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Structural Vector Autoregressive Analysis (Themes in Modern Econometrics)
by Lutz Kilian Helmut LütkepohlStructural vector autoregressive (VAR) models are important tools for empirical work in macroeconomics, finance, and related fields. This book not only reviews the many alternative structural VAR approaches discussed in the literature, but also highlights their pros and cons in practice. It provides guidance to empirical researchers as to the most appropriate modeling choices, methods of estimating, and evaluating structural VAR models. The book traces the evolution of the structural VAR methodology and contrasts it with other common methodologies, including dynamic stochastic general equilibrium (DSGE) models. It is intended as a bridge between the often quite technical econometric literature on structural VAR modeling and the needs of empirical researchers. The focus is not on providing the most rigorous theoretical arguments, but on enhancing the reader's understanding of the methods in question and their assumptions. Empirical examples are provided for illustration.
Structurally Unstable Quadratic Vector Fields of Codimension One
by Joan C. Artés Jaume Llibre Alex C. RezendeOriginating from research in the qualitative theory of ordinary differential equations, this book follows the authors’ work on structurally stable planar quadratic polynomial differential systems. In the present work the authors aim at finding all possible phase portraits in the Poincaré disc, modulo limit cycles, of planar quadratic polynomial differential systems manifesting the simplest level of structural instability. They prove that there are at most 211 and at least 204 of them.
Structure and Dynamics of Asymmetric Interactions
by Naohito ChinoThis book integrates the fundamentals of asymmetric multidimensional scaling, spectral graph theory, graph embedding theory, and various dynamical systems theories, that deal with the static and dynamic aspects of asymmetric phenomena. In this way, it provides a comprehensive introduction to theories and methods for analyzing phenomena observed universally in social, behavioral, economical, geographical, biological, neural, chemical reaction and other networks. The topics addressed in here include the notions of asymmetric similarity matrices, graph spectra, dimension reduction, and difference and differential equations to describe the dynamics of networks, bifurcation of vector fields, Mandelbrot sets, fractals and chaos, and Hilbert spaces. Illustrated by carefully chosen examples and supported by extensive simulation studies, the book is highly recommended to readers who seek to discover static asymmetric structures among members or nodes. It also appeals to those who want to understand the kinds of dynamics that are theoretically possible in their research domains.
Structure and Geometry of Lie Groups
by Joachim Hilgert Karl-Hermann NeebThis self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.
Structure and Properties of Clusters: from a few Atoms to Nanoparticles
by George MaroulisThis volume on Clusters brings together contributions from a large number of specialists. A central element for all contributions is the use of advanced computational methodologies and their application to various aspects of structure, reactivity and properties of clusters. The size of clusters varies from a few atoms to nanoparticles.
The Structure and Stability of Persistence Modules
by Frédéric Chazal Vin De Silva Marc Glisse Steve OudotThis book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations. Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.
Structure of Approximate Solutions of Optimal Control Problems
by Alexander J. ZaslavskiThis title examines the structure of approximate solutions of optimal control problems considered on subintervals of a real line. Specifically at the properties of approximate solutions which are independent of the length of the interval. The results illustrated in this book look into the so-called turnpike property of optimal control problems. The author generalizes the results of the turnpike property by considering a class of optimal control problems which is identified with the corresponding complete metric space of objective functions. This establishes the turnpike property for any element in a set that is in a countable intersection which is open everywhere dense sets in the space of integrands; meaning that the turnpike property holds for most optimal control problems. Mathematicians working in optimal control and the calculus of variations and graduate students will find this book useful and valuable due to its presentation of solutions to a number of difficult problems in optimal control and presentation of new approaches, techniques and methods.
The Structure of Complex Lie Groups (Chapman & Hall/CRC Research Notes in Mathematics Series)
by Dong Hoon LeeComplex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts
Structure of Medium Mass Nuclei: Deformed Shell Model and Spin-Isospin Interacting Boson Model
by V K Kota R SahuMedium heavy nuclei with mass number A=60-90 exhibit a variety of complex collective properties, provide a laboratory for double beta decay studies, and are a region of all heavy N=Z nuclei. This book discusses these three aspects of nuclear structure using Deformed Shell Model and the Spin-Isospin Invariant Interacting Boson Model naturally generated by fermionic SO(8) symmetry. Using these two models, the book describes properties of medium heavy nuclei with mass number A=60-90. It provides a good reference for future nuclear structure experiments using radioactive ion beam (RIB) facilities. Various results obtained by the authors and other research groups are also explained in this book.
