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Kernel Functions and Elliptic Differential Equations in Mathematical Physics (Dover Books on Mathematics #Volume 4)
by Stefan Bergman Menahem SchifferThis text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.The two-part treatment begins with a survey of boundary value problems occurring in certain branches of theoretical physics. It introduces fundamental solutions in a heuristic way and examines their physical significance. Many concepts can be unified by concentrating upon these particular kernels, and the text explains the common mathematical background of widely varying theories, such as those of heat conduction, hydrodynamics, electrostatics, magnetostatics, and elasticity. In addition to its intrinsic interest, this material provides illustrations and exact mathematical formulation of the problems and the methods. The second part is confined to a rather special type of partial differential equation, which is dealt with in the greatest detail so that students can make applications and generalizations to similar problems.
Kernel Methods for Machine Learning with Math and Python: 100 Exercises for Building Logic
by Joe SuzukiThe most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than relying on knowledge or experience. This textbook addresses the fundamentals of kernel methods for machine learning by considering relevant math problems and building Python programs. The book’s main features are as follows:The content is written in an easy-to-follow and self-contained style.The book includes 100 exercises, which have been carefully selected and refined. As their solutions are provided in the main text, readers can solve all of the exercises by reading the book.The mathematical premises of kernels are proven and the correct conclusions are provided, helping readers to understand the nature of kernels.Source programs and running examples are presented to help readers acquire a deeper understanding of the mathematics used.Once readers have a basic understanding of the functional analysis topics covered in Chapter 2, the applications are discussed in the subsequent chapters. Here, no prior knowledge of mathematics is assumed.This book considers both the kernel for reproducing kernel Hilbert space (RKHS) and the kernel for the Gaussian process; a clear distinction is made between the two.
Kernel Methods for Machine Learning with Math and R: 100 Exercises for Building Logic
by Joe SuzukiThe most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than relying on knowledge or experience. This textbook addresses the fundamentals of kernel methods for machine learning by considering relevant math problems and building R programs. The book’s main features are as follows:The content is written in an easy-to-follow and self-contained style.The book includes 100 exercises, which have been carefully selected and refined. As their solutions are provided in the main text, readers can solve all of the exercises by reading the book.The mathematical premises of kernels are proven and the correct conclusions are provided, helping readers to understand the nature of kernels.Source programs and running examples are presented to help readers acquire a deeper understanding of the mathematics used.Once readers have a basic understanding of the functional analysis topics covered in Chapter 2, the applications are discussed in the subsequent chapters. Here, no prior knowledge of mathematics is assumed.This book considers both the kernel for reproducing kernel Hilbert space (RKHS) and the kernel for the Gaussian process; a clear distinction is made between the two.
Kernel Mode Decomposition and the Programming of Kernels (Surveys and Tutorials in the Applied Mathematical Sciences #8)
by Houman Owhadi Clint Scovel Gene Ryan YooThis monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework.Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the context of additive Gaussian processes.It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems.
Kernel Ridge Regression in Clinical Research
by Aeilko H. Zwinderman Ton J. CleophasIBM (international business machines) has published in its SPSS statistical software 2022 update a very important novel regression method entitled Kernel Ridge Regression (KRR). It is an extension of the currently available regression methods, and is suitable for pattern recognition in high dimensional data, particularly, when alternative methods fail. Its theoretical advantages are plenty and include thekernel trick for reduced arithmetic complexity,estimation of uncertainty by Gaussians unlike histograms,corrected data-overfit by ridge regularization,availability of 8 alternative kernel density models for datafit.A very exciting and wide array of preliminary KRR research has already been published by major disciplines (like studies in quantum mechanics and nuclear physics, studies of molecular affinity / dynamics, atomisation energy studies, but also forecasting economics studies, IoT (internet of things) studies for e-networks, plant stress response studies, big data streaming studies, etc). In contrast, it is virtually unused in clinical research. This edition is the first textbook and tutorial of kernel ridge regressions for medical and healthcare students as well as recollection / update bench, and help desk for professionals. Each chapter can be studied as a standalone, and, using, real as well as hypothesized data, it tests the performance of the novel methodology against traditional regression analyses. Step by step analyses of over 20 data files stored at Supplementary Files at Springer Interlink are included for self-assessment. We should add that the authors are well qualified in their field. Professor Zwinderman is past-president of the International Society of Biostatistics (2012-2015) and Professor Cleophas is past-president of the American College of Angiology (2000-2002). From their expertise they should be able to make adequate selections of modern KRR methods for the benefit of physicians, students, and investigators. The authors have been working and publishing together for 24 years and their research can be characterized as a continued effort to demonstrate that clinical data analysis is not mathematics but rather a discipline at the interface of biology and mathematics.
