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.
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.
Linear Algebra for Pattern Processing
Linear algebra is one of the most basic foundations of a wide range of scientific domains, and most textbooks of linear algebra are written by mathematicians. However, this book is specifically intended to students and researchers of pattern information processing, analyzing signals such as images and exploring computer vision and computer graphics applications. The author himself is a researcher of this domain. Such pattern information processing deals with a large amount of data, which are represented by high-dimensional vectors and matrices. There, the role of linear algebra is not merely numerical computation of large-scale vectors and matrices. In fact, data processing is usually accompanied with "geometric interpretation." For example, we can think of one data set being "orthogonal" to another and define a "distance" between them or invoke geometric relationships such as "projecting" some data onto some space. Such geometric concepts not only help us mentally visualize abstracthigh-dimensional spaces in intuitive terms but also lead us to find what kind of processing is appropriate for what kind of goals. First, we take up the concept of "projection" of linear spaces and describe "spectral decomposition," "singular value decomposition," and "pseudoinverse" in terms of projection. As their applications, we discuss least-squares solutions of simultaneous linear equations and covariance matrices of probability distributions of vector random variables that are not necessarily positive definite. We also discuss fitting subspaces to point data and factorizing matrices in high dimensions in relation to motion image analysis. Finally, we introduce a computer vision application of reconstructing the 3D location of a point from three camera views to illustrate the role of linear algebra in dealing with data with noise. This book is expected to help students and researchers of pattern information processing deepen the geometric understanding of linear algebra.
On the Design of Game-Playing Agents
Evolving agents to play games is a promising technology. It can provide entertaining opponents for games like Chess or Checkers, matched to a human opponent as an alternative to the perfect and unbeatable opponents embodied by current artifical intelligences. Evolved agents also permit us to explore the strategy space of mathematical games like Prisoner's Dilemma and Rock-Paper-Scissors. This book summarizes, explores, and extends recent work showing that there are many unsuspected factors that must be controlled in order to create a plausible or useful set of agents for modeling cooperation and conflict, deal making, or other social behaviors. The book also provides a proposal for an agent training protocol that is intended as a step toward being able to train humaniform agents--in other words, agents that plausibly model human behavior.
Sound Synthesis, Propagation, and Rendering
This book gives a broad overview of research on sound simulation driven by a variety of applications. Vibrating objects produce sound, which then propagates through a medium such as air or water before finally being heard by a listener. As a crucial sensory channel, sound plays a vital role in many applications. There is a well-established research community in acoustics that has studied the problems related to sound simulation for six decades. Some of the earliest work was motivated by the design of concert halls, theaters, or lecture rooms with good acoustic characteristics. These problems also have been investigated in other applications, including noise control and sound design for urban planning, building construction, and automotive applications. Moreover, plausible or realistic sound effects can improve the sense of presence in a virtual environment or a game. In these applications, sound can provide important clues such as source directionality and spatial size. The book first surveys various sound synthesis methods, including harmonic synthesis, texture synthesis, spectral analysis, and physics-based synthesis. Next, it provides an overview of sound propagation techniques, including wave-based methods, geometric-based methods, and hybrid methods. The book also summarizes various techniques for sound rendering. Finally, it surveys some recent trends, including the use of machine learning methods to accelerate sound simulation and the use of sound simulation techniques for other applications such as speech recognition, source localization, and computer-aided design.
