This book presents a detailed study of the Lanczos potential in general relativity by using tetrad formalisms. It demonstrates that these formalisms offer some simplifications over the tensorial methods, and investigates a general approach to finding the Lanczos potential for algebraic space-time by translating all the tensorial relations concerning the Lanczos potential into the language of tetrad formalisms and using the Newman-Penrose and Geroch-Held-Penrose formalisms. In addition, the book obtains the Lanczos potential for perfect fluid space-time, and applies the results to cosmological models of the universe. In closing, it highlights other methods, apart from tetrad formalisms, for finding the Lanczos potential, as well as further applications of the Newman-Penrose formalism. Given its scope, the book will be of interest to pure mathematicians, theoretical physicists and cosmologists, and will provide common ground for communication among these scientific communities.

This book offers a detailed description of the histogram probabilistic multi-hypothesis tracker (H-PMHT), providing an accessible and intuitive introduction to the mathematical mechanics of H-PMHT as well as a definitive reference source for the existing literature on the method. Beginning with basic concepts, the authors then move on to address extensions of the method to a broad class of tracking problems. The latter chapters present applications using recorded data from experimental radar, sonar and video sensor systems. The book is supplemented with software that both furthers readers' understanding and acts as a toolkit for those who wish to apply the methods to their own problems.

While typically many approaches have been mainly mathematics focused, graph theory has become a tool used by scientists, researchers, and engineers in using modeling techniques to solve real-world problems. Graph Theory for Operations Research and Management: Applications in Industrial Engineering presents traditional and contemporary applications of graph theory in the areas of industrial engineering, management science, and applied operations research. This comprehensive collection of research introduces the useful basic concepts of graph theory in real world applications.

This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.

This book features a selection of articles based on the XXXV Bialowieza Workshop on Geometric Methods in Physics, 2016. The series of Bialowieza workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Bialowieza Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

The book offers a novel approach to the study of the complex dynamics of cities. It is based on (1) Synergetics as a science of cooperation and selforganization, (2) information theory including semantic and pragmatic aspects, and optimization principles, (3) a theory of steady state maintenance, and of (4) phase transition, i.e. qualitative changes of structure or behavior. From this novel theoretical vantage point, the book addresses particularly three issues that stand at the core of current discourse on cities: Urban Scaling, Smart Cities and City Planning. An important consequence of "the 21st century as the age of cities", is that the study of cities currently attracts scientists from a variety of disciplines, ranging from physics, mathematics and computer science, through urban studies, architecture, planning and human geography, to economics, psychology, sociology, public administration and more. The book is thus likely to attract scholars, researchers and students of these research domains, of complexity theories of cities, as well as of general complexity theory. In addition, it is directed also to practitioners of urbanism, city planning and urban design.

This book expands on the subject matter of 'Computational Electromagnetics and Model-Based Inversion: A Modern Paradigm for Eddy-Current Nondestructive Evaluation.' It includes (a) voxel-based inversion methods, which are generalizations of model-based algorithms; (b) a complete electromagnetic model of advanced composites (and other novel exotic materials), stressing the highly anisotropic nature of these materials, as well as giving a number of applications to nondestructive evaluation; and (c) an up-to-date discussion of stochastic integral equations and propagation-of-uncertainty models in nondestructive evaluation. As such, the book combines research started twenty-five years ago in advanced composites and voxel-based algorithms, but published in scattered journal articles, as well as recent research in stochastic integral equations. All of these areas are of considerable interest to the aerospace, nuclear power, civil infrastructure, materials characterization and biomedical industries. The book covers the topic of computational electromagnetics in eddy-current nondestructive evaluation (NDE) by emphasizing three distinct topics: (a) fundamental mathematical principles of volume-integral equations as a subset of computational electromagnetics, (b) mathematical algorithms applied to signal-processing and inverse scattering problems, and (c) applications of these two topics to problems in which real and model data are used. It is therefore more than an academic exercise and is valuable to users of eddy-current NDE technology in industries as varied as nuclear power, aerospace, materials characterization and biomedical imaging.

This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems.

Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

This textbook provides an introduction to the growing interdisciplinary field of computational science. It combines a foundational development of numerical methods with a variety of illustrative applications spread across numerous areas of science and engineering. The intended audience is the undergraduate who has completed introductory coursework in mathematics and computer science. Students gain computational acuity by authoring their own numerical routines and by practicing with numerical methods as they solve computational models. This education encourages students to learn the importance of answering: How expensive is a calculation, how trustworthy is a calculation, and how might we model a problem to apply a desired numerical method? The text is written in two parts. Part I provides a succinct, one-term inauguration into the primary routines on which a further study of computational science rests. The material is organized so that the transition to computational science from coursework in calculus, differential equations, and linear algebra is natural. Beyond the mathematical and computational content of Part I, students gain proficiency with elemental programming constructs and visualization, which are presented in MATLAB syntax. The focus of Part II is modeling, wherein students build computational models, compute solutions, and report their findings. The models purposely intersect numerous areas of science and engineering to demonstrate the pervasive role played by computational science.

Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems.

The book employs oscillatory dynamical systems to represent the Universe mathematically via constructing classical and quantum theory of damped oscillators. It further discusses isotropic and homogeneous metrics in the Friedman-Robertson-Walker Universe and shows their equivalence to non-stationary oscillators. The wide class of exactly solvable damped oscillator models with variable parameters is associated with classical special functions of mathematical physics. Combining principles with observations in an easy to follow way, it inspires further thinking for mathematicians and physicists. Contents Part I: Dissipative geometry and general relativity theory Pseudo-Riemannian geometry and general relativity Dynamics of universe models Anisotropic and homogeneous universe models Metric waves in a nonstationary universe and dissipative oscillator Bosonic and fermionic models of a Friedman-Robertson-Walker universe Time dependent constants in an oscillatory universe Part II: Variational principle for time dependent oscillations and dissipations Lagrangian and Hamilton descriptions Damped oscillator: classical and quantum theory Sturm-Liouville problem as a damped oscillator with time dependent damping and frequency Riccati representation of time dependent damped oscillators Quantization of the harmonic oscillator with time dependent parameters

The third edition of this handbook is designed to provide a broad coverage of the concepts, implementations, and applications in metaheuristics. The book's chapters serve as stand-alone presentations giving both the necessary underpinnings as well as practical guides for implementation. The nature of metaheuristics invites an analyst to modify basic methods in response to problem characteristics, past experiences, and personal preferences, and the chapters in this handbook are designed to facilitate this process as well. This new edition has been fully revised and features new chapters on swarm intelligence and automated design of metaheuristics from flexible algorithm frameworks. The authors who have contributed to this volume represent leading figures from the metaheuristic community and are responsible for pioneering contributions to the fields they write about. Their collective work has significantly enriched the field of optimization in general and combinatorial optimization in particular.Metaheuristics are solution methods that orchestrate an interaction between local improvement procedures and higher level strategies to create a process capable of escaping from local optima and performing a robust search of a solution space. In addition, many new and exciting developments and extensions have been observed in the last few years. Hybrids of metaheuristics with other optimization techniques, like branch-and-bound, mathematical programming or constraint programming are also increasingly popular. On the front of applications, metaheuristics are now used to find high-quality solutions to an ever-growing number of complex, ill-defined real-world problems, in particular combinatorial ones. This handbook should continue to be a great reference for researchers, graduate students, as well as practitioners interested in metaheuristics.

Artificial intelligence (AI) has become pervasive in most areas of research and applications. While computation can significantly reduce mental efforts for complex problem solving, effective computer algorithms allow continuous improvement of AI tools to handle complexity-in both time and memory requirements-for machine learning in large datasets. Meanwhile, data science is an evolving scientific discipline that strives to overcome the hindrance of traditional skills that are too limited to enable scientific discovery when leveraging research outcomes. Solutions to many problems in medicine and life science, which cannot be answered by these conventional approaches, are urgently needed for society. This edited book attempts to report recent advances in the complementary domains of AI, computation, and data science with applications in medicine and life science. The benefits to the reader are manifold as researchers from similar or different fields can be aware of advanced developments and novel applications that can be useful for either immediate implementations or future scientific pursuit. Features: Considers recent advances in AI, computation, and data science for solving complex problems in medicine, physiology, biology, chemistry, and biochemistry Provides recent developments in three evolving key areas and their complementary combinations: AI, computation, and data science Reports on applications in medicine and physiology, including cancer, neuroscience, and digital pathology Examines applications in life science, including systems biology, biochemistry, and even food technology This unique book, representing research from a team of international contributors, has not only real utility in academia for those in the medical and life sciences communities, but also a much wider readership from industry, science, and other areas of technology and education.

The topics in this volume include the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. Scattering theory (or collision theory as it is often called) is a fundamental area of theory and computation in both physics and chemistry. The correct formulation of scattering theory for two-body collisions is now well worked out, but systems with three or more particles still present fundamental unmet challenges, both in the formulations of the problem and in the interpretation of computational results. A key issue in the mathematical foundations is asymptotic completeness, which says that any state of a quantum system is a superposition of bound and scattering states. Key issues on the physical side are concerned with boundary conditions, electromagnetic fields, effective potentials and resonances.

Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics-the heat equation, the wave equation and Laplace's equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green's functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods.