Kernel Smoothing (ISSN #60)
by M.P. Wand M.C. JonesKernel smoothing refers to a general methodology for recovery of underlying structure in data sets. The basic principle is that local averaging or smoothing is performed with respect to a kernel function.This book provides uninitiated readers with a feeling for the principles, applications, and analysis of kernel smoothers. This is facilita
Kernel Smoothing: Principles, Methods and Applications
by Sucharita GhoshComprehensive theoretical overview of kernel smoothing methods with motivating examples Kernel smoothing is a flexible nonparametric curve estimation method that is applicable when parametric descriptions of the data are not sufficiently adequate. This book explores theory and methods of kernel smoothing in a variety of contexts, considering independent and correlated data e.g. with short-memory and long-memory correlations, as well as non-Gaussian data that are transformations of latent Gaussian processes. These types of data occur in many fields of research, e.g. the natural and the environmental sciences, and others. Nonparametric density estimation, nonparametric and semiparametric regression, trend and surface estimation in particular for time series and spatial data and other topics such as rapid change points, robustness etc. are introduced alongside a study of their theoretical properties and optimality issues, such as consistency and bandwidth selection. Addressing a variety of topics, Kernel Smoothing: Principles, Methods and Applications offers a user-friendly presentation of the mathematical content so that the reader can directly implement the formulas using any appropriate software. The overall aim of the book is to describe the methods and their theoretical backgrounds, while maintaining an analytically simple approach and including motivating examples—making it extremely useful in many sciences such as geophysics, climate research, forestry, ecology, and other natural and life sciences, as well as in finance, sociology, and engineering. A simple and analytical description of kernel smoothing methods in various contexts Presents the basics as well as new developments Includes simulated and real data examples Kernel Smoothing: Principles, Methods and Applications is a textbook for senior undergraduate and graduate students in statistics, as well as a reference book for applied statisticians and advanced researchers.
Key Concepts in Teaching Primary Mathematics (SAGE Key Concepts series)
by Derek HaylockCovering the key principles and concepts in the teaching and learning of mathematics in primary schools, this text provides trainee and practising teachers with a quick and easy reference to what they need to know for their course, and in the classroom. The entries are arranged alphabetically, and each contains a brief definition, followed by an explanation and discussion, practical examples and annotated suggestions for further reading. Examples of the wide-ranging material include: Anxiety about mathematics; Assessment for Learning; Cognitive conflict; Concept learning; Creativity in mathematics; Differentiation; Equivalence; Explanation; Investigation; Low attainment; Making connections; Meaningful context; Mental calculation; Numeracy; Play as a context for learning mathematics; Problem-solving; Questioning; Talk.
Key Demographics in Retirement Risk Management
by Leroy O StoneKey Demographics in Retirement Risk Management argues that the weakening of public and employer-sponsored social safety nets in several countries will permanently increase pre-retirees' risk-anxiety and create pressure towards readjustment of their expectations about the quality of their lives in retirement. The result will be to raise the priority of achieving effective comprehensive retirement related risk management. This achievement requires an emphasis upon the cascading of linked risks, and careful attention to the optimization of scarce resources used to manage those linked risks. Professional financial and retirement planning advisors comprise a key source of help. This book develops new knowledge concerning the factors that help to explain three important aspects of access to these professional advisors. The results of this analysis are used to illustrate the process of identifying distinctive population segments, key demographics, on the basis of multiple population attributes treated simultaneously. The illustration is further extended with an identification of distinctive population segments relative to performance on a composite indicator of the conduct of multiple retirement risk management activities. The book also discusses implications of the pattern of gender differences in preparedness to address retirement's challenges, highlighting subgroups of women in which inadequate preparedness is pronounced.
