Permutation Design


Book Description

In design, the problems that designers are called upon to solve can be regarded as a problem of permutations. A permutation is an ordered arrangement of elements in a set. In our case, the set is design and the elements are design components, such as lines, shapes, forms, or spaces. Traditionally, such arrangements are done by human designers who base their decision-making process either on intuition or on random sampling until a valid solution is found. However, in both cases the solution found may be an acceptable one but cannot be labeled as "the best possible solution" due to the subjective or arbitrary nature of the selection process. In contrast, by harnessing the potential of computational design, these elements can be arranged in all possible ways and then the best ones are chosen based on specific criteria. By presenting a complete list of permutation-based arrangements the "best solution" will eventually reveal itself by excluding all other possible solutions. This book comprehensively addresses theories, techniques, and examples of permutation design in order to fully demonstrate to the reader the full range of possibilities this method represents. The significance of such an approach to design is enormous, paradigmatic, and far-reaching. It provides an alternative method for design analysis, synthesis, and evaluation that is based on computational force rather than pure human intelligence alone. In contrast to human-based random sampling or intuition, permutation-based design offers the assurance of an optimum design since any possible alternative design can be eliminated. From a practical point of view, this methodology offers a paradigmatic shift away from the current state of design practice where arbitrariness, repetition, and redundancy often exist. From a theoretical viewpoint, this new paradigm will offer alternative insights into the value of human creativity, intuition, and intelligence.




A Chronicle of Permutation Statistical Methods


Book Description

The focus of this book is on the birth and historical development of permutation statistical methods from the early 1920s to the near present. Beginning with the seminal contributions of R.A. Fisher, E.J.G. Pitman, and others in the 1920s and 1930s, permutation statistical methods were initially introduced to validate the assumptions of classical statistical methods. Permutation methods have advantages over classical methods in that they are optimal for small data sets and non-random samples, are data-dependent, and are free of distributional assumptions. Permutation probability values may be exact, or estimated via moment- or resampling-approximation procedures. Because permutation methods are inherently computationally-intensive, the evolution of computers and computing technology that made modern permutation methods possible accompanies the historical narrative. Permutation analogs of many well-known statistical tests are presented in a historical context, including multiple correlation and regression, analysis of variance, contingency table analysis, and measures of association and agreement. A non-mathematical approach makes the text accessible to readers of all levels.




Permutation Tests


Book Description

A step-by-step guide to the application of permutation tests in biology, medicine, science, and engineering. The intuitive and informal style makes this manual ideally suitable for students and researchers approaching these methods for the first time. In particular, it shows how to handle the problems of missing and censored data, nonresponders, after-the-fact covariates, and outliers.




Permutation Groups and Combinatorial Structures


Book Description

The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.




Ideal Sequence Design in Time-Frequency Space


Book Description

This book develops theory and algorithms leading to systematic waveform design in time-frequency space. The key tool employed in the work is the Zak transform, which provides a two-dimensional image for sequences, the Fourier transform, convolution, and correlation, and allows for the design of sequences directly in Zak space. Application areas covered include pulse radars and sonars, multibeam radar and sonar imaging systems, remote dielectric material identification, and code division multiple-access communication systems. This is an excellent reference text for graduate students, researchers, and engineers in radar, sonar, and communication systems.




Product Design


Book Description

The discovery of market needs and the manufacture of a product to meet those needs are integral parts of the same process. Since most textbooks on new product development are written from either a marketing or an engineering perspective, it is important for students to encounter these two aspects of product development together in a single text. Product Design: Practical Methods for the Systematic Development of New Products covers the entire new product development process, from market research through concept design, embodiment design, design for manufacture, and product launch. Systematic and practical in its approach, the text offers both a structured management framework for product development and an extensive range of specific design methods. Chapters feature "Design Toolkits" that provide detailed guidance on systematic design methods, present examples with familiar products, and conclude with reviews of key concepts. This major text aims to turn the often haphazard and unstructured product design process into a quality-controlled, streamlined, and manageable procedure. It is ideal for students of engineering, design, and technology on their path to designing new products.




Permutation Tests for Complex Data


Book Description

Complex multivariate testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. As a result, modern statistics needs permutation testing for complex data with low sample size and many variables, especially in observational studies. The Authors give a general overview on permutation tests with a focus on recent theoretical advances within univariate and multivariate complex permutation testing problems, this book brings the reader completely up to date with today’s current thinking. Key Features: Examines the most up-to-date methodologies of univariate and multivariate permutation testing. Includes extensive software codes in MATLAB, R and SAS, featuring worked examples, and uses real case studies from both experimental and observational studies. Includes a standalone free software NPC Test Release 10 with a graphical interface which allows practitioners from every scientific field to easily implement almost all complex testing procedures included in the book. Presents and discusses solutions to the most important and frequently encountered real problems in multivariate analyses. A supplementary website containing all of the data sets examined in the book along with ready to use software codes. Together with a wide set of application cases, the Authors present a thorough theory of permutation testing both with formal description and proofs, and analysing real case studies. Practitioners and researchers, working in different scientific fields such as engineering, biostatistics, psychology or medicine will benefit from this book.




R in Action, Third Edition


Book Description

'R in Action' presents both the R system and the use cases that make it such a compelling package for business developers. The book begins by introducing the R language, and then moves on to various examples illustrating R's features.




Designs and Their Codes


Book Description

A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.