The Fixed Scale Transformation: Status and Perspectives L Pietronero 3. However, glasses may also be formed by c hemical vitrification, a process involving progressive polymerization or aggregation of the constituent molecules via the formation of irreversible or reversible chemical bonds. The Fourier transform ; 3. We describe a simple model to account for the presence of long-range power law correlations and the systematic variation of the scaling exponent α with evolution which is based upon a generalization of the classic Lévy walk. Advances in genomic sequence analysis and pattern discovery. The Fractal Laboratory Journal: a new challenge in the post-genomic era editorial. Fractal Landscapes in Biological Systems H E Stanley et al.
This publication contains state-of-the-art contributions exploring a spread of applications right across the disciplines, from physics and mathematics, through astronomy, biophysics, ecology and geography to image processing, medicine and turbulence. Using fractal geometry as a language, it has become possible to get a deeper insight into previously intractable problems. The polymerization and aggregation phenomena in reacting systems may become a valuable route to understand glass and gel formation. We develop asimple iterative model, basedonknownproperties ofpolymeric sequences, thatgenerates long-range nucleotide correlations froman initially noncorrelated coding region. West, University of North Texas, Bulletin of Mathematical Biology Read more.
A unique explanation of how to use fractal geometry in ecology and biology. Back in the early 1980s, he had returned from a Gordon Conference on fractals, where essentially a lot of pretty pictures had been presented, and was scratching his head trying to make sense of it. The conundrum of functional brain networks: small-world efficiency of fractal modularity. Entropic and Multifractal Analysis of Disordered Morphologies A Beghdadi et al. Abstract The fractal dimension can be used to quantify the shape of a natural curve. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable.
Glass formation is usually viewed in terms of physical vitrification: a liquid in a metastable state is cooled or compressed so as to avoid crystallization. The observed behaviors are confronted to those of reference models with known multifractal properties. Dimension of patterns -- 4. Due to the sensitivity of platelet shape change to preanalytical influencing factors, a highly standardized examination procedure is necessary in order to obtain reliable and reproducible results. Front Neuroanat 5: 1— 16.
The Fourier transform -- 6. Beginning with the foundations of measurement in Euclidian geometry, this book progresses from analogues in the geometry of random fractals to illustrative applications spanning the natural sciences. This volume is an essential resource for all natural scientists interested in working with fractals. J Transl Med 11: 36. In total, the fractal dimensions of 1200 nuclei were calculated. Fractal geometry: mathematical foundations and applications. Finally, we describe briefly some recent work showing that the noncoding sequences have certain statistical features in common with natural languages.
The system allows for the user independent examination of fractal and Euclidean geometrical properties from unfixed and unstained samples of soluble objects. Use of fractal theory in neuroscience: methods, advantages, and potential problems. Exploring wavelet transforms for morphological differentiation between functionally different cat retinal ganglion cells. This new method allows for the standardized continuous numerical classification of platelet shape and its dynamic change, which is useful for the analysis of altered platelet activity e. Abstract Platelet shape change is a dynamic membrane surface process that exhibits remarkable morphological heterogeneity.
Heterogeneity and organ-typical differentiation of endothelial cells seem to be dependent on cell-cell signaling within each organ. In: Rattey, F , editor. Nowadays, modern neurosciences admit the prevalence of fractal properties such as self-similarity in the brain at various levels of observation, from the microscale to the macroscale, in molecular, anatomic, functional, and pathological perspectives. Much material has been added to the chapter on renormalisation group ideas. A Cascade Model of Wave Turbulence with Applications to Surface Gravity and Capillary Waves R E Glazman 3. The results presented demonstrate the large intra and inter slide reproducibility and the ability of the system to clearly identify and separate smaller and larger particles as well as aggregates and objects out of focus. The evolution of the brain, the human nature of cortical circuits, and the intellectual creativity.
The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Consequently, the rise of what is broadly called the theory of complexity has gained tremendous momentum in the last decade or two. J Neurosci Res 65 5 : 439— 45. The fractal exponent describes the complexity of a shape and characterizes the scale-dependency of the pattern. J Neurosci Methods 56 2 : 133— 44. Scaling behaviour of density-dependent populations under random noise ; V.
Differentiating grades of microglia activation with fractal analysis. Beyond Classical Multifractal Analysis Using Wavelets: Uncovering a Multiplicative Process Hidden in the Geometrical Complexity of Diffusion Limited Aggregates A Arneodo et al. It can be used not only to generate biological structures e. Fractal geometry is a tool used to characterize irregularly shaped and complex figures. Supplemental Materials What is included with this book? Here we develop the Riemann -Darboux-Jordan theory. J Physiol 240 2 : 397— 419. We applied a box-counting algorithm to determine the fractal dimension of atypical nuclei in dysplastic cervical epithelium.