Space, Structure and Randomness - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Space, Structure and Randomness write by Michel Bilodeau. This book was released on 2007-12-23. Space, Structure and Randomness available in PDF, EPUB and Kindle. 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.
The Large Scale Structure of Space-Time
The Large Scale Structure of Space-Time - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Large Scale Structure of Space-Time write by S. W. Hawking. This book was released on 1975-02-27. The Large Scale Structure of Space-Time available in PDF, EPUB and Kindle. Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
Computability, Forcing and Descriptive Set Theory
Computability, Forcing and Descriptive Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computability, Forcing and Descriptive Set Theory write by Douglas Cenzer. This book was released on 2019-12-31. Computability, Forcing and Descriptive Set Theory available in PDF, EPUB and Kindle. This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium. Contents: Limits of the Kucerea-Gacs Coding Method (George Barmpalias and Andrew Lewis-Pye);Infinitary partition properties of sums of selective ultrafilters (Andreas Blass);Semiselective Coideals and Ramsey Sets (Carlos DiPrisco and Leonardo Pacheco);Survey on Topological Ramsey Spaces Dense in Forcings (Natasha Dobrinen);Higher Computability in the Reverse Mathematics of Borel Determinacy (Sherwood Hachtman);Computability and Definability (Valentina Harizanov);A Ramsey Space of Infinite Polyhedra and the Random Polyhedron (Jose G Mijares Palacios and Gabriel Padilla);Computable Reducibility for Cantor Space (Russell G Miller);Information vs Dimension - An Algorithmic Perspective (Jan Reimann); Readership: Graduate students and researchers interested in the interface between set theory and computability.
Modeling Social Behavior
Modeling Social Behavior - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modeling Social Behavior write by Paul Smaldino. This book was released on 2023-10-03. Modeling Social Behavior available in PDF, EPUB and Kindle. 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
Topics in Random Matrix Theory
Topics in Random Matrix Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topics in Random Matrix Theory write by Terence Tao. This book was released on 2012-03-21. Topics in Random Matrix Theory available in PDF, EPUB and Kindle. The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
