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What kind of dynamics is a piecewise linear system able to display? How may they generate heteroclinic chaos? How can the coexistence of attractors be designed and characterized? Is it necessary to have equilibrium points to generate chaotic behavior? Chaos theory and complex systems are interesting and evolving topics whose investigation from a theoretical and practical point of view constantly leads to arising questions. Interesting behaviors can be observed in self-excited attractors, hidden attractors and non-self-excited attractors.This book presents some fundamentals of linear system theory and recent approaches to design the three classes of chaotic attractors in piecewise linear systems. Each chapter presents a brief description and basic concepts to provide an overview of linear systems theory; chaos and multistability in integer linear systems; hidden and non-self-excited attractors; and fractional approaches. They also provide example systems to illustrate the concepts and design methods introduced. Some current topics under investigation are addressed from an integer order perspective to make the connection with the fractional order counterpart.This textbook provides a comprehensive introduction, methodologies, and analysis tools to study chaotic piecewise linear systems and will be suitable for undergraduate or graduate students interested in the field of chaos and complex dynamics.

The subject of this monograph is to describe orbits of slowly chaotic motion. The study of geodesic flow on the unit torus is motivated by the irrational rotation sequence, where the most outstanding result is the Kronecker-Weyl equidistribution theorem and its time-quantitative enhancements, including superuniformity. Another important result is the Khinchin density theorem on superdensity, a best possible form of time-quantitative density. The purpose of this monograph is to extend these classical time-quantitative results to some non-integrable flat dynamical systems.The theory of dynamical systems is on the most part about the qualitative behavior of typical orbits and not about individual orbits. Thus, our study deviates from, and indeed is in complete contrast to, what is considered the mainstream research in dynamical systems. We establish non-trivial results concerning explicit individual orbits and describe their long-term behavior in a precise time-quantitative way. Our non-ergodic approach gives rise to a few new methods. These are based on a combination of ideas in combinatorics, number theory, geometry and linear algebra.Approximately half of this monograph is devoted to a time-quantitative study of two concrete simple non-integrable flat dynamical systems. The first concerns billiard in the L-shape region which is equivalent to geodesic flow on the L-surface. The second concerns geodesic flow on the surface of the unit cube. In each, we give a complete description of time-quantitative equidistribution for every geodesic with a quadratic irrational slope.

About sixty years ago, the anomalous magnetic response of certain magnetic alloys drew the attention of theoretical physicists. It soon became clear that understanding these systems, now called spin glasses, would give rise to a new branch of statistical physics. As physical materials, spin glasses were found to be as useless as they were exotic. They have nevertheless been recognized as paradigmatic examples of complex systems with applications to problems as diverse as neural networks, amorphous solids, biological molecules, social and economic interactions, information theory and constraint satisfaction problems.This book presents an encyclopaedic overview of the broad range of these applications. More than 30 contributions are compiled, written by many of the leading researchers who have contributed to these developments over the last few decades. Some timely and cutting-edge applications are also discussed. This collection serves well as an introduction and summary of disordered and glassy systems for advanced undergraduates, graduate students and practitioners interested in the topic.

How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects?There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc.This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems.

A Practical Guide on Security and Privacy in Cyber-Physical Systems offers an in-depth look at the recent security and privacy challenges of Cyber-Physical Systems (CPS) in multiple application domains. It provides readers with a comprehensive view of system architecture for cybersecurity systems before actual implementation.The book first presents a systematic overview on several CPS applications covering standard architectures before zooming into each of the layers of the architectureal design to describe the underpinning technological, security, and privacy issues currently facing some CPS research groups. The guiding principles that should be followed while planning future innovations for such mission-critical systems are also covered.This book captures the latest advancements from many different fields and is a well-balanced combination of academic contributions and industrial applications in CPS. Written for students and professionals at all levels, this book presents the best practices for individuals who want to advance their research and development in this exciting area.

This book reinforces an understanding of Economics by showing how basic mathematics is used to construct models of the economy. By taking wide-ranging examples drawn for virtually all areas of economics, it shows how model-building is an indispensable aid to understanding economics.The mathematical techniques used in the book are fairly rudimentary - optimisation methods and equation-solving are the primary tools used. A brief explanation of constrained optimisation using Lagrange multipliers is provided. Throughout, the emphasis is on how these techniques are fruitfully deployed in constructing economic models and solving economic problems. It bridges the gap between mathematical analysis and economic logic. For readers, it builds confidence in constructing their own models for purposes of analysis. The book is well-suited for self-study.

Launched in 2013, the journal Unmanned Systems has published more than 200 articles reporting on the state-of-art development in the field. This review volume has selected the 15 best articles of the journal to mark its 10-year anniversary as well as the progress achieved in the field of unmanned systems in the last decade.The articles selected in this celebratory volume cover all subjects related to the development of automatic machine systems in unmanned hardware platforms (aerial, ground, underwater and unconventional platforms), unmanned software systems, energy systems, modelling and control, communications systems, computer vision systems, sensing and information processing, navigation and path planning, computing, information fusion, multi-agent systems, mission management, machine intelligence, artificial intelligence, and innovative application case studies.An analytical review that examines the selected articles under the human cognitive perceptual cycle, to perceive, learn, remember, and think about information is also included in this collection.

