Locally computable (NC0) functions are "simple" functions for which every bit of the output can be computed by reading a small number of bits of their input. The study of locally computable cryptography attempts to construct cryptographic functions that achieve this strong notion of simplicity and simultaneously provide a high level of security. Such constructions are highly parallelizable and they can be realized by Boolean circuits of constant depth.

This book establishes, for the first time, the possibility of local implementations for many basic cryptographic primitives such as one-way functions, pseudorandom generators, encryption schemes and digital signatures. It also extends these results to other stronger notions of locality, and addresses a wide variety of fundamental questions about local cryptography. The author's related thesis was honorably mentioned (runner-up) for the ACM Dissertation Award in 2007, and this book includes some expanded sections and proofs, and notes on recent developments.

The book assumes only a minimal background in computational complexity and cryptography and is therefore suitable for graduate students or researchers in related areas who are interested in parallel cryptography. It also introduces general techniques and tools which are likely to interest experts in the area.

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.

In the last decade, both scholars and practitioners have sought novel ways to address the problem of cybersecurity. Innovative outcomes have included applications such as blockchain as well as creative methods for cyber forensics, software development, and intrusion prevention. Accompanying these technological advancements, discussion on cyber matters at national and international levels has focused primarily on the topics of law, policy, and strategy. The objective of these efforts is typically to promote security by establishing agreements among stakeholders on regulatory activities. Varying levels of investment in cyberspace, however, comes with varying levels of risk; in some ways, this can translate directly to the degree of emphasis for pushing substantial change. At the very foundation or root of cyberspace systems and processes are tenets and rules governed by principles in mathematics. Topics such as encrypting or decrypting file transmissions, modeling networks, performing data analysis, quantifying uncertainty, measuring risk, and weighing decisions or adversarial courses of action represent a very small subset of activities highlighted by mathematics. To facilitate education and a greater awareness of the role of mathematics in cyber systems and processes, a description of research in this area is needed. Mathematics in Cyber Research aims to familiarize educators and young researchers with the breadth of mathematics in cyber-related research. Each chapter introduces a mathematical sub-field, describes relevant work in this field associated with the cyber domain, provides methods and tools, as well as details cyber research examples or case studies. Features One of the only books to bring together such a diverse and comprehensive range of topics within mathematics and apply them to cyber research. Suitable for college undergraduate students or educators that are either interested in learning about cyber-related mathematics or intend to perform research within the cyber domain. The book may also appeal to practitioners within the commercial or government industry sectors. Most national and international venues for collaboration and discussion on cyber matters have focused primarily on the topics of law, policy, strategy, and technology. This book is among the first to address the underpinning mathematics.

Device-independent quantum cryptography is a method for exchanging secret messages over potentially insecure quantum communication channels, such as optical fibers. In contrast to conventional quantum cryptography, security is guaranteed even if the devices used by the communication partners, such as photon sources and detectors, deviate from their theoretical specifications. This is of high practical relevance, for attacks to current implementations of quantum cryptography exploit exactly such deviations. Device-independent cryptography is however technologically so demanding that it looked as if experimental realizations are out of reach. In her thesis, Rotem Arnon-Friedman presents powerful information-theoretic methods to prove the security of device-independent quantum cryptography. Based on them, she is able to establish security in a parameter regime that may be experimentally achievable in the near future. Rotem Arnon-Friedman's thesis thus provides the theoretical foundations for an experimental demonstration of device-independent quantum cryptography.

rd This book constitutes a collection of extended versions of papers presented at the 23 IFIP TC7 Conference on System Modeling and Optimization, which was held in C- cow, Poland, on July 23-27, 2007. It contains 7 plenary and 22 contributed articles, the latter selected via a peer reviewing process. Most of the papers are concerned with optimization and optimal control. Some of them deal with practical issues, e. g. , p- formance-based design for seismic risk reduction, or evolutionary optimization in structural engineering. Many contributions concern optimization of infini- dimensional systems, ranging from a general overview of the variational analysis, through optimization and sensitivity analysis of PDE systems, to optimal control of neutral systems. A significant group of papers is devoted to shape analysis and opti- zation. Sufficient optimality conditions for ODE problems, and stochastic control methods applied to mathematical finance, are also investigated. The remaining papers are on mathematical programming, modeling, and information technology. The conference was the 23rd event in the series of such meetings biennially org- ized under the auspices of the Seventh Technical Committee "Systems Modeling and Optimization" of the International Federation for Information Processing (IFIP TC7).

