Acyclic Models


Book Description

Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book is the first attempt to put together in a concise form this important technique and to include all the necessary background. It presents a brief introduction to category theory and homological algebra. The author then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology. The volume could be used as a text for a course that combines homological algebra and algebraic topology. Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. It is also suitable as a reference work for researchers.




Introduction to Structural Equation Modeling Using IBM SPSS Statistics and Amos


Book Description

This comprehensive Second Edition offers readers a complete guide to carrying out research projects involving structural equation modeling (SEM). Updated to include extensive analysis of AMOS′ graphical interface, a new chapter on latent curve models and detailed explanations of the structural equation modeling process, this second edition is the ideal guide for those new to the field. The book includes: Learning objectives, key concepts and questions for further discussion in each chapter. Helpful diagrams and screenshots to expand on concepts covered in the texts. Real life examples from a variety of disciplines to show how SEM is applied in real research contexts. Exercises for each chapter on an accompanying companion website. A new glossary. Assuming no previous experience of the subject, and a minimum of mathematical knowledge, this is the ideal guide for those new to SEM and an invaluable companion for students taking introductory SEM courses in any discipline. Niels J. Blunch was formerly in the Department of Marketing and Statistics at the University of Aarhus, Denmark




Lectures on Algebraic Topology


Book Description

This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applica tions of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions.




Introduction to Structural Equation Modeling Using IBM SPSS Statistics and EQS


Book Description

This student orientated guide to structural equation modeling promotes theoretical understanding and inspires students with the confidence to successfully apply SEM. Assuming no previous experience, and a minimum of mathematical knowledge, this is an invaluable companion for students taking introductory SEM courses in any discipline. Niels Blunch shines a light on each step of the structural equation modeling process, providing a detailed introduction to SPSS and EQS with a focus on EQS′ excellent graphical interface. He also sets out best practice for data entry and programming, and uses real life data to show how SEM is applied in research. The book includes: Learning objectives, key concepts and questions for further discussion in each chapter. Helpful diagrams and screenshots to expand on concepts covered in the texts. A wide variety of examples from multiple disciplines and real world contexts. Exercises for each chapter on an accompanying . A detailed glossary. Clear, engaging and built around key software, this is an ideal introduction for anyone new to SEM.




Elements of Homology Theory


Book Description

The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.




Introduction to Homotopy Theory


Book Description

Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.




A History of Algebraic and Differential Topology, 1900 - 1960


Book Description

This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet




New Frontiers in Artificial Intelligence


Book Description

This book constitutes the thoroughly refereed post-proceedings of four workshops held as satellite events of the JSAI International Symposia on Artificial Intelligence 2010, in Tokyo, Japan, in November 2010. The 28 revised full papers with four papers for the following four workshops presented were carefully reviewed and selected from 70 papers. The papers are organized in sections Logic and Engineering of Natural Language Semantics (LENLS), Juris-Informatics (JURISIN), Advanced Methodologies for Bayesian Networks (AMBN), and Innovating Service Systems (ISS).




Fixed Point Theory


Book Description

The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS




Statistics and Causality


Book Description

b”STATISTICS AND CAUSALITYA one-of-a-kind guide to identifying and dealing with modern statistical developments in causality Written by a group of well-known experts, Statistics and Causality: Methods for Applied Empirical Research focuses on the most up-to-date developments in statistical methods in respect to causality. Illustrating the properties of statistical methods to theories of causality, the book features a summary of the latest developments in methods for statistical analysis of causality hypotheses. The book is divided into five accessible and independent parts. The first part introduces the foundations of causal structures and discusses issues associated with standard mechanistic and difference-making theories of causality. The second part features novel generalizations of methods designed to make statements concerning the direction of effects. The third part illustrates advances in Granger-causality testing and related issues. The fourth part focuses on counterfactual approaches and propensity score analysis. Finally, the fifth part presents designs for causal inference with an overview of the research designs commonly used in epidemiology. Statistics and Causality: Methods for Applied Empirical Research also includes: New statistical methodologies and approaches to causal analysis in the context of the continuing development of philosophical theories End-of-chapter bibliographies that provide references for further discussions and additional research topics Discussions on the use and applicability of software when appropriate Statistics and Causality: Methods for Applied Empirical Research is an ideal reference for practicing statisticians, applied mathematicians, psychologists, sociologists, logicians, medical professionals, epidemiologists, and educators who want to learn more about new methodologies in causal analysis. The book is also an excellent textbook for graduate-level courses in causality and qualitative logic.