Introduction to Logic, Third Edition
This book is a gentle but rigorous introduction to Formal Logic. It is intended primarily for use at the college level. However, it can also be used for advanced secondary school students, and it can be used at the start of graduate school for those who have not yet seen the material.The approach to teaching logic used here emerged from more than 20 years of teaching logic to students at Stanford University and from teaching logic to tens of thousands of others via online courses on the World Wide Web. The approach differs from that taken by other books in logic in two essential ways, one having to do with content, the other with form.Like many other books on logic, this one covers logical syntax and semantics and proof theory plus induction. However, unlike other books, this book begins with Herbrand semantics rather than the more traditional Tarskian semantics. This approach makes the material considerably easier for students to understand and leaves them with a deeper understanding of what logic is all about.In addition to this text, there are online exercises (with automated grading), online logic tools and applications, online videos of lectures, and an online forum for discussion. They are available at http: //intrologic.stanford.edu/
Digital Heritage Reconstruction Using Super-Resolution and Inpainting
Heritage sites across the world have witnessed a number of natural calamities, sabotage and damage from visitors, resulting in their present ruined condition. Many sites are now restricted to reduce the risk of further damage. Yet these masterpieces are significant cultural icons and critical markers of past civilizations that future generations need to see. A digitally reconstructed heritage site could diminish further harm by using immersive navigation or walkthrough systems for virtual environments. An exciting key element for the viewer is observing fine details of the historic work and viewing monuments in their undamaged form. This book presents image super-resolution methods and techniques for automatically detecting and inpainting damaged regions in heritage monuments, in order to provide an enhanced visual experience. The book presents techniques to obtain higher resolution photographs of the digitally reconstructed monuments, and the resulting images can serve as input to immersive walkthrough systems. It begins with the discussion of two novel techniques for image super-resolution and an approach for inpainting a user-supplied region in the given image, followed by a technique to simultaneously perform super-resolution and inpainting of given missing regions. It then introduces a method for automatically detecting and repairing the damage to dominant facial regions in statues, followed by a few approaches for automatic crack repair in images of heritage scenes. This book is a giant step toward ensuring that the iconic sites of our past are always available, and will never be truly lost.
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.
Aspects of Differential Geometry II
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and K瓣hler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincar矇 duality, and the K羹nneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology ofcompact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.
Statistics is Easy! 2nd Edition
Statistics is the activity of inferring results about a population given a sample. Historically, statistics books assume an underlying distribution to the data (typically, the normal distribution) and derive results under that assumption. Unfortunately, in real life, one cannot normally be sure of the underlying distribution. For that reason, this book presents a distribution-independent approach to statistics based on a simple computational counting idea called resampling. This book explains the basic concepts of resampling, then system atically presents the standard statistical measures along with programs (in the language Python) to calculate them using resampling, and finally illustrates the use of the measures and programs in a case study. The text uses junior high school algebra and many examples to explain the concepts. Th e ideal reader has mastered at least elementary mathematics, likes to think procedurally, and is comfortable with computers. Table of Contents: The Basic Idea/ Pragmatic Considerations when Using Resampling / Terminology / The Essential Stats / Case Study: New Mexico's 2004 Presidential Ballots / References / Bias Corrected Confidence Intervals / Appendix B
The Fundamentals of Analysis for Talented Freshmen
This book assumes the students know some of the basic facts about Calculus. We are very rigorous and expose them to the proofs and the ideas which produce them. In three chapters, this book covers these number systems and the material usually found in a junior-senior advanced Calculus course. It is designed to be a one-semester course for "talented" freshmen. Moreover, it presents a way of thinking about mathematics that will make it much easier to learn more of this subject and be a good preparation for more of the undergraduate curriculum.
The Integral
This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to provide a quick but accurate (and detailed) introduction to all aspects of modern integration theory. It should be accessible to any student who has had calculus and some exposure to upper division mathematics. Table of Contents: Introduction / The Riemann Integral / The Lebesgue Integral / Comparison of the Riemann and Lebesgue Integrals / Other Theories of the Integral
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.
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
Fast Start Integral Calculus
This book introduces integrals, the fundamental theorem of calculus, initial value problems, and Riemann sums. It introduces properties of polynomials, including roots and multiplicity, and uses them as a framework for introducing additional calculus concepts including Newton's method, L'H繫pital's Rule, and Rolle's theorem. Both the differential and integral calculus of parametric, polar, and vector functions are introduced. The book concludes with a survey of methods of integration, including u-substitution, integration by parts, special trigonometric integrals, trigonometric substitution, and partial fractions.
