High Level Structures for Quantum Computing
This book is concerned with the models of quantum computation. Information processing based on the rules of quantum mechanics provides us with new opportunities for developing more efficient algorithms and protocols. However, to harness the power offered by quantum information processing it is essential to control the behavior of quantum mechanical objects in a precise manner. As this seems to be conceptually difficult at the level of quantum states and unitary gates, high-level quantum programming languages have been proposed for this purpose. The aim of this book is to provide an introduction to abstract models of computation used in quantum information theory. Starting from the abstract models of Turing machine and finite automata, we introduce the models of Boolean circuits and Random Access Machine and use them to present quantum programming techniques and quantum programming languages. Table of Contents: Introduction / Turing machines / Quantum Finite State Automata / Computational Circuits / Random Access Machines / Quantum Programming Environment / Quantum Programming Languages / Imperative quantum programming / Functional Quantum Programming / Outlook
Automated Verification of Concurrent Search Structures
Search structures support the fundamental data storage primitives on key-value pairs: insert a pair, delete by key, search by key, and update the value associated with a key. Concurrent search structures are parallel algorithms to speed access to search structures on multicore and distributed servers. These sophisticated algorithms perform fine-grained synchronization between threads, making them notoriously difficult to design correctly. Indeed, bugs have been found both in actual implementations and in the designs proposed by experts in peer-reviewed publications. The rapid development and deployment of these concurrent algorithms has resulted in a rift between the algorithms that can be verified by the state-of-the-art techniques and those being developed and used today. The goal of this book is to show how to bridge this gap in order to bring the certified safety of formal verification to high-performance concurrent search structures. Similar techniques and frameworks can be applied to concurrent graph and network algorithms beyond search structures.
Linked Data
The World Wide Web has enabled the creation of a global information space comprising linked documents. As the Web becomes ever more enmeshed with our daily lives, there is a growing desire for direct access to raw data not currently available on the Web or bound up in hypertext documents. Linked Data provides a publishing paradigm in which not only documents, but also data, can be a first class citizen of the Web, thereby enabling the extension of the Web with a global data space based on open standards - the Web of Data. In this Synthesis lecture we provide readers with a detailed technical introduction to Linked Data. We begin by outlining the basic principles of Linked Data, including coverage of relevant aspects of Web architecture. The remainder of the text is based around two main themes - the publication and consumption of Linked Data. Drawing on a practical Linked Data scenario, we provide guidance and best practices on: architectural approaches to publishing Linked Data; choosing URIs and vocabularies to identify and describe resources; deciding what data to return in a description of a resource on the Web; methods and frameworks for automated linking of data sets; and testing and debugging approaches for Linked Data deployments. We give an overview of existing Linked Data applications and then examine the architectures that are used to consume Linked Data from the Web, alongside existing tools and frameworks that enable these. Readers can expect to gain a rich technical understanding of Linked Data fundamentals, as the basis for application development, research or further study. Table of Contents: List of Figures / Introduction / Principles of Linked Data / The Web of Data / Linked Data Design Considerations / Recipes for Publishing Linked Data / Consuming Linked Data / Summary and Outlook
Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition
This synthesis lecture presents an intuitive introduction to the mathematics of motion and deformation in computer graphics. Starting with familiar concepts in graphics, such as Euler angles, quaternions, and affine transformations, we illustrate that a mathematical theory behind these concepts enables us to develop the techniques for efficient/effective creation of computer animation. This book, therefore, serves as a good guidepost to mathematics (differential geometry and Lie theory) for students of geometric modeling and animation in computer graphics. Experienced developers and researchers will also benefit from this book, since it gives a comprehensive overview of mathematical approaches that are particularly useful in character modeling, deformation, and animation.
The Envisionment and Discovery Collaboratory (EDC)
The Envisionment and Discovery Collaboratory (EDC) is a long-term research platform exploring immersive socio-technical environments in which stakeholders can collaboratively frame and solve problems and discuss and make decisions in a variety of application domains and different disciplines. The knowledge to understand, frame, and solve these problems does not already exist, but is constructed and evolves in ongoing interactions and collaborations among stakeholders coming from different disciplines providing a unique and challenging environment to study, foster, and support human-centered informatics, design, creativity, and learning. At the social level, the EDC is focused on the collaborative construction of artifacts rather than the sharing of individually constructed items. It brings individuals together in face-to-face meetings, encouraging and supporting them to engage, individually and collectively, in action and reflection. At the technological level, the EDC integrates tabletop computing environments, tangible objects, sketching support, geographic information systems, visualization software, and an envisioned virtual implementation. This book is based on 20 years of research and development activities that brought together interdisciplinary teams of researchers, educators, designers, and practitioners from different backgrounds. The EDC originated with the merging of two research paradigms from disparate disciplines to build on the strengths, approaches, and perspectives of each. This book describes the artifacts and scenarios that were developed, with the goal of providing inspiration for human-centered informatics not focused on technologies in search of a purpose but on the development of systems supporting stakeholders to explore personally meaningful problems. These developments have inspired numerous research and teaching activities. The challenges, prototypical systems, and lessons learned represent important milestones in the development and evolution of the EDC that are relevant for future research activities and practices in human-centered informatics.
