Download or read book Fractal Dimensions of Networks written by Eric Rosenberg and published by Springer Nature. This book was released on 2020-07-07 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current interest in fractal dimensions of networks is the result of more than a century of previous research on dimensions. Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the “classic” theory of dimensions of geometric objects. The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. Since almost all of the major concepts in fractal dimensions originated in the study of sets, the book achieves this goal by first clearly presenting, with an abundance of examples and illustrations, the theory and algorithms for sets, and then showing how the theory and algorithms have been applied to networks. Thus, the book presents the classical theory and algorithms for the box counting dimension for sets, and then presents the box counting dimension for networks. All the major fractal dimensions are studied, e.g., the correlation dimension, the information dimension, the Hausdorff dimension, the multifractal spectrum, as well as many lesser known dimensions. Algorithm descriptions are accompanied by worked examples, many applications of the methods are presented, and many exercises, ranging in difficulty from easy to research level, are included.
Download or read book A Survey of Fractal Dimensions of Networks written by Eric Rosenberg and published by Springer. This book was released on 2018-05-29 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many different fractal dimensions have been proposed for networks. In A Survey of Fractal Dimensions of Networks the theory and computation of the most important of these dimensions are reviewed, including the box counting dimension, the correlation dimension, the mass dimension, the transfinite fractal dimension, the information dimension, the generalized dimensions (which provide a way to describe multifractals), and the sandbox method (for approximating the generalized dimensions). The book describes the use of diameter-based and radius-based boxes, and presents several heuristic methods for box counting, including greedy coloring, random sequential node burning, and a method for computing a lower bound. We also discuss very recent results on resolving ambiguity in the calculation of the information dimension and the generalized dimensions, and on the non-monotonicity of the generalized dimensions. Anyone interested in the theory and application of networks will want to read this Brief. This includes anyone studying, e.g., social networks, telecommunications networks, transportation networks, ecological networks, food chain networks, network models of the brain, or financial networks.
Download or read book Fractal Dimension for Fractal Structures written by Manuel Fernández-Martínez and published by Springer. This book was released on 2019-04-23 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.
Download or read book A Random Walk Through Fractal Dimensions written by Brian H. Kaye and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin
Download or read book Fractals A Very Short Introduction written by Kenneth Falconer and published by OUP Oxford. This book was released on 2013-09-26 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Download or read book Fractal Physiology written by James B Bassingthwaighte and published by Springer. This book was released on 2013-05-27 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.
Download or read book Modelling of Flow and Transport in Fractal Porous Media written by Jianchao Cai and published by Elsevier. This book was released on 2020-11-05 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important resource explores recent theoretical advances and modelling on fluids transport in fractal porous systems and presents a systematic understanding of the characterization of complex microstructure and transport mechanism in fractal porous media. Modelling of Flow and Transport in Fractal Porous Media shows how fractal theory and technology, combined with other modern experiments and numerical simulation methods, will assist researchers and practitioners in modelling of transport properties of fractal porous media, such as fluid flow, heat and mass transfer, mechanical characteristics, and electrical conductivity. Presents the main methods and technologies for transport characterization of fractal porous media, including soils, reservoirs and artificial materials Provides the most recent theoretical advances in modelling of fractal porous media, including gas and vapor transport in fibrous materials, nonlinear seepage flow in hydrocarbon reservoirs, mass transfer of porous nanofibers, and fractal mechanics of unsaturated soils Includes multidisciplinary examples of applications of fractal theory to aid researchers and practitioners in characterizing various porous media structures
Download or read book Fractals in Probability and Analysis written by Christopher J. Bishop and published by Cambridge University Press. This book was released on 2017 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Download or read book Fat Crystal Networks written by Alejandro G. Marangoni and published by CRC Press. This book was released on 2004-12-27 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first authoritative source on the subject, this reference discusses the various levels of structure that influence the macroscopic physical properties of fat crystal networks. Fat Crystal Networks summarizes 50 years of structural research in the field, as well as a wealth of information on fat crystal networks pertinent to real-world challenge
Download or read book The Geometry of Fractal Sets written by K. J. Falconer and published by Cambridge University Press. This book was released on 1985 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.
Download or read book The Fractal Geometry of the Brain written by Antonio Di Ieva and published by Springer. This book was released on 2016-08-03 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. Will bring an understanding of fractals to clinicians and researchers also if they do not have a mathematical background, and will serve as a good tool for teaching the translational applications of computational models to students and scholars of different disciplines. This comprehensive collection is organized in four parts: (1) Basics of fractal analysis; (2) Applications of fractals to the basic neurosciences; (3) Applications of fractals to the clinical neurosciences; (4) Analysis software, modeling and methodology.
Download or read book Fractals in Geophysics written by SCHOLZ and published by Birkhäuser. This book was released on 2013-11-22 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 131 (1989), No. 1
Download or read book Graph Colourings written by Roy Nelson and published by Longman Publishing Group. This book was released on 1990 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nine papers on graph colourings, presented by speakers at a one-day meeting at the Open University in December 1988. The topics presented have been chosen to cover as wide a field as possible within the area of graph colourings. Each paper contains a cetain amount of survey material to put the results of the paper into perspective, as well as a discussion of new results. It is not the aim of this book to present a succession of highly technical research papers which would be better in a specialized journal.
Download or read book The Fractal Dimension of Architecture written by Michael J. Ostwald and published by Birkhäuser. This book was released on 2016-09-01 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.
Download or read book Complexity written by Melanie Mitchell and published by Oxford University Press. This book was released on 2009-04-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: What enables individually simple insects like ants to act with such precision and purpose as a group? How do trillions of neurons produce something as extraordinarily complex as consciousness? In this remarkably clear and companionable book, leading complex systems scientist Melanie Mitchell provides an intimate tour of the sciences of complexity, a broad set of efforts that seek to explain how large-scale complex, organized, and adaptive behavior can emerge from simple interactions among myriad individuals. Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. Richly illustrated, Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.
Download or read book Fractals in Physics written by L. Pietronero and published by Elsevier. This book was released on 2012-12-02 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals in Physics
