Media
ISBN 13 : 3319000802
Total Pages : 129 pages
Book Rating : 4.3/5 (19 download)
Download or read book Hypergraph Theory written by Alain Bretto and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.
Author : Demeter Krupka
Publisher : Elsevier
ISBN 13 : 0080954154
Total Pages : 544 pages
Book Rating : 4.0/5 (89 download)
Download or read book Introduction to Global Variational Geometry written by Demeter Krupka and published by Elsevier. This book was released on 2009-06-15 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces
Author : Qionghai Dai
Publisher : Springer Nature
ISBN 13 : 9819901855
Total Pages : 251 pages
Book Rating : 4.8/5 (199 download)
Download or read book Hypergraph Computation written by Qionghai Dai and published by Springer Nature. This book was released on 2023-06-16 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book discusses the theory and methods of hypergraph computation. Many underlying relationships among data can be represented using graphs, for example in the areas including computer vision, molecular chemistry, molecular biology, etc. In the last decade, methods like graph-based learning and neural network methods have been developed to process such data, they are particularly suitable for handling relational learning tasks. In many real-world problems, however, relationships among the objects of our interest are more complex than pair-wise. Naively squeezing the complex relationships into pairwise ones will inevitably lead to loss of information which can be expected valuable for learning tasks. Hypergraph, as a generation of graph, has shown superior performance on modelling complex correlations compared with graph. Recent years have witnessed a great popularity of researches on hypergraph-related AI methods, which have been used in computer vision, social media analysis, etc. We summarize these attempts as a new computing paradigm, called hypergraph computation, which is to formulate the high-order correlations underneath the data using hypergraph, and then conduct semantic computing on the hypergraph for different applications. The content of this book consists of hypergraph computation paradigms, hypergraph modelling, hypergraph structure evolution, hypergraph neural networks, and applications of hypergraph computation in different fields. We further summarize recent achievements and future directions on hypergraph computation in this book.
Author : Claude Berge
Publisher :
ISBN 13 : 9780720424508
Total Pages : 0 pages
Book Rating : 4.4/5 (245 download)
Download or read book Graphs and Hypergraphs written by Claude Berge and published by . This book was released on 1976 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter J. Cameron
Publisher : Cambridge University Press
ISBN 13 : 0521211603
Total Pages : 153 pages
Book Rating : 4.5/5 (212 download)
Download or read book Parallelisms of Complete Designs written by Peter J. Cameron and published by Cambridge University Press. This book was released on 1976-06-10 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present an investigation of a condition similar to Euclid's parallel axiom for subsets of finite sets. The background material to the theory of parallelisms is introduced and the author then describes the links this theory has with other topics from the whole range of combinatorial theory and permutation groups. These include network flows, perfect codes, Latin squares, block designs and multiply-transitive permutation groups, and long and detailed appendices are provided to serve as introductions to these various subjects. Many of the results are published for the first time.
Author : Marcus Greferath
Publisher : Springer
ISBN 13 : 3319702939
Total Pages : 443 pages
Book Rating : 4.3/5 (197 download)
Download or read book Network Coding and Subspace Designs written by Marcus Greferath and published by Springer. This book was released on 2018-01-29 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by experts from universities and major research laboratories, addresses the hot topic of network coding, a powerful scheme for information transmission in networks that yields near-optimal throughput. It introduces readers to this striking new approach to network coding, in which the network is not simply viewed as a mechanism for delivering packets, but rather an algebraic structure named the subspace, which these packets span. This leads to a new kind of coding theory, employing what are called subspace codes. The book presents selected, highly relevant advanced research output on: Subspace Codes and Rank Metric Codes; Finite Geometries and Subspace Designs; Application of Network Coding; Codes for Distributed Storage Systems. The outcomes reflect research conducted within the framework of the European COST Action IC1104: Random Network Coding and Designs over GF(q). Taken together, they offer communications engineers, R&D engineers, researchers and graduate students in Mathematics, Computer Science, and Electrical Engineering a comprehensive reference guide to the construction of optimal network codes, as well as efficient encoding and decoding schemes for a given network code.
