This contributed volume explores the achievements gained and the remaining puzzling questions by applying dynamical systems theory to the linguistic inquiry. In particular, the book is divided into three parts, each one addressing one of the following topics: 1) Facing complexity in the right way: mathematics and complexity 2) Complexity and theory of language 3) From empirical observation to formal models: investigation of specific linguistic phenomena, like enunciation, deixis, or the meaning of the metaphorical phrases The application of complexity theory to describe cognitive phenomena is a recent and very promising trend in cognitive science. At the time when dynamical approaches triggered a paradigm shift in cognitive science some decade ago, the major topic of research were the challenges imposed by classical computational approaches dealing with the explanation of cognitive phenomena like consciousness, decision making and language. The target audience primarily comprises researchers and experts in the field but the book may also be beneficial for graduate and post-graduate students who want to enter the field.

Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones. This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlab (R) illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study.

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sproessig's work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sproessig throughout his career.

This book introduces the basic fundamentals, models, emulators and analyses of mem-elements in the circuit theory with applications. The book starts reviewing the literature on mem-elements, models and their recent applications. It presents mathematical models, numerical results, circuit simulations, and experimental results for double-loop hysteresis behavior of mem-elements. The authors introduce a generalized memristor model in the fractional-order domain under different input and different designs for emulator-based mem-elements, with circuit and experimental results. The basic concept of memristive-based relaxation-oscillators in the circuit theory is also covered. The reader will moreover find in this book information on memristor-based multi-level digital circuits, memristor-based multi-level multiplier and memcapacitor-based oscillators and synaptic circuits.

This new edition of a well-received textbook provides a concise introduction to both the theoretical and experimental aspects of quantum information at the graduate level. While the previous edition focused on theory, the book now incorporates discussions of experimental platforms. Several chapters on experimental implementations of quantum information protocols have been added: implementations using neutral atoms, trapped ions, optics, and solidstate systems are each presented in its own chapter. Previous chapters on entanglement, quantum measurements, quantum dynamics, quantum cryptography, and quantum algorithms have been thoroughly updated, and new additions include chapters on the stabilizer formalism and the Gottesman-Knill theorem as well as aspects of classical and quantum information theory. To facilitate learning, each chapter starts with a clear motivation to the topic and closes with exercises and a recommended reading list. Quantum Information Processing: Theory and Implementation will be essential to graduate students studying quantum information as well as and researchers in other areas of physics who wish to gain knowledge in the field.

In 1983 O.J. Boxma and the author have published a research monograph on Boundary Value Problems in Queueing System Analysis. The continuation of that research is described in the present monograph. The technique developed in the 1983-monograph has appeared to be quite powerful in the construction of explicit expressions for the generating functions and/or Laplace-Stieltjes transforms of characteristic distributions needed in the performance evaluation of stoachistic models stemming from computer system and telecommunication engineering. The book covers the following topics: One- Dimensional Random Walks; Two-Dimensional Random Walks; the Two-Dimensional Workload Process; and the N-Dimensional Random Walk.

Given a conservative dynamical system of classical physics, how does one find a variational principle for it? Is there a canonical recipe for such a principle? The case of particle mechanics was settled by Lagrange in 1788; this text treats continuous systems. Recipes devised are algebraic in nature, and this book develops all the mathematical tools found necessary after the minute examination of the adiabatic fluid dynamics in the introduction. These tools include: Lagrangian and Hamiltonian formalisms, Legendre transforms, dual spaces of Lie algebras and associated 2-cocycles; and linearized and Z2-graded versions of all of these. The following typical physical systems, together with their Hamiltonian structures, are discussed: Classical Magnetohydro-dynamics with its Hall deformation; Multifluid Plasma; Superfluid He-4 (both irrotational and rotating) and 3He-A; Quantum fluids; Yang-Mills MHD; Spinning fluids; Spin Glass; Extended YM Plasma; A Lattice Gas. Detailed motivations, easy-to-follow arguments, open problems, and over 300 exercises help the reader.

The book includes articles from eminent international scientists discussing a wide spectrum of topics of current importance in mathematics and statistics and their applications. It presents state-of-the-art material along with a clear and detailed review of the relevant topics and issues concerned. The topics discussed include message transmission, colouring problem, control of stochastic structures and information dynamics, image denoising, life testing and reliability, survival and frailty models, analysis of drought periods, prediction of genomic profiles, competing risks, environmental applications and chronic disease control. It is a valuable resource for researchers and practitioners in the relevant areas of mathematics and statistics.

