A smart city utilizes ICT technologies to improve the working effectiveness, share various data with the citizens, and enhance political assistance and societal wellbeing. The fundamental needs of a smart and sustainable city are utilizing smart technology for enhancing municipal activities, expanding monetary development, and improving citizens' standards of living. Data-Driven Mathematical Modeling in Smart Cities discusses new mathematical models in smart and sustainable cities using big data, visualization tools in mathematical modeling, machine learning-based mathematical modeling, and more. It further delves into privacy and ethics in data analysis. Covering topics such as deep learning, optimization-based data science, and smart city automation, this premier reference source is an excellent resource for mathematicians, statisticians, computer scientists, civil engineers, government officials, students and educators of higher education, librarians, researchers, and academicians.

An increasing body of literature concerns the economics of those highly appreciated qualities of life that are not easily provided by market exchange. Today these problems are visible as never before, for example environmental problems. But already at the dawn of industrial society the problem had been observed by Rousseau. His statements on the economy claim to take these problems into account with due importance. In this way his economic philosophy concerns a different domain of the economy from, for example, Adam Smith's work. Rousseau's philosophy attempts to consider phenomena later labeled information asymmetries and information costs, bargaining, collective good problems. Some of Rousseau's most puzzling social proposals (on theater, women, music, etc.) can be explained by his well-argued conviction that an optimal economy demands a high social morale, a communicative morale. He proposes an economic philosophy for the most important properties of richness - such as experiencing the unique, and being free although dependent on others (empowerment). It is for the adult capable of true deliberation, not for the trifle of the innocent child. He develops a concept of richness that is close to the Aristotelian capability-concept, later explored by Amartya Sen. Rousseau's economic philosophy has not been treated in a monograph before. The book should be rewarding to those interested in social theory, the history of social and economic thought, problems at the margins of market exchange, e.g. cultural economics, environmental economics, students of Rousseau and the thought of the 18th century, welfare economic theory in the direction of Arrow or Sen, and Poanyi's and others' theses about the transition from selfsufficiency to market.

One of the main goals of optimal control theory is to provide a theoretical basis for choosing an appropriate controller for whatever system is under consideration by the researcher or engineer. Two popular norms that have proved useful are known as H-2 and H - infinity control. The first has been particularly applicable to problems arising in the aerospace industry. However, most industrial problems are badly modeled and the second norm proved to be more appropriate when the actual conditions of the problem did not conform to the stipulated conditions of the theory. This book takes the topic of H-infinity control as a point of departure and pursues an improved controller design which has been suggested in the mainstream of robust control. Its main theme, minimum entropy control, provides a means of trading off some of the features of other control problems. The book is aimed at research workers in networking systems as well as those in operator theory and linear multivariable control. The use of stochastic methods makes the book also of importance to the circuits and systems community. CONTENTS: Preface Introduction Preliminaries Induced Operator Norms Discrete-Time Entropy Connections With Related Optimal Control Problems Minimum Entropy Control Continuous-Time Entropy A. Proof of Theorem B. Proof of Theorem Bibliography Notation Index"

This book discusses recent developments and the latest research in statistics and its applications, primarily in agriculture and industry, survey sampling and biostatistics, gathering articles on a wide variety of topics. Written by leading academics, scientists, researchers and scholars from around the globe to mark the platinum jubilee of the Department of Statistics, University of Calcutta in 2016, the book is a valuable resource for statisticians, aspiring researchers and professionals across educational levels and disciplines.

Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.

For the last decade, the author has been working to extend continuum mechanics to treat moving boundaries in materials focusing, in particular, on problems of metallurgy. This monograph presents a rational treatment of the notion of configurational forces; it is an effort to promote a new viewpoint. Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture. The work should be of interest to materials scientists, mechanicians, and mathematicians.

