This book reconsiders key issues, such as description and explanation, which affect data analytics. For starters: the soul does not exist. Once released from this cumbersome roommate, we are left with complex biological systems: namely, ourselves, who must configure their environment in terms of worlds that are compatible with what they sense. Far from supplying yet another cosmogony, the book provides the cultivated reader with computational tools for describing and understanding data arising from his surroundings, such as climate parameters or stock market trends, even the win/defeat story of his son football team. Besides the superposition of the very many universes considered by quantum mechanics, we aim to manage families of worlds that may have generated those data through the key feature of their compatibility. Starting from a sharp engineering of ourselves in term of pairs consisting of genome plus a neuron ensemble, we toss this feature in different cognitive frameworks within a span of exploitations ranging from probability distributions to the latest implementations of machine learning. From the perspective of human society as an ensemble of the above pairs, the book also provides scientific tools for analyzing the benefits and drawbacks of the modern paradigm of the world as a service.

This innovative textbook brings together modern concepts in mathematical epidemiology, computational modeling, physics-based simulation, data science, and machine learning to understand one of the most significant problems of our current time, the outbreak dynamics and outbreak control of COVID-19. It teaches the relevant tools to model and simulate nonlinear dynamic systems in view of a global pandemic that is acutely relevant to human health. If you are a student, educator, basic scientist, or medical researcher in the natural or social sciences, or someone passionate about big data and human health: This book is for you! It serves as a textbook for undergraduates and graduate students, and a monograph for researchers and scientists. It can be used in the mathematical life sciences suitable for courses in applied mathematics, biomedical engineering, biostatistics, computer science, data science, epidemiology, health sciences, machine learning, mathematical biology, numerical methods, and probabilistic programming. This book is a personal reflection on the role of data-driven modeling during the COVID-19 pandemic, motivated by the curiosity to understand it.

The book discusses hidden symmetries in the Anti-de Sitter/conformal field theory (AdS/CFT) duality. This duality is a modern concept that asserts an exact duality between conformally invariant quantum field theories and string theories in higher dimensional Anti-de Sitter spaces, and in this way provides a completely new tool for the study of strongly coupled quantum field theories. In this setting, the book focuses on the Wilson loop, an important observable in four-dimensional maximally supersymmetric gauge theory. The dual string description using minimal surfaces enables a systematic study of the hidden symmetries of the loop. The book presents major findings, including the discovery of a master symmetry for strings in general symmetric spaces, its relation to the Yangian symmetry algebra and its action on the minimal surfaces appearing in the dual string description of the Wilson loop. Moreover, it clarifies why certain symmetries are not present on the gauge theory side for purely bosonic Wilson loops and, lastly, how the supersymmetrization of the minimal surface problem for type IIB superstrings can be undertaken. As such, it substantially increases our understanding and use of infinite dimensional symmetries occurring in the AdS/CFT correspondence.

This book contains contributions from leading researchers in biomechanics, nanomechanics, tribology, contact mechanics, materials science and applications on various experimental techniques including atomic force microscopy (AFM) for studying soft, biomimetic and biological materials and objects. Biologists, physicists, researchers applying methods of contact mechanics and researchers testing materials using indentation techniques along with many other applied scientists will find this book a useful addition to their libraries. Moreover, several reviews in this book are written as introductions to several important and rather sophisticated research areas such as depth-sensing indentation, studying of biological cells by AFM probes, mechanics of adhesive contact and contact between viscoelastic (hereditary elastic) solids. The book containing new theoretical models, results of experimental studies and numerical simulations, along with reviews of above mentioned areas of contact mechanics in application to biological systems, would be beneficial for researchers in many areas of biology, medicine, engineering, mechanics and biomimetics.

This book summarizes recent inventions, provides guidelines and recommendations, and demonstrates many practical applications of homomorphic encryption. This collection of papers represents the combined wisdom of the community of leading experts on Homomorphic Encryption. In the past 3 years, a global community consisting of researchers in academia, industry, and government, has been working closely to standardize homomorphic encryption. This is the first publication of whitepapers created by these experts that comprehensively describes the scientific inventions, presents a concrete security analysis, and broadly discusses applicable use scenarios and markets. This book also features a collection of privacy-preserving machine learning applications powered by homomorphic encryption designed by groups of top graduate students worldwide at the Private AI Bootcamp hosted by Microsoft Research. The volume aims to connect non-expert readers with this important new cryptographic technology in an accessible and actionable way. Readers who have heard good things about homomorphic encryption but are not familiar with the details will find this book full of inspiration. Readers who have preconceived biases based on out-of-date knowledge will see the recent progress made by industrial and academic pioneers on optimizing and standardizing this technology. A clear picture of how homomorphic encryption works, how to use it to solve real-world problems, and how to efficiently strengthen privacy protection, will naturally become clear.

This book's aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book discusses application of Markov chains and transient mappings, Charlie-Simpson numerical algorithm, models represented by nonlinear reaction-diffusion-type partial differential equations, and related techniques. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments. Both graduate students and researchers of computational biology and oncologists will benefit by studying this book. Researchers of cancer studies and biological sciences will also find this work helpful.

This book is dedicated for engineers and researchers who would like to increase the knowledge in area of mobile mapping systems. Therefore, the flow of the derived information is divided into subproblems corresponding to certain mobile mapping data and related observations' equations. The proposed methodology is not fulfilling all SLAM aspects evident in the literature, but it is based on the experience within the context of the pragmatic and realistic applications. Thus, it can be supportive information for those who are familiar with SLAM and would like to have broader overview in the subject. The novelty is a complete and interdisciplinary methodology for large-scale mobile mapping applications. The contribution is a set of programming examples available as supportive complementary material for this book. All observation equations are implemented, and for each, the programming example is provided. The programming examples are simple C++ implementations that can be elaborated by students or engineers; therefore, the experience in coding is not mandatory. Moreover, since the implementation does not require many additional external programming libraries, it can be easily integrated with any mobile mapping framework. Finally, the purpose of this book is to collect all necessary observation equations and solvers to build computational system capable providing large-scale maps.

With relevant, timely topics, this book gathers carefully selected, peer-reviewed scientific works and offers a glimpse of the state-of-the-art in disaster prevention research, with an emphasis on challenges in Latin America. Topics include studies on surface frost, an extreme meteorological event that occasionally affects parts of Argentina, Bolivia, Peru, and southern Brazil, with serious impacts on local economies; near-ground pollution concentration, which affects many industrial, overpopulated cities within Latin America; disaster risk reduction and management, which are represented by mathematical models designed to assess the potential impact of failures in complex networks; and the intricate dynamics of international armed conflicts, which can be modeled with the help of stochastic theory. The book offers a valuable resource for professors, researchers, and students from both mathematical and environmental sciences, civil defense coordinators, policymakers, and stakeholders.

This book discusses supply chain management, focusing on developments within modelling the dynamic behaviour of the supply chain. Aimed at postgraduate students, researchers and practitioners, this book provides an in-depth knowledge of the dynamics of supply chains. Business trends such as the globalisation process and the increase of competition across many industrial sectors have forced companies to concentrate on their core competences and to outsource those activities in which they do not excel. As a consequence, companies no longer produce and distribute their goods in isolation, but being part of a supply chain or supply network, i.e. a set of interrelated companies who ultimately deliver the goods and services to the final customer. Despite the prevalence of supply chains as the primary form of production and distribution, their performance can be seriously hampered by the complex dynamics resulting from the collaboration and coordination (or lack thereof) among their members. This book provides the reader with modelling tools to understand, analyse and improve the dynamic behaviour of supply chains. It assembles seminal works on supply chain models and recent developments on the topic in order to provide a comprehensive, unified vision of the field for researchers and practitioners who wish to grasp the challenges of supply chain management. Aside presenting the main elements, equations and performance indicators governing the dynamics of a supply chain, and the book addresses issues such as the effect of timely and accurately sharing the information across members, the influence of restrictions on the productive capacities of their members, or the impact of the variability of the lead times, among others. Furthermore, more complex supply chain structures such as non-serial supply networks or closed-loop supply chains are modelled and discussed. Relevant managerial insights regarding the causes of supply chain underperformance, as well as avenues to improve their efficiency can be extracted from the resulting models.

Scattering amplitudes are fundamental and rich observables in quantum field theory. Based on the observation that, for massless particles of spin-one or more, scattering amplitudes are much simpler than expected from traditional Feynman diagram techniques, the broad aim of this work is to understand and exploit this hidden structure. It uses methods from twistor theory to provide new insights into the correspondence between scattering amplitudes in supersymmetric Yang-Mills theory and null polygonal Wilson loops. By additionally exploiting the symmetries of the problem, the author succeeds in developing new ways of computing scattering amplitudes.

Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in chemical engineering, and business process management are included to aide researchers and graduate students in mathematics, computer science, engineering, economics, and business management.

In this book, the author deals with the mathematical modelling, nonlinear control and performance evaluation of a conceptual anti-aircraft gun based mobile air defence system engaging an attacking three-dimensional aerial target. This book is of interest to academic faculty, graduate students and industry professionals working in the fields of mathematical modelling and control, ground vehicles, mobile air defence systems and other related topics.

This book deals with several types of multi-dimensional control problems in the face of data uncertainty for vector cases-multi-dimensional multi-objective control problem with uncertain objective functionals, uncertain constraint functionals, and uncertain objective as well as constraint functionals, uncertain multi-dimensional multi-objective control problem with semi-infinite constraints, uncertain dual multi-dimensional multi-objective variational control problem, and second-order PDE&PDI constrained robust optimization problem. The book provides the solution approaches-an exact l1 penalty function approach, modified objective approach, robust approach-in the simplest way to solve the recent developing optimization problems in the sense of uncertainty.

Industrial Mathematics is a relatively recent discipline. It is concerned primarily with transforming technical, organizational and economic problems posed by indus try into mathematical problems; "solving" these problems byapproximative methods of analytical and/or numerical nature; and finally reinterpreting the results in terms of the original problems. In short, industrial mathematics is modelling and scientific computing of industrial problems. Industrial mathematicians are bridge-builders: they build bridges from the field of mathematics to the practical world; to do that they need to know about both sides, the problems from the companies and ideas and methods from mathematics. As mathematicians, they have to be generalists. If you enter the world of indus try, you never know which kind of problems you will encounter, and which kind of mathematical concepts and methods you will need to solve them. Hence, to be a good "industrial mathematician" you need to know a good deal of mathematics as well as ideas already common in engineering and modern mathematics with tremen dous potential for application. Mathematical concepts like wavelets, pseudorandom numbers, inverse problems, multigrid etc., introduced during the last 20 years have recently started entering the world of real applications. Industrial mathematics consists of modelling, discretization, analysis and visu alization. To make a good model, to transform the industrial problem into a math ematical one such that you can trust the prediction of the model is no easy task."

This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill. Features: This book provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics such as the nature of theorem proving; examines the field of software engineering, including software reliability and dependability and describes formal methods; investigates probability and statistics and presents an overview of operations research and financial mathematics.

This book reports on advanced theories and methods in three related fields of research: applied physics, system science and computers. It is organized in three parts, the first of which covers applied physics topics, including lasers and accelerators; condensed matter, soft matter and materials science; nanoscience and quantum engineering; atomic, molecular, optical and plasma physics; as well as nuclear and high-energy particle physics. It also addresses astrophysics, gravitation, earth and environmental science, as well as medical and biological physics. The second and third parts focus on advances in computers and system science, respectively, and report on automatic circuit control, power systems, computer communication, fluid mechanics, simulation and modeling, software engineering, data structures and applications of artificial intelligence among other areas. Offering a collection of contributions presented at the 2nd International Conference on Applied Physics, System Science and Computers (APSAC), held in Dubrovnik, Croatia on September 27-29, 2017, the book bridges the gap between applied physics and electrical engineering. It not only to presents new methods, but also promotes collaborations between different communities working on related topics at the interface between physics and engineering, with a special focus on communication, data modeling and visualization, quantum information, applied mechanics as well as bio and geophysics.

This book, to reflect the system's diverse, relevant characteristics, uses three different mathematical tools, namely probability theory, fuzzy theory and random fuzzy theory, to model and analyze the reliability of each system. Reliability system engineering is an interdisciplinary area that chiefly focuses on the lifecycle characteristics of products and involves many fields of basic mathematics, technical science and management science. In recent years, there have been many books on reliability theory, but comparatively few on the reliability of mathematical models, or the reliability of mathematical models based on single probability theory or fuzzy theory. The findings presented here will not only enrich and expand traditional reliability theory, but also promote the development of related disciplines, lending the book considerable theoretical significance.

This book uses kinematics, mechanics, mathematics, and so on, to systematically propose the fixturing performance evaluation and fixturing layout planning method. The proposed method is a novel method, including the analysis method of locating determination, the analysis method of workpiece stability, the analysis method of clamping reasonability, the analysis method of workpiece attachment/detachment, the analysis method of locating accuracy, and the planning algorithm of locating point layout, the planning algorithm of clamping force, and so forth. It can enrich and develop the basic theory of computer aided fixture design, change the empirical method of fixture design. The combination of theoretical analysis and mathematical modeling technology can resolve the key problems in the process of fixture design, which will play a certain role in promoting the progress of manufacturing technology, improving the precision and level of product manufacturing, and meeting the higher and higher requirements of mechanical manufacturing industry.