Vivo
The world of scholarship is changing rapidly. Increasing demands on scholars, the growing size and complexity of questions and problems to be addressed, and advances in sophistication of data collection, analysis, and presentation require new approaches to scholarship. A ubiquitous, open information infrastructure for scholarship, consisting of linked open data, open-source software tools, and a community committed to sustainability are emerging to meet the needs of scholars today. This book provides an introduction to VIVO, http: //vivoweb.org/, a tool for representing information about research and researchers -- their scholarly works, research interests, and organizational relationships. VIVO provides an expressive ontology, tools for managing the ontology, and a platform for using the ontology to create and manage linked open data for scholarship and discovery. Begun as a project at Cornell and further developed by an NIH funded consortium, VIVO is now being established as an open-source project with community participation from around the world. By the end of 2012, over 20 countries and 50 organizations will provide information in VIVO format on more than one million researchers and research staff, including publications, research resources, events, funding, courses taught, and other scholarly activity. The rapid growth of VIVO and of VIVO-compatible data sources speaks to the fundamental need to transform scholarship for the 21st century. Table of Contents: Scholarly Networking Needs and Desires / The VIVO Ontology / Implementing VIVO and Filling It with Life / Case Study: University of Colorado at Boulder / Case Study: Weill Cornell Medical College / Extending VIVO / Analyzing and Visualizing VIVO Data / The Future of VIVO: Growing the Community
Virtual Material Acquisition and Representation for Computer Graphics
This book provides beginners in computer graphics and related fields a guide to the concepts, models, and technologies for realistic rendering of material appearance. It provides a complete and thorough overview of reflectance models and acquisition setups, along with providing a selection of the available tools to explore, visualize, and render the reflectance data. Reflectance models are under continuous development, since there is still no straightforward solution for general material representations. Every reflectance model is specific to a class of materials. Hence, each has strengths and weaknesses, which the book highlights in order to help the reader choose the most suitable model for any purpose. The overview of the acquisition setups will provide guidance to a reader who needs to acquire virtual materials and will help them to understand which measurement setup can be useful for a particular purpose, while taking into account the performance and the expected cost derived fromthe required components. The book also describes several recent open source software solutions, useful for visualizing and manipulating a wide variety of reflectance models and data.
A Guide to Visual Multi-Level Interface Design From Synthesis of Empirical Study Evidence
Displaying multiple levels of data visually has been proposed to address the challenge of limited screen space. Although many previous empirical studies have addressed different aspects of this question, the information visualization research community does not currently have a clearly articulated consensus on how, when, or even if displaying data at multiple levels is effective. To shed more light on this complex topic, we conducted a systematic review of 22 existing multi-level interface studies to extract high-level design guidelines. To facilitate discussion, we cast our analysis findings into a four-point decision tree: (1) When are multi-level displays useful? (2) What should the higher visual levels display? (3) Should the different visual levels be displayed simultaneously, or one at a time? (4) Should the visual levels be embedded in a single display, or separated into multiple displays? Our analysis resulted in three design guidelines: (1) the number of levels in display anddata should match; (2) high visual levels should only display task-relevant information; (3) simultaneous display, rather than temporal switching, is suitable for tasks with multi-level answers. Table of Contents: Introduction / Terminology / Methodology / Summary of Studies / Decision 1: Single or Multi-level Interface? / Decision 2: How to Create the High-Level Displays? / Decision 3: Simultaneous or Temporal Displays of the Multiple Visual Levels / Decision 4: How to Spatially Arrange the Visual Levels, Embedded or Separate? / Limitations of Study / Design Recommendations / Discussion and Future Work
Storing Clocked Programs Inside DNA
In the history of modern computation, large mechanical calculators preceded computers. A person would sit there punching keys according to a procedure and a number would eventually appear. Once calculators became fast enough, it became obvious that the critical path was the punching rather than the calculation itself. That is what made the stored program concept vital to further progress. Once the instructions were stored in the machine, the entire computation could run at the speed of the machine. This book shows how to do the same thing for DNA computing. Rather than asking a robot or a person to pour in specific strands at different times in order to cause a DNA computation to occur (by analogy to a person punching numbers and operations into a mechanical calculator), the DNA instructions are stored within the solution and guide the entire computation. We show how to store straight line programs, conditionals, loops, and a rudimentary form of subroutines. To achieve this goal, the book proposes a complete language for describing the intrinsic topology of DNA complexes and nanomachines, along with the dynamics of such a system. We then describe dynamic behavior using a set of basic transitions, which operate on a small neighborhood within a complex in a well-defined way. These transitions can be formalized as purely syntactical functions of the string representations. Building on that foundation, the book proposes a novel machine motif which constitutes an instruction stack, allowing for the clocked release of an arbitrary sequence of DNA instruction or data strands. The clock mechanism is built of special strands of DNA called ""tick"" and ""tock."" Each time a ""tick"" and ""tock"" enter a DNA solution, a strand is released from an instruction stack (by analogy to the way in which as a clock cycle in an electronic computer causes a new instruction to enter a processing unit). As long as there remain strands on the stack, the next cycle will release a new instruction strand. Regardless of the actual strand or component to be released at any particular clock step, the ""tick"" and ""tock"" fuel strands remain the same, thus shifting the burden of work away from the end user of a machine and easing operation. Pre-loaded stacks enable the concept of a stored program to be realized as a physical DNA mechanism. A conceptual example is given of such a stack operating a walker device. The stack allows for a user to operate such a clocked walker by means of simple repetition of adding two fuel types, in contrast to the previous mechanism of adding a unique fuel -- at least 12 different types of strands -- for each step of the mechanism. We demonstrate by a series of experiments conducted in Ned Seeman's lab that it is possible to ""initialize"" a clocked stored program DNA machine. We end the book with a discussion of the design features of a programming language for clocked DNA programming. There is a lot left to do. Table of Contents: Introduction / Notation / A Topological Description of DNA Computing / Machines and Motifs / Experiment: Storing Clocked Programs in DNA / A Clocked DNA Programming Language
![IB Math AA [Analysis and Approaches] Internal Assessment](https://cdn.kingstone.com.tw/english/images/product/1552/9781999611552m.webp "IB Math AA [Analysis and Approaches] Internal Assessment")
IB Math AA [Analysis and Approaches] Internal Assessment
This book is an extensive guide to the IB Mathematics Analysis and Approaches Internal Assessment component. It provides IB Diploma students with tips, resources, and ideas to help them maximize their marks on their IA. Our guide makes frequent reference to the grading matrix and the format that your IA should follow, as well as highlighting details which you must bear in mind when carrying out your investigation. There is a 50-page introductory section which includes step-by-step advice on: - Structure: how to plan your Math IA the ideal way- Ideas: an exhaustive list of excellent sources and inspirational websites- Assessment: maximizing your marks with one eye on the grading criterion- Technology: which tools can be used to improve your IA Alongside the extensive guide, we have included SEVEN excellent student IA which have scored near-perfect marks after being moderated, including several 20/20 explorations.
The Complexity of Noise
In quantum computing, where algorithms exist that can solve computational problems more efficiently than any known classical algorithms, the elimination of errors that result from external disturbances or from imperfect gates has become the "holy grail", and a worldwide quest for a large scale fault-tolerant, and computationally superior, quantum computer is currently taking place. Optimists rely on the premise that, under a certain threshold of errors, an arbitrary long fault-tolerant quantum computation can be achieved with only moderate (i.e., at most polynomial) overhead in computational cost. Pessimists, on the other hand, object that there are in principle (as opposed to merely technological) reasons why such machines are still inexistent, and that no matter what gadgets are used, large scale quantum computers will never be computationally superior to classical ones. Lacking a complete empirical characterization of quantum noise, the debate on the physical possibility of such machines invites philosophical scrutiny. Making this debate more precise by suggesting a novel statistical mechanical perspective thereof is the goal of this project. Table of Contents: Introduction / The Curse of the Open System / To Balance a Pencil on Its Tip / Universality at All Cost / Coda
Time-Fractional Order Biological Systems with Uncertain Parameters
The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, ��������λ����μ controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters. However, in real-lifeapplications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge. In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globe.
Negative Quantum Channels
This book is a brief introduction to negative quantum channels, i.e., linear, trace-preserving (and consistent) quantum maps that are not completely positive. The flat and sharp operators are introduced and explained. Complete positivity is presented as a mathematical property, but it is argued that complete positivity is not a physical requirement of all quantum operations. Negativity, a measure of the lack of complete positivity, is proposed as a tool for empirically testing complete positivity assumptions. Table of Contents: Preface / Acknowledgments / Introduction and Definition of Terms / Tomography / Non-Positive Reduced Dynamics / Complete Positivity / Physical Motivation of Complete Positivity / Measures of Complete Positivity / Negative Channels / Negative Climates with Diagonal Composite Dynamics / Rabi Channels / Physical Motivations for Sharp Operations / Negative Qubit Channel Examples with Multi-Qubit Baths / Proposed Experimental Demonstration of Negativity / Implications of Negative Channels / Uses for Negative Channels / Conclusions / Bibliography / Author's Biography
Replicated Data Management for Mobile Computing
