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Virtual Turning Points
by Naofumi Honda Takahiro Kawai Yoshitsugu TakeiThe discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi-Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M. V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H. L. Berk, W. M. Nevins, and K. V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary.
Virtual Work Approach to Mechanical Modeling
by Jean SalençonThis book is centred about the Principle of virtual work and the related method for mechanical modelling. It aims at showing and enhancing the polyvalence and versatility of the virtual work approach in the mechanical modelling process. The virtual work statement is set as the principle at the root of a force modelling method that can be implemented on any geometrical description. After experimentally induced hypotheses have been made on the geometrical parameters that describe the concerned system and subsystems, the method provides a unifying framework for building up consistently associated force models where external and internal forces are introduced through their virtual rates of work. Systems described as three-dimensional, curvilinear or planar continua are considered: force models are established with the corresponding equations of motion; the validation process points out that enlarging the domain of relevance of the model for practical applications calls for an enrichment of the geometrical description that takes into account the underlying microstructure.
Virtuelle und mögliche Welten in Physik und Philosophie
by Hans J. PirnerWas sind mögliche Welten und was haben Entwicklungen der modernen Physik mit Ideen über mögliche Welten in der Philosophie zu tun? In der Beantwortung dieser Fragen entwickelt das vorliegende Werk das wissenschaftliche Weltbild im Vergleich mit möglichen Welten und gelangt so zu einem besseren Verständnis unserer einzigen wirklichen Welt. Dazu beschreibt der Autor die kreativen Ideen, die zur klassischen Physik, zur Quantenphysik und zur Erforschung des Ursprungs des Weltalls geführt haben. Er lädt den Leser ein, mit ihm über die Versuche in der modernen Physik nachzudenken, Parallelwelten und neue Universen einzuführen. Man erfährt, wie in Physik und Philosophie mögliche Welten als Instrumente verwendet werden, um unsere Erkenntnisse zu erweitern. Es wird erläutert, wie man sich mögliche Welten auch außerhalb der Physik vorzustellen hat und welchen Anforderungen diesen genügen. Unter diesem Gesichtspunkt analysiert der Autor abschließend die Zukunftsvisionen der Science-Fiction Literatur und die neuesten Erkenntnisse über künstliche, virtuelle und hybride Welten. Anhänge mit vertieftem physikalischen Hintergrund und ein ausführliches Glossar unterstützen die interessierten Lesern und Leserinnen dabei, einen Überblick über die vielfältigen Begriffe und Sachverhalte zu behalten.
Virus Host Cell Genetic Material Transport: Computational ODE/PDE Modeling with R
by William E. SchiesserThe reproduction and spread of a virus during an epidemic proceeds when the virus attaches to a host cell and viral genetic material (VGM) (protein, DNA, RNA) enters the cell, then replicates, and perhaps mutates, in the cell. The movement of the VGM across the host cell outer membrane and within the host cell is a spatiotemporal dynamic process that is modeled in this book as a system of ordinary and partial differential equations (ODE/PDEs). The movement of the virus proteins through the cell membrane is modeled as a diffusion process expressed by the diffusion PDE (Fick’s second law). Within the cell, the time variation of the VGM is modeled as ODEs. The evolution of the dependent variables is computed by the numerical integration of the ODE/PDEs starting from zero initial conditions (ICs). The departure of the dependent variables from zero is in response to the virus protein concentration at the outer membrane surface (the point at which the virus binds to the host cell). The numerical integration of the ODE/PDEs is performed with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The ODE/PDE dependent variables are displayed graphically with basic R plotting utilities. The R routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the ODE/PDE model, such as changes in the parameters and the form of the model equations.