Structure of Nucleon Excited States from Lattice QCD (Springer Theses)
by Finn M. StokesQuantum Chromodynamics (QCD) describes the interactions between elementary quarks and gluons as they compose the nucleons at the heart of atomic structure. The interactions give rise to complexity that can only be examined via numerical simulations on supercomputers. This work provides an introduction to the numerical simulations of lattice QCD and establishes new formalisms relevant to understanding the structure of nucleons and their excited states. The research opens with an examination of the non-trivial QCD vacuum and the emergence of “centre domains.” The focus then turns to establishing a novel Parity-Expanded Variational Analysis (PEVA) technique solving the important problem of isolating baryon states moving with finite momentum. This seminal work provides a foundation for future calculations of baryon properties. Implementation of the PEVA formalism discloses important systematic errors in conventional calculations and reveals the structure of nucleon excited states from the first principles of QCD for the first time.
Structure of Solutions of Variational Problems
by Alexander J. ZaslavskiStructure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line. Results on properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems in the calculus of variations are illustrated throughout this book. This book also contains significant results and information about the turnpike property of the variational problems. This well-known property is a general phenomenon which holds for large classes of variational problems. The author examines the following in relation to the turnpike property in individual (non-generic) turnpike results, sufficient and necessary conditions for the turnpike phenomenon as well as in the non-intersection property for extremals of variational problems. This book appeals to mathematicians working in optimal control and the calculus as well as with graduate students.
Structure-Preserving Algorithms for Oscillatory Differential Equations
by Bin Wang Xiong You Xinyuan WuStructure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations. The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph.D student of Nanjing University and University of Cambridge.
Structure-Preserving Algorithms for Oscillatory Differential Equations II
by Xinyuan Wu Kai Liu Wei ShiThis book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics and electronics. To accurately simulate the true behavior of such systems, a numerical algorithm must preserve as much as possible their key structural properties: time-reversibility, oscillation, symplecticity, and energy and momentum conservation. The book describes novel advances in RKN methods, ERKN methods, Filon-type asymptotic methods, AVF methods, and trigonometric Fourier collocation methods. The accuracy and efficiency of each of these algorithms are tested via careful numerical simulations, and their structure-preserving properties are rigorously established by theoretical analysis. The book also gives insights into the practical implementation of the methods. This book is intended for engineers and scientists investigating oscillatory systems, as well as for teachers and students who are interested in structure-preserving algorithms for differential equations.
Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics
by Peter BetschThis book focuses on structure-preserving numerical methodsfor flexible multibody dynamics, including nonlinear elastodynamics andgeometrically exact models for beams and shells. It also deals with the newlyemerging class of variational integrators as well as Lie-group integrators. Itdiscusses two alternative approaches to the discretization in space ofnonlinear beams and shells. Firstly, geometrically exact formulations, whichare typically used in the finite element community and, secondly, the absolutenodal coordinate formulation, which is popular in the multibody dynamicscommunity. Concerning the discretization in time, the energy-momentum methodand its energy-decaying variants are discussed. It also addresses a number ofissues that have arisen in the wake of the structure-preserving discretizationin space. Among them are the parameterization of finite rotations, theincorporation of algebraic constraints and the computer implementation of thevarious numerical methods. The practical application of structure-preservingmethods is illustrated by a number of examples dealing with, among others,nonlinear beams and shells, large deformation problems, long-term simulationsand coupled thermo-mechanical multibody systems. In addition it links novel timeintegration methods to frequently used methods in industrial multibody systemsimulation.
Structure Theory for Canonical Classes of Finite Groups
by Wenbin GuoThis book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described - e. g. , the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems.
Structured Biological Modelling: A New Approach to Biophysical Cell Biology
by Michael Kraus Bernhard WolfStructured Biological Modelling presents a straightforward introduction for computer-aided analysis, mathematical modelling, and simulation of cell biological systems. This unique guide brings together the physiological, structural, molecular biological, and theoretical aspects of the signal transduction network that regulates growth and proliferation in normal and tumor cells. It provides comprehensive survey of functional and theoretical features of intracellular signal processing and introduces the concept of cellular self-organization. Exemplified by oscillatory calcium waves, strategies for the design of computer experiments are presented that can assist or even substitute for time-consuming biological experiments. The presented minimal model for proliferation-associated signal transduction clearly shows the alterations of the cellular signal network involved in neoplastic growth. This book will be useful to cell and molecular biologists, oncologists, physiologists, theoretical biologists, computer scientists, and all other researchers and students studying functional aspects of cellular signaling.
Structured Controllers for Uncertain Systems
by Rosario ToscanoStructured Controllers for Uncertain Systems focuses on the development of easy-to-use design strategies for robust low-order or fixed-structure controllers (particularly the industrially ubiquitous PID controller). These strategies are based on a recently-developed stochastic optimization method termed the "Heuristic Kalman Algorithm" (HKA) the use of which results in a simplified methodology that enables the solution of the structured control problem without a profusion of user-defined parameters. An overview of the main stochastic methods employable in the context of continuous non-convex optimization problems is also provided and various optimization criteria for the design of a structured controller are considered; H , H2, and mixed H2/H each merits a chapter to itself. Time-domain-performance specifications can be easily incorporated in the design.