This book presents selected peer-reviewed contributions from the International Work-Conference on Time Series, ITISE 2017, held in Granada, Spain, September 18-20, 2017. It discusses topics in time series analysis and forecasting, including advanced mathematical methodology, computational intelligence methods for time series, dimensionality reduction and similarity measures, econometric models, energy time series forecasting, forecasting in real problems, online learning in time series as well as high-dimensional and complex/big data time series. The series of ITISE conferences provides a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing computer science, mathematics, statistics and econometrics.

Stochastic hydrogeology, which emerged as a research area in the late 1970s, involves the study of subsurface, geological variability on flow and transport processes and the interpretation of observations using existing theories. Lacking, however, has been a rational framework for modeling the impact of the processes that take place in heterogeneous media and for incorporating it in predictions and decision-making. This book provides this important framework. It covers the fundamental and practical aspects of stochastic hydrogeology, coupling theoretical aspects with examples, case studies, and guidelines for applications.

All traditional implementation techniques for functional languages fail to avoid useless repetition of work. They are not "optimal" in their implementation of sharing, often causing a catastrophic, exponential explosion in reduction time. Optimal reduction is an innovative graph reduction technique for functional expressions, introduced by Lamping in 1990, that solves the sharing problem. This work, the first on the subject, is a comprehensive account by two of its leading exponents. Practical implementation aspects are fully covered as are the mathematical underpinnings of the subject. The relationship to the pioneering work of Lévy and to Girard's more recent "Geometry of Interaction" are explored; optimal reduction is thereby revealed as a prime example of how a beautiful mathematical theory can lead to practical benefit. The book is essentially self-contained, requiring no more than basic familiarity with functional languages. It will be welcomed by graduate students and research workers in lambda calculus, functional programming or linear logic.

This new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its 'pyramidal' graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids are the central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid.

Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of 'false' contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences.

This book describes the mathematical aspects of the semantics of programming languages. The main goals are to provide formal tools to assess the meaning of programming constructs in both a language-independent and a machine-independent way and to prove properties about programs, such as whether they terminate, or whether their result is a solution of the problem they are supposed to solve. In order to achieve this the authors first present, in an elementary and unified way, the theory of certain topological spaces that have proved of use in the modeling of various families of typed lambda calculi considered as core programming languages and as meta-languages for denotational semantics. This theory is now known as Domain Theory, and was founded as a subject by Scott and Plotkin. One of the main concerns is to establish links between mathematical structures and more syntactic approaches to semantics, often referred to as operational semantics, which is also described. This dual approach has the double advantage of motivating computer scientists to do some mathematics and of interesting mathematicians in unfamiliar application areas from computer science.

This book presents best selected research papers presented at the Thirteenth International Conference on Applied Mathematics and Mechanics in the Aerospace Industry (AMMAI 2020), held from September 6 to September 13, 2020, at the Alushta Health and Educational Center (The Republic of Crimea). The book is dedicated to solving actual problems of applied mechanics using modern computer technology including smart paradigms. Physical and mathematical models, numerical methods, computational algorithms, and software complexes are discussed, which allow to carry out high-precision mathematical modeling in fluid, gas, and plasma mechanics, in general mechanics, deformable solid mechanics, in strength, destruction and safety of structures, etc. Technologies and software systems that provide effective solutions to the problems at various multi-scale levels are considered. Special attention is paid to the training of highly qualified specialists for the aviation and space industry. The book is recommended for specialists in the field of applied mathematics and mechanics, mathematical modeling, information technologies, and developers of modern applied software systems.

