Successful development of effective computational systems is a challenge for IT developers across sectors due to uncertainty issues that are inherently present within computational problems. Soft computing proposes one such solution to the problem of uncertainty through the application of generalized set structures including fuzzy sets, rough sets, and multisets. The Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing presents double blind peer-reviewed and original research on soft computing applications for solving problems of uncertainty within the computing environment. Emphasizing essential concepts on generalized and hybrid set structures that can be applied across industries for complex problem solving, this timely resource is essential to engineers across disciplines, researchers, computer scientists, and graduate-level students.

Within the field of modeling complex objects in natural sciences, which considers systems that consist of a large number of interacting parts, a good tool for analyzing and fitting models is the theory of random evolutionary systems, considering their asymptotic properties and large deviations. In Random Evolutionary Systems we consider these systems in terms of the operators that appear in the schemes of their diffusion and the Poisson approximation. Such an approach allows us to obtain a number of limit theorems and asymptotic expansions of processes that model complex stochastic systems, both those that are autonomous and those dependent on an external random environment. In this case, various possibilities of scaling processes and their time parameters are used to obtain different limit results.

Succinct and understandable, this book is a step-by-step guide to the mathematics and construction of electrical load forecasting models. Written by one of the world's foremost experts on the subject, Electrical Load Forecasting provides a brief discussion of algorithms, their advantages and disadvantages and when they are best utilized. The book begins with a good description of the basic theory and models needed to truly understand how the models are prepared so that they are not just blindly plugging and chugging numbers. This is followed by a clear and rigorous exposition of the statistical techniques and algorithms such as regression, neural networks, fuzzy logic, and expert systems. The book is also supported by an online computer program that allows readers to construct, validate, and run short and long term models.

An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics.

Communicable diseases have been an important part of human history. Epidemics afflicted populations, causing many deaths before gradually fading away and emerging again years after. Epidemics of infectious diseases are occurring more often, and spreading faster and further than ever, in many different regions of the world. The scientific community, in addition to its accelerated efforts to develop an effective treatment and vaccination, is also playing an important role in advising policymakers on possible non-pharmacological approaches to limit the catastrophic impact of epidemics using mathematical and machine learning models. Controlling Epidemics With Mathematical and Machine Learning Models provides mathematical and machine learning models for epidemical diseases, with special attention given to the COVID-19 pandemic. It gives mathematical proof of the stability and size of diseases. Covering topics such as compartmental models, reproduction number, and SIR model simulation, this premier reference source is an essential resource for statisticians, government officials, health professionals, epidemiologists, sociologists, students and educators of higher education, librarians, researchers, and academicians.

Basic Optics: Principles and Concepts addresses in great detail the basic principles of the science of optics, and their related concepts. The book provides a lucid and coherent presentation of an extensive range of concepts from the field of optics, which is of central relevance to several broad areas of science, including physics, chemistry, and biology. With its extensive range of discourse, the book's content arms scientists and students with knowledge of the essential concepts of classical and modern optics. It can be used as a reference book and also as a supplementary text by students at college and university levels and will, at the same time, be of considerable use to researchers and teachers. The book is composed of nine chapters and includes a great deal of material not covered in many of the more well-known textbooks on the subject. The science of optics has undergone major changes in the last fifty years because of developments in the areas of the optics of metamaterials, Fourier optics, statistical optics, quantum optics, and nonlinear optics, all of which find their place in this book, with a clear presentation of their basic principles. Even the more traditional areas of ray optics and wave optics are elaborated within the framework of electromagnetic theory, at a level more fundamental than what one finds in many of the currently available textbooks. Thus, the eikonal approximation leading to ray optics, the Lagrangian and Hamiltonian formulations of ray optics, the quantum theoretic interpretation of interference, the vector and dyadic diffraction theories, the geometrical theory of diffraction, and similar other topics of basic relevance are presented in clear terms. The presentation is lucid and elegant, capturing the essential magic and charm of physics. All this taken together makes the book a unique text, of major contemporary relevance, in the field of optics. Avijit Lahiri is a well-known researcher, teacher, and author, with publications in several areas of physics, and with a broad range of current interests, including physics and the philosophy of science.

The development of man's understanding of planetary motions is the crown jewel of Newtonian mechanics. This book offers a concise but self-contained handbook-length treatment of this historically important topic for students at about the third-year-level of an undergraduate physics curriculum. After opening with a review of Kepler's three laws of planetary motion, it proceeds to analyze the general dynamics of 'central force' orbits in spherical coordinates, how elliptical orbits satisfy Newton's gravitational law, and how the geometry of ellipses relates to physical quantities, such as energy and momentum. Exercises are provided, and derivations are set up in such a way that readers can gain analytic practice by filling in the missing steps. A brief bibliography lists sources for readers who wish to pursue further study on their own.

Medical imaging is one of the heaviest funded biomedical engineering research areas. The second edition of Pattern Recognition and Signal Analysis in Medical Imaging brings sharp focus to the development of integrated systems for use in the clinical sector, enabling both imaging and the automatic assessment of the resultant data. Since the first edition, there has been tremendous development of new, powerful technologies for detecting, storing, transmitting, analyzing, and displaying medical images. Computer-aided analytical techniques, coupled with a continuing need to derive more information from medical images, has led to a growing application of digital processing techniques in cancer detection as well as elsewhere in medicine. This book is an essential tool for students and professionals, compiling and explaining proven and cutting-edge methods in pattern recognition for medical imaging.