The energy momentum tensor (EMT) is one of the most fundamental observables in physics. Recently, a novel method to define EMT on the basis of the gradient-flow formalism has been proposed. It turned out that the EMT operator can be constructed even on the lattice with the method, which enables non-perturbative computations. This approach has been successfully applied to the analyses on thermodynamic quantities. This book presents the study on spatial EMT distributions around static charges via the gradient flow in lattice simulations based on SU(3) Yang-Mills theory. Static charges are employed as probes to explore complex quantum systems, and EMT then characterizes the response of vacuum as well as hot medium under the existence of the charges, which significantly provides profound and novel insights into the non-perturbative phenomena, such as the confinement of quarks. In addition, the book treats the study on the EMT distribution around a magnetic vortex in the Abelian-Higgs model, which is compared with the lattice result. These achievements open up various future studies for revealing non-trivial aspects of the strong interaction. The book also includes well-organized reviews on general properties of EMT, lattice gauge theory and the gradient-flow formalism with its application to the definition of EMT. They are useful for students and young researchers as a brief introduction to this field.

This proceedings volume features top contributions in modern statistical methods from Statistics 2021 Canada, the 6th Annual Canadian Conference in Applied Statistics, held virtually on July 15-18, 2021. Papers are contributed from established and emerging scholars, covering cutting-edge and contemporary innovative techniques in statistics and data science. Major areas of contribution include Bayesian statistics; computational statistics; data science; semi-parametric regression; and stochastic methods in biology, crop science, ecology and engineering. It will be a valuable edited collection for graduate students, researchers, and practitioners in a wide array of applied statistical and data science methods.

This thesis presents the first isotope-shift measurement of bound-electron g-factors of highly charged ions and determines the most precise value of the electron mass in atomic mass units, which exceeds the value in the literature by a factor of 13. As the lightest fundamental massive particle, the electron is one of nature's few central building blocks. A precise knowledge of its intrinsic properties, such as its mass, is mandatory for the most accurate tests in physics - the Quantum Electrodynamics tests that describe one of the four established fundamental interactions in the universe. The underlying measurement principle combines a high-precision measurement of the Larmor-to-cyclotron frequency ratio on a single hydrogen-like carbon ion studied in a Penning trap with very accurate calculations of the so-called bound-electron g-factor. For the isotope-shift measurement, the bound-electron g-factors of two lithium-like calcium isotopes have been measured with relative uncertainties of a few 10^{-10}, constituting an as yet unrivaled level of precision for lithium-like ions.

This book offers a theoretical description of topological matter in terms of effective field theories, and in particular topological field theories, focusing on two main topics: topological superconductors and topological insulators.Even though there is vast literature on these subjects, the book fills an important gap by providing a concise introduction to both topological order and symmetry-protected phases using a modern mathematical language, and developing the theoretical concepts by highlighting the physics and the physical properties of the systems. Further, it discusses in detail the topological interactions for topologically ordered matter, and the response to smooth external fields for symmetry protected matter. The book also covers more specialized topics that cannot be found elsewhere. Specifically, the response of superconductors to geometry, including the newly discovered geo-Meissner effect; and a correction to the usual Meissner effect, only present in the topologically interesting chiral superconductors.

This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

It is not intuitive to accept that there exists a link between quantum physical systems and cognitive systems. However, recent research has shown that cognitive systems and collective (social) systems, including biology, exhibit uncertainty which can be successfully modelled with quantum probability. The use of such probability allows for the modelling of situations which typically violate the laws of classical probability. The Palgrave Handbook of Quantum Models in Social Science is is a unique volume that brings together contributions from leading experts on key topics in this new and emerging field. Completely self-contained, it begins with an introductory section which gathers all the fundamental notions required to be able to understand later chapters. The handbook then moves on to address some of the latest research and applications for quantum methods in social science disciplines, including economics, politics and psychology. It begins with the issue of how the quantum mechanical framework can be applied to economics. Chapters devoted to this topic range from how Fisher information can be argued to play a role in economics, to the foundations and application of quantum game theory. The handbook then progresses in considering how belief states can be updated with the theory of quantum measurements (and also with more general methods). The practical use of the Hilbert space (and Fock space) in decision theory is then introduced, and open quantum systems are also considered. The handbook also treats a model of neural oscillators that reproduces some of the features of quantum cognition. Other contributions delve into causal reasoning using quantum Bayes nets and the role of quantum probability in modelling so called affective evaluation. The handbook is rounded off with two chapters which discuss the grand challenges which lie ahead of us. How can the quantum formalism be justified in social science and is the traditional quantum formalism too restrictive? Finally, a question is posed: whether there is a necessary role for quantum mathematical models to go beyond physics. This book will bring the latest and most cutting edge research on quantum theory to social science disciplines. Students and researchers across the discipline, as well as those in the fields of physics and mathematics will welcome this important addition to the literature.

