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Author: John E. Hilliard
Publisher: Springer Science & Business Media
ISBN: 9781402016875
Category : Computers
Languages : en
Pages : 512
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Book Description
Somebody had to do it. The Chinese speak of deep water wells called "grandfather wells" because they take three generations of diggers to complete. Imagine the thought of such a well being abandoned incomplete by the third generation. What a loss! This book is like a grandfather well except that it has taken only two generations, John Hilliard's and mine, to finish. When I saw his manuscript lying in a heap, I decided that I must spend the time to put it and his notes into a publishable form. Now, it is done. This book is mostly about performing spatial measurements through the statistical sampling of images; it is a text on classical stereology as John Hilliard saw it. His vision of the subject was broad. Consequently, its title is broad too. It presents this subject and some of its modem extensions from the classical perspective of the one of the founders of the field, and my first advisor at Northwestern University, John Hilliard. There is nothing new in this book but much that may have been lost over time. It rediscovers many useful discussions about such subjects as the variances of stereo logical measurements, anisotropy etc. It recovers some of the dialogues between John Hilliard and his students on such topics as fractals and Monte Carlo simulations. It recaptures a little of John Hilliard's unique and subtle wit.
Author: John E. Hilliard
Publisher: Springer Science & Business Media
ISBN: 9781402016875
Category : Computers
Languages : en
Pages : 512
Get Book Here
Book Description
Somebody had to do it. The Chinese speak of deep water wells called "grandfather wells" because they take three generations of diggers to complete. Imagine the thought of such a well being abandoned incomplete by the third generation. What a loss! This book is like a grandfather well except that it has taken only two generations, John Hilliard's and mine, to finish. When I saw his manuscript lying in a heap, I decided that I must spend the time to put it and his notes into a publishable form. Now, it is done. This book is mostly about performing spatial measurements through the statistical sampling of images; it is a text on classical stereology as John Hilliard saw it. His vision of the subject was broad. Consequently, its title is broad too. It presents this subject and some of its modem extensions from the classical perspective of the one of the founders of the field, and my first advisor at Northwestern University, John Hilliard. There is nothing new in this book but much that may have been lost over time. It rediscovers many useful discussions about such subjects as the variances of stereo logical measurements, anisotropy etc. It recovers some of the dialogues between John Hilliard and his students on such topics as fractals and Monte Carlo simulations. It recaptures a little of John Hilliard's unique and subtle wit.
Author: Rolf Schneider
Publisher: Springer Science & Business Media
ISBN: 354078859X
Category : Mathematics
Languages : en
Pages : 692
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Book Description
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.
Author: Volker Schmidt
Publisher: Springer
ISBN: 3319100645
Category : Mathematics
Languages : en
Pages : 484
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Book Description
This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.
Author: Eva B. Vedel Jensen
Publisher: Springer
ISBN: 3319519514
Category : Mathematics
Languages : en
Pages : 469
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Book Description
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
Author: Sung Nok Chiu
Publisher: John Wiley & Sons
ISBN: 1118658256
Category : Mathematics
Languages : en
Pages : 561
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Book Description
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. This edition: Presents a wealth of models for spatial patterns and related statistical methods. Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas. Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments. Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes 700 new references. Is written in an accessible style enabling non-mathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.
Author: Evgeny Spodarev
Publisher: Springer
ISBN: 3642333052
Category : Mathematics
Languages : en
Pages : 470
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Book Description
This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.
Author: Vitor Balestro
Publisher: Springer Nature
ISBN: 3031505077
Category :
Languages : en
Pages : 1195
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Book Description
Author: B. S. Daya Sagar
Publisher: Springer Nature
ISBN: 3030850404
Category : Science
Languages : en
Pages : 1744
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Book Description
The Encyclopedia of Mathematical Geosciences is a complete and authoritative reference work. It provides concise explanation on each term that is related to Mathematical Geosciences. Over 300 international scientists, each expert in their specialties, have written around 350 separate articles on different topics of mathematical geosciences including contributions on Artificial Intelligence, Big Data, Compositional Data Analysis, Geomathematics, Geostatistics, Geographical Information Science, Mathematical Morphology, Mathematical Petrology, Multifractals, Multiple Point Statistics, Spatial Data Science, Spatial Statistics, and Stochastic Process Modeling. Each topic incorporates cross-referencing to related articles, and also has its own reference list to lead the reader to essential articles within the published literature. The entries are arranged alphabetically, for easy access, and the subject and author indices are comprehensive and extensive.
Author: Eva B. Vedel Jensen
Publisher: World Scientific
ISBN: 9789810224547
Category : Mathematics
Languages : en
Pages : 272
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Book Description
This book provides a unified exposition of local-stereological methods developed within the last 15 years. The object of local stereology is to draw inference about quantitative parameters of spatial structures which can be regarded as neighbourhoods of points, called reference points. The model example is a biological cell which can be regarded as a neighbourhood of its nucleus. In local stereology, information from sections through the reference point is used. Only very weak assumptions are needed for the structure under study. For instance, specific cell shape assumptions are not necessary.In order to reach a broader audience, the book has been written not only for specialists in stereology, integral geometry and geometric measure theory. In particular, Chapter 1 is an elementary introduction to stereology and the book contains about 75 illustrations. The theory of local steroelogy involves, however, advanced mathematical tools, which constitute an important part of the book.Local-stereological methods are now in world-wide use in the microscopical study of biological tissue, and this invaluable book also contains a description of how the local methods are used in practice.
Author: Peter R. Mouton
Publisher: JHU Press
ISBN: 0801899850
Category : Science
Languages : en
Pages : 195
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Book Description
This update to Peter R. Mouton's pioneering work provides bioscientists with the concepts needed in order to apply the principles and practices of unbiased stereology to research involving biological tissues. Mouton starts with a brief explanation of the history and theory of the process before defining the terms, concepts, and tools of unbiased stereological procedures. He compares and contrasts the procedures with less-exacting approaches to quantitative analysis of biological structure using specific examples from biomedical literature. The book incorporates existing best practices with new methodologies, such as the Rare Event Protocol, while simplifying the dense, often difficult literature on the Subject to show the utility and importance of unbiased stereology. This clear, insightful guide goes a step further than other books on this Subject by demonstrating not only how to use unbiased stereology but also how to interpret and present the results. Written by the official U.S. representative to the International Society for Stereology, this is the most complete, up-to-date resource on the science of unbiased stereology. Those new to bioscience research as well as experienced practitioners will find that Mouton's explanations are the perfect companion for stereology courses and workshops.