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.

Living Culturally Responsive Mathematics Education with/in Indigenous Communities explores challenges and possibilities across international contexts, involving Indigenous and non-Indigenous scholars, teachers and Elders responding to calls for improved education for all Indigenous students. Authors from Australia, New Zealand, United States, Micronesia, and Canada explore the nature of culturally responsive mathematics education. Chapters highlight the importance of relationships with communities and the land, each engaging critically with ideas of culturally responsive education, exploring what this stance might mean and how it is lived in local contexts within global conversations. Education researchers and teacher educators will find a living pathway where scholars, educators, youth and community members critically take-up culturally responsive teachings and the possibilities and challenges that arise along the journey. Contributors are: Dayle Anderson, Dora Andre-Ihrke, Jo-ann Archibald Q'um Q'um Xiiem, Maria Jose Athie-Martinez, Robin Averill, Trevor Bills, Beatriz A. Camacho, A. J. (Sandy) Dawson, Dwayne Donald, Herewini Easton, Tauvela Fale, Amanda Fritzlan, Florence Glanfield, Jodie Hunter, Roberta Hunter, Newell Margaret Johnson, Julie Kaomea, Robyn Jorgensen, Jerry Lipka, Lisa Lunney Borden, Dora Miura, Sharon Nelson-Barber, Cynthia Nicol, Gladys Sterenberg, Marama Taiwhati, Pania Te Maro, Jennifer S. Thom, David Wagner, Evelyn Yanez, and Joanne Yovanovich.

Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments.

Topology Optimization in Engineering Structure Design explores the recent advances and applications of topology optimization in engineering structures design, with a particular focus on aircraft and aerospace structural systems. To meet the increasingly complex engineering challenges provided by rapid developments in these industries, structural optimization techniques have developed in conjunction with them over the past two decades. The latest methods and theories to improve mechanical performances and save structural weight under static, dynamic and thermal loads are summarized and explained in detail here, in addition to potential applications of topology optimization techniques such as shape preserving design, smart structure design and additive manufacturing. These new design strategies are illustrated by a host of worked examples, which are inspired by real engineering situations, some of which have been applied to practical structure design with significant effects. Written from a forward-looking applied engineering perspective, the authors not only summarize the latest developments in this field of structure design but also provide both theoretical knowledge and a practical guideline. This book should appeal to graduate students, researchers and engineers, in detailing how to use topology optimization methods to improve product design.

Mathematic Modelling: Improving the Implementation, Monitoring and Evaluation of Interventions, Part B, the latest volume in the Advances in Parasitology series contains comprehensive and up-to-date reviews in the field of mathematic modeling and its implementation within parasitology. The series includes medical studies of parasites of major influence, such as Plasmodium falciparum and trypanosomes, along with reviews of more traditional areas, such as zoology, taxonomy, and life history, all of which shape current thinking and applications.

Domain theory, a subject that arose as a response to natural concerns in the semantics of computation, studies ordered sets which possess an unusual amount of mathematical structure. This book explores its connection with quantum information science and the concept that relates them: disorder. This is not a literary work. It can be argued that its subject, domain theory and quantum information science, does not even really exist, which makes the scope of this alleged 'work' irrelevant. BUT, it does have a purpose and to some extent, it can also be said to have a method. I leave the determination of both of those largely to you, the reader. Except to say, I am hoping to convince the uninitiated to take a look. A look at what? Twenty years ago, I failed to satisfactorily prove a claim that I still believe: that there is substantial domain theoretic structure in quantum mechanics and that we can learn a lot from it. One day it will be proven to the point that people will be comfortable dismissing it as a 'well-known' idea that many (possibly including themselves) had long suspected but simply never bothered to write down. They may even call it "obvious!" I will not bore you with a brief history lesson on why it is not obvious, except to say that we have never been interested in the difficulty of proving the claim only in establishing its validity. This book then documents various attempts on my part to do just that.

When it comes to data collection and analysis, ranked set sampling (RSS) continues to increasingly be the focus of methodological research. This type of sampling is an alternative to simple random sampling and can offer substantial improvements in precision and efficient estimation. There are different methods within RSS that can be further explored and discussed. On top of being efficient, RSS is cost-efficient and can be used in situations where sample units are difficult to obtain. With new results in modeling and applications, and a growing importance in theory and practice, it is essential for modeling to be further explored and developed through research. Ranked Set Sampling Models and Methods presents an innovative look at modeling survey sampling research and new models of RSS along with the future potentials of it. The book provides a panoramic view of the state of the art of RSS by presenting some previously known and new models. The chapters illustrate how the modeling is to be developed and how they improve the efficiency of the inferences. The chapters highlight topics such as bootstrap methods, fuzzy weight ranked set sampling method, item count technique, stratified ranked set sampling, and more. This book is essential for statisticians, social and natural science scientists, physicians and all the persons involved with the use of sampling theory in their research along with practitioners, researchers, academicians, and students interested in the latest models and methods for ranked set sampling.