ISBN: 978-1-119-71668-6 May 2021 384 Pages
Hardcover
To date, much of the application of IRT has been in the field of educational measurement, where for example, IRT has been used extensively by the Educational Testing Service for the development of scholastic aptitude tests. IRT has played a major role in all major college and graduate school admission tests (SAT, ACT, GRE, GMAT, MCAT, …). Unlike traditional tests based on classical test theory that summarizes the test result by a simple counting operation of number of correct responses, IRT provides model-based measurements in which the difficulty of the items, discrimination of high and low levels of the underlying latent variable(s) and the corresponding ability of the respondents can be estimated. In IRT scoring of tests, a certain number of items can be arbitrarily added, deleted, or replaced without losing comparability of scores on the scale. Only the precision of measurement at some points on the scale is affected. This property of scaled measurement, as opposed to counts of events, is the most salient advantage of IRT over classical methods of educational and psychological measurement. The evolution of IRT is now going beyond educational measurement. Recent advances in multidimensional extensions of IRT and computerized adaptive testing are leading to major advances in patient reported outcome measures of physical and emotional well being. In mental health research, IRT is now leading to a major paradigm shift in the screening and measurement of mental health disorders, substance abuse and suicidality, one of the leading causes of death in the world. Multidimensional IRT extends the tools used to evaluate essentially unidimensional constructs such as mathematical ability to the measurement of complex traits such as depression, anxiety and psychosis. In the next five years we expect that the use of multidimensional IRT for the measurement of complex traits will extend to other areas of health sciences and to problems in marketing research and practice where rapid adaptive tests administered through the internet will be able to precisiely measure consumer affinity for different products, events, and market sectors. The methods described in this book will provide the foundation for these future developments.
ISBN: 978-1-119-58242-7 May 2021 656 Pages
Hardcover
A rich examination of the technologies supporting?secure?digital information transfers from a respected leader in the field
As technology continues to advance, Cryptography, Information Theory, and Error-Correction: A Handbook for the Twenty-First Century is an indispensable resource for anyone interested in the secure exchange of financial information. Identity theft, cybercrime, and other security issues have taken center stage as information becomes easier to access. Three disciplines offer solutions to these digital challenges: cryptography, information theory, and error-correction, all of which are addressed in this book.
This book is geared toward a broad audience of professionals working at financial institutions, law firms and governments who need updated information to make critical decisions. The book s discussions will also be of?interest to those involved?in blockchains as well as those working in companies developing and applying security for new products, like self-driving cars.The second edition is also an authoritative overview for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, and entrepreneurs.
It is an excellent reference for both graduate and undergraduate students of mathematics, computer science, cybersecurity, and engineering. Six new chapters?cover?current?topics like Internet of Things security,?new identities in information theory, blockchains,?cryptocurrency, compression, and cloud computing and storage. Increased security and applicable research in elliptic curve cryptography are also featured. The book also:
Shares vital, new research in the field of information theory
Provides quantum cryptography updates?
Includes over 350 worked examples and problems for greater understanding of ideas.
Cryptography, Information Theory, and Error-Correction guides readers in their understanding of reliable tools that can be used to store or transmit digital information safely.
ISBN: 978-1-119-38784-8
July 2021 300 Pages
This book presents a unified approach to modelling functional data when spatial and spatio-temporal correlations are present. The editors link together for the first time the wide research areas of geostatistics and functional data analysis to provide the reader with a new area called geostatistical functional data analysis that will bring new insights and new open questions to researchers coming from both scientific fields.
Leading experts in the field, the Editors have put together a collection of chapters covering state-of-the-art methods in this area. The individual chapters combine formal statements of the results including mathematical proofs with informal and naive statements of classical and new results.This book serves the scientific community to know what has been done so far, and to know what type of open questions need of future answers.
After an introduction and brief overview, the book includes the following:
A detailed exposition of the spatial kriging methodology when dealing with functions.
A detailed exposition of more classical statistical techniques already adapted to the functional case and now extended in the right way to handle spatial correlations. Learning ANOVA, regression, clustering methods is crucial for a correct use of the statistical methods when the spatial correlation is present among a collection of curves sampled in a region.
A thorough guide to understanding similarities and differences between spatio-temporal data analysis and functional data analysis. The reader will be guided in terms of modelling and computational issues.