Key Labor Market Indicators: Analysis with Household Survey Data
by Michael Lokshin Ina Pietschmann Sajaia Evangelia Bourmpoula Steven KapsosKey Labor Market Indicators: Analysis with Household Survey Data is an introduction to labor market indicator analysis and a guide for analyzing household survey data using the ADePT ILO (International Labour Organization) Labor Market Indicators Module. The analytical framework and approach taken up in this book are based on the ILO's Key Indicators of the Labour Market (KILM). KILM indicators provide a strong basis on which to address key questions related to productive employment and decent work. The ADePT ILO Labor Market Indicators Module is a powerful tool for producing and analyzing KILM indicators using household survey data. The software allows researchers and practitioners to automate data production, to minimize data production errors, and to quickly produce a wide range of labor market data from labor force surveys or other household surveys that contain labor market information. ABOUT ADePT Streamlined Analysis with ADePT Software is a series that provides academics, students, and policy practitioners with a theoretical foundation, practical guidelines, and software tools for applied analysis in various areas of economic research. ADePT Platform is a software package developed in the research department of the World Bank (see www.worldbank.org/adept). The series examines such topics as sector performance and inequality in education, the effectiveness of social transfers, labor market conditions, the effects of macroeconomic shocks on income distribution and labor market outcomes, child anthropometrics, and gender inequalities.
Key Stage 3 Mastering Mathematics Book 1
by Sophie Goldie Luke RobinsonWith small steps and our carefully crafted questions, every pupil will achieve greater progress.Designed to be used flexibly, this second edition textbook has been updated to include more Mastery-style questions and whole-class activities. Whether you follow a full Mastery scheme, choose to use Mastery aspects or you're just looking for quality resources, our three textbooks support the way you want to teach.Each book gradually builds on prior knowledge, developing pupils' confidence, fluency, reasoning and problem-solving skills.· Secure understanding with differentiated questions and worked examples that build on prior knowledge, following the 'do it, secure it, deepen it' Mastery structure· Recap skills and topics from Key Stage 2, ensuring a smooth transition to Key Stage 3· Target key skills using the fluency, reasoning and problem-solving markers in the margin· Build confidence with starter activities and warm-up questions to introduce each concept· Develop reasoning skills using non-examples, where pupils identify mistakes in sample answers· Track progress through review questions, building key skills and knowledge· Benefit from the expertise of UK Mastery trained subject specialists with over 30 years of teaching experience· Cover the full UK National Curriculum and all four strands - number, algebra, geometry and measures, statistics and probability - within our three restructured textbooks for Key Stage 3Our flexible, Mastery-led approachOur flexible approach allows you to teach maths your way. You can choose to focus on building understanding using the graduated questions or take a Mastery approach to exposition using manipulatives and 'concrete, pictorial, abstract' in the optional class activities.Answers will be provided online.
Key Stage 3 Mastering Mathematics Book 2
by Sophie Goldie Luke Robinson Andrew GintyWith small steps and our carefully crafted questions, every pupil will achieve greater progress.Designed to be used flexibly, this second edition textbook has been updated to include more Mastery-style questions and whole-class activities. Whether you follow a full Mastery scheme, choose to use Mastery aspects or you're just looking for quality resources, our three textbooks support the way you want to teach.Each book gradually builds on prior knowledge, developing pupils' confidence, fluency, reasoning and problem-solving skills.· Secure understanding with differentiated questions and worked examples that build on prior knowledge, following the 'do it, secure it, deepen it' Mastery structure, building on prior knowledge from Book 1· Target key skills using the fluency, reasoning and problem-solving markers in the margin· Build confidence with starter activities and warm-up questions to introduce each concept· Develop reasoning skills using non-examples, where pupils identify mistakes in sample answers· Track progress through review questions, building key skills and knowledge· Benefit from the expertise of UK Mastery trained subject specialists with over 30 years of teaching experience· Cover the full UK National Curriculum and all four strands - number, algebra, geometry and measures, statistics and probability - within our three restructured textbooks for Key Stage 3Our flexible, Mastery-led approachOur flexible approach allows you to teach maths your way. You can choose to focus on building understanding using the graduated questions or take a Mastery approach to exposition using manipulatives and 'concrete, pictorial, abstract' in the optional class activities.Answers will be provided online.