A long-standing unsolved problem in economic theory is how economic equilibria are attained. Price Dynamics in Equilibrium Models: The Search for Equilibrium and the Emergence of Endogenous Fluctuations considers a number of adjustment processes in different economic models and investigates their dynamical behaviour. Two important themes arising in this context are bounded rationality' and nonlinear dynamics'. Important sub-themes of the book are the following: how do boundedly rational agents interact with their environment and does this interaction in some sense lead to rational outcomes (which may or may not correspond to equilibria)? The second sub-theme deals with the consequences of the nonlinear dynamical nature of many adjustment processes. The results presented in this volume indicate that endogenous fluctuations are the rule rather than the exception in the search for equilibrium. The book uses the theory of nonlinear dynamics to analyze the dynamics of the different economic models. Due to the complexity of most of the models, an important role is played by computational methods. In particular, at regular instances the models are analyzed by numerical simulations and some computer-assisted proofs are provided. It also covers a wide range of dynamical models from economic theory. Most of these models merge the theory of nonlinear economic dynamics with the theory of bounded rationality. The book is written for anyone with an interest in economic theory in general and bounded rationality and endogenous fluctuations in particular. It is entirely self-contained and accessible to readers with only a limited knowledge of economic theory.

This is a book describing electronic structure theory and application within the framework of a methodology implemented in the computer code RSPt. In 1986, when the code that was to become RSPt was developed enough to be useful, it was one of the ?rst full-potential, all-electron, relativistic implem- tations of DFT (density functional theory). While RSPt was documented p- asitically in many publications describing the results of its application, it was many years before a publication explicitly describing aspects of the method appeared. In the meantime, several excellent all-electron, full-potential me- ods had been developed, published, and become available. So why a book about RSPt now? The code that became RSPt was initially developed as a personal research tool, rather than a collaborative e?ort or as a product. As such it required some knowledge of its inner workings to use, and as it was meant to be m- imally ?exible, the code required experience to be used e?ectively. These - tributes inhibited, but did not prevent, the spread of RSPt as a research tool. While applicable across the periodic table, the method is particularly useful in describing a wide range of materials, including heavier elements and c- pounds, and its ?exibility provides targeted accuracy and a convenient and accurate framework for implementing and assessing the e?ect of new models.

Quantum machine learning investigates how quantum computers can be used for data-driven prediction and decision making. The books summarises and conceptualises ideas of this relatively young discipline for an audience of computer scientists and physicists from a graduate level upwards. It aims at providing a starting point for those new to the field, showcasing a toy example of a quantum machine learning algorithm and providing a detailed introduction of the two parent disciplines. For more advanced readers, the book discusses topics such as data encoding into quantum states, quantum algorithms and routines for inference and optimisation, as well as the construction and analysis of genuine ``quantum learning models''. A special focus lies on supervised learning, and applications for near-term quantum devices.

A major outstanding problem in physics is understanding the nature of the dark energy that is driving the accelerating expansion of the Universe. This thesis makes a significant contribution by demonstrating, for the first time, using state-of-the-art computer simulations, that the interpretation of future galaxy survey measurements is far more subtle than is widely assumed, and that a major revision to our models of these effects is urgently needed. The work contained in the thesis was used by the WiggleZ dark energy survey to measure the growth rate of cosmic structure in 2011 and had a direct impact on the design of the surveys to be conducted by the European Space Agency's Euclid mission, a 650 million euro project to measure dark energy.

This textbook offers a clear and comprehensive introduction to analytical mechanics, one of the core components of undergraduate physics courses. The book starts with a thorough introduction into Lagrangian mechanics, detailing the d'Alembert principle, Hamilton's principle and conservation laws. It continues with an in-depth explanation of Hamiltonian mechanics, illustrated by canonical and Legendre transformation, the generalization to quantum mechanics through Poisson brackets and all relevant variational principles. Finally, the Hamilton-Jacobi theory and the transition to wave mechanics are presented in detail. Ideally suited to undergraduate students with some grounding in classical mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this series cover the complete core curriculum of theoretical physics at undergraduate level. Each volume is self-contained and provides all the material necessary for the individual course topic. Numerous problems with detailed solutions support a deeper understanding. Wolfgang Nolting is famous for his refined didactical style and has been referred to as the "German Feynman" in reviews.