Managing data in a mobile computing environment invariably involves caching or replication. In many cases, a mobile device has access only to data that is stored locally, and much of that data arrives via replication from other devices, PCs, and services. Given portable devices with limited resources, weak or intermittent connectivity, and security vulnerabilities, data replication serves to increase availability, reduce communication costs, foster sharing, and enhance survivability of critical information. Mobile systems have employed a variety of distributed architectures from client-server caching to peer-to-peer replication. Such systems generally provide weak consistency models in which read and update operations can be performed at any replica without coordination with other devices. The design of a replication protocol then centers on issues of how to record, propagate, order, and filter updates. Some protocols utilize operation logs, whereas others replicate state. Systems might provide best-effort delivery, using gossip protocols or multicast, or guarantee eventual consistency for arbitrary communication patterns, using recently developed pairwise, knowledge-driven protocols. Additionally, systems must detect and resolve the conflicts that arise from concurrent updates using techniques ranging from version vectors to read-write dependency checks. This lecture explores the choices faced in designing a replication protocol, with particular emphasis on meeting the needs of mobile applications. It presents the inherent trade-offs and implicit assumptions in alternative designs. The discussion is grounded by including case studies of research and commercial systems including Coda, Ficus, Bayou, Sybase's iAnywhere, and Microsoft's Sync Framework. Table of Contents: Introduction / System Models / Data Consistency / Replicated Data Protocols / Partial Replication / Conflict Management / Case Studies / Conclusions / Bibliography
Controlling Energy Demand in Mobile Computing Systems
This lecture provides an introduction to the problem of managing the energy demand of mobile devices. Reducing energy consumption, primarily with the goal of extending the lifetime of battery-powered devices, has emerged as a fundamental challenge in mobile computing and wireless communication. The focus of this lecture is on a systems approach where software techniques exploit state-of-the-art architectural features rather than relying only upon advances in lower-power circuitry or the slow improvements in battery technology to solve the problem. Fortunately, there are many opportunities to innovate on managing energy demand at the higher levels of a mobile system. Increasingly, device components offer low power modes that enable software to directly affect the energy consumption of the system. The challenge is to design resource management policies to effectively use these capabilities. The lecture begins by providing the necessary foundations, including basic energy terminology andwidely accepted metrics, system models of how power is consumed by a device, and measurement methods and tools available for experimental evaluation. For components that offer low power modes, management policies are considered that address the questions of when to power down to a lower power state and when to power back up to a higher power state. These policies rely on detecting periods when the device is idle as well as techniques for modifying the access patterns of a workload to increase opportunities for power state transitions. For processors with frequency and voltage scaling capabilities, dynamic scheduling policies are developed that determine points during execution when those settings can be changed without harming quality of service constraints. The interactions and tradeoffs among the power management policies of multiple devices are discussed. We explore how the effective power management on one component of a system may have either a positive or negative impact on overall energy consumption or on the design of policies for another component. The important role that application-level involvement may play in energy management is described, with several examples of cross-layer cooperation. Application program interfaces (APIs) that provide information flow across the application-OS boundary are valuable tools in encouraging development of energy-aware applications. Finally, we summarize the key lessons of this lecture and discuss future directions in managing energy demand.
Interactive Gpu-Based Visualization of Large Dynamic Particle Data
Prevalent types of data in scientific visualization are volumetric data, vector field data, and particle-based data. Particle data typically originates from measurements and simulations in various fields, such as life sciences or physics. The particles are often visualized directly, that is, by simple representants like spheres. Interactive rendering facilitates the exploration and visual analysis of the data. With increasing data set sizes in terms of particle numbers, interactive high-quality visualization is a challenging task. This is especially true for dynamic data or abstract representations that are based on the raw particle data. This book covers direct particle visualization using simple glyphs as well as abstractions that are application-driven such as clustering and aggregation. It targets visualization researchers and developers who are interested in visualization techniques for large, dynamic particle-based data. Its explanations focus on GPU-accelerated algorithms for high-performance rendering and data processing that run in real-time on modern desktop hardware. Consequently, the implementation of said algorithms and the required data structures to make use of the capabilities of modern graphics APIs are discussed in detail. Furthermore, it covers GPU-accelerated methods for the generation of application-dependent abstract representations. This includes various representations commonly used in application areas such as structural biology, systems biology, thermodynamics, and astrophysics.
Principles of Blockchain Systems
This book is the first to present the state of the art and provide technical focus on the latest advances in the foundations of blockchain systems. It is a collaborative work between specialists in cryptography, distributed systems, formal languages, and economics, and addresses hot topics in blockchains from a theoretical perspective: cryptographic primitives, consensus, formalization of blockchain properties, game theory applied to blockchains, and economical issues. This book reflects the expertise of the various authors, and is intended to benefit researchers, students, and engineers who seek an understanding of the theoretical foundations of blockchains.
Basic Topology 2
1. Background on Topology, Analysis and Algebra.- 2. Topological Groups.- 3. Topology of Manifolds.- 4. Lie Groups and Lie Algebra.- 5. Brief History of Topological Groups, Manifold and Lie Groups.
Differential Equations
This new edition is re-organized to make it more useful and more accessible. The most frequently taught topics are now up front. And the major applications are isolated in their own chapters. This makes this edition the most useable and flexible of any previous editions.