Key Stage 3 Mastering Mathematics Book 3
by Heather Davis Sophie Goldie Luke RobinsonWith small steps and our carefully crafted questions, every pupil will achieve greater progress.Designed to be used flexibly, this second edition textbook has been updated to include more Mastery-style questions and whole-class activities. Whether you follow a full Mastery scheme, choose to use Mastery aspects or you're just looking for quality resources, our three textbooks support the way you want to teach.Each book gradually builds on prior knowledge, developing pupils' confidence, fluency, reasoning and problem-solving skills.· Secure understanding with differentiated questions and worked examples that follow the 'do it, secure it, deepen it' Mastery structure, building on prior knowledge from Book 2· Target key skills using the fluency, reasoning and problem-solving markers in the margin· Build confidence with starter activities and warm-up questions to introduce each concept· Develop reasoning skills using non-examples, where pupils identify mistakes in sample answers· Track progress through review questions, building key skills and knowledge so students will be prepared for the next step up to GCSE· Benefit from the expertise of UK Mastery trained subject specialists with over 30 years of teaching experience· Cover the full UK National Curriculum and all four strands - number, algebra, geometry and measures, statistics and probability - within our three restructured textbooks for Key Stage 3Our flexible, Mastery-led approachOur flexible approach allows you to teach maths your way. You can choose to focus on building understanding using the graduated questions or take a Mastery approach to exposition using manipulatives and 'concrete, pictorial, abstract' in the optional class activities.Answers will be provided online.
Key Stage 3 Mastering Mathematics Develop and Secure Practice Book 1
by Frances CarrBuild key fluency and reasoning skills and prepare for problem-solving with extra practice. This book is packed with questions that take small steps to enable sustained progress and is perfect for intervention.- Bridge the gap from KS2 to KS3 by recapping the key skills and content needed for KS3- Develop knowledge and understanding with practice questions that get progressively more difficult following a Mastery approach to learning- Support pupils with helpful reminders and explanations alongside hints for trickier questions- Help to engage pupils with questions that relate maths to outside of the classroom and plenty of colourful images- Enable home learning with answers available online
Key Stage 3 Mastering Mathematics Develop and Secure Practice Book 2
by Frances CarrBuild key fluency, reasoning and problem-solving skills with extra practice. This book is packed with questions that take small steps to enable sustained progress and is perfect for intervention.- Develop knowledge and understanding with practice questions that get progressively more difficult following a Mastery approach to learning- Support pupils with helpful reminders and explanations alongside hints for trickier questions- Help to engage pupils with questions that relate maths to outside of the classroom and plenty of colourful images- Enable home learning with answers available online
Key Stage 3 Mastering Mathematics Develop and Secure Practice Book 3
by Frances CarrBuild key fluency, reasoning and problem-solving skills with extra practice. This book is packed with questions that take small steps to enable sustained progress and is perfect for intervention.- Develop knowledge and understanding with practice questions that get progressively more difficult following a Mastery approach to learning- Support pupils with helpful reminders and explanations alongside hints for trickier questions- Help to engage pupils with questions that relate maths to outside of the classroom and plenty of colourful images- Enable home learning with answers available online
Key Stage 3 Mastering Mathematics Extend Practice Book 1
by Heather DavisStrengthen problem-solving skills and challenge more able pupils through extra practice. This book is packed with questions that are perfect for extension activities and learning beyond the curriculum.- Ensure sustained progress and greater depth for more able pupils with challenging practice questions designed to improve their fluency, reasoning and problem-solving skills- Follow a Mastery approach to learning with questions that get progressively more difficult through small steps - Promote conceptual understanding with questions that encourage pupils to apply and reflect on their knowledge- Enable home learning with answers available online
Key Stage 3 Mastering Mathematics Extend Practice Book 2
by Heather DavisStrengthen problem-solving skills and challenge more able pupils through extra practice. This book is packed with questions that are perfect for extension activities and learning beyond the curriculum.- Ensure sustained progress and greater depth for more able pupils with challenging practice questions designed to improve their fluency, reasoning and problem-solving skills- Follow a Mastery approach to learning with questions that get progressively more difficult through small steps - Promote conceptual understanding with questions that encourage pupils to apply and reflect on their knowledge- Enable home learning with answers available online
Key Stage 3 Mastering Mathematics Extend Practice Book 3
by Heather DavisStrengthen problem-solving skills and challenge more able pupils through extra practice. This book is packed with questions that are perfect for extension activities and learning beyond the curriculum.- Ensure sustained progress and greater depth for more able pupils with challenging practice questions designed to improve their fluency, reasoning and problem-solving skills- Follow a Mastery approach to learning with questions that get progressively more difficult through small steps - Promote conceptual understanding with questions that encourage pupils to apply and reflect on their knowledge- Enable home learning with answers available online
Kidney and Kidney Tumor Segmentation: MICCAI 2023 Challenge, KiTS 2023, Held in Conjunction with MICCAI 2023, Vancouver, BC, Canada, October 8, 2023, Proceedings (Lecture Notes in Computer Science #14540)
by Andrew Wood Nicholas Heller Fabian Isensee Nikolaos Papanikolopoulos Christopher Weight Tim Rädsch Resha TeipaulThis book constitutes the Third International Challenge on Kidney and Kidney Tumor Segmentation, KiTS 2023, which was held in conjunction with the 26th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2023. The challenge took place in Vancouver, BC, Canada, on October 8, 2023. The 22 contributions presented in this book were carefully reviewed and selected from 29 submissions. This challenge aims to develop the best system for automatic semantic segmentation of kidneys, renal tumors and renal cysts.
