Series: Springer Texts in Statistics
2012, 2012, XXXII, 536 p.
Hardcover version
ISBN 978-1-4614-3899-1
Due: August 31, 2012
.This book provides a description of the most important theoretical concepts and features of linear mixed models (LMMs) and their implementation in R
All the classes of linear models presented in the book are illustrated using real-life data
Provides information crucial to data from many fields including biostatistics, public health, psychometrics, educational measurement, and sociology
A step-by-step approach is used to describe the R tools for LMMs
Linear mixed-effects models (LMMs) are an important class of statistical models that can be used to analyze correlated data. Such data are encountered in a variety of fields including biostatistics, public health, psychometrics, educational measurement, and sociology. This book aims to support a wide range of uses for the models by applied researchers in those and other fields by providing state-of-the-art descriptions of the implementation of LMMs in R. To help readers to get familiar with the features of the models and the details of carrying them out in R, the book includes a review of the most important theoretical concepts of the models. The presentation connects theory, software and applications. It is built up incrementally, starting with a summary of the concepts underlying simpler classes of linear models like the classical regression model, and carrying them forward to LMMs. A similar step-by-step approach is used to describe the R tools for LMMs. All the classes of linear models presented in the book are illustrated using real-life data. The book also introduces several novel R tools for LMMs, including new class of variance-covariance structure for random-effects, methods for influence diagnostics and for power calculations. They are included into an R package that should assist the readers in applying these and other methods presented in this text.
Introduction.- Linear Models for Independent Observations.- Linear Fixed-effects Models for Correlated Data.- Linear Mixed-effects Models.
Series: Geometry and Computing, Tentative volume 8
2012, 2012, Approx. 220 p.
Hardcover
ISBN 978-3-642-31793-4
Due: November 30, 2012
.Defines geometric algebra computing as the geometrically intuitive development of algorithms with a focus on their efficient implementation
Author anticipates the forthcoming widespread adoption of parallel processor technology
New computing platforms can benefit from the inherent optimization and parallelization of the techniques described
The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics.
This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications.
The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.
Chap. 1 Introduction.- Chap. 2 Mathematical Introduction.- Chap. 3 The Conformal Geometric Algebra.- Chap. 4 Maple and the Identification of Quaternions and Other Algebras.- Chap. 5 Fitting of Planes or Spheres into Point Sets.- Chap. 6 Geometric Algebra Tutorial Using CLUCalc.- Chap. 7 Inverse Kinematics of a Simple Robot.- Chap. 8 Robot Grasping an Object.- Chap. 9 Efficient Computer Animation Application in CGA.- Chap. 10 Using Gaalop for Performant Geometric Algebra Computing.- Chap. 11 Collision Detection Using the Gaalop Precompiler.- Chap. 12 Gaalop Precompiler for GPGPUs.- Chap. 13 Molecular Dynamics Using Gaalop GPC for OpenCL.- Chap. 14 Geometric Algebra Computers.
Series: SpringerBriefs in Statistics, Vol. 12
2012, 2012, XI, 57 p. 9 illus.
Softcover
ISBN 978-1-4614-4737-5
Due: August 31, 2012
In statistics, the Kalman filter is a mathematical method whose purpose is to use a series of measurements observed over time, containing random variations and other inaccuracies, and produce estimates that tend to be closer to the true unknown values than those that would be based on a single measurement alone. This Brief offers developments on Kalman filtering subject to general linear constraints. There are essentially three types of contributions: new proofs for results already established; new results within the subject; and applications in investment analysis and macroeconomics, where the proposed methods are illustrated and evaluated. The Brief has a short chapter on linear state space models and the Kalman filter, aiming to make the book self-contained and to give a quick reference to the reader (notation and terminology). The prerequisites would be a contact with time series analysis in the level of Hamilton (1994) or Brockwell & Davis (2002) and also with linear state models and the Kalman filter ? each of these books has a chapter entirely dedicated to the subject. The book is intended for graduate students, researchers and practitioners in statistics (specifically: time series analysis and econometrics).
Introduction.- Linear state space models and the Kalman filtering: a briefing.- Restricted Kalman filtering: theoretical issues.- Restricted Kalman filtering: methodological issues.- Applications.- Further Extensions.
2012, 2012, Approx. 120 p. 8 illus.
Hardcover
ISBN 978-3-642-30987-8
Due: September 2012
.Unique collection of material on the topic
Clear and as simple as possible presentation
Wide range of problems considered
Along with general theorems and constructions their most important special cases are considered in detail
This vital contribution to the mathematical literature on combinatorics, algebra and differential equations develops two fundamental finiteness properties of the semigroup Z_(?0)^n that elucidate key aspects of theories propounded by, among others, Hilbert and Kouchnirenko.
The authors provide explanations for numerous results in the field that appear at first glance to be unrelated. The first finiteness property relates to the fact that Z_(?0)^n can be represented in the form of a finite union of shifted n-dimensional octants, while the second asserts that any co-ideal of the semigroup can be represented as a finite, disjoint union of shifted co-ordinate octants.
The applications of their work include proof that Hilbert’s implication that dimension d of the affine variety X equals the degree of Hilbert’s polynomial can be developed until its degree X equates to the leading coefficient of the Hilbert polynomial multiplied by d. The volume is a major forward step in this field
I Geometry and combinatorics of semigroups.- 1 Elementary geometry of the semigroup Zn>0.- 2 Properties of an ordered semigroup.- 3 Hilbert functions and their analogues.- II Applications: 4 Kouchnirenko`s theorem on number of solutions of a polynomial system of equations. On the Grothendieck groups of the semigroup of finite subsets of Zn and compact subsets of Rn.- 5 Differential Grobner bases and analytical theory of partial differential equations.- 6 On the Convergence of Formal Solutions of a System of Partial Differential Equations.- A Hilbert and Hilbert-Samuel polynomials and Partial Differential Equations.- References
Series: SpringerBriefs in Mathematics
2012, 2012, XII, 86 p. 51 illus., 34 in color.
Softcover
ISBN 978-1-4614-4486-2
Due: September 30, 2012
Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light.
The reader is assumed to have taken a senior level course in analysis and a basic course in topology. Advanced undergraduate and graduate students, and researchers working in this area will find this brief useful. ?
Content Level ≫ Research
Keywords ≫ Inverse limit - Mapping Theorems - attractors in dynamical systems - backward economics - set-valued function
Related subjects ≫ Applications - Dynamical Systems & Differential Equations - Geometry & Topology
1. Basics.- 2. Connectedness.- 3. Mapping verses Set-valued Functions.-
4. Mapping Theorems.- 5. Dimension.- 6. Problems.-Index.