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A Handbook of Model Categories

Author: Scott Balchin

Publisher: Springer Nature

Published: 2021-10-29

Total Pages: 326

ISBN-13: 3030750353

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.

Model Categories

Author: Mark Hovey

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 229

ISBN-13: 0821843613

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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.

Handbook of Algebraic Topology

Author: I.M. James

Publisher: Elsevier

Published: 1995-07-18

Total Pages: 1336

ISBN-13: 0080532985

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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.

Handbook of Model Checking

Author: Edmund M. Clarke

Publisher: Springer

Published: 2018-05-18

Total Pages: 1212

ISBN-13: 3319105752

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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.

Handbook of Model-Based Systems Engineering

Author: Azad M. Madni

Publisher: Springer Nature

Published: 2023-07-25

Total Pages: 1362

ISBN-13: 3030935825

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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.

Handbook of Structural Equation Modeling

Author: Rick H. Hoyle

Publisher: Guilford Publications

Published: 2023-02-17

Total Pages: 801

ISBN-13: 1462544649

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"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"--

Handbook of Diagnostic Classification Models

Author: Matthias von Davier

Publisher: Springer Nature

Published: 2019-10-11

Total Pages: 656

ISBN-13: 3030055841

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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.

Springer Handbook of Model-Based Science

Author: Lorenzo Magnani

Publisher: Springer

Published: 2017-05-22

Total Pages: 1180

ISBN-13: 3319305263

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This handbook offers the first comprehensive reference guide to the interdisciplinary field of model-based reasoning. It highlights the role of models as mediators between theory and experimentation, and as educational devices, as well as their relevance in testing hypotheses and explanatory functions. The Springer Handbook merges philosophical, cognitive and epistemological perspectives on models with the more practical needs related to the application of this tool across various disciplines and practices. The result is a unique, reliable source of information that guides readers toward an understanding of different aspects of model-based science, such as the theoretical and cognitive nature of models, as well as their practical and logical aspects. The inferential role of models in hypothetical reasoning, abduction and creativity once they are constructed, adopted, and manipulated for different scientific and technological purposes is also discussed. Written by a group of internationally renowned experts in philosophy, the history of science, general epistemology, mathematics, cognitive and computer science, physics and life sciences, as well as engineering, architecture, and economics, this Handbook uses numerous diagrams, schemes and other visual representations to promote a better understanding of the concepts. This also makes it highly accessible to an audience of scholars and students with different scientific backgrounds. All in all, the Springer Handbook of Model-Based Science represents the definitive application-oriented reference guide to the interdisciplinary field of model-based reasoning.

Handbook of Homotopy Theory

Author: Haynes Miller

Publisher: CRC Press

Published: 2020-01-23

Total Pages: 982

ISBN-13: 1351251619

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The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Homotopy Type Theory: Univalent Foundations of Mathematics

Author:

Publisher: Univalent Foundations

Published:

Total Pages: 484

ISBN-13:

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