This book examines discrete dynamical systems with memory-nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.

This book presents up-to-date research developments and novel methodologies to solve various stability and control problems of dynamic systems with time delays. First, it provides the new introduction of integral and summation inequalities for stability analysis of nominal time-delay systems in continuous and discrete time domain, and presents corresponding stability conditions for the nominal system and an applicable nonlinear system. Next, it investigates several control problems for dynamic systems with delays including H(infinity) control problem Event-triggered control problems; Dynamic output feedback control problems; Reliable sampled-data control problems. Finally, some application topics covering filtering, state estimation, and synchronization are considered. The book will be a valuable resource and guide for graduate students, scientists, and engineers in the system sciences and control communities.

This thesis describes the stand-alone discovery and measurement of the Higgs boson in its decays to two W bosons using the Run-I ATLAS dataset. This is the most precise measurement of gluon-fusion Higgs boson production and is among the most significant results attained at the LHC. The thesis provides an exceptionally clear exposition on a complicated analysis performed by a large team of researchers. Aspects of the analysis performed by the author are explained in detail; these include new methods for evaluating uncertainties on the jet binning used in the analysis and for estimating the background due to associated production of a W boson and an off-shell photon. The thesis also describes a measurement of the WW cross section, an essential background to Higgs boson production. The primary motivation of the LHC was to prove or disprove the existence of the Higgs boson. In 2012, CERN announced this discovery and the resultant ATLAS publication contained three decay channels: gg, ZZ, and WW.

Clifford algebras are assuming now an increasing role in theoretical physics. Some of them predominantly larger ones are used in elementary particle theory, especially for a unification of the fundamental interactions. The smaller ones are promoted in more classical domains. This book is intended to demonstrate usefulness of Clifford algebras in classical electrodynamics. Written with a pedagogical aim, it begins with an introductory chapter devoted to multivectors and Clifford algebra for the three-dimensional space. In a later chapter modifications are presented necessary for higher dimension and for the pseudoeuclidean metric of the Minkowski space.Among other advantages one is worth mentioning: Due to a bivectorial description of the magnetic field a notion of force surfaces naturally emerges, which reveals an intimate link between the magnetic field and the electric currents as its sources. Because of the elementary level of presentation, this book can be treated as an introductory course to electromagnetic theory. Numerous illustrations are helpful in visualizing the exposition. Furthermore, each chapter ends with a list of problems which amplify or further illustrate the fundamental arguments.

This monograph deals with the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations that describe their evolution in time under varying loads. A work in four parts, the first is an introduction to continuum mechanics, including classical fluid mechanics, linear and non-linear elasticity. The second part considers continuum thermodynamics and its use to derive constitutive equations of materials with memory, including viscoelastic solids, fluids, heat conductors and some examples of non-simple materials. In the third part, free energies for materials with linear memory constitutive relations are discussed. The concept of a minimal state is introduced. Explicit formulae are presented for the minimum and related free energies. The final part deals with existence, uniqueness, and stability results for the integrodifferential equations describing the dynamical evolution of viscoelastic materials, including a new approach based on minimal states rather than histories. There are also chapters on the controllability of thermoelastic systems with memory, the Saint-Venant problem for viscoelastic materials and on the theory of inverse problems. The second edition includes a new chapter on thermoelectromagnetism as well as recent findings on minimal states and free energies. It considers the case of minimum free energies for non-simple materials and dielectrics, together with an introduction to fractional derivative models.

