Structure And Randomness

Structure and Randomness
by Terence Tao

“In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein’s equation E = mc[superscript 2], or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article.

Space, Structure and Randomness
by Michel Bilodeau, Fernand Meyer, Michel Schmitt

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.


Structure and Randomness
by Terence Tao

There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and non-rigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as to who learned such folklore mathematics. But today, such bits and pieces can be communicated effectively and efficiently via the semiformal medium of research blogging. This book grew from such a blog. In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein’s equation $E=mc^2$, or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article. While the articles vary widely in subject matter and level, they should be broadly accessible to readers with a general graduate mathematics background; the focus in many articles is on the “big picture” and on informal discussion, with technical details largely being left to the referenced literature.

Geometry, Structure and Randomness in Combinatorics
by Jiří Matousek, Jaroslav Nešetřil, Marco Pellegrini

​This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.

Computational Analysis of Randomness in Structural Mechanics
by Christian Bucher

Proper treatment of structural behavior under severe loading – such as the performance of a high-rise building during an earthquake – relies heavily on the use of probability-based analysis and decision-making tools. Proper application of these tools is significantly enhanced by a thorough understanding of the underlying theoretical and computational concepts as provided by this book.

Detailing the computational aspects of stochastic analysis within the field of structural mechanics, this book first presents a few motivating examples that demonstrate the various random effects within the context of simple structural analysis models. It moreover briefly reviews the fundamental concepts from continuum mechanics and puts them in the perspective of modern numerical tools, such as the finite element method. More advanced topics are developed step by step while gradually increasing the complexity of the structural and probabilistic analyses.

This volume is intended for structural analysts and advanced students who wish to explore the benefits of stochastic analysis. It will provide researchers and decision makers working on structural and infrastructural systems with the necessary probabilistic information needed for strategic developments in construction, inspection and maintenance.


Fooled by Randomness
by Nassim Nicholas Taleb

Fooled by Randomness is a standalone book in Nassim Nicholas Taleb’s landmark Incerto series, an investigation of opacity, luck, uncertainty, probability, human error, risk, and decision-making in a world we don’t understand. The other books in the series are The Black Swan, Antifragile, Skin in the Game, and The Bed of Procrustes.

Fooled by Randomness is the word-of-mouth sensation that will change the way you think about business and the world. Nassim Nicholas Taleb–veteran trader, renowned risk expert, polymathic scholar, erudite raconteur, and New York Times bestselling author of The Black Swan–has written a modern classic that turns on its head what we believe about luck and skill.

This book is about luck–or more precisely, about how we perceive and deal with luck in life and business. Set against the backdrop of the most conspicuous forum in which luck is mistaken for skill–the world of trading–Fooled by Randomness provides captivating insight into one of the least understood factors in all our lives. Writing in an entertaining narrative style, the author tackles major intellectual issues related to the underestimation of the influence of happenstance on our lives.

The book is populated with an array of characters, some of whom have grasped, in their own way, the significance of chance: the baseball legend Yogi Berra; the philosopher of knowledge Karl Popper; the ancient world’s wisest man, Solon; the modern financier George Soros; and the Greek voyager Odysseus. We also meet the fictional Nero, who seems to understand the role of randomness in his professional life but falls victim to his own superstitious foolishness.

However, the most recognizable character of all remains unnamed–the lucky fool who happens to be in the right place at the right time–he embodies the “survival of the least fit.” Such individuals attract devoted followers who believe in their guru’s insights and methods. But no one can replicate what is obtained by chance.

Are we capable of distinguishing the fortunate charlatan from the genuine visionary? Must we always try to uncover nonexistent messages in random events? It may be impossible to guard ourselves against the vagaries of the goddess Fortuna, but after reading Fooled by Randomness we can be a little better prepared.

Named by Fortune One of the Smartest Books of All Time

A Financial Times Best Business Book of the Year


Advances in Computation and Intelligence
by Jingnan Liu, Zhihua Cai, Chengyu Hu, Zhuo Kang, Yong Liu

LNCS 6382 is the ?rst volume of the proceedings of the Fifth International Symposium on Intelligence Computation and Applications (ISICA 2010)held in Wuhan, China, October 22–24, 2010. Fifty-three papers among 267 submissions were selected and included in LNCS 6382. The symposium featured the most up-to-date research in ant colony and particle swarm optimization, di?erential evolution, distributed computing, – netic algorithms, multi-agent systems, multi-objective and dynamic optimi- tion, robot intelligence, statistical learning, and system design. LNCS 6382 is dedicated to the memory of Lishan Kang. ISICA conferences were one of the ?rst series of international conferences on computational intel- gence that combine elements of learning, adaptation, evolution and fuzzy logic to create programs as alternative solutions to arti?cial intelligence. The idea for ISICA came about after Lishan Kang organized on international symposium on evolutionary computation at Wuhan University in 2000. After he was – vited to be the Director of the School of Computer Science, China University of Geosciences, he wondered whether he could establish such discussion forums on computational intelligence at China University of Geosciences. With support from his university, the School of Computer Science organizedthe ?rst ISICA in 2005, in which some of the leading ?gures from the scienti?c computing world were invited, including H. -P. Schwefel, Germany, M. Schoenauer, France, D. J. Evans, UK, T. Higuchi, Japan, Z. Michalewicz, Australia, and X. Yao, UK.

Compactness and Contradiction
by Terence Tao

There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter

Statistics in Musicology
by Jan Beran

Traditionally, statistics and music are not generally associated with each other. However, …intelligent… music software, computer digitization, and other advanced techniques and technologies have precipitated the need for standard statistical models to answer basic musicological questions. Statistics In Musicology presents an unprecedented introduction to statistical and mathematical methods developed for use in music analysis, music theory, and performance theory. It explores concrete methods for data generation and numerical encoding of musical data and serves as a practical reference for a wide audience, including statisticians, mathematicians, musicologists, and musicians.


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