A Handbook Of Model Categories

Author : Scott Balchin
Publisher : Springer Nature
ISBN 13 : 3030750353
Total Pages : 326 pages
Book Rating : 4.50/5 ( download)

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Download or read book A Handbook of Model Categories written by Scott Balchin and published by Springer Nature. This book was released on 2021-10-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.

Author : Mark Hovey
Publisher : American Mathematical Soc.
ISBN 13 : 0821843613
Total Pages : 229 pages
Book Rating : 4.11/5 ( download)

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Download or read book Model Categories written by Mark Hovey and published by American Mathematical Soc.. This book was released on 2007 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model categories are used as a tool for inverting certain maps in a category in a controllable manner. They are useful in diverse areas of mathematics. This book offers a comprehensive study of the relationship between a model category and its homotopy category. It develops the theory of model categories, giving a development of the main examples.

Author : I.M. James
Publisher : Elsevier
ISBN 13 : 0080532985
Total Pages : 1336 pages
Book Rating : 4.81/5 ( download)

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Download or read book Handbook of Algebraic Topology written by I.M. James and published by Elsevier. This book was released on 1995-07-18 with total page 1336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

Author : Edmund M. Clarke
Publisher : Springer
ISBN 13 : 3319105752
Total Pages : 1212 pages
Book Rating : 4.58/5 ( download)

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Download or read book Handbook of Model Checking written by Edmund M. Clarke and published by Springer. This book was released on 2018-05-18 with total page 1212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model checking is a computer-assisted method for the analysis of dynamical systems that can be modeled by state-transition systems. Drawing from research traditions in mathematical logic, programming languages, hardware design, and theoretical computer science, model checking is now widely used for the verification of hardware and software in industry. The editors and authors of this handbook are among the world's leading researchers in this domain, and the 32 contributed chapters present a thorough view of the origin, theory, and application of model checking. In particular, the editors classify the advances in this domain and the chapters of the handbook in terms of two recurrent themes that have driven much of the research agenda: the algorithmic challenge, that is, designing model-checking algorithms that scale to real-life problems; and the modeling challenge, that is, extending the formalism beyond Kripke structures and temporal logic. The book will be valuable for researchers and graduate students engaged with the development of formal methods and verification tools.

Author : Azad M. Madni
Publisher : Springer Nature
ISBN 13 : 3030935825
Total Pages : 1362 pages
Book Rating : 4.25/5 ( download)

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Download or read book Handbook of Model-Based Systems Engineering written by Azad M. Madni and published by Springer Nature. This book was released on 2023-07-25 with total page 1362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook brings together diverse domains and technical competences of Model Based Systems Engineering (MBSE) into a single, comprehensive publication. It is intended for researchers, practitioners, and students/educators who require a wide-ranging and authoritative reference on MBSE with a multidisciplinary, global perspective. It is also meant for those who want to develop a sound understanding of the practice of systems engineering and MBSE, and/or who wish to teach both introductory and advanced graduate courses in systems engineering. It is specifically focused on individuals who want to understand what MBSE is, the deficiencies in current practice that MBSE overcomes, where and how it has been successfully applied, its benefits and payoffs, and how it is being deployed in different industries and across multiple applications. MBSE engineering practitioners and educators with expertise in different domains have contributed chapters that address various uses of MBSE and related technologies such as simulation and digital twin in the systems lifecycle. The introductory chapter reviews the current state of practice, discusses the genesis of MBSE and makes the business case. Subsequent chapters present the role of ontologies and meta-models in capturing system interdependencies, reasoning about system behavior with design and operational constraints; the use of formal modeling in system (model) verification and validation; ontology-enabled integration of systems and system-of-systems; digital twin-enabled model-based testing; system model design synthesis; model-based tradespace exploration; design for reuse; human-system integration; and role of simulation and Internet-of-Things (IoT) within MBSE.

Author : Matthias von Davier
Publisher : Springer Nature
ISBN 13 : 3030055841
Total Pages : 656 pages
Book Rating : 4.44/5 ( download)

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Download or read book Handbook of Diagnostic Classification Models written by Matthias von Davier and published by Springer Nature. This book was released on 2019-10-11 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook provides an overview of major developments around diagnostic classification models (DCMs) with regard to modeling, estimation, model checking, scoring, and applications. It brings together not only the current state of the art, but also the theoretical background and models developed for diagnostic classification. The handbook also offers applications and special topics and practical guidelines how to plan and conduct research studies with the help of DCMs. Commonly used models in educational measurement and psychometrics typically assume a single latent trait or at best a small number of latent variables that are aimed at describing individual differences in observed behavior. While this allows simple rankings of test takers along one or a few dimensions, it does not provide a detailed picture of strengths and weaknesses when assessing complex cognitive skills. DCMs, on the other hand, allow the evaluation of test taker performance relative to a potentially large number of skill domains. Most diagnostic models provide a binary mastery/non-mastery classification for each of the assumed test taker attributes representing these skill domains. Attribute profiles can be used for formative decisions as well as for summative purposes, for example in a multiple cut-off procedure that requires mastery on at least a certain subset of skills. The number of DCMs discussed in the literature and applied to a variety of assessment data has been increasing over the past decades, and their appeal to researchers and practitioners alike continues to grow. These models have been used in English language assessment, international large scale assessments, and for feedback for practice exams in preparation of college admission testing, just to name a few. Nowadays, technology-based assessments provide increasingly rich data on a multitude of skills and allow collection of data with respect to multiple types of behaviors. Diagnostic models can be understood as an ideal match for these types of data collections to provide more in-depth information about test taker skills and behavioral tendencies.

