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Finding Ghosts in Your Data: Anomaly Detection Techniques with Examples in Python
by Kevin FeaselDiscover key information buried in the noise of data by learning a variety of anomaly detection techniques and using the Python programming language to build a robust service for anomaly detection against a variety of data types. The book starts with an overview of what anomalies and outliers are and uses the Gestalt school of psychology to explain just why it is that humans are naturally great at detecting anomalies. From there, you will move into technical definitions of anomalies, moving beyond "I know it when I see it" to defining things in a way that computers can understand.The core of the book involves building a robust, deployable anomaly detection service in Python. You will start with a simple anomaly detection service, which will expand over the course of the book to include a variety of valuable anomaly detection techniques, covering descriptive statistics, clustering, and time series scenarios. Finally, you will compare your anomaly detection service head-to-head with a publicly available cloud offering and see how they perform.The anomaly detection techniques and examples in this book combine psychology, statistics, mathematics, and Python programming in a way that is easily accessible to software developers. They give you an understanding of what anomalies are and why you are naturally a gifted anomaly detector. Then, they help you to translate your human techniques into algorithms that can be used to program computers to automate the process. You’ll develop your own anomaly detection service, extend it using a variety of techniques such as including clustering techniques for multivariate analysis and time series techniques for observing data over time, and compare your service head-on against a commercial service.What You Will LearnUnderstand the intuition behind anomaliesConvert your intuition into technical descriptions of anomalous dataDetect anomalies using statistical tools, such as distributions, variance and standard deviation, robust statistics, and interquartile rangeApply state-of-the-art anomaly detection techniques in the realms of clustering and time series analysisWork with common Python packages for outlier detection and time series analysis, such as scikit-learn, PyOD, and tslearnDevelop a project from the ground up which finds anomalies in data, starting with simple arrays of numeric data and expanding to include multivariate inputs and even time series dataWho This Book Is ForFor software developers with at least some familiarity with the Python programming language, and who would like to understand the science and some of the statistics behind anomaly detection techniques. Readers are not required to have any formal knowledge of statistics as the book introduces relevant concepts along the way.
Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers
by Amir D. Aczel“A captivating story, not just an intellectual quest but a personal one . . . gripping [and] filled with the passion and wonder of numbers.” —The New York TimesVirtually everything in our lives is digital, numerical, or quantified. But the story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is the saga of Amir Aczel’s lifelong obsession: to find the original sources of our numerals, perhaps the greatest abstraction the human mind has ever created.Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross-examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride.The history begins with Babylonian cuneiform numbers, followed by Greek and Roman letter numerals. Then Aczel asks: Where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures.While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from.“A historical adventure that doubles as a surprisingly engaging math lesson . . . rip-roaring exploits and escapades.” —Publishers Weekly
Finding the Speed of Light: The 1676 Discovery That Dazzled The World
by Mark WestonKirkus Star Mark Weston’s high-interest story and Rebecca Evans’s colorful graphics make scientific discovery the coolest thing this side of Jupiter. More than two centuries before Einstein, using a crude telescope and a mechanical timepiece, Danish astronomer Ole Romer measured the speed of light with astounding accuracy. How was he able to do this when most scientists didn’t even believe that light traveled? Like many paradigm-shattering discoveries, Romer’s was accidental. Night after night he was timing the disappearance and reappearance of Jupiter’s moon Io behind the huge, distant planet. Eventually he realized that the discrepancies in his measurements could have only one explanation: Light had a speed, and it took longer to reach Earth when Earth was farther from Jupiter. All he needed then to calculate light’s speed was some fancy geometry.
Fingerübungen der Physik: Repetitorium und Übungsbuch mit Lösungen und MATLAB-Programmen
by Michael Kaschke Holger CartariusDieses Lehr- und Lernbuch erscheint in mehreren Bänden und ist gleichsam ein Repetitorium als auch Arbeitsbuch zu wenig behandelten Kapiteln des Physikstudiums. In diesem Band wird die Physik der Bewegung von Körpern und des Kontinuums behandelt. Zahlreiche spannende Probleme aus dem Alltag, der Physikgeschichte und der modernen Forschung werden sowohl anschaulich erklärt als auch mathematisch-physikalisch beschrieben. Die ausführlichen Lösungsvorschläge mit MATLAB-Programmen dienen dabei als „Fingerübungen“ für ein tieferes physikalisches Verständnis. Der Inhalt Physik der Bewegung – Physik des Kontinuums Die Zielgruppe Das Buch richtet sich an alle, die Freude an der Physik haben und diese für verschiedene Fragestellungen anwenden wollen. Besonderen Nutzen daraus werden Studierende und Promovierende der Physik, Mathematik und Ingenieurswissenschaften, ebenso wie des Lehramtes für naturwissenschaftliche Fächer gewinnen. Genauso ist das Buch für Dozentinnen und Dozenten der Physik an Hochschulen und Universitäten gedacht, aber auch für Lehrkräfte der Physik an Gymnasien, die aus dem Fundus der Übungen und Beispiele Anregungen für eigene Problemstellungen und Projekte gewinnen können. Vorkenntnisse Das Physikwissen des Bachelor-Studiums stellt in etwa die Grundlage dar, auf der das Buch aufbaut. Eine Reihe von Kapiteln lassen sich auch mit den Kenntnissen eines Leistungskurses Physik an den Gymnasien erschließen. Die Übungsaufgaben sind nach 3 Schwierigkeitsklassen gegliedert.