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
Game Theory
This book is a formalization of collected notes from an introductory game theory course taught at Queen's University. The course introduced traditional game theory and its formal analysis, but also moved to more modern approaches to game theory, providing a broad introduction to the current state of the discipline. Classical games, like the Prisoner's Dilemma and the Lady and the Tiger, are joined by a procedure for transforming mathematical games into card games. Included is an introduction and brief investigation into mathematical games, including combinatorial games such as Nim. The text examines techniques for creating tournaments, of the sort used in sports, and demonstrates how to obtain tournaments that are as fair as possible with regards to playing on courts. The tournaments are tested as in-class learning events, providing a novel curriculum item. Example tournaments are provided at the end of the book for instructors interested in running a tournament in their own classroom.The book is appropriate as a text or companion text for a one-semester course introducing the theory of games or for students who wish to get a sense of the scope and techniques of the field.
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
![IB Math AI [Applications and Interpretation] Internal Assessment](https://cdn.kingstone.com.tw/english/images/product/1569/9781999611569.webp "IB Math AI [Applications and Interpretation] Internal Assessment")
IB Math AI [Applications and Interpretation] Internal Assessment
This book is an extensive guide to the IB Mathematics Applications and Interpretation 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.
Applications of Affine and Weyl Geometry
Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and K瓣hler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need---proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting. The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with K瓣hler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and K瓣hler geometry. Another feature of the book is that we have tried wherever possibleto find the original references in the subject for possible historical interest. Thus, we have cited the seminal papers of Levi-Civita, Ricci, Schouten, and Weyl, to name but a few exemplars. We have also given different proofs of various results than those that are given in the literature, to take advantage of the unified treatment of the area given herein.
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
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.
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.
Fast Start Differential Calculus
This book reviews the algebraic prerequisites of calculus, including solving equations, lines, quadratics, functions, logarithms, and trig functions. It introduces the derivative using the limit-based definition and covers the standard function library and the product, quotient, and chain rules. It explores the applications of the derivative to curve sketching and optimization and concludes with the formal definition of the limit, the squeeze theorem, and the mean value theorem.
A Gyrovector Space Approach to Hyperbolic Geometry
The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. These novel analogies that this book captures stem from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Remarkably, the mere introduction of Thomas gyration turns Euclidean geometry into hyperbolic geometry, and reveals mystique analogies that the two geometries share. Accordingly, Thomas gyration gives rise to the prefix "gyro" that isextensively used in the gyrolanguage of this book, giving rise to terms like gyrocommutative and gyroassociative binary operations in gyrogroups, and gyrovectors in gyrovector spaces. Of particular importance is the introduction of gyrovectors into hyperbolic geometry, where they are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrilateral the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrilateral the two diagonals of which intersect at their midpoints. Table of Contents: Gyrogroups / Gyrocommutative Gyrogroups / Gyrovector Spaces / Gyrotrigonometry
Translating Euclid
Translating Euclid reports on an effort to transform geometry for students from a stylus-and-clay-tablet corpus of historical theorems to a stimulating computer-supported collaborative-learning inquiry experience. The origin of geometry was a turning point in the pre-history of informatics, literacy, and rational thought. Yet, this triumph of human intellect became ossified through historic layers of systematization, beginning with Euclid's organization of the Elements of geometry. Often taught by memorization of procedures, theorems, and proofs, geometry in schooling rarely conveys its underlying intellectual excitement. The recent development of dynamic-geometry software offers an opportunity to translate the study of geometry into a contemporary vernacular. However, this involves transformations along multiple dimensions of the conceptual and practical context of learning. Translating Euclid steps through the multiple challenges involved in redesigning geometry education to take advantage of computer support. Networked computers portend an interactive approach to exploring dynamic geometry as well as broadened prospects for collaboration. The proposed conception of geometry emphasizes the central role of the construction of dependencies as a design activity, integrating human creation and mathematical discovery to form a human-centered approach to mathematics. This book chronicles an iterative effort to adapt technology, theory, pedagogy and practice to support this vision of collaborative dynamic geometry and to evolve the approach through on-going cycles of trial with students and refinement of resources. It thereby provides a case study of a design-based research effort in computer-supported collaborative learning from a human-centered informatics perspective.