This book documents ongoing research and theorizing in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people's everyday lives as well as sophisticated new problems for society at large. Mathematical tradition in China that emphasizes algorithm and computation has now seen a renaissance in mathematical modelling and applications where China has made significant progress with its economy, science and technology. In recent decades, teaching and learning of mathematical modelling as well as contests in mathematical modelling have been flourishing at different levels of education in China. Today, teachers and researchers in China become keener to learn from their colleagues from Western countries and other parts of the world in research and teaching of mathematical modelling and applications. The book provides a dialogue and communication between colleagues from across the globe with new impetus and resources for mathematical modelling education and its research in both West and East with new ideas on modelling teaching and practices, inside and outside classrooms. All authors of this book are members of the International Community of Teachers of Mathematical Modelling and Applications (ICTMA), the peak research body into researching the teaching, assessing and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace. The book is of interest to researchers, mathematics educators, teacher educators, education administrators, policy writers, curriculum developers, professional developers, in-service teachers and pre-service teachers including those interested in mathematical literacy.

Mathematical Models and Algorithms for Power System Optimization helps readers build a thorough understanding of new technologies and world-class practices developed by the State Grid Corporation of China, the organization responsible for the world's largest power distribution network. This reference covers three areas: power operation planning, electric grid investment and operational planning and power system control. It introduces economic dispatching, generator maintenance scheduling, power flow, optimal load flow, reactive power planning, load frequency control and transient stability, using mathematic models including optimization, dynamic, differential and difference equations.

Financial analysis, modellng, simulation and knowledge engineering have become essential to the survival of every enterprise. This thorough and comprehensive book looks at the development and use of financial models for analysis and decision-making, showing the reader how to apply these methods in his or her own work.

Introduction to Modeling in Physiology and Medicine, Second Edition, develops a clear understanding of the fundamental principles of good modeling methodology. Sections show how to create valid mathematical models that are fit for a range of purposes. These models are supported by detailed explanation, extensive case studies, examples and applications. This updated edition includes clearer guidance on the mathematical prerequisites needed to achieve the maximum benefit from the material, a greater detail regarding basic approaches to modeling, and discussions on non-linear and stochastic modeling. The range of case study material has been substantially extended, with examples drawn from recent research experience. Key examples include a cellular model of insulin secretion and its extension to the whole-body level, a model of insulin action during a meal/oral glucose tolerance test, a large-scale simulation model of type 1 diabetes and its use in in silico clinical trials and drug trials.

This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics. The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.

The intention of this collection agrees with the purposes of the homonymous mini-symposium (MS) at ICIAM-2019, which were to overview the essentials of geometric calculus (GC) formalism, to report on state-of-the-art applications showcasing its advantages and to explore the bearing of GC in novel approaches to deep learning. The first three contributions, which correspond to lectures at the MS, offer perspectives on recent advances in the application GC in the areas of robotics, molecular geometry, and medical imaging. The next three, especially invited, hone the expressiveness of GC in orientation measurements under different metrics, the treatment of contact elements, and the investigation of efficient computational methodologies. The last two, which also correspond to lectures at the MS, deal with two aspects of deep learning: a presentation of a concrete quaternionic convolutional neural network layer for image classification that features contrast invariance and a general overview of automatic learning aimed at steering the development of neural networks whose units process elements of a suitable algebra, such as a geometric algebra. The book fits, broadly speaking, within the realm of mathematical engineering, and consequently, it is intended for a wide spectrum of research profiles. In particular, it should bring inspiration and guidance to those looking for materials and problems that bridge GC with applications of great current interest, including the auspicious field of GC-based deep neural networks.

This book introduces the reliability modelling and optimization of warm standby systems. Warm standby is an attractive redundancy technique, as it consumes less energy than hot standby and switches into the active state faster than cold standby. Since a warm standby component experiences different failure rates in the standby state and active state, the reliability evaluation is challenging and the existing works are only restricted to very special cases. By adapting the decision diagrams, this book proposes the methodology to evaluate the reliability of different types of warm standby systems and studies the reliability optimization. Compared with existing works, the proposed methods allow the system to have an arbitrary number of components and allow the failure time distribution of components to observe arbitrary distributions. From this book, the readers can not only learn how to evaluate and optimize the reliability of warm standby systems but also use the methods to study the reliability of other complex systems.