Benoit Mandelbrot A Life In Many Dimensions
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Benoit Mandelbrot A Life In Many Dimensions
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Author : Michael Frame
language : en
Publisher: World Scientific
Release Date : 2015-03-02
Benoit Mandelbrot A Life In Many Dimensions written by Michael Frame and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-02 with Mathematics categories.
This is a collection of articles, many written by people who worked with Mandelbrot, memorializing the remarkable breadth and depth of his work in science and the arts. Contributors include mathematicians, physicists, biologists, economists, and engineers, as expected; and also artists, musicians, teachers, an historian, an architect, a filmmaker, and a comic. Some articles are quite technical, others entirely descriptive. All include stories about Benoit.Also included are chapters on fractals and music by Charles Wuorinen and by Harlan Brothers, on fractals and finance by Richard Hudson and by Christian Walter, on fractal invisibility cloaks by Nathan Cohen, and a personal reminiscence by Aliette Mandelbrot.While he is known most widely for his work in mathematics and in finance, Benoit influenced almost every field of modern intellectual activity. No other book captures the breadth of all of Benoit's accomplishments.
Extreme Events In Finance
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Author : Francois Longin
language : en
Publisher: John Wiley & Sons
Release Date : 2016-10-17
Extreme Events In Finance written by Francois Longin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-17 with Business & Economics categories.
A guide to the growing importance of extreme value risk theory, methods, and applications in the financial sector Presenting a uniquely accessible guide, Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications features a combination of the theory, methods, and applications of extreme value theory (EVT) in finance and a practical understanding of market behavior including both ordinary and extraordinary conditions. Beginning with a fascinating history of EVTs and financial modeling, the handbook introduces the historical implications that resulted in the applications and then clearly examines the fundamental results of EVT in finance. After dealing with these theoretical results, the handbook focuses on the EVT methods critical for data analysis. Finally, the handbook features the practical applications and techniques and how these can be implemented in financial markets. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications includes: Over 40 contributions from international experts in the areas of finance, statistics, economics, business, insurance, and risk management Topical discussions on univariate and multivariate case extremes as well as regulation in financial markets Extensive references in order to provide readers with resources for further study Discussions on using R packages to compute the value of risk and related quantities The book is a valuable reference for practitioners in financial markets such as financial institutions, investment funds, and corporate treasuries, financial engineers, quantitative analysts, regulators, risk managers, large-scale consultancy groups, and insurers. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications is also a useful textbook for postgraduate courses on the methodology of EVTs in finance.
An Invitation To Fractal Geometry
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Author : Michel L. Lapidus
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-30
An Invitation To Fractal Geometry written by Michel L. Lapidus and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Mathematics categories.
This book offers a comprehensive exploration of fractal dimensions, self-similarity, and fractal curves. Aimed at undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book. Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to self-similar sets and their construction via the iteration of contraction mappings. The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including well-known fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a stand-alone resource and a gateway to deeper explorations in fractal geometry.
The Fractalist
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Author : Benoit Mandelbrot
language : en
Publisher: Vintage
Release Date : 2012-10-30
The Fractalist written by Benoit Mandelbrot and has been published by Vintage this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Biography & Autobiography categories.
A fascinating memoir from the man who revitalized visual geometry, and whose ideas about fractals have changed how we look at both the natural world and the financial world. Benoit Mandelbrot, the creator of fractal geometry, has significantly improved our understanding of, among other things, financial variability and erratic physical phenomena. In The Fractalist, Mandelbrot recounts the high points of his life with exuberance and an eloquent fluency, deepening our understanding of the evolution of his extraordinary mind. We begin with his early years: born in Warsaw in 1924 to a Lithuanian Jewish family, Mandelbrot moved with his family to Paris in the 1930s, where he was mentored by an eminent mathematician uncle. During World War II, as he stayed barely one step ahead of the Nazis until France was liberated, he studied geometry on his own and dreamed of using it to solve fresh, real-world problems. We observe his unusually broad education in Europe, and later at Caltech, Princeton, and MIT. We learn about his thirty-five-year affiliation with IBM’s Thomas J. Watson Research Center and his association with Harvard and Yale. An outsider to mainstream scientific research, he managed to do what others had thought impossible: develop a new geometry that combines revelatory beauty with a radical way of unfolding formerly hidden laws governing utter roughness, turbulence, and chaos. Here is a remarkable story of both the man’s life and his unparalleled contributions to science, mathematics, and the arts.