Structured Credit Portfolio Analysis, Baskets and CDOs (Chapman and Hall/CRC Financial Mathematics Series)
by Christian Bluhm Ludger OverbeckThe financial industry is swamped by credit products whose economic performance is linked to the performance of some underlying portfolio of credit-risky instruments, like loans, bonds, swaps, or asset-backed securities. Financial institutions continuously use these products for tailor-made long and short positions in credit risks. Based on a stead
Structured Decision Making: A Practical Guide to Environmental Management Choices
by Robin Gregory Lee Failing Michael Harstone Graham Long Tim McDaniels Dan OhlsonThis book outlines the creative process of making environmental management decisions using the approach called Structured Decision Making. It is a short introductory guide to this popular form of decision making and is aimed at environmental managers and scientists. This is a distinctly pragmatic label given to ways for helping individuals and groups think through tough multidimensional choices characterized by uncertain science, diverse stakeholders, and difficult tradeoffs. This is the everyday reality of environmental management, yet many important decisions currently are made on an ad hoc basis that lacks a solid value-based foundation, ignores key information, and results in selection of an inferior alternative. Making progress – in a way that is rigorous, inclusive, defensible and transparent – requires combining analytical methods drawn from the decision sciences and applied ecology with deliberative insights from cognitive psychology, facilitation and negotiation. The authors review key methods and discuss case-study examples based in their experiences in communities, boardrooms, and stakeholder meetings. The goal of this book is to lay out a compelling guide that will change how you think about making environmental decisions. Visit www.wiley.com/go/gregory/sdm to access the figures and tables from the book.
Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications (Springer INdAM Series #30)
by Dario Andrea Bini Fabio Di Benedetto Eugene Tyrtyshnikov Marc Van BarelThis book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.
Structured Object-Oriented Formal Language and Method: 10th International Workshop, SOFL+MSVL 2020, Singapore, March 1, 2021, Revised Selected Papers (Lecture Notes in Computer Science #12723)
by Jinyun Xue Fumiko Nagoya Shaoying Liu Zhenhua DuanThis book constitutes the refereed workshop proceedings of the 10th International Workshop on Structured Object-Oriented Formal Language and Method, SOFL+MSVL 2020, held in Singapore, in March 2021. The 13 revised full papers included in the volume were carefully reviewed and selected from 24 submissions. They are organized in the following topical sections: modeling and specification; model checking; specification and verification; and testing and formal verification.Due to the Corona pandemic this event was held virtually.
Structured Stochastic Matrices of M/G/1 Type and Their Applications
by Marcel F. NeutsThis book deals with Markov chains and Markov renewal processes (M/G/1 type). It discusses numerical difficulties which are apparently inherent in the classical analysis of a variety of stochastic models by methods of complex analysis.
Structures and Algorithms: Mathematics And The Nature Of Knowledge (Logic, Argumentation And Reasoning Ser. #15)
by Jens Erik FenstadThis book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy (or methodology) of science, which employ a syntactic approach, the author’s approach is model theoretic or structural. Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and algorithms is mathematics. But viewing “mathematics” as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what “mathematics” should actually mean. Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2–6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind. Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author’s analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book’s closing chapter. The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society.
Structures and Dynamics of Interfacial Water: Input from Theoretical Vibrational Sum-frequency Spectroscopy (Springer Theses)
by Fujie TangThis book focuses on the study of the interfacial water using molecular dynamics simulation and experimental sum frequency generation spectroscopy. It proposes a new definition of the free O-H groups at water-air interface and presents research on the structure and dynamics of these groups. Furthermore, it discusses the exponential decay nature of the orientation distribution of the free O-H groups of interfacial water and ascribes the origin of the down pointing free O-H groups to the presence of capillary waves on the surface. It also describes how, based on this new definition, a maximum surface H-bond density of around 200 K at ice surface was found, as the maximum results from two competing effects. Lastly, the book discusses the absorption of water molecules at the water–TiO2 interface. Providing insights into the combination of molecular dynamics simulation and experimental sum frequency generation spectroscopy, it is a valuable resource for researchers in the field.
Structures Mères: Semantics, Mathematics, and Cognitive Science (Studies in Applied Philosophy, Epistemology and Rational Ethics #57)
by Alberto Peruzzi Silvano Zipoli CaianiThis book reports on cutting-edge concepts related to Bourbaki’s notion of structures mères. It merges perspectives from logic, philosophy, linguistics and cognitive science, suggesting how they can be combined with Bourbaki’s mathematical structuralism in order to solve foundational, ontological and epistemological problems using a novel category-theoretic approach. By offering a comprehensive account of Bourbaki’s structuralism and answers to several important questions that have arisen in connection with it, the book provides readers with a unique source of information and inspiration for future research on this topic.