Discrete Distributions in Engineering and the Applied Sciences
This is an introductory book on discrete statistical distributions and its applications. It discusses only those that are widely used in the applications of probability and statistics in everyday life. The purpose is to give a self-contained introduction to classical discrete distributions in statistics. Instead of compiling the important formulas (which are available in many other textbooks), we focus on important applications of each distribution in various applied fields like bioinformatics, genomics, ecology, electronics, epidemiology, management, reliability, etc., making this book an indispensable resource for researchers and practitioners in several scientific fields. Examples are drawn from different fields. An up-to-date reference appears at the end of the book. Chapter 1 introduces the basic concepts on random variables, and gives a simple method to find the mean deviation (MD) of discrete distributions. The Bernoulli and binomial distributions are discussedin detail in Chapter 2. A short chapter on discrete uniform distribution appears next. The next two chapters are on geometric and negative binomial distributions. Chapter 6 discusses the Poisson distribution in-depth, including applications in various fields. Chapter 7 is on hypergeometric distribution. As most textbooks in the market either do not discuss, or contain only brief description of the negative hypergeometric distribution, we have included an entire chapter on it. A short chapter on logarithmic series distribution follows it, in which a theorem to find the kth moment of logarithmic distribution using (k-1)th moment of zero-truncated geometric distribution is presented. The last chapter is on multinomial distribution and its applications. The primary users of this book are professionals and practitioners in various fields of engineering and the applied sciences. It will also be of use to graduate students in statistics, research scholars in science disciplines, and teachers of statistics, biostatistics, biotechnology, education, and psychology.
Numerical Integration of Space Fractional Partial Differential Equations
Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. The Caputo derivative is defined as a convolution integral. Thus, rather than being local (with a value at a particular point in space), the Caputo derivative is non-local (it is based on an integration in space), which is one of the reasons that it has properties not shared by integer derivatives. A principal objective of the two volumes is to provide the reader with a set of documented R routines that are discussed in detail, and can be downloaded and executed without having to first study the details of the relevant numerical analysis and then code a set of routines. In the first volume, the emphasis is on basic concepts of SFPDEs and the associated numerical algorithms. The presentation is not as formal mathematics, e.g., theorems and proofs. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.
Essays in Constructive Mathematics
This collection of essays aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it. All definitions and proofs are based on finite algorithms, which pave illuminating paths to nontrivial results, primarily in algebra, number theory, and the theory of algebraic curves. The second edition adds a new set of essays that reflect and expand upon the first. The topics covered derive from classic works of nineteenth-century mathematics, among them Galois's theory of algebraic equations, Gauss's theory of binary quadratic forms, and Abel's theorems about integrals of rational differentials on algebraic curves. Other topics include Newton's diagram, the fundamental theorem of algebra, factorization of polynomials over constructive fields, and the spectral theorem for symmetric matrices, all treated using constructive methods in the spirit of Kronecker. In this second edition, the essays of the first edition are augmented with newessays that give deeper and more complete accounts of Galois's theory, points on an algebraic curve, and Abel's theorem. Readers will experience the full power of Galois's approach to solvability by radicals, learn how to construct points on an algebraic curve using Newton's diagram, and appreciate the amazing ideas introduced by Abel in his 1826 Paris memoir on transcendental functions. Mathematical maturity is required of the reader, and some prior knowledge of Galois theory is helpful. But experience with constructive mathematics is not necessary; readers should simply be willing to set aside abstract notions of infinity and explore deep mathematics via explicit constructions.
Two Arguments for the Identity of Indiscernibles
The Principle of Identity of Indiscernibles is the thesis that, necessarily, no two (concrete) objects differ only numerically. This is the weakest version of the Principle of Identity of Indiscernibles. Gonzalo Rodriguez-Pereyra argues that there is no trivial version of the Principle of Identity of Indiscernibles, since what is usually known as the trivial version of the principle is consistent with objects differing only numerically. He provides two positive arguments for the Principle: one based on broadly Humean considerations excluding a certain kind of necessary connection between distinct objects, and the other based on ideas about what grounds the having of certain properties by objects. This book also presents two new arguments against restricted versions of the principle according to which, necessarily, no two objects can be purely qualitatively indiscernible or intrinsically purely qualitatively indiscernible. It is further argued that one of the arguments for the weakest version of the principle can be extended to abstract objects. The conclusion is drawn that, necessarily, there are no objects, whether abstract or concrete, that differ only numerically.
Libraries and the Semantic Web
This book covers the concept of the Semantic Web--what it is, the components that comprise it, including Linked Data, and the various ways that libraries are engaged in contributing to its development in making library resources and services ever more accessible to end-users.
Truth and Knowledge
We look at problems of truth and knowledge from various angles. Insufficient information may prevent the direct use of certain operations, as the use of probability in legal reasoning, so we have to take detours. We may have only contradictory information from different sources, and will use and adjust past reliability of the sources to evaluate the information.Conjectures about homogenousness of the domain may also help.On a more formal level, we extend the formal semantics of counterfactual conditionals to analogical reasoning, and examine Yablo's Paradox using various concepts and examples.