Inverse Obstacle Scattering with Non-Over-Determined Scattering Data
The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ����(����;����;����), where ����(����;����;����) is the scattering amplitude, ����;���� ���� ����簡 is the direction of the scattered, incident wave, respectively, ����簡 is the unit sphere in the ℝ3 and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is ����(����): = ����(����;����₀;����₀). By sub-index 0 a fixed value of a variable is denoted. It is proved in this book that the data ����(����), known for all ���� in an open subset of ����簡, determines uniquely the surface ���� and the boundary condition on ����. This condition can be the Dirichlet, or the Neumann, or the impedance type. The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown ����. There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.
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
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
Jordan Canonical Form
Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. The JCF of a linear transformation, or of a matrix, encodes all of the structural information about that linear transformation, or matrix. This book is a careful development of JCF. After beginning with background material, we introduce Jordan Canonical Form and related notions: eigenvalues, (generalized) eigenvectors, and the characteristic and minimum polynomials. We decide the question of diagonalizability, and prove the Cayley-Hamilton theorem. Then we present a careful and complete proof of the fundamental theorem: Let V be a finite-dimensional vector space over the field of complex numbers C, and let T: V → V be a linear transformation. Then T has a Jordan Canonical Form. This theorem has an equivalent statement in terms of matrices: Let A be a square matrix with complex entries. Then A is similar to a matrix J in Jordan Canonical Form, i.e., there is an invertible matrix P and a matrix J in Jordan Canonical Form with A = PJP-1. We further present an algorithm to find P and J, assuming that one can factor the characteristic polynomial of A. In developing this algorithm we introduce the eigenstructure picture (ESP) of a matrix, a pictorial representation that makes JCF clear. The ESP of A determines J, and a refinement, the labeled eigenstructure picture (ℓESP) of A, determines P as well. We illustrate this algorithm with copious examples, and provide numerous exercises for the reader. Table of Contents: Fundamentals on Vector Spaces and Linear Transformations / The Structure of a Linear Transformation / An Algorithm for Jordan Canonical Form and Jordan Basis
The Geometry of Walker Manifolds
This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then pass to the 4 dimensional setting as a gateway to higher dimensions. Since the book is aimed at a very general audience (and in particular to an advanced undergraduate or to a beginning graduate student), no more than a basic course in differential geometry is required in the way of background. To keep our treatment as self-contained as possible, we shall begin with two elementary chapters that provide an introduction to basic aspects of pseudo-Riemannian geometry before beginning on our study of Walker geometry. An extensive bibliography is provided for further reading. Math subject classifications: Primary: 53B20 -- (PACS: 02.40.Hw) Secondary: 32Q15, 51F25, 51P05, 53B30, 53C50, 53C80, 58A30, 83F05, 85A04 Table of Contents: Basic Algebraic Notions / Basic Geometrical Notions / Walker Structures / Three-Dimensional Lorentzian Walker Manifolds / Four-Dimensional Walker Manifolds / The Spectral Geometry of the Curvature Tensor / Hermitian Geometry / Special Walker Manifolds
![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.
Virtual Crowds
There are many applications of computer animation and simulation where it is necessary to model virtual crowds of autonomous agents. Some of these applications include site planning, education, entertainment, training, and human factors analysis for building evacuation. Other applications include simulations of scenarios where masses of people gather, flow, and disperse, such as transportation centers, sporting events, and concerts. Most crowd simulations include only basic locomotive behaviors possibly coupled with a few stochastic actions. Our goal in this survey is to establish a baseline of techniques and requirements for simulating large-scale virtual human populations. Sometimes, these populations might be mutually engaged in a common activity such as evacuation from a building or area; other times they may be going about their individual and personal agenda of work, play, leisure, travel, or spectator. Computational methods to model one set of requirements may not mesh well withgood approaches to another. By including both crowd and individual goals and constraints into a comprehensive computational model, we expect to simulate the visual texture and contextual behaviors of groups of seemingly sentient beings. Table of Contents: Introduction / Crowd Simulation Methodology Survey / Individual Differences in Crowds / Framework (HiDAC + MACES + CAROSA) / HiDAC: Local Motion / MACES: Wayfinding with Communication and Roles / CAROSA: Functional Crowds / Initializing a Scenario / Evaluating Crowds
An Introduction to Laplacian Spectral Distances and Kernels
In geometry processing and shape analysis, several applications have been addressed through the properties of the Laplacian spectral kernels and distances, such as commute time, biharmonic, diffusion, and wave distances. Within this context, this book is intended to provide a common background on the definition and computation of the Laplacian spectral kernels and distances for geometry processing and shape analysis. To this end, we define a unified representation of the isotropic and anisotropic discrete Laplacian operator on surfaces and volumes; then, we introduce the associated differential equations, i.e., the harmonic equation, the Laplacian eigenproblem, and the heat equation. Filtering the Laplacian spectrum, we introduce the Laplacian spectral distances, which generalize the commute-time, biharmonic, diffusion, and wave distances, and their discretization in terms of the Laplacian spectrum. As main applications, we discuss the design of smooth functions and the Laplacian smoothing of noisy scalar functions. All the reviewed numerical schemes are discussed and compared in terms of robustness, approximation accuracy, and computational cost, thus supporting the reader in the selection of the most appropriate with respect to shape representation, computational resources, and target application.
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
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
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.
An Introduction to Numerical Methods for the Physical Sciences
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.
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.
Applied Mathematics with Open-Source Software
This book is aimed at a broad segment of readers who wish to learn how to use open-source software to solve problems in applied mathematics.Each chapter starts with a problem, gives an overview of the relevant theory, shows a solution approach in R and in Python, and finally gives wider context by including a number of published references.
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.
Almost Periodic and Almost Automorphic Functions in Abstract Spaces
This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and applications to evolution equations. Several generalizations have since been introduced in the literature, including the study of almost automorphic sequences, and the interplay between almost periodicity and almost automorphic has been exposed for the first time in light of operator theory, complex variable functions and harmonic analysis methods. As such, the time has come for a second edition to this work, which was one of the most cited books of the year 2001.This new edition clarifies and improves upon earlier materials, includes many relevant contributions and references in new and generalized concepts and methods, and answers the longtime open problem, "What is the number of almost automorphic functions that are not almost periodic in the sense of Bohr?" Open problems in non-locally convex valued almost periodic and almost automorphic functions are also indicated.As in the first edition, materials are presented in a simplified and rigorous way. Each chapter is concluded with bibliographical notes showing the original sources of the results and further reading.
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.
Srinivasa Ramanujan
This book offers a unique account on the life and works of Srinivasa Ramanujan-often hailed as the greatest "natural" mathematical genius. Sharing valuable insights into the many stages of Ramanujan's life, this book provides glimpses into his prolific research on highly composite numbers, partitions, continued fractions, mock theta functions, arithmetic, and hypergeometric functions which led the author to discover a new summation theorem. It also includes the list of Ramanujan's collected papers, letters and other material present at the Wren Library, Trinity College in Cambridge, UK. This book is a valuable resource for all readers interested in Ramanujan's life, work and indelible contributions to mathematics.
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.
Complete Data Analysis Using R
This book gets you up and running with using R in your research project, focusing on data analysis.