This book presents a unified study of dynamically coupled systems involving a rigid body and an ideal fluid flow from the perspective of Lagrangian and Hamiltonian mechanics. It compiles theoretical investigations on the topic of dynamically coupled systems using a framework grounded in Kirchhoff's equations. The text achieves a balance between geometric mechanics, or the modern theories of reduction of Lagrangian and Hamiltonian systems, and classical fluid mechanics, with a special focus on the applications of these principles. Following an introduction to Kirchhoff's equations of motion, the book discusses several extensions of Kirchhoff's work, particularly related to vortices. It addresses the equations of motions of these systems and their Lagrangian and Hamiltonian formulations. The book is suitable to mathematicians, physicists and engineers with a background in Lagrangian and Hamiltonian mechanics and theoretical fluid mechanics. It includes a brief introductory overview of geometric mechanics in the appendix.

This open access book presents theoretical framework and sample applications of variant construction. The first part includes the components variant logic, variant measurements, and variant maps, while the second part covers sample applications such as variation with functions, variant stream ciphers, quantum interference, classical/quantum random sequences, whole DNA sequences, and multiple-valued pulse sequences. Addressing topics ranging from logic and measuring foundation to typical applications and including various illustrated maps, it is a valuable guide for theoretical researchers in discrete mathematics; computing-, quantum- and communication scientists; big data engineers; as well as graduate and upper undergraduate students.

This book provides detailed descriptions of big data solutions for activity detection and forecasting of very large numbers of moving entities spread across large geographical areas. It presents state-of-the-art methods for processing, managing, detecting and predicting trajectories and important events related to moving entities, together with advanced visual analytics methods, over multiple heterogeneous, voluminous, fluctuating and noisy data streams from moving entities, correlating them with data from archived data sources expressing e.g. entities' characteristics, geographical information, mobility patterns, mobility regulations and intentional data. The book is divided into six parts: Part I discusses the motivation and background of mobility forecasting supported by trajectory-oriented analytics, and includes specific problems and challenges in the aviation (air-traffic management) and the maritime domains. Part II focuses on big data quality assessment and processing, and presents novel technologies suitable for mobility analytics components. Next, Part III describes solutions toward processing and managing big spatio-temporal data, particularly enriching data streams and integrating streamed and archival data to provide coherent views of mobility, and storing of integrated mobility data in large distributed knowledge graphs for efficient query-answering. Part IV focuses on mobility analytics methods exploiting (online) processed, synopsized and enriched data streams as well as (offline) integrated, archived mobility data, and highlights future location and trajectory prediction methods, distinguishing between short-term and more challenging long-term predictions. Part V examines how methods addressing data management, data processing and mobility analytics are integrated in big data architectures with distinctive characteristics compared to other known big data paradigmatic architectures. Lastly, Part VI covers important ethical issues that research on mobility analytics should address. Providing novel approaches and methodologies related to mobility detection and forecasting needs based on big data exploration, processing, storage, and analysis, this book will appeal to computer scientists and stakeholders in various application domains.

This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.

This book presents the state of the art in High Performance Computing on modern supercomputer architectures. It addresses trends in hardware and software development in general, as well as the future of High Performance Computing systems and heterogeneous architectures. The contributions cover a broad range of topics, from improved system management to Computational Fluid Dynamics, High Performance Data Analytics, and novel mathematical approaches for large-scale systems. In addition, they explore innovative fields like coupled multi-physics and multi-scale simulations. All contributions are based on selected papers presented at the 24th Workshop on Sustained Simulation Performance, held at the University of Stuttgart's High Performance Computing Center in Stuttgart, Germany in December 2016 and the subsequent Workshop on Sustained Simulation Performance, held at the Cyberscience Center, Tohoku University, Japan in March 2017.

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.

This thesis focuses on an unresolved problem in particle and nuclear physics: the relation between two important non-perturbative phenomena in quantum chromodynamics (QCD) - quark confinement and chiral symmetry breaking. The author develops a new analysis method in the lattice QCD, and derives a number of analytical formulae to express the order parameters for quark confinement, such as the Polyakov loop, its fluctuations, and the Wilson loop in terms of the Dirac eigenmodes closely related to chiral symmetry breaking. Based on the analytical formulae, the author analytically as well as numerically shows that at finite temperatures there is no direct one-to-one correspondence between them. The thesis describes this extraordinary achievement using the first-principle analysis, and proposes a possible new phase in which quarks are confined and chiral symmetry is restored.

This is the proceedings of ARK 2018, the 16th International Symposium on Advances in Robot Kinematics, that was organized by the Group of Robotics, Automation and Biomechanics (GRAB) from the University of Bologna, Italy. ARK are international symposia of the highest level organized every two years since 1988. ARK provides a forum for researchers working in robot kinematics and stimulates new directions of research by forging links between robot kinematics and other areas.The main topics of the symposium of 2018 were: kinematic analysis of robots, robot modeling and simulation, kinematic design of robots, kinematics in robot control, theories and methods in kinematics, singularity analysis, kinematic problems in parallel robots, redundant robots, cable robots, over-constrained linkages, kinematics in biological systems, humanoid robots and humanoid subsystems.