An introduction to the world of quarks and leptons, and of their interactions governed by fundamental symmetries of nature, as well as an introduction to the connection that exists between worlds of the infinitesimally small and the infinitely large.The book begins with a simple presentation of the theoretical framework, the so-called Standard Model, which evolved gradually since the 1960s. The key experiments establishing it as the theory of elementary particle physics, but also its missing pieces and conceptual weaknesses are introduced. The book proceeds with the extraordinary story of the Large Hadron Collider at CERN - the largest purely scientific project ever realized. Conception, design and construction by worldwide collaborations of the detectors of size and complexity without precedent in scientific history are discussed. The book then offers the reader a state-of-the art (2020) appreciation of the depth and breadth of the physics exploration performed by the LHC experiments: the study of new forms of matter, the understanding of symmetry-breaking phenomena at the fundamental level, the exciting searches for new physics such as dark matter, additional space dimensions, new symmetries, and more. The adventure of the LHC culminated in the discovery of the Higgs boson in 2012 (Nobel Prize in Physics in 2013). The last chapter of this book describes the plans for the LHC during the next 15 years of exploitation and improvement, and the possible evolution of the field and future collider projects under consideration.The authors are researchers from CERN, CEA and CNRS (France), and deeply engaged in the LHC program: D Denegri in the CMS experiment, C Guyot, A Hoecker and L Roos in the ATLAS experiment. Some of them are involved since the inception of the project. They give a lively and accessible inside view of this amazing scientific and human adventure.

This book introduces readers to the giant clam's biology, taxonomy and systematics, ecological and cultural significance, threats and challenges, and conservation solutions. The highlight of this book is the species identification guide containing descriptions of 12 known giant clam species accompanied by accurate hand-drawn shell illustrations and live photographs of specimens for comparison. Detailed information is summarised in a visual key on the distinctive features of the individual species, with notes on their ecology, geographic distribution, taxonomy and morphology. This book also includes other useful natural history information to spur the reader's interest in these magnificent animals.With the most comprehensive information presented concisely, this book allows readers to identify a particular giant clam readily and confidently, as well as the other species that it may easily be confused with, confirm that the species occurs in a specific area, and access general information on the biology and ecology of the species. It is a valuable resource for researchers, students, the SCUBA diving community, managers of marine resources, and the public.

The chapters in the book focus on recent developments in the field of technological innovation and entrepreneurship. It is structured in three parts. The focus is on innovation and entrepreneurial ecosystems, digital technologies and innovation, as well as responses to pandemics resulting from external shocks.Carefully selected on the basis of relevance and rigor, the chapters in the book take the readers through various trending research topics.

High-energy particle accelerators are as diverse as their uses, which range from scientific research in fields such as high-energy physics, materials science and the life sciences, to applications in industry and medicine. Despite the diversity of accelerators, the particle beams that they are designed to produce behave in ways that share many common features. Beam Dynamics in High Energy Particle Accelerators aims to provide an introduction to phenomena regularly encountered when working with beams in accelerators; from the basic principles of motion of relativistic particles in electromagnetic fields, to instabilities that can affect beam quality in machines operating at high current. This book assumes no prior experience with accelerator physics and develops the subject in a way that provides a solid foundation for more advanced study of specific topics.As well as including numerous revisions and improvements in the text, this second edition features substantial new material, including sections on fringe fields in multipole magnets, Verlet integration for particle tracking, and measurement of beam emittances. References and discussions of current topics have been updated. As with the first edition, the aim is to provide practical and powerful tools and techniques for the study of beam dynamics, while emphasizing the elegance of the subject and helping the reader develop a deep understanding of the relevant physics.

Digital forensics deals with the investigation of cybercrimes. With the growing deployment of cloud computing, mobile computing, and digital banking on the internet, the nature of digital forensics has evolved in recent years, and will continue to do so in the near future.This book presents state-of-the-art techniques to address imminent challenges in digital forensics. In particular, it focuses on cloud forensics, Internet-of-Things (IoT) forensics, and network forensics, elaborating on innovative techniques, including algorithms, implementation details and performance analysis, to demonstrate their practicality and efficacy. The innovations presented in this volume are designed to help various stakeholders with the state-of-the-art digital forensics techniques to understand the real world problems. Lastly, the book will answer the following questions: How do the innovations in digital forensics evolve with the emerging technologies? What are the newest challenges in the field of digital forensics?