Author : Rick H. Hoyle
Publisher : Guilford Publications
ISBN 13 : 1462544649
Total Pages : 801 pages
Book Rating : 4.46/5 ( download)

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Download or read book Handbook of Structural Equation Modeling written by Rick H. Hoyle and published by Guilford Publications. This book was released on 2023-02-17 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible volume presents both the mechanics of structural equation modeling (SEM) and specific SEM strategies and applications. The editor, along with an international group of contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, including new and emerging topics in SEM. Each chapter provides conceptually oriented descriptions, fully explicated analyses, and engaging examples that reveal modeling possibilities for use with readers' data. Many of the chapters also include access to data and syntax files at the companion website, allowing readers to try their hands at reproducing the authors' results"--

Author :
Publisher : Univalent Foundations
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4./5 ( download)

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Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Michael L. Nering
Publisher : Routledge
ISBN 13 : 1135168717
Total Pages : 349 pages
Book Rating : 4.11/5 ( download)

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Download or read book Handbook of Polytomous Item Response Theory Models written by Michael L. Nering and published by Routledge. This book was released on 2011-01-19 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive Handbook focuses on the most used polytomous item response theory (IRT) models. These models help us understand the interaction between examinees and test questions where the questions have various response categories. The book reviews all of the major models and includes discussions about how and where the models originated, conceptually and in practical terms. Diverse perspectives on how these models can best be evaluated are also provided. Practical applications provide a realistic account of the issues practitioners face using these models. Disparate elements of the book are linked through editorial sidebars that connect common ideas across chapters, compare and reconcile differences in terminology, and explain variations in mathematical notation. These sidebars help to demonstrate the commonalities that exist across the field. By assembling this critical information, the editors hope to inspire others to use polytomous IRT models in their own research so they too can achieve the type of improved measurement that such models can provide. Part 1 examines the most commonly used polytomous IRT models, major issues that cut across these models, and a common notation for calculating functions for each model. An introduction to IRT software is also provided. Part 2 features distinct approaches to evaluating the effectiveness of polytomous IRT models in various measurement contexts. These chapters appraise evaluation procedures and fit tests and demonstrate how to implement these procedures using IRT software. The final section features groundbreaking applications. Here the goal is to provide solutions to technical problems to allow for the most effective use of these models in measuring educational, psychological, and social science abilities and traits. This section also addresses the major issues encountered when using polytomous IRT models in computerized adaptive testing. Equating test scores across different testing contexts is the focus of the last chapter. The various contexts include personality research, motor performance, health and quality of life indicators, attitudes, and educational achievement. Featuring contributions from the leading authorities, this handbook will appeal to measurement researchers, practitioners, and students who want to apply polytomous IRT models to their own research. It will be of particular interest to education and psychology assessment specialists who develop and use tests and measures in their work, especially researchers in clinical, educational, personality, social, and health psychology. This book also serves as a supplementary text in graduate courses on educational measurement, psychometrics, or item response theory.

Author : Philip S. Hirschhorn
Publisher : American Mathematical Soc.
ISBN 13 : 0821849174
Total Pages : 482 pages
Book Rating : 4.70/5 ( download)

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Download or read book Model Categories and Their Localizations written by Philip S. Hirschhorn and published by American Mathematical Soc.. This book was released on 2003 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps, called weak equivalences, and then passing to the homotopy category by localizing with respect to the weak equivalences, i.e., by creating a new category in which the weak equivalences are isomorphisms. Quillen defined a model category to be a category together with a class of weak equivalences and additional structure useful for describing the homotopy category in terms of the original category. This allows you to make constructions analogous to those used to study the homotopy theory of topological spaces. A model category has a class of maps called weak equivalences plus two other classes of maps, called cofibrations and fibrations. Quillen's axioms ensure that the homotopy category exists and that the cofibrations and fibrations have extension and lifting properties similar to those of cofibration and fibration maps of topological spaces. During the past several decades the language of model categories has become standard in many areas of algebraic topology, and it is increasingly being used in other fields where homotopy theoretic ideas are becoming important, including modern algebraic $K$-theory and algebraic geometry. All these subjects and more are discussed in the book, beginning with the basic definitions and giving complete arguments in order to make the motivations and proofs accessible to the novice. The book is intended for graduate students and research mathematicians working in homotopy theory and related areas.