Kinder thematisieren Differenzerfahrungen: Eine rekonstruktive Studie unter besonderer Berücksichtigung der Sachunterrichtsdidaktik und des Sozialen Lernens (Sachlernen & kindliche Bildung – Bedingungen, Strukturen, Kontexte)
by Florian SchrumpfWelches Potenzial hat der Sachunterricht für die Thematisierung kindlicher Differenzerfahrungen? Und kann in diesem Zusammenhang der Begriff des Sozialen Lernens didaktische und forschungsmethodologische Impulse für die fachdidaktische Forschung zu Differenzerfahrungen bereithalten? Florian Schrumpf geht in dem vorliegenden Buch diesen Fragen nach und entfaltet seine Argumentation durch Überlegungen zum Passungsverhältnis zwischen Sachunterrichtsdidaktik und Sozialem Lernen. Die bildungstheoretische Diskussion wird dabei mit einem soziologischen Zugang zu Kinderkulturen verbunden: Ein empirisches Forschungsvorhaben rekonstruiert das Sprechen über Differenz von Kindern in Gruppendiskussionen. Aus den theoretischen und empirischen Erkenntnissen werden für die Sachunterrichtsdidaktik und das Soziale Lernen didaktische Konsequenzen gezogen. Abschließend werden das Gruppendiskussionsverfahren sowie die Dokumentarische Methode hinsichtlich ihrer Potenziale und Herausforderungen für die fachdidaktische Forschung mit Kindern kritisch reflektiert.
Kindergarten Math With Confidence Instructor Guide (Math with Confidence #1)
by Kate SnowComprehensive coverage of all essential kindergarten math topics. With this scripted, open-and-go program, parents can help their children master all the concepts typically covered in kindergarten: counting to 100 writing numbers beginning addition and subtraction shapes and patterns coins, time, and measurement Carefully-sequenced, confidence-building lessons will help children develop a strong understanding of math, step by step. Daily review will ensure they fully master what they have learned. With this blend of conceptual understanding and traditional skill practice, children will be well-prepared for first grade. This book is the Instructor Guide to Kindergarten Math With Confidence: Student Workbook
Kindergarten Math With Confidence Student Workbook (Math With Confidence Ser. #2)
by Kate SnowQuick and easy workbook pages will help children review and practice what they've learned. They'll also develop children's fine-motor skills and help them get used to pencil-and-paper work, which will prepare them for greater independence in first grade. This simple, beautiful, age-appropriate workbook is colorfully illustrated by Itamar Katz. This Student Workbook accompanies Kindergarten Math With Confidence: Instructor Guide .
Kinderlosigkeit im Alter – (k)ein Thema?!: Eine biographische Perspektive auf die sozialen Beziehungen und Generativität kinderloser älterer Menschen
by Katrin AlertDie Studie zeigt die Vielfältigkeit kinderloser Lebensentwürfe und -verläufe auf. Dabei wird insbesondere das Phänomen erworbene Kinderlosigkeit differenzierter als in vielen bisherigen Untersuchungen beleuchtet. Zudem wird der Prozesscharakter von Kinderlosigkeit deutlich herausgearbeitet und gezeigt, dass mit dem zeitlichen Abstand im Alter die Entstehung der eigenen Kinderlosigkeit zum Teil eine Umdeutung erfährt, um von den kinderlosen Älteren sinnhaft in die Biographie gefügt werden zu können.Die AutorinKatrin Alert ist derzeit Geschäftsführerin des Forschungskollegs Wohlbefinden bis ins hohe Alter (gefördert vom Ministerium für Kultur und Wissenschaft des Landes Nordrhein-Westfalen) mit zehn Doktorand*innen an der Universität zu Köln.