Relevance Logics and other Tools for Reasoning. Essays in Honor of J. Michael Dunn
This book honors J. Michael Dunn, who was a preeminent relevance logician. Dunn's careerspanned over 50 years and his research results had an impact on philosophy, mathematics and informatics. Dunn often used algebraic techniques in his research into logics such as relevance, orthomodular and substructural logics. He invented the logic R-mingle and the sequent calculus LR+; he proved crucial theorems about 2-valued first-order logic and non-classical higher-order logics - among many other results. The papers in this volume touch upon topics that Dunn was concerned with. Some authors were students or colleagues of Dunn; some other authors had not met Dunn in person, but share his research interests. None of the articles published here have appeared in print before; indeed, most of the papers were written specifically for this collection. The diversity of the themes of the articles reflects the scope of Dunn's own research in logic. It will also ensure that anybody with an interest in logic - whether a student, a logician or a scholar in another field - will find reading this book a worthwhile endeavor. The editor, Katalin Bimb籀 was the 14th Ph.D. student of J. Michael Dunn at Indiana University in Bloomington, IN, U.S.A.; currently, she is a professor of philosophy at the University of Alberta in Canada.
Analytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field
The investigation of the behavior of ferromagnetic particles in an external magnetic field is important for use in a wide range of applications in magnetostatics problems, from biomedicine to engineering. To the best of the author's knowledge, the systematic analysis for this kind of investigation is not available in the current literature. Therefore, this book contributes a complete solution for investigating the behavior of two ferromagnetic spherical particles, immersed in a uniform magnetic field, by obtaining exact mathematical models on a boundary value problem. While there are a vast number of common numerical and analytical methods for solving boundary value problems in the literature, the rapidly growing complexity of these solutions causes increase usage of the computer tools in practical cases. We analytically solve the boundary value problem by using a special technique called a bispherical coordinates system and the numerical computations were obtained by a computer tool. In addition to these details, we will present step-by-step instructions with simple explanations throughout the book, in an effort to act as inspiration in the reader's own modeling for relevant applications in science and engineering. On the other hand, the resulting analytical expressions will constitute benchmark solutions for specified geometric arrangements, which are beneficial for determining the validity of other relevant numerical techniques. The generated results are analyzed quantitatively as well as qualitatively in various approaches. Moreover, the methodology of this book can be adopted for real-world applications in the fields of ferrohydrodynamics, applied electromagnetics, fluid dynamics, electrical engineering, and so forth. Higher-level university students, academics, engineers, scientists, and researchers involved in the aforementioned fields are the intended audience for this book.
Transition to Advanced Mathematics
This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics.
Facets of Algebraic Geometry: Volume 2
Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.
Mathematical Logic
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fra簿ss矇's characterization of elementary equivalence, Lindstr繹m's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
Facets of Algebraic Geometry: Volume 1
Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the first of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.
Emmy Noether - Mathematician Extraordinaire
Although she was famous as the "mother of modern algebra," Emmy Noether's life and work have never been the subject of an authoritative scientific biography. Emmy Noether - Mathematician Extraordinaire represents the most comprehensive study of this singularly important mathematician to date. Focusing on key turning points, it aims to provide an overall interpretation of Noether's intellectual development while offering a new assessment of her role in transforming the mathematics of the twentieth century.Hermann Weyl, her colleague before both fled to the United States in 1933, fully recognized that Noether's dynamic school was the very heart and soul of the famous G繹ttingen community. Beyond her immediate circle of students, Emmy Noether's lectures and seminars drew talented mathematicians from all over the world. Four of the most important were B.L. van der Waerden, Pavel Alexandrov, Helmut Hasse, and Olga Taussky. Noether's classic papers on ideal theory inspiredvan der Waerden to recast his research in algebraic geometry. Her lectures on group theory motivated Alexandrov to develop links between point set topology and combinatorial methods. Noether's vision for a new approach to algebraic number theory gave Hasse the impetus to pursue a line of research that led to the Brauer-Hasse-Noether Theorem, whereas her abstract style clashed with Taussky's approach to classical class field theory during a difficult time when both were trying to find their footing in a foreign country.Although similar to Proving It Her Way: Emmy Noether, a Life in Mathematics, this lengthier study addresses mathematically minded readers. Thus, it presents a detailed analysis of Emmy Noether's work with Hilbert and Klein on mathematical problems connected with Einstein's theory of relativity. These efforts culminated with her famous paper "Invariant Variational Problems," published one year before she joined the G繹ttingen faculty in 1919.
Computational Topology for Data Analysis
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions - like zigzag persistence and multiparameter persistence - and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Pop-Up Geometry
Anyone browsing at the stationery store will see an incredible array of pop-up cards available for any occasion. The workings of pop-up cards and pop-up books can be remarkably intricate. Behind such designs lies beautiful geometry involving the intersection of circles, cones, and spheres, the movements of linkages, and other constructions. The geometry can be modelled by algebraic equations, whose solutions explain the dynamics. For example, several pop-up motions rely on the intersection of three spheres, a computation made every second for GPS location. Connecting the motions of the card structures with the algebra and geometry reveals abstract mathematics performing tangible calculations. Beginning with the nephroid in the 19th-century, the mathematics of pop-up design is now at the frontiers of rigid origami and algorithmic computational complexity. All topics are accessible to those familiar with high-school mathematics; no calculus required. Explanations are supplemented by 140+ figures and 20 animations.