Covers computational methods in design and fluid dynamics with a focus on computational fluid dynamics Explains advanced material applications and manufacturing in labs using novel alloys and introduces properties in material Discusses fabrication of graphene reinforced magnesium metal matrix for orthopedic applications Illustrates simulation and optimization gear transmission, heat sink and heat exchangers application Provides unique problem-solution approach including solutions, methodology, experimental setup, and results validation

This book offers an introduction to ten key topics in quantum information science and quantum coherent phenomena, aimed at graduate-student level. The chapters cover some of the most recent developments in this dynamic research field where theoretical and experimental physics, combined with computer science, provide a fascinating arena for groundbreaking new concepts in information processing.

The book addresses both the theoretical and experimental aspects of the subject, and clearly demonstrates how progress in experimental techniques has stimulated a great deal of theoretical effort and vice versa. Experiments are shifting from simply preparing and measuring quantum states to controlling and manipulating them, and the book outlines how the first real applications, notably quantum key distribution for secure communication, are starting to emerge. The chapters cover quantum retrodiction, ultracold quantum gases in optical lattices, optomechanics, quantum algorithms, quantum key distribution, quantum control based on measurement, orbital angular momentum of light, entanglement theory, trapped ions and quantum metrology, and open quantum systems subject to decoherence.

The contributing authors have been chosen not just on the basis of their scientific expertise, but also because of their ability to offer pedagogical and well-written contributions which will be of interest to students and established researchers.

This book presents fundamental concepts of optimization problems and its real-world applications in various fields. The core concepts of optimization, formulations and solution procedures of various real-world problems are provided in an easy-to-read manner. The unique feature of this book is that it presents unified knowledge of the modelling of real-world decision-making problems and provides the solution procedure using the appropriate optimization techniques. The book will help students, researchers, and faculty members to understand the need for optimization techniques for obtaining optimal solution for the decision-making problems. It provides a sound knowledge of modelling of real-world problems using optimization techniques. It is a valuable compendium of several optimization techniques for solving real-world application problems using optimization software LINGO. The book is useful for academicians, practitioners, students and researchers in the field of OR. It is written in simple language with a detailed explanation of the core concepts of optimization techniques. Readers of this book will understand the formulation of real-world problems and their solution procedures obtained using the appropriate optimization techniques.

Universal codes efficiently compress sequences generated by stationary and ergodic sources with unknown statistics, and they were originally designed for lossless data compression. In the meantime, it was realized that they can be used for solving important problems of prediction and statistical analysis of time series, and this book describes recent results in this area. The first chapter introduces and describes the application of universal codes to prediction and the statistical analysis of time series; the second chapter describes applications of selected statistical methods to cryptography, including attacks on block ciphers; and the third chapter describes a homogeneity test used to determine authorship of literary texts. The book will be useful for researchers and advanced students in information theory, mathematical statistics, time-series analysis, and cryptography. It is assumed that the reader has some grounding in statistics and in information theory.

This book presents selected peer-reviewed contributions from the International Conference on Time Series and Forecasting, ITISE 2018, held in Granada, Spain, on September 19-21, 2018. The first three parts of the book focus on the theory of time series analysis and forecasting, and discuss statistical methods, modern computational intelligence methodologies, econometric models, financial forecasting, and risk analysis. In turn, the last three parts are dedicated to applied topics and include papers on time series analysis in the earth sciences, energy time series forecasting, and time series analysis and prediction in other real-world problems. The book offers readers valuable insights into the different aspects of time series analysis and forecasting, allowing them to benefit both from its sophisticated and powerful theory, and from its practical applications, which address real-world problems in a range of disciplines. The ITISE conference series provides a valuable forum for scientists, engineers, educators and students to discuss the latest advances and implementations in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing computer science, mathematics, statistics and econometrics.