This book presents the latest results related to shells characterize and design shells, plates, membranes and other thin-walled structures, a multidisciplinary approach from macro- to nanoscale is required which involves the classical disciplines of mechanical/civil/materials engineering (design, analysis, and properties) and physics/biology/medicine among others. The book contains contributions of a meeting of specialists (mechanical engineers, mathematicians, physicists and others) in such areas as classical and non-classical shell theories. New trends with respect to applications in mechanical, civil and aero-space engineering, as well as in new branches like medicine and biology are presented which demand improvements of the theoretical foundations of these theories and a deeper understanding of the material behavior used in such structures.

This book is concerned with topological and differential properties of multivalued mappings and marginal functions. Beside this applica- tions to the sensitivity analysis of optimization problems, in particular nonlinear programming problems with perturbations, are studied. The elaborated methods are primarily obtained by theories and concepts of two former Soviet Union researchers, Demyanov and Rubinov. Con- sequently, a significant part of the presented results have never been published in English before. Based on the use of directional derivatives as a key tool in studying nonsmooth functions and multifunctions, these results can be considered as a further development of quasidifferential calculus created by Demyanov and Rubinov. In contrast to other research in this field, especially the recent publica- tion by Bonnans and Shapiro, this book analyses properties of marginal functions associated with optimization problems under quite general con- straints defined by means of multivalued mappings. A unified approach to directional differentiability of functions and multifunctions forms the base of the volume.

Recent achievements in hardware and software developments have enabled the introduction of a revolutionary technology: in-memory data management. This technology supports the flexible and extremely fast analysis of massive amounts of data, such as diagnoses, therapies, and human genome data. This book shares the latest research results of applying in-memory data management to personalized medicine, changing it from computational possibility to clinical reality. The authors provide details on innovative approaches to enabling the processing, combination, and analysis of relevant data in real-time. The book bridges the gap between medical experts, such as physicians, clinicians, and biological researchers, and technology experts, such as software developers, database specialists, and statisticians. Topics covered in this book include - amongst others - modeling of genome data processing and analysis pipelines, high-throughput data processing, exchange of sensitive data and protection of intellectual property. Beyond that, it shares insights on research prototypes for the analysis of patient cohorts, topology analysis of biological pathways, and combined search in structured and unstructured medical data, and outlines completely new processes that have now become possible due to interactive data analyses.

Computer simulations of economic systems are slowly gaining ground within the economic profession. However, such a process is hindered by a lack of communication among researchers who do not share a common language. For its object-oriented structure and its versatility, Swarm has the necessary characteristics to become a credible universal language of agent-based simulations. Economic Simulations in Swarm collects a series of original articles in such domains as macro and micro economics, industrial organization, monetary theory, and finance, all linked by a common denominator: the use of the Swarm simulation platform. Swarm, a standard set of program libraries, allows users to construct simulations where a collection of heterogeneous independent agents or elements interact through discrete events. This volume offers the first extensive tutorial to the use of these software libraries developed at the Santa Fe Institute as part of the ongoing research into complexity. The editors conceived the idea of this book while visiting the Santa Fe Institute as members of the Working Group on Adaptive and Computable Economics'. Francesco Luna is a specialist in Computable Economics, and Benedikt Stefansson is an active contributor to the Swarm community.

The great interest in photonic crystals and their applications in the last 15 years is being expressed in the publishing of a large number of monographs, collections, textbooks and tutorials, where existing knowledge concerning - eration principles of photonic crystal devices and microstructured ?bers, their mathematicaldescription,well-knownandnovelapplicationsofsuchtechno- gies in photonics and optical communications are presented. They challenges authors of new books to cover the gaps still existing in the literature and highlight and popularize of already known material in a new and original manner. Authorsofthisbookbelievethatthenextsteptowardswideapplicationof photoniccrystalsisthesolutionofmanypracticalproblemsofdesignandc- putation of the speci?c photonic crystal-based devices aimed at the speci?c technicalapplication.Inordertomakethisstep,itisnecessarytoincreasethe number of practitioners who can solve such problems independently. The aim of this book is to extend the group of researchers, developers and students, who could practically use the knowledge on the physics of photonic crystals together with the knowledge and skills of independent calculation of basic characteristics of photonic crystals and modeling of various elements of - tegrated circuits and optical communication systems created on the basis of photonic crystals. The book is intended for quali?ed readers, specialists in the ?eld of optics and photonics, students of higher courses, master degree students and PhD students. As an introduction to the snopest, the book contains the basics of wave optics and radiation propagation in simple guiding media such as planar waveguides and step-index ?bers.