Fractal Geometry Complex Dimensions And Zeta Functions
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Author : Michel L. Lapidus
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-20
Fractal Geometry Complex Dimensions And Zeta Functions written by Michel L. Lapidus 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 2012-09-20 with Mathematics categories.
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Key Features of this Second Edition: The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula The method of Diophantine approximation is used to study self-similar strings and flows Analytical and geometric methodsare used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions Throughout, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions, Second Edition will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.
The Fractal Geometry Of The Brain
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Author : Antonio Di Ieva
language : en
Publisher: Springer Nature
Release Date : 2024-03-12
The Fractal Geometry Of The Brain written by Antonio Di Ieva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-12 with Science categories.
The new edition of the highly popular, The Fractal Geometry of the Brain, reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. It brings an understanding of fractals to clinicians and researchers even if they do not have a mathematical background, and it serves as a valuable tool for teaching the translational applications of computational fractal-based models to both students and scholars. As a consequence of the novel research developed at Professor Di Ieva's laboratory and other centers around the world, the second edition will explore the use of computational fractal-based analysis in many clinical disciplines and different fields of research, including neurology and neurosurgery, neuroanatomy and psychology, magnetoencephalography (MEG), eye-tracking devices (for the fractal computational characterization of “scanpaths”),deep learning in image analysis, radiomics for the characterization of brain MRIs, characterization of neuropsychological and psychiatric diseases and traits, signal complexity analysis in time series, and functional MRI, amongst others.
Kitchen Science Fractals A Lab Manual For Fractal Geometry
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Author : Michael Frame
language : en
Publisher: World Scientific
Release Date : 2021-10-04
Kitchen Science Fractals A Lab Manual For Fractal Geometry written by Michael Frame and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-04 with Young Adult Nonfiction categories.
This book provides a collection of 44 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking fractals, videofeedback, and fractal networks of resistors and oscillators.
Fractal Worlds
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Author : Michael Frame
language : en
Publisher: Yale University Press
Release Date : 2016-06-21
Fractal Worlds written by Michael Frame and has been published by Yale University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-21 with Mathematics categories.
Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.
Stargazing In The Atomic Age
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Author : Anne Goldman
language : en
Publisher: University of Georgia Press
Release Date : 2021-01-15
Stargazing In The Atomic Age written by Anne Goldman and has been published by University of Georgia Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-15 with categories.
A Kirkus Best Book of the Year During World War II, with apocalypse imminent, a group of well-known Jewish scientists and artists sidestepped despair by challenging themselves to solve some of the most difficult questions posed by our age. Many had just fled Europe. Others were born in the United States to immigrants who had escaped Russia’s pogroms. Alternately celebrated as mavericks and dismissed as eccentrics, they trespassed the boundaries of their own disciplines as the entrance to nations slammed shut behind them. In Stargazing in the Atomic Age, Anne Goldman interweaves personal and intellectual history in exuberant essays that cast new light on these figures and their virtuosic thinking. In lyric, lucent sentences that dance between biography and memoir as they connect innovation in science with achievement in the arts, Goldman yokes the central dramas of the modern age with the brilliant thinking of earlier eras. Here, Einstein plays Mozart to align mathematical principle with the music of the spheres and Rothko paints canvases whose tonalities echo the stark prose of Genesis. Nearby, Bellow evokes the dirt and dazzle of the Chicago streets, while upon the heels of World War II, Chagall illuminates stained glass no less buoyant than the effervescent notes of Gershwin's Rhapsody in Blue. In these essays, Goldman reminds readers that Jewish history offers as many illustrations of accomplishment as of affliction. At the same time, she gestures toward the ways in which experiments in science and art that defy partisanship can offer us inspiration during a newly divisive era.
Analysis Probability And Mathematical Physics On Fractals
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Author : Patricia Alonso Ruiz
language : en
Publisher: World Scientific
Release Date : 2020-02-26
Analysis Probability And Mathematical Physics On Fractals written by Patricia Alonso Ruiz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-26 with Mathematics categories.
In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.