Cycle Index Of Uncertain Random Graph

With the increasing of the complexity of a system, there is a variety of indeterminacy in the practical applications of graph theory. We focus on uncertain random graph, in which some edges exist with degrees in probability measure and others exist with degrees in uncertain measure. In this paper, the chance theory is applied to construct the cycle index of an uncertain random graph. Then a method to calculate the cycle index of an uncertain random graph is presented. We also discuss some properties of the cycle index.

An essential resource work for understanding how to design and develop smart applications for present and future problems of the field of agriculture.— Dr. Deepak Gupta, Maharaja Agrasen Institute of Technology, Delhi, India As a result of the advances in Artificial Intelligence (AI), many aspects of daily life have been transformed by smart digital technology. Advanced intelligent algorithms can provide powerful solutions to real-world problems. Smart applications have become commonplace. All areas of life are being changed by smart tools developed to deal with complex issues challenging both humanity and the earth. Artificial Intelligence and Smart Agriculture Applications presents the latest smart agriculture applications developed across the globe. It covers a broad array of solutions using data science and AI to attack problems facing agriculture worldwide. Features: Application of drones and sensors in advanced farming A cloud-computing model for implementing smart agriculture Conversational AI for farmer's advisory communications Intelligent fuzzy logic to predict global warming’s effect on agriculture Machine learning algorithms for mapping soil macronutrient elements variability A smart IoT framework for soil fertility enhancement AI applications in pest management A model using Python for predicting rainfall The book examines not only present solutions but also potential future outcomes. It looks at the role of AI-based algorithms and the almost infinite combinations of variables for agricultural applications. Researchers, public and private sector representatives, agriculture scientists, and students can use this book to develop sustainable and solutions for smart agriculture. This book’s findings are especially important as the planet is facing unprecedented environmental challenges from over-farming and climate change due to global warming.

This book is intended to present the milestones in the progression of uncertain Data envelopment analysis (DEA). Chapter 1 gives some basic introduction to uncertain theories, including probability theory, credibility theory, uncertainty theory and chance theory. Chapter 2 presents a comprehensive review and discussion of basic DEA models. The stochastic DEA is introduced in Chapter 3, in which the inputs and outputs are assumed to be random variables. To obtain the probability distribution of a random variable, a lot of samples are needed to apply the statistics inference approach. Chapter 4 and 5 provide two uncertain DEA methods to evaluate the DMUs with limited or insufficient statistical data, named fuzzy DEA and uncertain DEA. In order to evaluate the DMUs in which uncertainty and randomness appear simultaneously, the hybrid DEA based on chance theory is presented in Chapter 6.

The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.

Life-cycle analysis is a systemic tool for efficient and effective service life management of deteriorating structures. In the last few decades, theoretical and practical approaches for life-cycle performance and cost analysis have been developed extensively due to increased demand on structural safety and service life extension. This book presents the state-of-the-art in life-cycle analysis and maintenance optimization for fatigue-sensitive structures. Both theoretical background and practical applications have been provided for academics, engineers and researchers. Concepts and approaches of life-cycle performance and cost analysis developed in recent decades are presented. The major topics covered include (a) probabilistic concepts of life-cycle performance and cost analysis, (b) inspection, monitoring and maintenance for fatigue cracks, (c) estimation of fatigue crack detection, (d) optimum inspection and monitoring planning, (e) multi-objective life-cycle optimization, and (f) decision making in life-cycle analysis. Life-cycle optimization covered in the book considers probability of fatigue crack detection, fatigue crack damage detection time, maintenance times, probability of failure, service life and total life-cycle cost. For the practical application and integration of recently developed approaches for inspection and maintenance planning, efficient and effective multi-objective optimization and decision making are presented. This book will help engineers engaged in civil and marine structures including students, researchers and practitioners with reliable and cost-effective maintenance planning of fatigue-sensitive structures, and to develop more advanced approaches and techniques in the field of life-cycle maintenance optimization and safety of structures under various aging and deteriorating conditions. Key Features: Provides the state-of-the-art in life-cycle cost analysis and optimization for fatigue-sensitive structures Provides a solid foundation of theoretical backgrounds and practical applications both for academics and practicing engineers and researchers Covers illustrative examples and recent development for optimum service life management Deals with various structures such as bridges and ships subjected to fatigue .

A unified, modern treatment of the theory of random graphs-including recent results and techniques Since its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book. Poised to stimulate research for years to come, this new work covers developments of the last decade, providing a much-needed, modern overview of this fast-growing area of combinatorics. Written by three highly respected members of the discrete mathematics community, the book incorporates many disparate results from across the literature, including results obtained by the authors and some completely new results. Current tools and techniques are also thoroughly emphasized. Clear, easily accessible presentations make Random Graphs an ideal introduction for newcomers to the field and an excellent reference for scientists interested in discrete mathematics and theoretical computer science. Special features include: * A focus on the fundamental theory as well as basic models of random graphs * A detailed description of the phase transition phenomenon * Easy-to-apply exponential inequalities for large deviation bounds * An extensive study of the problem of containing small subgraphs * Results by Bollobas and others on the chromatic number of random graphs * The result by Robinson and Wormald on the existence of Hamilton cycles in random regular graphs * A gentle introduction to the zero-one laws * Ample exercises, figures, and bibliographic references

Life-Cycle and Sustainability of Civil Infrastructure Systems contains the lectures and papers presented at the Third International Symposium on Life-Cycle Civil Engineering (IALCCE 2012) held in one of Vienna‘s most famous venues, the Hofburg Palace, October 3rd-6th, 2012. This volume consists of a book of extended abstracts (516 pp) and a DVD-ROM

This is a new edition of a now classic text. The addition of two new sections, numerous new results and over 150 references mean that this represents an up-to-date account of random graph theory. Suitable for mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics.