Fractals in Biology and Medicine

Author: Gabriele A. Losa,Danilo Merlini,Theo F. Nonnenmacher,Ewald R. Weibel

Publisher: Birkhäuser

ISBN: 3034881193

Category: Mathematics

Page: 362

View: 9954

In March 2000 leading scientists gathered at the Centro Seminariale Monte Verità, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This volume highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes.

Fractals in Biology and Medicine

Author: Gabriele A. Losa,Danilo Merlini,Theo F. Nonnenmacher,Ewald R. Weibel

Publisher: Springer Science & Business Media

ISBN: 3764374128

Category: Mathematics

Page: 314

View: 3827

This volume is number four in a series of proceedings volumes from the International Symposia on Fractals in Biology and Medicine in Ascona, Switzerland which have been inspired by the work of Benoît Mandelbrot seeking to extend the concepts towards the life sciences. It highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions.

Fractals in Biology and Medicine

Author: Gabriele A. Losa,Theo F. Nonnenmacher

Publisher: Springer Science & Business Media

ISBN: 9783764371722

Category: Computers

Page: 314

View: 6911

This book is a compilation of the presentations given at the Fourth International Symposium on Fractals in Biology and Medicine held in Ascona, Switzerland on 10-13 March 2004 and was dedicated to Professor Benoît Mandelbrot in honour of this 80th birthday. The symposium was the fourth of a series that originated back in 1993, always in Ascona. This title highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal, abnormal and tumoral conditions.

Fractals in Biology and Medicine

III

Author: Gabriele A. Losa,Danilo Merlini,Theo F. Nonnenmacher,Ewald R. Weibel

Publisher: Springer Science & Business Media

ISBN: 9783764364748

Category: Mathematics

Page: 362

View: 8730

In March 2000 leading scientists gathered at the Centro Seminariale Monte Verità, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference was held over a four-day period and provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This Volume III in the MBI series highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes. Many biological objects, previously considered as hopelessly far from any quantitative description, are now being investigated by means of fractal methods. Researchers currently used fractals both as theoretical tools, to shed light on living systems` self-organization and evolution, and as useful techniques, capable of quantitatively analyzing physiological and pathological cell states, shapes and ultrastructures. The book should be of interest to researchers and students from Molecular and C

Fractals in Biology and Medicine

Author: Theo F. Nonnenmacher,Gabriele A. Losa,Ewald R. Weibel

Publisher: Birkhäuser

ISBN: 9783764329891

Category: Science

Page: 397

View: 9895

"Fractals in Biology and Medicine" explores the potential of fractal geometry for describing and understanding biological organisms, their development and growth as well as their structural design and functional properties. It extends these notions to assess changes associated with disease in the hope to contribute to the understanding of pathogenetic processes in medicine. The book is the first comprehensive presentation of the importance of the new concept of fractal geometry for biological and medical sciences. It collates in a logical sequence extended papers based on invited lectures and free communications presented at a symposium in Ascona, Switzerland, attended by leading scientists in this field, among them the originator of fractal geometry, Benoit Mandelbrot. "Fractals in Biology and Medicine" begins by asking how the theoretical construct of fractal geometry can be applied to biomedical sciences and then addresses the role of fractals in the design and morphogenesis of biological organisms as well as in molecular and cell biology. The consideration of fractal structure in understanding metabolic functions and pathological changes is a particularly promising avenue for future research.

Fractal Symmetry of Protein Exterior

Author: Anirban Banerji

Publisher: Springer Science & Business Media

ISBN: 303480654X

Category: Science

Page: 55

View: 9354

The essential question that fractal dimensions attempt to answer is about the scales in Nature. For a system as non-idealistic and complex as a protein, studying scale-invariance becomes particularly important. Fractal Symmetry of Protein Exterior investigates the diverse facets of the various scales at which we describe protein biophysical and biochemical phenomena. Although these ideas are entirely mathematical, mathematical expositions have been avoided, unless the use of some expressions becomes absolutely obligatory. A first chapter introduce into fractal dimensions, protein exteriors and to methods to study the roughness of surfaces. The main topics covered in the following chapters include: protein-protein interaction interfaces; protein surface-roughness and local shape as well as adhesion on protein and other rough biomolecular surfaces.

Fractal Physiology

Author: James B Bassingthwaighte,Larry S Liebovitch,Bruce J. West

Publisher: Springer

ISBN: 1461475724

Category: Medical

Page: 384

View: 3735

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.

Fractal Physiology and Chaos in Medicine

Author: Bruce J. West

Publisher: World Scientific

ISBN: 9814417807

Category: Chaotic behavior in systems

Page: 345

View: 6254

This exceptional book is concerned with the application of fractals and chaos, as well as other concepts from nonlinear dynamics to biomedical phenomena. Herein we seek to communicate the excitement being experienced by scientists upon making application of these concepts within the life sciences. Mathematical concepts are introduced using biomedical data sets and the phenomena being explained take precedence over the mathematics.In this new edition what has withstood the test of time has been updated and modernized; speculations that were not borne out have been expunged and the breakthroughs that have occurred in the intervening years are emphasized. The book provides a comprehensive overview of a nascent theory of medicine, including a new chapter on the theory of complex networks as they pertain to medicine.

Fractal Modelling

Growth and Form in Biology

Author: Jaap A. Kaandorp

Publisher: Springer Science & Business Media

ISBN: 3642579221

Category: Science

Page: 209

View: 5294

In this book, methods from fractal geometry are applied to model growth forms, taking as a case study a type of growth process which can be found among various taxonomic classes such as sponges and corals. These models can be used, for example, to understand the amazing variety of forms to be found in a coral reef and to simulate their growth with 2D and 3D geometrical objects. Models which mimic the growth of forms and the environmental influence on the growth process are also useful for ecologists, as a combination of simulation models together with the actual growth forms can be used to detect the effects of slow changes in the environment.

Physics in Biology and Medicine

Author: Paul Davidovits

Publisher: Academic Press

ISBN: 012386514X

Category: Science

Page: 352

View: 6464

Physics in Biology and Medicine, Fourth Edition, covers topics in physics as they apply to the life sciences, specifically medicine, physiology, nursing and other applied health fields. This is a concise introductory paperback that provides practical techniques for applying knowledge of physics to the study of living systems and presents material in a straightforward manner requiring very little background in physics or biology. Applicable courses are Biophysics and Applied Physics. This new edition discusses biological systems that can be analyzed quantitatively, and how advances in the life sciences have been aided by the knowledge of physical or engineering analysis techniques. The volume is organized into 18 chapters encompassing thermodynamics, electricity, optics, sound, solid mechanics, fluid mechanics, and atomic and nuclear physics. Each chapter provides a brief review of the background physics before focusing on the applications of physics to biology and medicine. Topics range from the role of diffusion in the functioning of cells to the effect of surface tension on the growth of plants in soil and the conduction of impulses along the nervous system. Each section contains problems that explore and expand some of the concepts. The text includes many figures, examples and illustrative problems and appendices which provide convenient access to the most important concepts of mechanics, electricity, and optics in the body. Physics in Biology and Medicine will be a valuable resource for students and professors of physics, biology, and medicine, as well as for applied health workers. Provides practical techniques for applying knowledge of physics to the study of living systems Presents material in a straight forward manner requiring very little background in physics or biology Includes many figures, examples and illustrative problems and appendices which provide convenient access to the most important concepts of mechanics, electricity, and optics in the body

Fractals

Applications in Biological Signalling and Image Processing

Author: Dinesh Kumar,Sridhar P. Arjunan,Behzad Aliahmad

Publisher: CRC Press

ISBN: 1351678388

Category: Mathematics

Page: 190

View: 3977

The book provides an insight into the advantages and limitations of the use of fractals in biomedical data. It begins with a brief introduction to the concept of fractals and other associated measures and describes applications for biomedical signals and images. Properties of biological data in relations to fractals and entropy, and the association with health and ageing are also covered. The book provides a detailed description of new techniques on physiological signals and images based on the fractal and chaos theory. The aim of this book is to serve as a comprehensive guide for researchers and readers interested in biomedical signal and image processing and feature extraction for disease risk analyses and rehabilitation applications. While it provides the mathematical rigor for those readers interested in such details, it also describes the topic intuitively such that it is suitable for audience who are interested in applying the methods to healthcare and clinical applications. The book is the outcome of years of research by the authors and is comprehensive and includes other reported outcomes.

Fractals and Multifractals in Ecology and Aquatic Science

Author: Laurent Seuront

Publisher: CRC Press

ISBN: 9781420004243

Category: Nature

Page: 360

View: 8476

Ecologists sometimes have a less-than-rigorous background in quantitative methods, yet research within this broad field is becoming increasingly mathematical. Written in a step-by-step fashion, Fractals and Multifractals in Ecology and Aquatic Science provides scientists with a basic understanding of fractals and multifractals and the techniques for utilizing them when analyzing ecological phenomenon. With illustrations, tables, and graphs on virtually every page – several in color – this book is a comprehensive source of state-of-the-art ecological scaling and multiscaling methods at temporal and spatial scales, respectfully ranging from seconds to months and from millimeters to thousands of kilometers. It illustrates most of the data analysis techniques with real case studies often based on original findings. It also incorporates descriptions of current and new numerical techniques to analyze and deepen understanding of ecological situations and their solutions. Includes a Wealth of Applications and Examples This book also includes nonlinear analysis techniques and the application of concepts from chaos theory to problems of spatial and temporal patterns in ecological systems. Unlike other books on the subject, Fractals and Multifractals in Ecology and Aquatic Science is readily accessible to researchers in a variety of fields, such as microbiology, biology, ecology, hydrology, geology, oceanography, social sciences, and finance, regardless of their mathematical backgrounds. This volume demystifies the mathematical methods, many of which are often regarded as too complex, and allows the reader to access new and promising concepts, procedures, and related results.

Fractals and Chaos Simplified for the Life Sciences

Author: Larry S. Liebovitch

Publisher: OUP USA

ISBN: N.A

Category: Science

Page: 284

View: 8650

There is a growing interest on the part of undergraduate and graduate students and investigators in applying fractals and chaos (nonlinear dynamics) to a variety of problems in biology and medicine. This book explains fractals and chaos and illustrates their use with examples from biomedical research. The author presents the material in a unique style that doesn't require a strong background in mathematics. The ideas are presented in a straightforward way without technical jargon. One concept at a time is explained in a set of facing pages, with text on the left page and graphics on the right page. The graphics pages can be copied directly on to transparencies for teaching.

Lindenmayer Systems, Fractals, and Plants

Author: Przemyslaw Prusinkiewicz,James Hanan

Publisher: Springer Science & Business Media

ISBN: 1475714289

Category: Mathematics

Page: 122

View: 4702

1-systems are a mathematical formalism which was proposed by Aristid 1indenmayer in 1968 as a foundation for an axiomatic theory of develop ment. The notion promptly attracted the attention of computer scientists, who investigated 1-systems from the viewpoint of formal language theory. This theoretical line of research was pursued very actively in the seventies, resulting in over one thousand publications. A different research direction was taken in 1984 by Alvy Ray Smith, who proposed 1-systems as a tool for synthesizing realistic images of plants and pointed out the relationship between 1-systems and the concept of fractals introduced by Benoit Mandel brot. The work by Smith inspired our studies of the application of 1-systems to computer graphics. Originally, we were interested in two problems: • Can 1-systems be used as a realistic model of plant species found in nature? • Can 1-systems be applied to generate images of a wide class of fractals? It turned out that both questions had affirmative answers. Subsequently we found that 1-systems could be applied to other areas, such as the generation of tilings, reproduction of a geometric art form from East India, and synthesis of musical scores based on an interpretation of fractals. This book collects our results related to the graphical applications of- systems. It is a corrected version of the notes which we prepared for the ACM SIGGRAPH '88 course on fractals.

Fractal Geometry in Biological Systems

An Analytical Approach

Author: Philip M. Iannaccone,Mustafa Khokha

Publisher: CRC Press

ISBN: 9780849376368

Category: Science

Page: 384

View: 5993

Fractal Geometry in Biological Systems was written by the leading experts in the field of mathematics and the biological sciences together. It is intended to inform researchers in the bringing about the fundamental nature of fractals and their widespread appearance in biological systems. The chapters explain how the presence of fractal geometry can be used in an analytical way to predict outcomes in systems, to generate hypotheses, and to help design experiments. The authors make the mathematics accessible to a wide audience and do not assume prior experience in this area.

Application of Chaos and Fractals to Computer Vision

Author: Michael E. Farmer

Publisher: Bentham Science Publishers

ISBN: 1608059006

Category: Computers

Page: 340

View: 4720

This book provides a thorough investigation of the application of chaos theory and fractal analysis to computer vision. The field of chaos theory has been studied in dynamical physical systems, and has been very successful in providing computational models for very complex problems ranging from weather systems to neural pathway signal propagation. Computer vision researchers have derived motivation for their algorithms from biology and physics for many years as witnessed by the optical flow algorithm, the oscillator model underlying graphical cuts and of course neural networks. These algorithms are very helpful for a broad range of computer vision problems like motion segmentation, texture analysis and change detection. The contents of this book include chapters in biological vision systems, foundations of chaos and fractals, behavior of images and image sequences in phase space, mathematical measures for analyzing phase space, applications to pre-attentive vision and applications to post-attentive vision. This book is intended for graduate students, upper division undergraduates, researchers and practitioners in image processing and computer vision. The readers will develop a solid understanding of the concepts of chaos theory and their application to computer vision. Readers will be introduced to a new way of thinking about computer vision problems from the perspective of complex dynamical systems. This new approach will provide them a deeper understanding of the various phenomena present in complex image scenes.

Self-Organized Biological Dynamics and Nonlinear Control

Toward Understanding Complexity, Chaos and Emergent Function in Living Systems

Author: Jan Walleczek

Publisher: Cambridge University Press

ISBN: 9780521624367

Category: Science

Page: 428

View: 2640

Collection of articles on the impact of nonlinear science on biology.

The Fractal Geometry of the Brain

Author: Antonio Di Ieva

Publisher: Springer

ISBN: 1493939955

Category: Medical

Page: 585

View: 6023

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.

Chaos and Fractals in Engineering

Author: Masao Nakagawa

Publisher: World Scientific

ISBN: 9789810238339

Category: Mathematics

Page: 944

View: 4469

This book is written for all engineers, graduate students and beginners working in the application fields, and for experimental scientists in general. It is not presented as a purely theoretical treatise but shows mathematics at a workshop, so to speak, through important applications originating in a deep pure mathematical theory. Widely spread subjects which the author has encountered hitherto are briefly addressed in the book, as chaos and fractal science is a frontier of new research fields nowadays.