Space, Structure and Randomness
Space, Structure and Randomness

Author: Michel Bilodeau

Publisher: Springer Science & Business Media

Published: 2007-12-23

Total Pages: 402

ISBN-13: 0387291156

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Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic. When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems. The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.

Stochastic Geometry, Spatial Statistics and Random Fields
Stochastic Geometry, Spatial Statistics and Random Fields

Author: Volker Schmidt

Publisher: Springer

Published: 2014-10-24

Total Pages: 484

ISBN-13: 3319100645

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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.

The Random Spatial Economy and its Evolution
The Random Spatial Economy and its Evolution

Author: Leslie Curry

Publisher: Taylor & Francis

Published: 2020-07-09

Total Pages: 461

ISBN-13: 0429764456

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First published in 1998, this volume, spanning a lifetime's research, is a highly innovative first attempt at a consistent theoretical approach to the elements, structures and dynamics of the geography of agents, settlements and trade. Cause and effect are replaced by chance within constraints. Populations are substituted for unreal representative individuals, variability for uniformity, probabilistic process for unique history. Ignorance is a major factor in interpersonal and inter-areal commercial relations so that the focus is on flows of information and their effects on the efficiency of the economy or, alternatively, on changes in its information content. Recent work on spatial arrangements in many physical and social sciences is incorporated but always interpreted from an overriding geographical viewpoint. Key concepts are locational potential, distance friction, mobility, diffusion, spatial pattern and texture, adaptability, efficiency, spatial interaction and dependence. Analytic methods include autocovariance and transfer functions, areal special densities and entropy. Various forms of self-organization of economic spatial patterns are examined.

Spatial Sampling with R
Spatial Sampling with R

Author: Dick J. Brus

Publisher: CRC Press

Published: 2022-09-26

Total Pages: 582

ISBN-13: 100060005X

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Scientific research often starts with data collection. However, many researchers pay insufficient attention to this first step in their research. The author, researcher at Wageningen University and Research, often had to conclude that the data collected by fellow researchers were suboptimal, or in some cases even unsuitable for their aim. One reason is that sampling is frequently overlooked in statistics courses. Another reason is the lack of practical textbooks on sampling. Numerous books have been published on the statistical analysis and modelling of data using R, but to date no book has been published in this series on how these data can best be collected. This book fills this gap. Spatial Sampling with R presents an overview of sampling designs for spatial sample survey and monitoring. It shows how to implement the sampling designs and how to estimate (sub)population- and space-time parameters in R. Key features Describes classical, basic sampling designs for spatial survey, as well as recently developed, advanced sampling designs and estimators Presents probability sampling designs for estimating parameters for a (sub)population, as well as non-probability sampling designs for mapping Gives comprehensive overview of model-assisted estimators Covers Bayesian approach to sampling design Illustrates sampling designs with surveys of soil organic carbon, above-ground biomass, air temperature, opium poppy Explains integration of wall-to-wall data sets (e.g. remote sensing images) and sample data Data and R code available on github Exercises added making the book suitable as a textbook for students The target group of this book are researchers and practitioners of sample surveys, as well as students in environmental, ecological, agricultural science or any other science in which knowledge about a population of interest is collected through spatial sampling. This book helps to implement proper sampling designs, tailored to their problems at hand, so that valuable data are collected that can be used to answer the research questions.

Mathematics of Random Phenomena
Mathematics of Random Phenomena

Author: P. Krée

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 452

ISBN-13: 9400947704

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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.

Spatial Analysis with R
Spatial Analysis with R

Author: Tonny J. Oyana

Publisher: CRC Press

Published: 2020-08-31

Total Pages: 355

ISBN-13: 1000173453

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In the five years since the publication of the first edition of Spatial Analysis: Statistics, Visualization, and Computational Methods, many new developments have taken shape regarding the implementation of new tools and methods for spatial analysis with R. The use and growth of artificial intelligence, machine learning and deep learning algorithms with a spatial perspective, and the interdisciplinary use of spatial analysis are all covered in this second edition along with traditional statistical methods and algorithms to provide a concept-based problem-solving learning approach to mastering practical spatial analysis. Spatial Analysis with R: Statistics, Visualization, and Computational Methods, Second Edition provides a balance between concepts and practicums of spatial statistics with a comprehensive coverage of the most important approaches to understand spatial data, analyze spatial relationships and patterns, and predict spatial processes. New in the Second Edition: Includes new practical exercises and worked-out examples using R Presents a wide range of hands-on spatial analysis worktables and lab exercises All chapters are revised and include new illustrations of different concepts using data from environmental and social sciences Expanded material on spatiotemporal methods, visual analytics methods, data science, and computational methods Explains big data, data management, and data mining This second edition of an established textbook, with new datasets, insights, excellent illustrations, and numerous examples with R, is perfect for senior undergraduate and first-year graduate students in geography and the geosciences.

Tensor-Valued Random Fields for Continuum Physics
Tensor-Valued Random Fields for Continuum Physics

Author: Anatoliy Malyarenko

Publisher: Cambridge University Press

Published: 2019

Total Pages: 313

ISBN-13: 1108429858

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Presents a complete description of homogenous and isotropic tensor-valued random fields, including the problems of continuum physics, mathematical tools and applications.

Random Graphs and Complex Networks: Volume 2
Random Graphs and Complex Networks: Volume 2

Author: Remco van der Hofstad

Publisher: Cambridge University Press

Published: 2024-02-08

Total Pages: 508

ISBN-13: 1316805581

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Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.

Applied Geospatial Data Science with Python
Applied Geospatial Data Science with Python

Author: David S. Jordan

Publisher: Packt Publishing Ltd

Published: 2023-02-28

Total Pages: 308

ISBN-13: 1803240342

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Intelligently connect data points and gain a deeper understanding of environmental problems through hands-on Geospatial Data Science case studies written in Python The book includes colored images of important concepts Key Features Learn how to integrate spatial data and spatial thinking into traditional data science workflows Develop a spatial perspective and learn to avoid common pitfalls along the way Gain expertise through practical case studies applicable in a variety of industries with code samples that can be reproduced and expanded Book DescriptionData scientists, when presented with a myriad of data, can often lose sight of how to present geospatial analyses in a meaningful way so that it makes sense to everyone. Using Python to visualize data helps stakeholders in less technical roles to understand the problem and seek solutions. The goal of this book is to help data scientists and GIS professionals learn and implement geospatial data science workflows using Python. Throughout this book, you’ll uncover numerous geospatial Python libraries with which you can develop end-to-end spatial data science workflows. You’ll learn how to read, process, and manipulate spatial data effectively. With data in hand, you’ll move on to crafting spatial data visualizations to better understand and tell the story of your data through static and dynamic mapping applications. As you progress through the book, you’ll find yourself developing geospatial AI and ML models focused on clustering, regression, and optimization. The use cases can be leveraged as building blocks for more advanced work in a variety of industries. By the end of the book, you’ll be able to tackle random data, find meaningful correlations, and make geospatial data models.What you will learn Understand the fundamentals needed to work with geospatial data Transition from tabular to geo-enabled data in your workflows Develop an introductory portfolio of spatial data science work using Python Gain hands-on skills with case studies relevant to different industries Discover best practices focusing on geospatial data to bring a positive change in your environment Explore solving use cases, such as traveling salesperson and vehicle routing problems Who this book is for This book is for you if you are a data scientist seeking to incorporate geospatial thinking into your workflows or a GIS professional seeking to incorporate data science methods into yours. You’ll need to have a foundational knowledge of Python for data analysis and/or data science.