By focusing on the mostly used variational methods, this monograph aspires to give a unified description and comparison of various ways of constructing conserved quantities for perturbations and to study symmetries in general relativity and modified theories of gravity. The main emphasis lies on the field-theoretical covariant formulation of perturbations, the canonical Noether approach and the Belinfante procedure of symmetrisation. The general formalism is applied to build the gauge-invariant cosmological perturbation theory, conserved currents and superpotentials to describe physically important solutions of gravity theories. Meticulous attention is given to the construction of conserved quantities in asymptotically-flat spacetimes as well as in asymptotically constant curvature spacetimes such as the Anti-de Sitter space. Significant part of the book can be used in graduate courses on conservation laws in general relativity. THE SERIES: DE GRUYTER STUDIES IN MATHEMATICAL PHYSICS The series is devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply, and develop further, with sufficient rigor, mathematical methods to given problems in physics. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.

This edited volume presents examples of social science research projects that employ new methods of quantitative analysis and mathematical modeling of social processes. This book presents the fascinating areas of empirical and theoretical investigations that use formal mathematics in a way that is accessible for individuals lacking extensive expertise but still desiring to expand their scope of research methodology and add to their data analysis toolbox. Mathematical Modeling of Social Relationships professes how mathematical modeling can help us understand the fundamental, compelling, and yet sometimes complicated concepts that arise in the social sciences. This volume will appeal to upper-level students and researchers in a broad area of fields within the social sciences, as well as the disciplines of social psychology, complex systems, and applied mathematics.

This thesis develops a nested sampling algorithm into a black box tool for directly calculating the partition function, and thus the complete phase diagram of a material, from the interatomic potential energy function. It represents a significant step forward in our ability to accurately describe the finite temperature properties of materials. In principle, the macroscopic phases of matter are related to the microscopic interactions of atoms by statistical mechanics and the partition function. In practice, direct calculation of the partition function has proved infeasible for realistic models of atomic interactions, even with modern atomistic simulation methods. The thesis also shows how the output of nested sampling calculations can be processed to calculate the complete PVT (pressure-volume-temperature) equation of state for a material, and applies the nested sampling algorithm to calculate the pressure-temperature phase diagrams of aluminium and a model binary alloy.

This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain. The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis and design method. Based on the parametric characteristic approach, nonlinear influence in the frequency domain can be investigated with a novel insight, i.e., alternating series, which is followed by some application results in vibration control. Magnitude bounds of frequency response functions of nonlinear systems can also be studied with a parametric characteristic approach, which result in novel parametric convergence criteria for any given parametric nonlinear model whose input-output relationship allows a convergent Volterra series expansion. This book targets those readers who are working in the areas related to nonlinear analysis and design, nonlinear signal processing, nonlinear system identification, nonlinear vibration control, and so on. It particularly serves as a good reference for those who are studying frequency domain methods for nonlinear systems.

This book presents a range of fundamentally new approaches to solving problems involving traditional molecular models. Fundamental molecular symmetry is shown to open new avenues for describing molecular dynamics beyond standard perturbation techniques. Traditional concepts used to describe molecular dynamics are based on a few fundamental assumptions, the ball-and-stick picture of molecular structure and the respective perturbative treatment of different kinds of couplings between otherwise separate motions. The book points out the conceptual limits of these models and, by focusing on the most essential idea of theoretical physics, namely symmetry, shows how to overcome those limits by introducing fundamentally new concepts. The book begins with an introduction to molecular symmetry in general, followed by a discussion of nuclear spin symmetry. Here, a new correlation between identical particle exchange and spin angular momentum symmetry of nuclei is exhibited. The central part of the book is the discussion of extremely floppy molecules, which are not describable in the framework of traditional theories. The book introduces a fundamentally new approach to describing the molecular dynamics of these molecules - the super-rotor model, which is based on a five-dimensional symmetry that has never been observed in molecules before. By applying the super-rotor theory to the prototype of floppy molecules, protonated methane, this model can consistently predict the symmetry and energy of low-energy states, which were characterized experimentally only a few years ago. The theoretical predictions agree with the experimental results, which makes the prospect of further developing the super-rotor theory and applying it to other molecules a promising one. In the final section, the book also covers the topic of ultrafast rotations, where usual quantum calculations reach their natural limits. A semi-classical method for determining rotational energies, developed in the early 1990s, is shown to be attachable to quantum calculations of the vibrational states. This new combined method is suitable for efficiently calculating ro-vibrational energies, even for molecular states with large angular momentum.