Author : Frank Kwang-ming Hwang
Publisher : World Scientific
ISBN 13 : 9814477869
Total Pages : 249 pages
Book Rating : 4.8/5 (144 download)
Download or read book Pooling Designs And Nonadaptive Group Testing: Important Tools For Dna Sequencing written by Frank Kwang-ming Hwang and published by World Scientific. This book was released on 2006-06-19 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pooling designs have been widely used in various aspects of DNA sequencing. In biological applications, the well-studied mathematical problem called “group testing” shifts its focus to nonadaptive algorithms while the focus of traditional group testing is on sequential algorithms. Biological applications also bring forth new models not previously considered, such as the error-tolerant model, the complex model, and the inhibitor model. This book is the first attempt to collect all the significant research on pooling designs in one convenient place.The coverage includes many real biological applications such as clone library screening, contig sequencing, exon boundary finding and protein-protein interaction detecting and introduces the mathematics behind it.
Author : Annegret Habel
Publisher : Springer Science & Business Media
ISBN 13 : 9783540560050
Total Pages : 236 pages
Book Rating : 4.5/5 (6 download)
Download or read book Hyperedge Replacement: Grammars and Languages written by Annegret Habel and published by Springer Science & Business Media. This book was released on 1992-12-08 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of graph grammars is theoretically attractive and well motivated byvarious applications. More than 20 years ago, the concept of graph grammars was introduced by A. Rosenfeld as a formulation of some problems in pattern recognition and image processing, as well as by H.J. Schneider as a method for data type specification. Within graph-grammar theory one maydistinguish the set-theoretical approach, the algebraic approach, and the logical approach. These approaches differ in the method in which graph replacement is described. Specific approaches, node replacement and hyperedge replacement, concern the basic units of a hypergraph, nodes and hyperedges. This monograph is mainly concerned with the hyperedge-replacement approach. Hyperedge-replacement grammars are introduced as a device for generating hypergraph languages including graph languages and string languages. The concept combines a context-free rewriting with a comparatively large generative power. The volume includes a foreword by H. Ehrig.
Author : Renate Klempien-Hinrichs
Publisher : BoD – Books on Demand
ISBN 13 : 3831126747
Total Pages : 181 pages
Book Rating : 4.8/5 (311 download)
Download or read book Context Free Hypergraph Grammars written by Renate Klempien-Hinrichs and published by BoD – Books on Demand. This book was released on 2002 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hongliang Zhang
Publisher : Springer
ISBN 13 : 3319604694
Total Pages : 70 pages
Book Rating : 4.3/5 (196 download)
Download or read book Hypergraph Theory in Wireless Communication Networks written by Hongliang Zhang and published by Springer. This book was released on 2017-07-24 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief focuses on introducing a novel mathematical framework, referred as hypergraph theory, to model and solve the multiple interferer scenarios for future wireless communication networks. First, in Chap. 1, the authors introduce the basic preliminaries of hypergraph theory in general, and develop two hypergraph based polynomial algorithms, i.e., hypergraph coloring and hypergraph clustering. Then, in Chaps. 2 and 3, the authors present two emerging applications of hypergraph coloring and hypergraph clustering in Device-to-Device (D2D) underlay communication networks, respectively, in order to show the advantages of hypergraph theory compared with the traditional graph theory. Finally, in Chap. 4, the authors discuss the limitations of using hypergraph theory in future wireless networks and briefly present some other potential applications. This brief introduces the state-of-the-art research on the hypergraph theory and its applications in wireless communications. An efficient framework is provided for the researchers, professionals and advanced level students who are interested in the radio resource allocation in the heterogeneous networks to solve the resource allocation and interference management problems.
Author : C. Berge
Publisher :
ISBN 13 : 9783662163054
Total Pages : 304 pages
Book Rating : 4.1/5 (63 download)
Download or read book Hypergraph Seminar written by C. Berge and published by . This book was released on 2014-01-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 396 pages
Book Rating : 4.3/5 (91 download)
Download or read book Ars Combinatoria written by and published by . This book was released on 2007 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : N S Narasimha Sastry
Publisher : World Scientific
ISBN 13 : 9814467855
Total Pages : 281 pages
Book Rating : 4.8/5 (144 download)
Download or read book Perspectives In Mathematical Science Ii: Pure Mathematics written by N S Narasimha Sastry and published by World Scientific. This book was released on 2009-07-01 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of invited articles by distinguished Mathematicians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute, during the year 2007. These articles provide a current perspective of different areas of research, emphasizing the major challenging issues. Given the very significant record of the Institute in research in the areas of Statistics, Probability and Mathematics, distinguished authors have very admirably responded to the invitation. Some of the articles are written keeping students and potential new entrants to an area of mathematics in mind. This volume is thus very unique and gives a perspective of several important aspects of mathematics.