The information here allows the reader not only to fully understand kriging methods, but to use the most innovative functional methods adapted to spatially correlated functions, to deal with spatio-temporal datasets from a functional perspective, and to being able to handle massive databases from a more computational perspective. This book provides a complete an up-to-date account to deal with functional data that is spatially correlated, but also includes the most innovative developments in different open avenues in this field.
Hardback
Published: 09 March 2021
480 Pages | 8
234x153mm
ISBN: 9780198868781
Paperback
ISBN: 9780198868798
Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces.
Fundamentals of Mathematical Analysis is an extensive study of metric spaces,
including the core topics of completeness, compactness and function spaces,
with a good number of applications. The later chapters consist of an introduction
to general topology, a classical treatment of Banach and Hilbert spaces,
the elements of operator theory, and a deep account of measure and integration
theories. Several courses can be based on the book. This book is suitable
for a two-semester course on analysis, and material can be chosen to design
one-semester courses on topology or real analysis. It is designed as an
accessible classical introduction to the subject and aims to achieve excellent
breadth and depth and contains an abundance of examples and exercises.
The topics are carefully sequenced, the proofs are detailed, and the writing
style is clear and concise. The only prerequisites assumed are a thorough
understanding of undergraduate real analysis and linear algebra, and a
degree of mathematical maturity
1:Preliminaries
2:Set Theory
3:Vector Spaces
4:The Metric Topology
5:Essentials of General Topology
6:Banach Spaces
7:Hilbert Spaces
8:Integration Theory
Multi disciplinary approach - helps the combinatorist tackle theoretical physics issues and vice versa.
This book helps the combinatorists learn how combinatorial techniques can be used to tackle theoretical physics issues.
Variety of topics, including algebraic, analytical combinatorics, non-commutative quantum field theory, tensor models, quantum gravity.
Aims to help the theoretical physicists learn how theoretical physics techniques can be used to tackle combinatorial problems
Hardback
Published: 16 April 2021
416 Pages | Graphs and line drawings
246x171mm
ISBN: 9780192895493
Users, especially instructors adopting this book, will find its reach wide and deep enough for a number of courses
The sequencing is largely linear but logical. Users do not have to look for supplemental material elsewhere
The proofs are detailed although the writing style is concise. Contains an abundance of examples and exercises
The interplay between combinatorics and theoretical physics is a recent trend which appears to us as particularly natural, since the unfolding of new ideas in physics is often tied to the development of combinatorial methods, and, conversely, problems in combinatorics have been successfully tackled using methods inspired by theoretical physics. We can thus speak nowadays of an emerging domain of Combinatorial Physics.
The interference between these two disciplines is moreover an interference of multiple facets. Its best known manifestation (both to combinatorialists and theoretical physicists) has so far been the one between combinatorics and statistical physics, as statistical physics relies on an accurate counting of the various states or configurations of a physical system.
But combinatorics and theoretical physics interact in various other ways. This book is mainly dedicated to the interactions of combinatorics (algebraic, enumerative, analytic) with (commutative and non-commutative) quantum field theory and tensor models, the latter being seen as a quantum field theoretical generalisation of matrix models.
1:Introduction
2:Graphs, maps and polynomials
3:Quantum field theory (QFT)
4:Tree weights and renormalization in QFT
5:Combinatorial QFT and the Jacobian Conjecture
6:Fermionic QFT, Grassmann calculus and combinatorics
7:Analytic combinatorics and QFT
8:Algebraic combinatorics and QFT
9:QFT on the non-commutative Moyal space and combinatorics
10:Quantum gravity, Group Field Theory and combinatorics
11:From random matrices to random tensors
12:Random tensor models - the U(N)D-invariant model
13:Random tensor models - the multi-orientable (MO) model
14:Random tensor models - the O(N)3 invariant model
15:The Sachdev-Ye-Kitaev holographic model
16:SYK-like tensor models
Appendix
A:Examples of tree weights
B:Renormalization of the Grosse-Wulkenhaar model, one-loop examples
C:The B+ operator in Moyal QFT, two-loop examples
D:Explicit examples of GFT tensor Feynman integral computations
E:Coherent states of SU(2)
F:Proof of the double scaling limit of the U(N)D??invariant tensor model
G:Proof of Theorem 15.3.2
H:Proof of Theorem 16.1.1
J:Summary of results on the diagrammatics of the coloured SYK model and of the Gurau-Witten model
Bibliography