Visibility-based Optimal Path and Motion Planning
by Paul Keng-Chieh WangThis monograph deals with various visibility-based path and motion planning problems motivated by real-world applications such as exploration and mapping planetary surfaces, environmental surveillance using stationary or mobile robots, and imaging of global air/pollutant circulation. The formulation and solution of these problems call for concepts and methods from many areas of applied mathematics including computational geometry, set-covering, non-smooth optimization, combinatorial optimization and optimal control. Emphasis is placed on the formulation of new problems and methods of approach to these problems. Since geometry and visualization play important roles in the understanding of these problems, intuitive interpretations of the basic concepts are presented before detailed mathematical development. The development of a particular topic begins with simple cases illustrated by specific examples, and then progresses forward to more complex cases. The intended readers of this monograph are primarily students and researchers in engineering, computer science and applied mathematics. An understanding of the mathematical development of the main results requires only basic knowledge of mathematical analysis, control, and optimization theories. Some exercises with various degrees of difficulty are provided at the end of the main chapters. The material presented here may serve as a portion of an introductory course or seminar on visibility-based optimal path and motion planning problems with the objective of stimulating interest and further studies in this relatively new area.
Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series)
by Douglas Fisher John Hattie Dr Nancy Frey Linda M. Gojak Sara Delano Moore William L. MellmanRich tasks, collaborative work, number talks, problem-based learning, direct instruction…with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in “visible” learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.
Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series)
by Douglas Fisher John Hattie Dr Nancy Frey Linda M. Gojak Sara Delano Moore William L. MellmanRich tasks, collaborative work, number talks, problem-based learning, direct instruction…with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in “visible” learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.
Visible Thinking in the K–8 Mathematics Classroom
by Ted H. Hull Don S. Balka Ruth Harbin MilesSeeing is believing with this interactive approach to math instruction Do you ever wish your students could read each other’s thoughts? Now they can—and so can you! This newest book by veteran mathematics educators provides instructional strategies for maximizing students’ mathematics comprehension by integrating visual thinking into the classroom. Included are numerous grade-specific sample problems for teaching essential concepts such as number sense, fractions, and estimation. Among the many benefits of visible thinking are: Interactive student-to-student learning; Increased class participation; Development of metacognitive thinking and problem-solving skills.
Vision in Elementary Mathematics (Dover Books on Mathematics)
by W. W. SawyerHere is a presentation of elementary mathematics that anyone can appreciate, especially anyone with a capacity for imagination. As the title suggests, the author's technique relies on visual elements, and his approach employs the most graphic and least forbidding aspects of mathematics. Most people, he observes, possess a direct vision that permits them to "see" the smaller numbers; with the larger numbers, however, vision fails and mental chaos ensues. In addressing this difficulty, both for those who like recreational mathematics and particularly for teachers, the author suggests a variety of methods already used by many effective teachers -- techniques of visualizing, dramatizing, and analyzing numbers that attract and retain the attention and understanding of children. His topics range from basic multiplication and division to algebra, encompassing word problems, graphs, negative numbers, fractions, and many other practical applications of elementary mathematics.
Visions of Infinity: The Great Mathematical Problems
by Ian StewartIt is one of the wonders of mathematics that, for every problem mathematicians solve, another awaits to perplex and galvanize them. Some of these problems are new, while others have puzzled and bewitched thinkers across the ages. <P><P>Such challenges offer a tantalizing glimpse of the field's unlimited potential, and keep mathematicians looking toward the horizons of intellectual possibility. In Visions of Infinity, celebrated mathematician Ian Stewart provides a fascinating overview of the most formidable problems mathematicians have vanquished, and those that vex them still. He explains why these problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole. The three-century effort to prove Fermat's last theorem-first posited in 1630, and finally solved by Andrew Wiles in 1995-led to the creation of algebraic number theory and complex analysis. The Poincaré conjecture, which was cracked in 2002 by the eccentric genius Grigori Perelman, has become fundamental to mathematicians' understanding of three-dimensional shapes. But while mathematicians have made enormous advances in recent years, some problems continue to baffle us. Indeed, the Riemann hypothesis, which Stewart refers to as the "Holy Grail of pure mathematics," and the P/NP problem, which straddles mathematics and computer science, could easily remain unproved for another hundred years. An approachable and illuminating history of mathematics as told through fourteen of its greatest problems, Visions of Infinity reveals how mathematicians the world over are rising to the challenges set by their predecessors-and how the enigmas of the past inevitably surrender to the powerful techniques of the present.