The book provides a survey of numerical methods for acoustics, namely the finite element method (FEM) and the boundary element method (BEM). It is the first book summarizing FEM and BEM (and optimization) for acoustics. The book shows that both methods can be effectively used for many other cases, FEM even for open domains and BEM for closed ones. Emphasis of the book is put on numerical aspects and on treatment of the exterior problem in acoustics, i.e. noise radiation.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

In the present edition I have included "Supplements and Problems" located at the end of each chapter. This was done with the aim of illustrating the possibilities of the methods contained in the book, as well as with the desire to make good on what I have attempted to do over the course of many years for my students-to awaken their creativity, providing topics for independent work. The source of my own initial research was the famous two-volume book Methods of Mathematical Physics by D. Hilbert and R. Courant, and a series of original articles and surveys on partial differential equations and their applications to problems in theoretical mechanics and physics. The works of K. o. Friedrichs, which were in keeping with my own perception of the subject, had an especially strong influence on me. I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space. This desire was successfully realized thanks to the introduction of various classes of general solutions and to an elaboration of the methods of proof for the corresponding uniqueness theorems. This was accomplished on the basis of comparatively simple integral inequalities for arbitrary functions and of a priori estimates of the solutions of the problems without enlisting any special representations of those solutions.

The finite element method is a numerical method widely used in engineering. This reference text is the first to discuss finite element methods for structures with large stochastic variations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will find this a very useful reference

Volume 21 provides the basis of the MHD theory in two extended reviews. The first review deals with high-temperature plasma equilibrium and stability in conventional stellarators (the steady state three-dimensional magnetic confinement systems). The second review considers the processes in the stationary plasma thrusters (SPT) created by one of the authors, A.I Morozov. In spite of the three-dimensional nature of stellarators, the author of the review, V.D. Pustovitov, has been able to give a concise presentation of basic ideas and results of the rather complicated theory of stellarators, both for specialists and for students in this field. The results of experimental and theoretical investigations of a new type of discharge device, SPT, are presented in the second review. Plasma thrusters generate quasi-neutral multi-ampere streams of ions with particle energies of 50 - 1000eV. They are most widely known as electric propulsion thrusters for spacecraft, and have been mounted onboard more than 50 Russian satellites. In addition, the SPTs are now used in technological systems for processing the surface layers of various products.

This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particular reaction-diffusion systems are studied where the medium is in turn either spatially inhomogeneous, compositionally heterogeneous or spatially discrete. Applications span a vast range of interdisciplinary fields and the systems considered can be as different as human or animal groups migrating under external influences, population ecology and evolution, complex chemical reactions, or networks of biological cells. Several chapters treat these applications in detail.

One of the major concerns of theoretical computer science is the classifi cation of problems in terms of how hard they are. The natural measure of difficulty of a function is the amount of time needed to compute it (as a function of the length of the input). Other resources, such as space, have also been considered. In recursion theory, by contrast, a function is considered to be easy to compute if there exists some algorithm that computes it. We wish to classify functions that are hard, i.e., not computable, in a quantitative way. We cannot use time or space, since the functions are not even computable. We cannot use Turing degree, since this notion is not quantitative. Hence we need a new notion of complexity-much like time or spac that is quantitative and yet in some way captures the level of difficulty (such as the Turing degree) of a function."

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations."Stationary Oscillations of Elastic Plates"" "studies the latter in the context ofstationaryvibrations of thin elastic plates. The techniquespresented herereduce the complexity of classical elasticity to a system of two independent variables, modeling problemsof flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely solvable integral equations.

The book isintended foran audiencewith a knowledge of advanced calculus and some familiarity with functional analysis. It is a valuable resource for professionals in pure and applied mathematics, and for theoretical physicists and mechanical engineerswhose work involveselastic plates. Graduate students in these fieldscan also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations."