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Sparse Polynomial Approximation of High-Dimensional Functions
Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions.These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data.This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods.These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering.It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations.It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing.It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code.The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
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Evaluation in Today’s World : Respecting Diversity, Improving Quality, and Promoting Usability
Recipient of a 2021 Most Promising New Textbook Award from the Textbook & Academic Authors Association (TAA) Evaluation in Today’s World: Respecting Diversity, Improving Quality, and Promoting Usability is a timely and comprehensive textbook that guides students, practitioners, and users of evaluations in understanding evaluation purposes, theories, methodologies, and challenges within today’s sociocultural and political context.Veronica G. Thomas and Patricia B. Campbell include discussions of evaluation history, frameworks, models, types, planning, and methods, through a social justice, diversity, and inclusive lens.The authors focus on ethics in diverse cultural contexts, help readers understand how social problems and programs get politicized and, sometimes, framed through a racialized lens, show how to engage stakeholders in the evaluation process, and communicate results in culturally appropriate ways. Included with this title: The password-protected Instructor Resource Site (formally known as SAGE Edge) offers access to all text-specific resources, including a test bank and editable, chapter-specific PowerPoint® slides.
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Usability Testing of Medical Devices
Usability Testing of Medical Devices covers the nitty-gritty of usability test planning, conducting, and results reporting.The book also discusses the government regulations and industry standards that motivate many medical device manufacturers to conduct usability tests. Since publication of the first edition, the FDA and other regulatory groups have modified their regulations and expectations regarding how medical device manufacturers should approach usability testing.Reflecting these changes, this Second Edition provides updated guidance to readers with an interest or direct role in conducting a usability test of a medical device or system.Key updates involve the 2011 FDA guidance on human factors engineering, requirements set forth by the third edition of IEC 60601 and closely related IEC 62366-1:2015, linking usability test tasks to risk analysis results, and analyzing root causes of use errors that occur during usability tests.Written by seasoned human factors specialists, Usability Testing of Medical Devices, Second Edition is an informative, practical, and up-to-date handbook for conducting usability tests of medical devices.The book helps ensure a smooth and painless development process—and thus, safe and effective medical devices.
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Argumentation : Analysis and Evaluation
This book concentrates on argumentation as it emerges in ordinary discourse, whether the discourse is institutionalized or strictly informal.Crucial concepts from the theory of argumentation are systematically discussed and explained with the help of examples from real-life discourse and texts.The basic principles are explained that are instrumental in the analysis and evaluation of argumentative discourse.Methodical instruments are offered for identifying differences of opinion, analyzing and evaluating argumentation and presenting arguments in oral and written discourse.Attention is also paid to the way in which arguers attempt to be not just reasonable, but effective as well, by maneuvering strategically.In addition, the book provides a great variety of exercises and assignments to improve the student’s skill in presenting argumentation. The authors begin their treatment of argumentation theory at the same juncture where argumentation also starts in practice: The difference of opinion that occasions the evolvement of the argumentation.Each chapter begins with a short summary of the essentials and ends with a number of exercises that students can use to master the material.Argumentation is the first introductory textbook of this kind.It is intended as a general introduction for students who are interested in a proper conduct of argumentative discourse.Suggestions for further reading are made for each topic and several extra assignments are added to the exercises. Special features:• A concise and complete treatment of both the theoretical backgrounds and the practice of argumentation analysis and evaluation. • Crucial concepts from pragmatics (speech act theory, Grice’s cooperative principle) presented in a non-technical way; introducing the theory of verbal communication. • The first textbook treatment of strategic maneuvering as a way of balancing being reasonable with being effective• Exercises and assignments based on real-life texts from a variety of contexts.
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What is the difference between a polynomial and a polynomial function?
A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division or roots. A polynomial function, on the other hand, is a specific type of function that can be defined by a polynomial expression. In other words, a polynomial function is a function that can be expressed as a polynomial. So, while a polynomial is simply an algebraic expression, a polynomial function is a specific type of mathematical function.
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What are polynomial functions?
Polynomial functions are mathematical functions that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. These functions can have multiple terms, each with a different power of the variable. Polynomial functions are continuous and smooth, and they can be used to model a wide range of real-world phenomena. They are commonly used in algebra, calculus, and other branches of mathematics to analyze and solve various problems.
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What is double polynomial division?
Double polynomial division is a method used to divide one polynomial by another polynomial. It involves dividing the leading term of the dividend by the leading term of the divisor to determine the first term of the quotient. This process is repeated for each subsequent term until the entire dividend is divided by the divisor. The result is a quotient and a remainder, if any.
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What is a polynomial space?
A polynomial space is a vector space whose elements are polynomials. In other words, it is a set of all polynomials of a certain degree, along with the operations of addition and scalar multiplication. The dimension of a polynomial space is determined by the highest degree of the polynomials in the space. Polynomial spaces are commonly used in mathematics and engineering to represent and manipulate functions and data.
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Validation of Analytical Methods for Pharmaceutical Analysis
This book provides a comprehensive guide on validating analytical methods.Key features: Full review of the available regulatory guidelines on validation and in particular, ICH. Sections of the guideline, Q2(R1), have been reproduced in this book with the kind permission of the ICH Secretariat; Thorough discussion of each of the validation characteristics (Specificity; Linearity; Range; Accuracy; Precision; Detection Limit; Quantitation Limit; Robustness; System Suitability) plus practical tips on how they may be studied; What to include in a validation protocol with advice on the experimental procedure to follow and selection of appropriate acceptance criteria; How to interpret and calculate the results of a validation study including the use of suitable statistical calculations; A fully explained case study demonstrating how to plan a validation study, what to include in the protocol, experiments to perform, setting acceptance criteria, interpretation of the results and reporting the study.
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Testing and Evaluation of Agricultural Machinery
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Enhancing Learning through Formative Assessment and Feedback
Assessment is a critical aspect of higher education because it has a range of powerful impacts on what staff and students do and how universities operate.Underpinned by relevant theory and practical advice this fully updated new edition takes into account the changing expectation of students in the context of an increasingly complex and shifting higher education environment to promote the role of formative assessment and formative feedback and its impact on shaping the student learning experience.Presented through the lens of contemporary perspectives, empirical evidence, and case studies across a broad range of subject disciplines, this new edition aims to encourage teaching and support staff to focus on the promotion of student learning through designing and embedding high-impact formative assessment processes and activities.Key content covers: the theoretical and philosophical aspects of formative assessment and formative feedback; the learning environment in which students undertake their learning activities, helping teachers develop appropriate formative assessment and provide effective formative feedback; the impact of formative assessment and formative feedback activities have on learning, teaching, and assessment design, as well as on the academic workload of tutors; the contemporary issues and challenges currently driving research into formative assessment; the use of technology in formative assessment and how different tools and technologies allow for the provision of effective and efficient formative feedback; the benefits of understanding how students respond to formative assessment and formative feedback as an opportunity to review the effectiveness of the teaching and learning methods and techniques; the integral role of formative assessment and formative feedback plays in postgraduate research settings; and how innovations in formative assessment and feedback inform key developments in large-scale assessment change.Aimed at both experienced and early career practitioners in higher education, this text is ideal reading for educators who wish to see a movement away from a higher education system driven by summative assessment to one where a more holistic approach to education positions learning standards rather than measurement and grades as central to effective assessment and, crucially, to return to a focus on student learners.
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Multivariable Feedback Control : Analysis and Design
Multivariable Feedback Control: Analysis and Design, Second Edition presents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems.Focusing on practical feedback control and not on system theory in general, this book provides the reader with insights into the opportunities and limitations of feedback control. Taking into account the latest developments in the field, this fully revised and updated second edition: * features a new chapter devoted to the use of linear matrix inequalities (LMIs); * presents current results on fundamental performance limitations introduced by RHP-poles and RHP-zeros; * introduces updated material on the selection of controlled variables and self-optimizing control; * provides simple IMC tuning rules for PID control; * covers additional material including unstable plants, the feedback amplifier, the lower gain margin and a clear strategy for incorporating integral action into LQG control; * includes numerous worked examples, exercises and case studies, which make frequent use of Matlab and the new Robust Control toolbox. Multivariable Feedback Control: Analysis and Design, Second Edition is an excellent resource for advanced undergraduate and graduate courses studying multivariable control.It is also an invaluable tool for engineers who want to understand multivariable control, its limitations, and how it can be applied in practice.The analysis techniques and the material on control structure design should prove very useful in the new emerging area of systems biology. Reviews of the first edition: "Being rich in insights and practical tips on controller design, the book should also prove to be very beneficial to industrial control engineers, both as a reference book and as an educational tool." Applied Mechanics Reviews "In summary, this book can be strongly recommended not only as a basic text in multivariable control techniques for graduate and undergraduate students, but also as a valuable source of information for control engineers." International Journal of Adaptive Control and Signal Processing
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Is 2x a polynomial function?
Yes, 2x is a polynomial function. A polynomial function is a function that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. In the case of 2x, it can be written as 2x^1, which fits the definition of a polynomial function.
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"Is my polynomial function correct?"
To determine if your polynomial function is correct, you should first check if it satisfies the given conditions or constraints. Then, you can verify if the function produces the expected output for a range of input values. Additionally, you can compare your function with other known correct polynomial functions to see if they match. If your function meets all these criteria, it is likely correct. However, it's always a good idea to double-check your work and seek feedback from others to ensure accuracy.
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What is the polynomial form?
The polynomial form is a mathematical expression consisting of variables, coefficients, and exponents. It is a sum of terms, where each term is a variable raised to a non-negative integer power, multiplied by a coefficient. The polynomial form is used to represent various mathematical functions and equations, and it can be manipulated through operations such as addition, subtraction, multiplication, and division. The degree of a polynomial is determined by the highest exponent of the variables present in the expression.
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What is a constant polynomial?
A constant polynomial is a polynomial function that has a degree of zero, meaning it does not contain any variables. It is simply a constant value, such as 5 or -3. Constant polynomials are represented in the form f(x) = c, where c is a constant value. These polynomials do not change in value as x varies, hence the term "constant."
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