Visual Analysis of Behaviour
by Shaogang Gong Tao XiangThis book presents a comprehensive treatment of visual analysis of behaviour from computational-modelling and algorithm-design perspectives. Topics: covers learning-group activity models, unsupervised behaviour profiling, hierarchical behaviour discovery, learning behavioural context, modelling rare behaviours, and "man-in-the-loop" active learning; examines multi-camera behaviour correlation, person re-identification, and "connecting-the-dots" for abnormal behaviour detection; discusses Bayesian information criterion, Bayesian networks, "bag-of-words" representation, canonical correlation analysis, dynamic Bayesian networks, Gaussian mixtures, and Gibbs sampling; investigates hidden conditional random fields, hidden Markov models, human silhouette shapes, latent Dirichlet allocation, local binary patterns, locality preserving projection, and Markov processes; explores probabilistic graphical models, probabilistic topic models, space-time interest points, spectral clustering, and support vector machines.
Visual Analytics for Dashboards: A Step-by-Step Guide to Principles and Practical Techniques
by Arshad KhanThis book covers the key principles, best practices, and practical techniques for designing and implementing visually compelling dashboards. It explores the various stages of the dashboard development process, from understanding user needs and defining goals, to selecting appropriate visual encodings, designing effective layouts, and employing interactive elements. It also addresses the critical aspect of data storytelling, examining how narratives and context can be woven into dashboards to deliver impactful insights and engage audiences. Visual Analytics for Dashboards is designed to cater to a wide range of readers, from beginners looking to grasp the fundamentals of visual analytics, to seasoned professionals seeking to enhance their dashboard design skills. For different types of readers, such as a data analyst, BI professional, data scientist, or simply someone interested in data visualization, this book aims to equip them with the knowledge and tools necessary to create impactful dashboards. What you’ll learn The principles of data visualization How to create effective dashboards Meet all the requirements for visual analytics/data visualization/dashboard courses Deepen understanding of data presentation and analysis How to use different kinds of tools for data analysis, such as scorecards and key performance indicators Who This Book Is For Business analysts, data analysts, BI professionals, end-users, executives, developers, as well as students in dashboards, data visualizations, and visual analytics courses.
Visual and Statistical Thinking: Displays of Evidence for Deicision Making
by Edward R. TufteThis booklet meant for students of quantitative thinking, reproduces chapter 2 of his other book Visual Explanations, Here we see two complex cases of the analysis and display of evidence--the celebrated investigation of a cholera epidemic by Dr. John Snow and the unfortunate decision to launch the space shuttle Challenger.
Visual Cryptography and Secret Image Sharing
by Stelvio Cimato Ching-Nung YangWith rapid progress in Internet and digital imaging technology, there are more and more ways to easily create, publish, and distribute images. Considered the first book to focus on the relationship between digital imaging and privacy protection, Visual Cryptography and Secret Image Sharing is a complete introduction to novel security methods and sharing-control mechanisms used to protect against unauthorized data access and secure dissemination of sensitive information. Image data protection and image-based authentication techniques offer efficient solutions for controlling how private data and images are made available only to select people. Essential to the design of systems used to manage images that contain sensitive data—such as medical records, financial transactions, and electronic voting systems—the methods presented in this book are useful to counter traditional encryption techniques, which do not scale well and are less efficient when applied directly to image files. An exploration of the most prominent topics in digital imaging security, this book discusses: Potential for sharing multiple secrets, Visual cryptography schemes—based either on the probabilistic reconstruction of the secret image, or on different logical operations for combining shared images, Inclusion of pictures in the distributed shares, Contrast enhancement techniques, Color-image visual cryptography, Cheating prevention, Alignment problems for image shares, Steganography and authentication In the continually evolving world of secure image sharing, a growing number of people are becoming involved as new applications and business models are being developed all the time. This contributed volume gives academicians, researchers, and professionals the insight of well-known experts on key concepts, issues, trends, and technologies in this emerging field.
