Space Structure And Randomness
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Space Structure And Randomness
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Author : Michel Bilodeau
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-23
Space Structure And Randomness written by Michel Bilodeau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-23 with Mathematics categories.
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
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Author : Volker Schmidt
language : en
Publisher: Springer
Release Date : 2014-10-24
Stochastic Geometry Spatial Statistics And Random Fields written by Volker Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-24 with Mathematics categories.
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
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Author : Leslie Curry
language : en
Publisher: Taylor & Francis
Release Date : 2020-07-09
The Random Spatial Economy And Its Evolution written by Leslie Curry and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-09 with Business & Economics categories.
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.
Random Patterns And Structures In Spatial Data
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Author : Radu Stoica
language : en
Publisher: CRC Press
Release Date : 2025-04-02
Random Patterns And Structures In Spatial Data written by Radu Stoica and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-02 with Mathematics categories.
The book presents a general mathematical framework able to detect and to characterise, from a morphological and statistical perspective, patterns hidden in spatial data. The mathematical tools employed are Gibbs Markov processes, maily marked point procesess with interaction, which permits us to reduce the complexity of the pattern. It presents the framework, step by step, in three major parts: modeling, simulation, and inference. Each of these parts contains a theoretical development followed by applications and examples. Features Presents mathematical foundations for tackling pattern detection and characterisation in spatial data using marked Gibbs point processes with interactions Includes application examples from cosmology, environmental sciences, geology, and social networks Presents theoretical and practical details for the presented algorithms in order to be correctly and efficiently used Provides access to C++ and R code to encourage the reader to experiment and to develop new ideas Includes references and pointers to mathematical and applied literature to encourage further study Random Patterns and Structures in Spatial Data is primarily aimed at researchers in mathematics, statistics, and the above-mentioned application domains. It is accessible for advanced undergraduate and graduate students and thus could be used to teach a course. It will be of interest to any scientific researcher interested in formulating a mathematical answer to the always challenging question: what is the pattern hidden in the data?
Large Space Structures Systems In The Space Station Era
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Author :
language : en
Publisher:
Release Date : 1992
Large Space Structures Systems In The Space Station Era written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Large space structures (Astronautics) categories.
Percolation In Spatial Networks
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Author : Bnaya Gross
language : en
Publisher: Cambridge University Press
Release Date : 2022-07-14
Percolation In Spatial Networks written by Bnaya Gross and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-14 with Science categories.
Percolation theory is a well studied process utilized by networks theory to understand the resilience of networks under random or targeted attacks. Despite their importance, spatial networks have been less studied under the percolation process compared to the extensively studied non-spatial networks. In this Element, the authors will discuss the developments and challenges in the study of percolation in spatial networks ranging from the classical nearest neighbors lattice structures, through more generalized spatial structures such as networks with a distribution of edge lengths or community structure, and up to spatial networks of networks.
Modeling Social Behavior
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Author : Paul E. Smaldino
language : en
Publisher: Princeton University Press
Release Date : 2023-10-03
Modeling Social Behavior written by Paul E. Smaldino and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-03 with Social Science categories.
A comprehensive introduction to mathematical and agent-based modeling of social behavior This book provides a unified, theory-driven introduction to key mathematical and agent-based models of social dynamics and cultural evolution, teaching readers how to build their own models, analyze them, and integrate them with empirical research programs. It covers a variety of modeling topics, each exemplified by one or more archetypal models, and helps readers to develop strong theoretical foundations for understanding social behavior. Modeling Social Behavior equips social, behavioral, and cognitive scientists with an essential tool kit for thinking about and studying complex social systems using mathematical and computational models. Combines both mathematical and agent-based modeling of social behavior Integrates cognitive science, social science, and cultural evolution Covers topics such as the philosophy of modeling, collective movement, segregation, contagion, polarization, the evolution of cooperation, the emergence of norms, networks, and the scientific process Discusses more advanced topics, including how to use models to build a more robust empirical research program An ideal introductory textbook for graduate students or advanced undergraduates An invaluable resource for practitioners
Random Graphs And Complex Networks Volume 2
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Author : Remco van der Hofstad
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-08
Random Graphs And Complex Networks Volume 2 written by Remco van der Hofstad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-08 with Mathematics categories.
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.
Spectral Theory Of Random Matrices
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Author : Vyacheslav L. Girko
language : en
Publisher: Academic Press
Release Date : 2016-08-23
Spectral Theory Of Random Matrices written by Vyacheslav L. Girko and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-23 with Computers categories.
Spectral Theory of Random Matrices
Probability For Deep Learning Quantum
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Author : Charles R. Giardina
language : en
Publisher: Elsevier
Release Date : 2025-01-21
Probability For Deep Learning Quantum written by Charles R. Giardina and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-21 with Computers categories.
Probability for Deep Learning Quantum provides readers with the first book to address probabilistic methods in the deep learning environment and the quantum technological area simultaneously, by using a common platform: the Many-Sorted Algebra (MSA) view. While machine learning is created with a foundation of probability, probability is at the heart of quantum physics as well. It is the cornerstone in quantum applications. These applications include quantum measuring, quantum information theory, quantum communication theory, quantum sensing, quantum signal processing, quantum computing, quantum cryptography, and quantum machine learning. Although some of the probabilistic methods differ in machine learning disciplines from those in the quantum technologies, many techniques are very similar. Probability is introduced in the text rigorously, in Komogorov's vision. It is however, slightly modified by developing the theory in a Many-Sorted Algebra setting. This algebraic construct is also used in showing the shared structures underlying much of both machine learning and quantum theory. Both deep learning and quantum technologies have several probabilistic and stochastic methods in common. These methods are described and illustrated using numerous examples within the text. Concepts in entropy are provided from a Shannon as well as a von-Neumann view. Singular value decomposition is applied in machine learning as a basic tool and presented in the Schmidt decomposition. Besides the in-common methods, Born's rule as well as positive operator valued measures are described and illustrated, along with quasi-probabilities. Author Charles R. Giardina provides clear and concise explanations, accompanied by insightful and thought-provoking visualizations, to deepen your understanding and enable you to apply the concepts to real-world scenarios. - Provides readers with a resource that is loaded with hundreds of well-crafted examples illustrating the difficult concepts pertaining to quantum and stochastic processes - Addresses probabilistic methods in the deep learning environment and in the quantum technological area - Includes a rigorous and precise presentation of the algebraic underpinning of both quantum and deep learning