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This volume presents the fundamentals of graph theory and then goes on to discuss specific chemical applications. Chapter 1 provides a historical setting for the current upsurge of interest in chemical graph theory. Chapter 2 gives a full background of the basic ideas and mathematical formalism of graph theory and includes such chemically relevant notions as connectedness, graph matrix representations, metric properties, symmetry and operations on graphs. This is followed by a discussion on chemical nomenclature and the trends in its rationalization by using graph theory, which has important implications for the storage and retrieval of chemical information. This volume also contains a detailed discussion of the relevance of graph-theoretical polynomials; it describes methodologies for the enumeration of isomers, incorporating the classical Polya method, as well as more recent approaches.
The book offers new concepts and ideas that broaden reader’s perception of modern science. Internationally established experts present the inspiring new science of complexity, which discovers new general laws covering wide range of science areas. The book offers a broader view on complexity based on the expertise of the related areas of chemistry, biochemistry, biology, ecology, and physics. Contains methodologies for assessing the complexity of systems that can be directly applied to proteomics and genomics, and network analysis in biology, medicine, and ecology.
This volume covers the rapidly developing field of complexity studies with the underlying theme that complexity is to be found everywhere. The volume discusses many chemical applications and offers a comprehensive coverage of complexity and the ways in which it may be measured, complexity indices, complexity measures based on Shannon's information theory, and thermodynamic complexity. Complexity: Introduction and Fundamentals provides a valuable source of reference for graduates and researchers for mathematical chemistry.
Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have brought together 27 chapters written by 68 internationally renowned experts in these two volumes. Each volume comprises a wise integration of mathematical and chemical concepts and covers numerous applications in the field of drug discovery, bioinformatics, chemoinformatics, computational biology, mathematical proteomics, and ecotoxicology. Volume 1 includes chapters on mathematical structural descriptors of molecules and biomolecules, applications of partially ordered sets...
Papers on Topological Model for Ecologically Industrial Systems, Bounds for the Harmonious Coloring of Myceilskians, Upper Singed Domination Number of Graphs, Existence Results of Unique Fixed Point in 2-Banach Spaces, Some Results in Fuzzy and Anti Fuzzy Group Theory, and other topics. Contributors: Linfan Mao, M. Kamal Kumar, B.O. Onasanya, S.A. Ilori, Buddhadev Pal, Arindam Bhattacharyya, Girish.V.R., P. Usha, H.B. Walikar, and others.
This ready reference discusses different methods for statistically analyzing and validating data created with high-throughput methods. As opposed to other titles, this book focusses on systems approaches, meaning that no single gene or protein forms the basis of the analysis but rather a more or less complex biological network. From a methodological point of view, the well balanced contributions describe a variety of modern supervised and unsupervised statistical methods applied to various large-scale datasets from genomics and genetics experiments. Furthermore, since the availability of sufficient computer power in recent years has shifted attention from parametric to nonparametric methods, the methods presented here make use of such computer-intensive approaches as Bootstrap, Markov Chain Monte Carlo or general resampling methods. Finally, due to the large amount of information available in public databases, a chapter on Bayesian methods is included, which also provides a systematic means to integrate this information. A welcome guide for mathematicians and the medical and basic research communities.
In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.
A collection of highly valuable statistical and computational approaches designed for developing powerful methods to analyze large-scale high-throughput data derived from studies of complex diseases. Such diseases include cancer and cardiovascular disease, and constitute the major health challenges in industrialized countries. They are characterized by the systems properties of gene networks and their interrelations, instead of individual genes, whose malfunctioning manifests in pathological phenotypes, thus making the analysis of the resulting large data sets particularly challenging. This is why novel approaches are needed to tackle this problem efficiently on a systems level. Written by computational biologists and biostatisticians, this book is an invaluable resource for a large number of researchers working on basic but also applied aspects of biomedical data analysis emphasizing the pathway level.
This book constitutes the first of 3 volumes of refereed conference proceedings of the 8th International Conference on Intelligent Computing, ICIC 2012, held in Huangshan, China, in July 2012. The 242 revised full papers presented were carefully reviewed and selected from 753 submissions. The 84 papers included in this volume are organized in topical sections on evolutionary learning and genetic algorithms, fuzzy theory and models, swarm intelligence and optimization, kernel methods and supporting vector machines, nature inspired computing and optimization, systems biology and computational biology, knowledge discovery and data mining, graph theory and algorithms, machine learning theory and...
The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe. The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.