A Clash of Civilisations is not inevitable, yet danger mounts the longer the West ignores its top forecaster. In 2023, the OECD sees China's economy as 27% bigger than the US: by mid-century 70%. India too will be larger, leaving America as No.3. Time to Get Real: listen to economists, especially development economists, and those in business who know China.Three giant shocks lurk right ahead for the West: economic, demographic and competence. 90% of the world's population will soon be non-Western: no more accepting exclusion from global decision making. After COVID, Afghanistan and domestic turmoil, many question Western competence to get things right, let alone avoid nuclear destruction.Economic size, not military might, is what counts among Great Powers. As leading military historian Paul Kennedy wrote, military strength is, 'inextricably intertwined with economic power and technological progress'. This need not threaten the West if understood and managed properly. Indeed, it would mitigate the real existential threats, from the environment to war. Otherwise nuclear conflict, Kissinger's 'Armageddon-like clash', is ever more likely.A New New World with growing muscle and some different ideas is emerging. How can the West best respond? The book proposes a Biden-Xi Grand Bargain, as Nixon struck with Mao. Grasp what Yin and Yang offer, as opposites can support each other for lasting mutual benefit.

Adam Smith, one of the founding fathers of contemporary economics, observed that religiosity is influenced by the extent of regulation in the "market" for religion. In countries where there is a state-sponsored religion, one can expect less overall religiosity than if the market were competitive and religions had to compete to increase their membership. Religion, he claims, is like other goods and services supplied in a market economy.Max Weber, one of the founding fathers of contemporary sociology, similarly proposed that religiosity and economic principles are strongly interconnected phenomena. Weber famously thought that Protestant religious beliefs about the importance of work, savings and trustworthiness played an important role in sparking the Industrial Revolution and accelerating economic growth in the Western World.This edited volume contains original contributions by eminent scholars in the new and emerging field of the economics of religion. The contributions expand upon the ground-breaking ideas of Adam Smith and Max Weber. The chapters also illuminate new directions for research in this relatively young, intellectually exciting, and rapidly growing multidisciplinary field of scientific inquiry

This book serves as an introduction to graph theory and its applications. It is intended for a senior undergraduate course in graph theory but is also appropriate for beginning graduate students in science or engineering. The book presents a rigorous (proof-based) introduction to graph theory while also discussing applications of the results for solving real-world problems of interest. The book is divided into four parts. Part 1 covers the combinatorial aspects of graph theory including a discussion of common vocabulary, a discussion of vertex and edge cuts, Eulerian tours, Hamiltonian paths and a characterization of trees. This leads to Part 2, which discusses common combinatorial optimization problems. Spanning trees, shortest path problems and matroids are all discussed, as are maximum flow problems. Part 2 ends with a discussion of graph coloring and a proof of the NP-completeness of the coloring problem. Part 3 introduces the reader to algebraic graph theory, and focuses on Markov chains, centrality computation (e.g., eigenvector centrality and page rank), as well as spectral graph clustering and the graph Laplacian. Part 4 contains additional material on linear programming, which is used to provide an alternative analysis of the maximum flow problem. Two appendices containing prerequisite material on linear algebra and probability theory are also provided.

Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.This second edition presents minimax properties with Lp risks, for a real p larger than one, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.

The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.

Digital transformation is happening across all industries worldwide, including in Singapore. This book seeks to provide insights on how small and medium enterprises (SMEs) can embark on their own journeys of digital transformation, while at the same time remaining agile in responding to industry and consumer needs. It will outline how firms can foster a culture of business transformation to improve efficiency and productivity; elaborate on how the COVID-19 pandemic has accelerated the digital transformation process, and how it has provided new opportunities; present a roadmap on how SMEs can navigate through the artificial and data analytics revolution; and provide recommendations on how SMEs can partner with institutes of higher learning. It concludes by elaborating on the skillsets and capabilities needed to drive digitalisation.

This book deals with two main topics. The first is a theory that aims to unify the many interpretations of probability presented in the literature. The second uses this comprehensive theory of probability to answer the questions of quantum mechanics that have long been debated. The entire book proposes original solutions that several experimental cases substantiate.

Islamic institutions have had a very long history, whose performance was muted during the Colonial Period. However, after the Second World War, the revival of the Islamic institutions began. Throughout its history, it had been assumed that these institutions are working for the betterment of humanity. Their target is to achieve a high level of the welfare for the concerned community. Historically these institutions were waqf, zakat and sadaqat. However from the last three decades, Islamic financial institutions have been established with the objective of providing interest- free products, transaction and services for Muslims. However there has been lot of criticism on the performance and role of these institutions. This becomes especially pertinent in a Muslim country like Indonesia, where there is a dire need to know that how these institutions are working and if it is possible for them to achieve the objectives of the Shari'ah. Some scholars have claimed that these institutions are performative and only serving 'lip service', and there are no significant differences between the Islamic and secular institutions where both kinds of institutions operate on the same foundations and differ only in use of technical terminologies. This volume aims to analyze some of the Islamic institutions which are operating in the world's biggest Muslim country, Indonesia, as a case study and analyze the contemporary Islamic Banking products and practices in the light of 'Maqasad al-Shari'ah'. The book's objective is to propose an improved system of Islamic institutions for Muslims to refer to. This volume will also analyze why these institutions are currently not able to comply with the Maqasad al Shari'ah and how it is possible to enhance the level of economic development, social wellbeing, individual freedom and equality, elimination of injustice and poverty, and achieve the other targets of the Maqasad through these institutions.