Finish Line Mathematics for The Common Core State Standards Grade 3
by Continental Press StaffThe Finish Line Mathematics for the Common Core State Standards workbook provides instruction and practice for the Common Core State Standards for Mathematics recently adopted by your state. Lessons emphasize rigor of text and higher-order thinking skills, and focus on development of the process skills. The format features instruction with step-by-step examples, guided practice, and independent work. Students will answer selected response, constructed-response, and extended-response questions. To align with the Common Core requirements, Finish Line practice builds on the underlying structure of mathematics to prepare students for algebra by the end of grade 7. Reviews at the end of each unit and a practice test at the end of the book help you monitor progress.
Finish Line Mathematics for the Common Core State Standards Grade 4
by Continental Press StaffFinish Line Mathematics for the Common Core State Standards will help you prepare for math tests. Each year in math class, you learn new skills and ideas. This book focuses on the math skills and ideas that are the most important for each grade. It is important to master the concepts you learn each year because mathematical ideas and skills build on each other. The things you learn this year will help you understand and master the skills you will learn next year.
Finite Approximations in Discrete-Time Stochastic Control: Quantized Models And Asymptotic Optimality (Systems And Control: Foundations And Applications Ser.)
by Serdar Yüksel Naci Saldi Tamás LinderIn a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.
Finite Automata
by Mark V. LawsonInterest in finite automata theory continues to grow, not only because of its applications in computer science, but also because of more recent applications in mathematics, particularly group theory and symbolic dynamics. The subject itself lies on the boundaries of mathematics and computer science, and with a balanced approach that does justice to
Finite Blaschke Products and Their Connections
by Javad Mashreghi Stephan Ramon Garcia William T. RossThis monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered.Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with the material. With much of the material previously scattered throughout mathematical history, this book presents a cohesive, comprehensive and modern exposition accessible to undergraduate students, graduate students, and researchers who have familiarity with complex analysis.
Finite Difference Computing with PDEs
by Svein Linge Hans Petter LangtangenThis easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology. This book is open access under a CC BY license.
Finite Difference Methods for Compressible Two-Fluid Dynamics (Forum for Interdisciplinary Mathematics)
by Khosro ShahbaziFinite Difference Methods for Compressible Two-Fluid Dynamics provides the essentials of high-order numerical methods for compressible single-fluid and two-fluid transport phenomena. This book can serve as a first course on the numerical methods for transport phenomena or fluid dynamics for students in mechanical, aerospace, and chemical engineering, applied mathematics, and physics at the senior level of an undergraduate or graduate degree. It also provides foundations and algorithmic details for implementing the most recent numerical schemes for compressible flows and extending them to include other physics, such as elasticity, reaction, and magnetohydrodynamics. The book's presented schemes enable computations for broad applications, including shock-induced interfacial instability and turbulence, shock-bubble interactions, and detonation, to name a few. For a broad reach and impact, the numerical schemes satisfy the simultaneous requirements of simplicity, extendibility, and efficiency on serial and parallel computers. The physics of the compressible single- and two-fluid system also guide the design and analysis of the numerical methods. The enabled direct numerical simulations also help obtain accurate data for tuning the emerging physics-based neuromorphic algorithms.
Finite Difference Methods,Theory and Applications
by Ivan Dimov István Faragó Lubin VulkovThis book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Finite Difference Methods, FDM 2014, held in Lozenetz, Bulgaria, in June 2014. The 36 revised full papers were carefully reviewed and selected from 62 submissions. These papers together with 12 invited papers cover topics such as finite difference and combined finite difference methods as well as finite element methods and their various applications in physics, chemistry, biology and finance.
Finite Difference Methods. Theory and Applications: 7th International Conference, FDM 2018, Lozenetz, Bulgaria, June 11-16, 2018, Revised Selected Papers (Lecture Notes in Computer Science #11386)
by Ivan Dimov István Faragó Lubin VulkovThis book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.