Pop-Up Geometry
Anyone browsing at the stationery store will see an incredible array of pop-up cards available for any occasion. The workings of pop-up cards and pop-up books can be remarkably intricate. Behind such designs lies beautiful geometry involving the intersection of circles, cones, and spheres, the movements of linkages, and other constructions. The geometry can be modelled by algebraic equations, whose solutions explain the dynamics. For example, several pop-up motions rely on the intersection of three spheres, a computation made every second for GPS location. Connecting the motions of the card structures with the algebra and geometry reveals abstract mathematics performing tangible calculations. Beginning with the nephroid in the 19th-century, the mathematics of pop-up design is now at the frontiers of rigid origami and algorithmic computational complexity. All topics are accessible to those familiar with high-school mathematics; no calculus required. Explanations are supplemented by 140+ figures and 20 animations.
Mathematical Modelling with Differential Equations
Mathematical Modelling with Differential Equations aims to introduce various strategies for modelling systems using differential equations. Some of these methodologies are elementary and quite direct to comprehend and apply while others are complex in nature and require thoughtful, deep contemplation. Many topics discussed in the chapter do not appear in any of the standard textbooks and this provides users an opportunity to consider a more general set of interesting systems that can be modelled. For example, the book investigates the evolution of a "toy universe," discusses why "alternate futures" exists in classical physics, constructs approximate solutions to the famous Thomas-Fermi equation using only algebra and elementary calculus, and examines the importance of "truly nonlinear" and oscillating systems. Features Introduces, defines, and illustrates the concept of "dynamic consistency" as the foundation of modelling. Can be used as the basis of an upper-level undergraduate course on general procedures for mathematical modelling using differential equations. Discusses the issue of dimensional analysis and continually demonstrates its value for both the construction and analysis of mathematical modelling.
Recent Developments of Function Spaces and Their Applications I
This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John-Nirenberg spaces, Sobolev spaces, and Besov and Triebel-Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calder籀n operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schr繹dinger equation.
Symmetry in Graphs
This is the first full-length book on the major theme of symmetry in graphs. Forming part of algebraic graph theory, this fast-growing field is concerned with the study of highly symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures, primarily by group-theoretic techniques. In practice the street goes both ways and these investigations shed new light on permutation groups and related algebraic structures. The book assumes a first course in graph theory and group theory but no specialized knowledge of the theory of permutation groups or vertex-transitive graphs. It begins with the basic material before introducing the field's major problems and most active research themes in order to motivate the detailed discussion of individual topics that follows. Featuring many examples and over 450 exercises, it is an essential introduction to the field for graduate students and a valuable addition to any algebraic graph theorist's bookshelf.
Studies in Inductive Logic and Probability, Volume II
Studies in Inductive Logic and Probability, Volume II--edited by Richard C. Jeffrey--delivers the long-awaited completion of Rudolf Carnap's "Basic System of Inductive Logic" and, with it, a definitive bridge between logical probability and modern Bayesian thought. Opening with the posthumous Part II of Carnap's program--on attribute spaces, confirmation across predicate families, and the celebrated λ-γ systems--the volume traces how exchangeability, similarity, and proximity reshape predictive inference beyond the straight rule. Jeffrey's editorial apparatus situates Carnap's late revisions and includes the originally withheld 禮21, offering a rare window onto the extensions Carnap envisaged but did not live to finish. Surrounding this keystone are landmark contributions that push the program into contemporary terrain. Hintikka and Niiniluoto secure positive confirmation for universal generalizations; Kuipers maps neighboring approaches; de Finetti's classic paper on partial exchangeability (in translation) anchors the treatment of analogy across families; Link and Diaconis-Freedman supply modern representation theorems; Fenstad reconnects logical languages with probabilistic semantics; and David Lewis's "Principal Principle" reweaves objective chance into subjective credence. Capped by Douglas Hoover's note on nonstandard measures, the collection is both capstone and launchpad--indispensable for philosophers of science, statisticians, and decision theorists who want Carnap's foundations rendered in the idiom that now governs rational belief and inductive learning. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1980.
Studies in Inductive Logic and Probability, Volume II
Studies in Inductive Logic and Probability, Volume II--edited by Richard C. Jeffrey--delivers the long-awaited completion of Rudolf Carnap's "Basic System of Inductive Logic" and, with it, a definitive bridge between logical probability and modern Bayesian thought. Opening with the posthumous Part II of Carnap's program--on attribute spaces, confirmation across predicate families, and the celebrated λ-γ systems--the volume traces how exchangeability, similarity, and proximity reshape predictive inference beyond the straight rule. Jeffrey's editorial apparatus situates Carnap's late revisions and includes the originally withheld 禮21, offering a rare window onto the extensions Carnap envisaged but did not live to finish. Surrounding this keystone are landmark contributions that push the program into contemporary terrain. Hintikka and Niiniluoto secure positive confirmation for universal generalizations; Kuipers maps neighboring approaches; de Finetti's classic paper on partial exchangeability (in translation) anchors the treatment of analogy across families; Link and Diaconis-Freedman supply modern representation theorems; Fenstad reconnects logical languages with probabilistic semantics; and David Lewis's "Principal Principle" reweaves objective chance into subjective credence. Capped by Douglas Hoover's note on nonstandard measures, the collection is both capstone and launchpad--indispensable for philosophers of science, statisticians, and decision theorists who want Carnap's foundations rendered in the idiom that now governs rational belief and inductive learning. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1980.
