Partitions

Partitions PDF Author: Frank Hwang
Publisher: World Scientific
ISBN: 9812770151
Category : Mathematics
Languages : en
Pages : 363

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Book Description
The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The OC clusteringOCO problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory OCo or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory."

Partitions

Partitions PDF Author: Frank Hwang
Publisher: World Scientific
ISBN: 9812770151
Category : Mathematics
Languages : en
Pages : 363

Get Book Here

Book Description
The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The OC clusteringOCO problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory OCo or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory."

Partitions: Optimality And Clustering - Vol Ii: Multi-parameter

Partitions: Optimality And Clustering - Vol Ii: Multi-parameter PDF Author: Frank Kwang-ming Hwang
Publisher: World Scientific
ISBN: 9814412368
Category : Mathematics
Languages : en
Pages : 302

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Book Description
The need for optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The “clustering” problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion.Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory — or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory.

Partitions: Optimality And Clustering - Volume I: Single-parameter

Partitions: Optimality And Clustering - Volume I: Single-parameter PDF Author: Frank Kwang-ming Hwang
Publisher: World Scientific
ISBN: 9814390992
Category : Mathematics
Languages : en
Pages : 363

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Book Description
The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The “clustering” problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion.Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory — or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory.

Inverse Problems: Tikhonov Theory And Algorithms

Inverse Problems: Tikhonov Theory And Algorithms PDF Author: Kazufumi Ito
Publisher: World Scientific
ISBN: 9814596213
Category : Mathematics
Languages : en
Pages : 330

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Book Description
Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.

Ordinary Differential Equations With Applications (Third Edition)

Ordinary Differential Equations With Applications (Third Edition) PDF Author: Sze-bi Hsu
Publisher: World Scientific
ISBN: 9811250766
Category : Mathematics
Languages : en
Pages : 378

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Book Description
Written in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras. A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.

Ordinary Differential Equations With Applications (2nd Edition)

Ordinary Differential Equations With Applications (2nd Edition) PDF Author: Sze-bi Hsu
Publisher: World Scientific Publishing Company
ISBN: 9814452920
Category : Mathematics
Languages : en
Pages : 312

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Book Description
During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers.This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.

Handbook of Discrete and Computational Geometry

Handbook of Discrete and Computational Geometry PDF Author: Csaba D. Toth
Publisher: CRC Press
ISBN: 1351645919
Category : Computers
Languages : en
Pages : 2354

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Book Description
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Evolving Fuzzy Systems - Methodologies, Advanced Concepts and Applications

Evolving Fuzzy Systems - Methodologies, Advanced Concepts and Applications PDF Author: Edwin Lughofer
Publisher: Springer
ISBN: 3642180876
Category : Technology & Engineering
Languages : en
Pages : 467

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Book Description
In today’s real-world applications, there is an increasing demand of integrating new information and knowledge on-demand into model building processes to account for changing system dynamics, new operating conditions, varying human behaviors or environmental influences. Evolving fuzzy systems (EFS) are a powerful tool to cope with this requirement, as they are able to automatically adapt parameters, expand their structure and extend their memory on-the-fly, allowing on-line/real-time modeling. This book comprises several evolving fuzzy systems approaches which have emerged during the last decade and highlights the most important incremental learning methods used. The second part is dedicated to advanced concepts for increasing performance, robustness, process-safety and reliability, for enhancing user-friendliness and enlarging the field of applicability of EFS and for improving the interpretability and understandability of the evolved models. The third part underlines the usefulness and necessity of evolving fuzzy systems in several online real-world application scenarios, provides an outline of potential future applications and raises open problems and new challenges for the next generation evolving systems, including human-inspired evolving machines. The book includes basic principles, concepts, algorithms and theoretic results underlined by illustrations. It is dedicated to researchers from the field of fuzzy systems, machine learning, data mining and system identification as well as engineers and technicians who apply data-driven modeling techniques in real-world systems.

Progress in Pattern Recognition, Image Analysis and Applications

Progress in Pattern Recognition, Image Analysis and Applications PDF Author: Alberto Sanfeliu
Publisher: Springer Science & Business Media
ISBN: 3540298509
Category : Computers
Languages : en
Pages : 1114

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Book Description
This book constitutes the refereed proceedings of the 10th Iberoamerican Congress on Pattern Recognition, CIARP 2005, held in Havana, Cuba in November 2005. The 107 revised full papers presented together with 3 keynote articles were carefully reviewed and selected from more than 200 submissions. The papers cover ongoing research and mathematical methods for pattern recognition, image analysis, and applications in such diverse areas as computer vision, robotics, industry, health, entertainment, space exploration, telecommunications, data mining, document analysis, and natural language processing and recognition.

Categorical Data Analysis

Categorical Data Analysis PDF Author: Alan Agresti
Publisher: John Wiley & Sons
ISBN: 1118710940
Category : Mathematics
Languages : en
Pages : 756

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Book Description
Praise for the Second Edition "A must-have book for anyone expecting to do research and/or applications in categorical data analysis." —Statistics in Medicine "It is a total delight reading this book." —Pharmaceutical Research "If you do any analysis of categorical data, this is an essential desktop reference." —Technometrics The use of statistical methods for analyzing categorical data has increased dramatically, particularly in the biomedical, social sciences, and financial industries. Responding to new developments, this book offers a comprehensive treatment of the most important methods for categorical data analysis. Categorical Data Analysis, Third Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial loglinear models for discrete data with normal regression for continuous data. This edition also features: An emphasis on logistic and probit regression methods for binary, ordinal, and nominal responses for independent observations and for clustered data with marginal models and random effects models Two new chapters on alternative methods for binary response data, including smoothing and regularization methods, classification methods such as linear discriminant analysis and classification trees, and cluster analysis New sections introducing the Bayesian approach for methods in that chapter More than 100 analyses of data sets and over 600 exercises Notes at the end of each chapter that provide references to recent research and topics not covered in the text, linked to a bibliography of more than 1,200 sources A supplementary website showing how to use R and SAS; for all examples in the text, with information also about SPSS and Stata and with exercise solutions Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and methodologists, such as biostatisticians and researchers in the social and behavioral sciences, medicine and public health, marketing, education, finance, biological and agricultural sciences, and industrial quality control.