Finite Element Analysis
by M Moatamedi Hassan A. KhawajaFinite element analysis has become the most popular technique for studying engineering structures in detail. It is particularly useful whenever the complexity of the geometry or of the loading is such that alternative methods are inappropriate. The finite element method is based on the premise that a complex structure can be broken down into finitely many smaller pieces (elements), the behaviour of each of which is known or can be postulated. These elements might then be assembled in some sense to model the behaviour of the structure. Intuitively this premise seems reasonable, but there are many important questions that need to be answered. In order to answer them it is necessary to apply a degree of mathematical rigour to the development of finite element techniques. The approach that will be taken in this book is to develop the fundamental ideas and methodologies based on an intuitive engineering approach, and then to support them with appropriate mathematical proofs where necessary. It will rapidly become clear that the finite element method is an extremely powerful tool for the analysis of structures (and for other field problems), but that the volume of calculations required to solve all but the most trivial of them is such that the assistance of a computer is necessary. As stated above, many questions arise concerning finite element analysis. Some of these questions are associated with the fundamental mathematical formulations, some with numerical solution techniques, and others with the practical application of the method. In order to answer these questions, the engineer/analyst needs to understand both the nature and limitations of the finite element approximation and the fundamental behaviour of the structure. Misapplication of finite element analysis programs is most likely to arise when the analyst is ignorant of engineering phenomena.
Finite Element Analysis for Biomedical Engineering Applications
by Z. C. YangFinite element analysis has been widely applied to study biomedical problems. This book aims to simulate some common medical problems using finite element advanced technologies, which establish a base for medical researchers to conduct further investigations. This book consists of four main parts: (1) bone, (2) soft tissues, (3) joints, and (4) implants. Each part starts with the structure and function of the biology and then follows the corresponding finite element advanced features, such as anisotropic nonlinear material, multidimensional interpolation, XFEM, fiber enhancement, UserHyper, porous media, wear, and crack growth fatigue analysis. The final section presents some specific biomedical problems, such as abdominal aortic aneurysm, intervertebral disc, head impact, knee contact, and SMA cardiovascular stent. All modeling files are attached in the appendixes of the book. This book will be helpful to graduate students and researchers in the biomedical field who engage in simulations of biomedical problems. The book also provides all readers with a better understanding of current advanced finite element technologies. Details finite element modeling of bone, soft tissues, joints, and implants Presents advanced finite element technologies, such as fiber enhancement, porous media, wear, and crack growth fatigue analysis Discusses specific biomedical problems, such as abdominal aortic aneurysm, intervertebral disc, head impact, knee contact, and SMA cardiovascular stent Explains principles for modeling biology Provides various descriptive modeling files
Finite Element Analysis of Composite Materials Using ANSYS
by Ever J. BarberoDesigning structures using composite materials poses unique challenges, especially due to the need for concurrent design of both material and structure. Students are faced with two options: textbooks that teach the theory of advanced mechanics of composites, but lack computational examples of advanced analysis, and books on finite element analysis
Finite Element Analysis of Composite Materials using Abaqus® (Composite Materials)
by Ever J. BarberoDeveloped from the author’s course on advanced mechanics of composite materials, Finite Element Analysis of Composite Materials with Abaqus® shows how powerful finite element tools tackle practical problems in the structural analysis of composites. This Second Edition includes two new chapters on "Fatigue" and "Abaqus Programmable Features" as well as a major update of chapter 10 "Delaminations" and significant updates throughout the remaining chapters. Furthermore, it updates all examples, sample code, and problems to Abaqus 2020. Unlike other texts, this one takes theory to a hands-on level by actually solving problems. It explains the concepts involved in the detailed analysis of composites, the mechanics needed to translate those concepts into a mathematical representation of the physical reality, and the solution of the resulting boundary value problems using Abaqus. The reader can follow a process to recreate every example using Abaqus graphical user interface (CAE) by following step-by-step directions in the form of pseudo-code or watching the solutions on YouTube. The first seven chapters provide material ideal for a one-semester course. Along with offering an introduction to finite element analysis for readers without prior knowledge of the finite element method, these chapters cover the elasticity and strength of laminates, buckling analysis, free edge stresses, computational micromechanics, and viscoelastic models for composites. Emphasizing hereditary phenomena, the book goes on to discuss continuum and discrete damage mechanics as well as delaminations and fatigue. The text also shows readers how to extend the capabilities of Abaqus via "user subroutines" and Python scripting. Aimed at advanced students and professional engineers, this textbook features 62 fully developed examples interspersed with the theory, 82 end-of-chapter exercises, and 50+ separate pieces of Abaqus pseudo-code that illustrate the solution of example problems. The author’s website offers the relevant Abaqus and MATLAB model files available for download, enabling readers to easily reproduce the examples and complete the exercises. Video recording of solutions to examples are available on YouTube with multilingual captions.
Finite Element Analysis of Rotating Beams
by Ranjan GanguliThis book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems - important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers - and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.
