March 23, 2016 by Chapman and Hall/CRC
Reference - 270 Pages - 25 B/W Illustrations
ISBN 9781482219593
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
Focuses on the computational processes that can be applied to a specified linear model
Discusses two classical topics in the state-space literature: model estimation and signal extraction
Describes many procedures to combine, decompose, aggregate, and disaggregate a state-space form
Covers the connection between mainstream time series models and the state-space representation
Provides source code, a complete user manual, and other materials related to the authors’ MATLAB toolbox on a supplementary website
The state-space approach provides a formal framework where any result or procedure developed for a basic model can be seamlessly applied to a standard formulation written in state-space form. Moreover, it can accommodate with a reasonable effort nonstandard situations, such as observation errors, aggregation constraints, or missing in-sample values.
Exploring the advantages of this approach, State-Space Methods for Time Series Analysis: Theory, Applications and Software presents many computational procedures that can be applied to a previously specified linear model in state-space form.
After discussing the formulation of the state-space model, the book illustrates the flexibility of the state-space representation and covers the main state estimation algorithms: filtering and smoothing. It then shows how to compute the Gaussian likelihood for unknown coefficients in the state-space matrices of a given model before introducing subspace methods and their application. It also discusses signal extraction, describes two algorithms to obtain the VARMAX matrices corresponding to any linear state-space model, and addresses several issues relating to the aggregation and disaggregation of time series. The book concludes with a cross-sectional extension to the classical state-space formulation in order to accommodate longitudinal or panel data. Missing data is a common occurrence here, and the book explains imputation procedures necessary to treat missingness in both exogenous and endogenous variables.
July 15, 2016 Forthcoming by CRC Press
Reference - 350 Pages
ISBN 9781498768290
* Gives an elementary geometrical construction of smooth resolutions of classical Schubert schemes of Grassmannian and Flag varieties and their relation to the Flag complex.
* Discusses the building of a reductive group to provide a geometric description of smooth resolutions of closures for Bruhat cells.
* Demonstrates how main constructions in Grothendieck's SGAIII regarding reductive group schemes may be used in an ordinary mathematical context.
* Provides an example of resolution of singularities valid in any characteristic p.
The first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck's SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.
Grassmannians and Flag Varieties. Schubert Cell Decomposition of Grassmannians and Flag Varieties. Resolution of Singularities of a Schubert Variety. The Singular Locus of a Schubert Variety. The Flag Complex. Configurations and Galleries Varieties. Configurations Varieties as Galleries Varieties. The Coxeter Complex. Minimal Generalized Galleries in a Coxeter Complex. Minimal Generalized Galleries in a Reductive Group Building. Parabolic Subgroups in a Reductive Group Scheme. Associated Schemes to the Relative Building. Incidence Type Schemes of the Relative Building. Smooth Resolutions of Schubert Schemes. Contracted Products and Galleries Configurations Schemes. Functoriality of Schubert Schemes Smooth Resolutions and Base Changes. About the Coxeter Complex. Generators and Relations and the Building of a Reductive Group.
September 15, 2016 Forthcoming by Chapman and Hall/CRC
Reference - 350 Pages - 100 B/W Illustrations
ISBN 9781498729505
Provides a dictionary and explanations of the tools and methods for pairing-based cryptography
Demonstrates how to implement a protocol
Includes both software and hardware implementations
Serves as a one-stop shop for algorithms, given an electronic target
Covers the necessary mathematical background
Pairings are interesting tools for cryptographers, because they provide new protocols such as identity-based cryptography, plus they allow the simplification of existing protocols such as signature schemes. The implementation of a pairing involves several levels of arithmetic: the arithmetic of finite fields, extensions of finite fields, the arithmetic of elliptic curves, and several algorithmic problems. This book provides various pairings available for cryptographic use, as well as the necessary mathematical background about finite fields and elliptic curves.
Introduction. Mathematical Background. Pairings. Pairing-Friendly Elliptic Curves. Miller's Algorithm. Arithmetic of Finite Fields. Final Exponentiation. Algorithms. Software Implementation. Hardware Implementation.
May 31, 2016 Forthcoming by A K Peters/CRC Press
Reference - 114 Pages - 292 B/W Illustrations
ISBN 9781498765343
Contains 50 completely novel origami photos as well as their crease patterns designed by computer
Explains how to design the origami using many figures and step-by-step explanations
Includes five "Let’s make it!" corners that guide readers in making simple 3D origami art
Covers recent origami topics, including the author’s techniques based on geometric theories
Provides the origami patterns on the author’s website
Easily Create Origami with Curved Folds and Surfaces
Origami-making shapes only through folding?reveals a fascinating area of
geometry woven with a variety of representations. The world of origami
has progressed dramatically since the advent of computer programs to perform
the necessary computations for origami design.
3D Origami Art presents the design methods underlying 3D creations derived from computation. It includes numerous photos and design drawings called crease patterns, which are available for download on the author’s website. Through the book’s clear figures and descriptions, readers can easily create geometric 3D structures out of a set of lines and curves drawn on a 2D plane.
The author uses various shapes of sheets such as rectangles and regular polygons, instead of square paper, to create the origami. Many of the origami creations have a 3D structure composed of curved surfaces, and some of them have complicated forms. However, the background theory underlying all the creations is very simple. The author shows how different origami forms are designed from a common theory.
Axisymmetric 3D Origami
Four Basic Types
Basic Crease Patterns
Flat-Pleat Cone Type
Flat-Pleat Cylinder Type
3D-Pleat Cone Type
3D-Pleat Cylinder Type
"Twist Closing" for Closing a Solid
Solid with Curved Surfaces
Stabilizing a Shape
Extension of Axisymmetric 3D Origami
Connecting Two 3D Origami Shapes (Cylinder Type)
Connecting Different 3D Origami Shapes (Cylinder Type)
Connecting Different 3D Origami Shapes (Cone Type)
Changing Pleat Orientation (Flat-Pleat Type)
Resizing Pleats (Cylinder Type)
Connecting Axisymmetric 3D Origami Shapes
Connecting and Tiling 3D-Pleat Type on a Plane
Connecting Flat-Pleat Type
Connecting Different 3D Origami Shapes
Making Use of Duality
Layering Dual Patterns
Making Use of Mirror Inversion
Cone-Based 3D Origami
Mirror Inversion on a Developable Surface
Specifying Mirror Planes by a Polygonal Line
Relation between Sweep Locus and Shape
Various Shapes
Application of Mirror Inversion
Curved Fold Units Combined Together
Inversion by Oblique Mirror Plane
Voronoi Origami
Tiling with Different Polygons
Origami by Voronoi Tiling
Various Origami Designs
Conclusion
Origami Design Techniques
Rigid Origami
Curved Folds and Curved Origami
Computational Origami
Origami with Thick Materials
Robots and Origami
Relation between Living Things and Origami
Origami and Mathematics
Origami and Education
Application of Origami to Industry
Others
Index