Algebraic Foundations for Applied Topology and Data Analysis
This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience. The required algebraic background is developed in detail. The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is a user's guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of software packages used in the field. Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students.
The Best Writing on Mathematics 2021
The year's finest mathematical writing from around the world This annual anthology brings together the year's finest mathematics writing from around the world--and you don't need to be a mathematician to enjoy the pieces collected here. These essays--from leading names and fresh new voices--delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice, and taking readers behind the scenes of today's hottest mathematical debates. Here, Viktor Bl疇sj繹 gives a brief history of "lockdown mathematics"; Yelda Nasifoglu decodes the politics of a seventeenth-century play in which the characters are geometric shapes; and Andrew Lewis-Pye explains the basic algorithmic rules and computational procedures behind cryptocurrencies. In other essays, Terence Tao candidly recalls the adventures and misadventures of growing up to become a leading mathematician; Natalie Wolchover shows how old math gives new clues about whether time really flows; and David Hand discusses the problem of "dark data"--information that is missing or ignored. And there is much, much more.
G繹del's Theorem: A Very Short Introduction
bVery Short Introductions: Brilliant, Sharp, Inspiring /b Kurt G繹del first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, nearly a century ago. The theorem challenged prevalent presuppositions about the nature of mathematics and was consequently of considerable mathematical interest, while also raising various deep philosophical questions. G繹del's Theorem has since established itself as a landmark intellectual achievement, having a profound impact on today's mathematical ideas. G繹del and his theorem have attracted something of a cult following, though his theorem is often misunderstood. This Very Short Introduction places the theorem in its intellectual and historical context, and explains the key concepts as well as common misunderstandings of what it actually states. A. W. Moore provides a clear statement of the theorem, presenting two proofs, each of which has something distinctive to teach about its content. Moore also discusses the most important philosophical implications of the theorem. In particular, Moore addresses the famous question of whether the theorem shows the human mind to have mathematical powers beyond those of any possible computer ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Computational Intelligence and Human-Computer Interaction
The present book contains all of the articles that were accepted and published in the Special Issue of MDPI's journal Mathematics titled "Computational Intelligence and Human-Computer Interaction: Modern Methods and Applications". This Special Issue covered a wide range of topics connected to the theory and application of different computational intelligence techniques to the domain of human-computer interaction, such as automatic speech recognition, speech processing and analysis, virtual reality, emotion-aware applications, digital storytelling, natural language processing, smart cars and devices, and online learning. We hope that this book will be interesting and useful for those working in various areas of artificial intelligence, human-computer interaction, and software engineering as well as for those who are interested in how these domains are connected in real-life situations.
Visual Category Theory, CoPart 1
This CoPart is a dual complement to Visual Category Theory Brick by Brick, Part 1. The original series translated abstract categorical concepts into the language of LEGO(R) bricks, and the CoPart series implement the opposite way of translating brick constructions to the standard diagram language of category theory that should benefit comprehension of definitions.Since usual categorical diagrams are black and white and occupy less space on paper, CoParts include additional color-enhanced diagrams in the spirit of brick constructions when arrow source and target parts use different colors.These CoParts from CoSeries (named after opposite categories with reversed arrows) keep the same 1-to-1 page correspondence between Parts and CoParts. Page layout is also similar: location of explanatory notes (written using standard mathematical notation) is the same - only bricks are replaced by letters, dots, and arrows. Therefore, this CoSeries can be used independently from the original series or together.The first CoPart covers the definition of categories, arrows, the composition and associativity of arrows, retracts, equivalence, covariant and contravariant functors, natural transformations, and 2-categories.
Differential Equations and Their Applications: Analysis from a Physicist's Viewpoint
This book is written for students and researchers who are fond of mathematics and the natural sciences. It consists of two parts. Part I presents the theory of analysis in which the mathematical theory is described not as an accomplished palace, but as a building under construction. It uncovers how a theory has been or is being constructed. In Part II, the theory of differential equations is applied to interesting practical problems, such as pursuit-line and tractrix, attack on an object from an airplane, an insect crawling along a stretching rubber rod, the SIR model of a virus infection, string vibration, circular membrane vibration, as well as the wind ripple, sand dune and wave phenomena on a highway. Furthermore, the problems of a one-dimensional lattice vibration, the keyboard percussion vibration and the eigenvalue problems in quantum mechanics, such as the Aharonov-Bohm effect, are also investigated in detail.