Visual Culture and Mathematics in the Early Modern Period (Visual Culture in Early Modernity)
by Ingrid Alexander-SkipnesDuring the early modern period there was a natural correspondence between how artists might benefit from the knowledge of mathematics and how mathematicians might explore, through advances in the study of visual culture, new areas of enquiry that would uncover the mysteries of the visible world. This volume makes its contribution by offering new interdisciplinary approaches that not only investigate perspective but also examine how mathematics enriched aesthetic theory and the human mind. The contributors explore the portrayal of mathematical activity and mathematicians as well as their ideas and instruments, how artists displayed their mathematical skills and the choices visual artists made between geometry and arithmetic, as well as Euclid’s impact on drawing, artistic practice and theory. These chapters cover a broad geographical area that includes Italy, Switzerland, Germany, the Netherlands, France and England. The artists, philosophers and mathematicians whose work is discussed include Leon Battista Alberti, Nicholas Cusanus, Marsilio Ficino, Francesco di Giorgio, Leonardo da Vinci and Andrea del Verrocchio, as well as Michelangelo, Galileo, Piero della Francesca, Girard Desargues, William Hogarth, Albrecht Dürer, Luca Pacioli and Raphael.
Visual Data Mining
by Russell K. AndersonA visual approach to data mining. Data mining has been defined as the search for useful and previously unknown patterns in large datasets, yet when faced with the task of mining a large dataset, it is not always obvious where to start and how to proceed. This book introduces a visual methodology for data mining demonstrating the application of methodology along with a sequence of exercises using VisMiner. VisMiner has been developed by the author and provides a powerful visual data mining tool enabling the reader to see the data that they are working on and to visually evaluate the models created from the data. Key features:Presents visual support for all phases of data mining including dataset preparation.Provides a comprehensive set of non-trivial datasets and problems with accompanying software.Features 3-D visualizations of multi-dimensional datasets.Gives support for spatial data analysis with GIS like features.Describes data mining algorithms with guidance on when and how to use.Accompanied by VisMiner, a visual software tool for data mining, developed specifically to bridge the gap between theory and practice.Visual Data Mining: The VisMiner Approach is designed as a hands-on work book to introduce the methodologies to students in data mining, advanced statistics, and business intelligence courses. This book provides a set of tutorials, exercises, and case studies that support students in learning data mining processes.In praise of the VisMiner approach: "What we discovered among students was that the visualization concepts and tools brought the analysis alive in a way that was broadly understood and could be used to make sound decisions with greater certainty about the outcomes"--Dr. James V. Hansen, J. Owen Cherrington Professor, Marriott School, Brigham Young University, USA"Students learn best when they are able to visualize relationships between data and results during the data mining process. VisMiner is easy to learn and yet offers great visualization capabilities throughout the data mining process. My students liked it very much and so did I." --Dr. Douglas Dean, Assoc. Professor of Information Systems, Marriott School, Brigham Young University, USA
The Visual Display of Quantitative Information
by Edward TufteThe classic book on statistical graphics, charts, tables. Theory and practice in the design of data graphics, 250 illustrations of the best (and a few of the worst) statistical graphics, with detailed analysis of how to display data for precise, effective, quick analysis. Design of the high-resolution displays, small multiples. Editing and improving graphics. The data-ink ratio. Time-series, relational graphics, data maps, multivariate designs. Detection of graphical deception: design variation vs. data variation. Sources of deception. Aesthetics and data graphical displays. This is the second edition of The Visual Display of Quantitative Information. Recently published, this new edition provides excellent color reproductions of the many graphics of William Playfair, adds color to other images, and includes all the changes and corrections accumulated during 17 printings of the first edition.