Finite Element Analysis of Structures through Unified Formulation
by Erasmo Carrera Marco Petrolo Enrico Zappino Maria CinefraThe finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another. Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same 'fundamental nucleus' that comes from geometrical relations and Hooke's law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D and 2D FEs that make use of 'real' physical surfaces rather than 'artificial' mathematical surfaces which are difficult to interface in CAD/CAE software. Key features: Covers how the refined formulation can be easily and conveniently used to analyse laminated structures, such as sandwich and composite structures, and to deal with multifield problems Shows the performance of different FE models through the 'best theory diagram' which allows different models to be compared in terms of accuracy and computational cost Introduces an axiomatic/asymptotic approach that reduces the computational cost of the structural analysis without affecting the accuracy Introduces an innovative 'component-wise' approach to deal with complex structures Accompanied by a website hosting the dedicated software package MUL2 (www.mul2.com) Finite Element Analysis of Structures Through Unified Formulation is a valuable reference for researchers and practitioners, and is also a useful source of information for graduate students in civil, mechanical and aerospace engineering.
Finite Element Approximation of Boundary Value Problems (Compact Textbooks in Mathematics)
by Franz ChoulyThis textbook provides an accessible introduction to the mathematical foundations of the finite element method for a broad audience. The author accomplishes this, in part, by including numerous exercises and illustrations. Each chapter begins with a clear outline to help make complex concepts more approachable without sacrificing depth. Structurally, the book begins with the simplest type of finite element method: low order, piecewise continuous, Lagrange finite elements. With this, crucial questions about the stability and approximation errors are answered. Of particular note is the author’s coverage of two specific topics that often go overlooked in introductory material. The first is the numerical treatment of boundary conditions, especially the Nitsche technique. The second is a detailed explanation of the discretization error using specific techniques of a posteriori error estimation. With the book’s compact yet thorough treatment of these areas, readers will have a clear understanding of how mathematical analysis tools can be used in practice. Finite Element Approximation of Boundary Value Problems will be suitable as a supplementary textbook in applied mathematics courses for graduate students, and may also be used for self-study.
Finite Element Method (Wiley-iste Ser.)
by Gilbert Touzot Emmanuel Lefrançois Gouri DhattThis book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences.The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus.The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.
Finite Element Method Analysis for Ice Class Vessels (Synthesis Lectures on Ocean Systems Engineering)
by Alexander Arnfinn OlsenThis book provides ship designers with clear guidance on alternative design procedures for hull side structures, power requirements, and propeller strength assessment based on the Finite Element Method for Baltic Ice Class Vessels. Through this comprehensive guide, readers will learn the intricacies of designing vessels capable of navigating the harsh ice conditions of the Baltic Sea. The chapters cover topics such as ice strengthening designs using direct calculation approaches, power requirement calculations for ice class vessels, and strength analysis of propellers. The authors present an expert analysis of these critical aspects, offering practical solutions and methodologies that are essential for marine engineers and naval architects. This book is a must-read for anyone involved in the design and construction of ice-class vessels, providing invaluable insights into the latest research and best practices in the field. This guide is indispensable for naval architects, marine engineering students, marine surveyors, and professionals working in maritime defense and shipping registries. It serves as a reference for academics and students in marine design and engineering, as well as a textbook for marine engineering courses. With contributions from experienced practitioners in the field, this book offers both theoretical perspectives and practical case studies that will benefit anyone involved in the design and operation of ice-class vessels.
Finite Element Method: Applications in Solids, Structures, and Heat Transfer (Mechanical Engineering)
by Michael R. GoszThe finite element method (FEM) is the dominant tool for numerical analysis in engineering, yet many engineers apply it without fully understanding all the principles. Learning the method can be challenging, but Mike Gosz has condensed the basic mathematics, concepts, and applications into a simple and easy-to-understand reference.Finite Element Method: Applications in Solids, Structures, and Heat Transfer navigates through linear, linear dynamic, and nonlinear finite elements with an emphasis on building confidence and familiarity with the method, not just the procedures. This book demystifies the assumptions made, the boundary conditions chosen, and whether or not proper failure criteria are used. It reviews the basic math underlying FEM, including matrix algebra, the Taylor series expansion and divergence theorem, vectors, tensors, and mechanics of continuous media.The author discusses applications to problems in solid mechanics, the steady-state heat equation, continuum and structural finite elements, linear transient analysis, small-strain plasticity, and geometrically nonlinear problems. He illustrates the material with 10 case studies, which define the problem, consider appropriate solution strategies, and warn against common pitfalls. Additionally, 35 interactive virtual reality modeling language files are available for download from the CRC Web site.For anyone first studying FEM or for those who simply wish to deepen their understanding, Finite Element Method: Applications in Solids, Structures, and Heat Transfer is the perfect resource.
Finite Element Methods
by Jonathan WhiteleyThis book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Finite Element Methods for Eigenvalue Problems (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Jiguang Sun Aihui ZhouThis book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.