Focuses on the latest research in the field of differential equations in engineering applications Discusses the most recent research findings that are occurring across different institutions Identifies the gaps in the knowledge of differential equations Presents the most fruitful areas for further research in advanced processes Offers the most forthcoming studies in modeling and simulation along with real-world case studies

the handbook is a valuable reference to researchers from industry and academia, as well as Masters and PhD students around the globe working in the metaheuristics and applications domain includes contributions from a variety of academics/researchers in the field of metaheuristics

This book presents the most important fault-tolerant distributed programming abstractions and their associated distributed algorithms, in particular in terms of reliable communication and agreement, which lie at the heart of nearly all distributed applications. These programming abstractions, distributed objects or services, allow software designers and programmers to cope with asynchrony and the most important types of failures such as process crashes, message losses, and malicious behaviors of computing entities, widely known under the term "Byzantine fault-tolerance". The author introduces these notions in an incremental manner, starting from a clear specification, followed by algorithms which are first described intuitively and then proved correct. The book also presents impossibility results in classic distributed computing models, along with strategies, mainly failure detectors and randomization, that allow us to enrich these models. In this sense, the book constitutes an introduction to the science of distributed computing, with applications in all domains of distributed systems, such as cloud computing and blockchains. Each chapter comes with exercises and bibliographic notes to help the reader approach, understand, and master the fascinating field of fault-tolerant distributed computing.

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book's content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum field theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.

This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop " Geometric and Numerical Foundations of Movements " held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.

The discussions and plans on all scienti?c, advisory, and political levels to realize an even larger "European Supercomputer" in Germany, where the hardware costs alone will be hundreds of millions Euro - much more than in the past - are getting closer to realization. As part of the strategy, the three national supercomputing centres HLRS (Stuttgart), NIC/JSC (Julic h) and LRZ (Munich) have formed the Gauss Centre for Supercomputing (GCS) as a new virtual organization enabled by an agreement between the Federal Ministry of Education and Research (BMBF) and the state ministries for research of Baden-Wurttem berg, Bayern, and Nordrhein-Westfalen. Already today, the GCS provides the most powerful high-performance computing - frastructure in Europe. Through GCS, HLRS participates in the European project PRACE (Partnership for Advances Computing in Europe) and - tends its reach to all European member countries. These activities aligns well with the activities of HLRS in the European HPC infrastructure project DEISA (Distributed European Infrastructure for Supercomputing Appli- tions) and in the European HPC support project HPC-Europa. Beyond that, HLRS and its partners in the GCS have agreed on a common strategy for the installation of the next generation of leading edge HPC hardware over the next ?ve years. The University of Stuttgart and the University of Karlsruhe have furth- more agreed to bundle their competences and resources.

Due to the fast growth of the Web and the difficulties in finding desired information, efficient and effective information retrieval systems have become more important than ever, and the search engine has become an essential tool for many people. The ranker, a central component in every search engine, is responsible for the matching between processed queries and indexed documents. Because of its central role, great attention has been paid to the research and development of ranking technologies. In addition, ranking is also pivotal for many other information retrieval applications, such as collaborative filtering, definition ranking, question answering, multimedia retrieval, text summarization, and online advertisement. Leveraging machine learning technologies in the ranking process has led to innovative and more effective ranking models, and eventually to a completely new research area called "learning to rank." Liu first gives a comprehensive review of the major approaches to learning to rank. For each approach he presents the basic framework, with example algorithms, and he discusses its advantages and disadvantages. He continues with some recent advances in learning to rank that cannot be simply categorized into the three major approaches - these include relational ranking, query-dependent ranking, transfer ranking, and semisupervised ranking. His presentation is completed by several examples that apply these technologies to solve real information retrieval problems, and by theoretical discussions on guarantees for ranking performance. This book is written for researchers and graduate students in both information retrieval and machine learning. They will find here the only comprehensive description of the state of the art in a field that has driven the recent advances in search engine development.

The aim of this book is to provide insight into Data Science and Artificial Learning Techniques based on Industry 4.0, conveys how Machine Learning & Data Science are becoming an essential part of industrial and academic research. Varying from healthcare to social networking and everywhere hybrid models for Data Science, Al, and Machine Learning are being used. The book describes different theoretical and practical aspects and highlights how new systems are being developed. Along with focusing on the research trends, challenges and future of AI in Data Science, the book explores the potential for integration of advanced AI algorithms, addresses the challenges of Data Science for Industry 4.0, covers different security issues, includes qualitative and quantitative research, and offers case studies with working models. This book also provides an overview of AI and Data Science algorithms for readers who do not have a strong mathematical background. Undergraduates, postgraduates, academicians, researchers, and industry professionals will benefit from this book and use it as a guide.