Visual Group Theory: A Computer-Oriented Geometric Introduction (Springer Undergraduate Mathematics Series)
by Stephan RosebrockThis textbook provides an introduction to group theory starting from the basics, relying on geometry to elucidate its various aspects. Groups naturally manifest as symmetries of geometric shapes, such as reflections and rotations. The book adopts this perspective to provide a straightforward, descriptive explanation, supported by examples and exercises in GAP, an open-source computer algebra system. It covers all of the key concepts of group theory, including homomorphisms, group operations, presentations, products of groups, and finite, abelian, and solvable groups. The topics include cyclic and symmetric groups, dihedral, orthogonal, and hyperbolic groups, as well as the significant notion of Cayley graphs. Self-contained and requiring little beyond high school mathematics, this book is aimed at undergraduate courses and features numerous exercises. It will also appeal to anyone interested in the geometric approach to group theory.
Visual Guide to Math (DK First Reference)
by DKKey math vocabulary and concepts for young children explained simply in this friendly and informative reference book.Clear, accessible pictures and diagrams support this first introduction to numbers, calculating, measuring, geometry, and data-collecting, making basic maths skills easier to understand. Packed with key terms and useful tips to help remember as well as practical examples of math in daily life, Visual Guide to Math is ideal even for reluctant kids. Place value, number bonds, multiplication tables, and fractions are just a few of the math concepts explained and reinforced in a variety of ways for children with different learning styles.Covering everything a young child needs to know, this unique reference book follows the curriculum and provides a strong foundation for math skills through the rest of the school years. A perfect homework help to support children as they take their first steps in math and build confidence.
A Visual Guide to Stata Graphics
by Michael MitchellA Visual Guide to Stata Graphics, Third Edition will teach you how to use Stata to make publication-quality graphics that will stand out and enhance your statistical results. With over 900 illustrated examples and quick-reference tabs, this book quickly guides you to the information you need for creating and customizing high-quality graphs for any type of statistical data.
A Visual Introduction to Differential Forms and Calculus on Manifolds
by Jon Pierre FortneyThis book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.
Visual Math Dict
by Don Balka Jack BanaThe most accessible and useful guide to math terms and procedures available, this reference has over 600 definitions and scores of additional resources including tables, rules and symbols.
Visual Mathematics and Cyberlearning
by Dragana Martinovic Zekeriya Karadag Viktor FreimanThis first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information and Communication Technologies. Here we present mathematics as a contemporary subject that is engaging, exciting and enlightening in new ways. For example, in the distributed environment of cyber space, mathematics learners play games, watch presentations on YouTube, create Java applets of mathematics simulations and exchange thoughts over the Instant Messaging tool. How should mathematics education resonate with these learners and technological novelties that excite them?
Visual Media Processing Using Matlab Beginner's Guide
by George SiogkasWritten in a friendly, Beginner's Guide format, showing the user how to use the digital media aspects of Matlab (image, video, sound) in a practical, tutorial-based style.This is great for novice programmers in any language who would like to use Matlab as a tool for their image and video processing needs, and also comes in handy for photographers or video editors with even less programming experience wanting to find an all-in-one tool for their tasks.
The Visual Neuroscience of Robotic Grasping
by Eris Chinellato Angel P. PobilThis book presents interdisciplinary research that pursues the mutual enrichment of neuroscience and robotics. Building on experimental work, and on the wealth of literature regarding the two cortical pathways of visual processing - the dorsal and ventral streams - we define and implement, computationally and on a real robot, a functional model of the brain areas involved in vision-based grasping actions. Grasping in robotics is largely an unsolved problem, and we show how the bio-inspired approach is successful in dealing with some fundamental issues of the task. Our robotic system can safely perform grasping actions on different unmodeled objects, denoting especially reliable visual and visuomotor skills. The computational model and the robotic experiments help in validating theories on the mechanisms employed by the brain areas more directly involved in grasping actions. This book offers new insights and research hypotheses regarding such mechanisms, especially for what concerns the interaction between the dorsal and ventral streams. Moreover, it helps in establishing a common research framework for neuroscientists and roboticists regarding research on brain functions.