Fractals and Hidden Symmetries in DNA

Cattani, Carlo

doi:10.1155/2010/507056

Cited by 88 publications

(72 citation statements)

References 43 publications

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“…In this paper, the BIIM was used to convert uni-dimensional symbolic sequences (such as DNA sequences) in 2-D images and to compute the FD and lacunarity. This method allows to visualize a typical patterns of nucleotide that looks like a fractal arrangement such as demonstrated by Cattani in recent works and in the study of complexity of Caenorhabditis elegans [2,19,[24][25][26].…”

Section: Biim Methodsmentioning

confidence: 99%

On the fractal analysis of gene sequences involved in atherosclerosis by binary image indicator matrix

Pierro¹

2015

Fractal Geometry and Nonlinear Analysis in Medicine and Biology

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In this paper, the gene sequences involved in Coronary Artery Disease (CAD) were analyzed by fractal analysis. In order to obtain a quantitative characterization of nucleotide patterns and to identify anomalies and singularities belonging to genes, the fractal dimension (FD) and lacunarity were studied as fractal parameters. To obtain accurateparametric values, the Binary Image Indicator Matrix (BIIM) was used. This method converts uni-dimensional sequences into 2-D images preserving the autocorrelation.The results show like the fractal values of genes CAD are very similar to the random sequences. In particular, all FD values fall in the range 1.20 -1.22 highlighting that the complexity/fractality is the same and suggesting that all genes equally contribute to the pathogenesis of atherosclerosis from statistical point a view. These results are in accordance with the biological studies that indicate CAD as a multi-factorial process, so that these values could be considered as characteristics for these genes.

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Section: Biim Methodsmentioning

confidence: 99%

On the fractal analysis of gene sequences involved in atherosclerosis by binary image indicator matrix

Pierro¹

2015

Fractal Geometry and Nonlinear Analysis in Medicine and Biology

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“…In recent years fractal geometry analysis has attracted attention of biologist as a useful and desirable tool to characterize the configuration and structure of biological structures. The considered issues include: fractal geometry analysis of configuration, structure and diffusion of proteins [24][25][26][27][28][29], fractal analysis of the DNA sequence, walks and aggregation [30][31][32][33][34] and fractal model of light scattering in biological tissue and cells [35]. (…”

Section: -1 Fractalitymentioning

confidence: 99%

Fractional Dynamics in Bioscience and Biomedicine and the Physics of Cancer

Nasrolahpour

2017

Preprint

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Almost all phenomena and structures in nature exhibit some degrees of fractionality or fractality. Fractional calculus and fractal theory are two interrelated concepts. In this article we study the memory effects in nature and particularly in biological structures. Based on this fact that natural way to incorporate memory effects in the modeling of various phenomena and dealing with complexities is using of fractional calculus, in this article we present different examples in various branch of science from cosmology to biology and we investigate this idea that are we able to describe all of such these phenomena using the well-know and powerful tool of fractional calculus. In particular we focus on fractional calculus approach as an effective tool for better understanding of physics of living systems and organism and especially physics of cancer.Keywords: Fractional Dynamics; Memory Effect; Biological Structures; Physics of Cancer IntroductionThe concept of memory effect plays an important role in a large number of phenomena in different contexts and systems from biological structures to cosmological phenomena. For instance: memory effects in nanoscale systems [1,2], optical memory effect [3], gravitational and cosmological memory effect (which means: the induction of a permanent change in the relative separation of the test particles when gravitational radiation passes through a configuration of test particles that make up a gravitational wave detector) [4], memory effects in gene regulatory networks [5], memory effects in economics [6] have been investigated. In addition other kinds of memory effect including: shape memory effect [7][8][9][10], magnetic shape memory effect [11] and temperature memory effect [12] have been also considered in recent years. In all above mentioned references authors have used the standard calculus, however nowadays it is well-known that a natural way to incorporate memory effects in the modeling of various phenomena is using of fractional calculus. On the other hand almost all phenomena and structures in nature exhibit some degrees and levels of fractionality or fractality (low or high level or something between them), also nowadays it is well-known that there is a close relation between fractality and fractionality. In this work we investigate this idea that are we able to describe all of such these phenomena using the well-know and powerful tool of fractional calculus. Therefore for this purpose in the following, concepts of fractality and fractional dynamics are briefly reviewed respectively in Sec. 2.Then in Sec. 3 we introduce fractional calculus as a powerful tool for modeling of memory effects in different context and we present some important applications. At last, in Sec. 4, we will present some conclusions.

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“…In an extensive work on analysis of fractal dimension of face according to the age, Yarlagadda et al developed a method that classified facial images into four categories i.e. child image [0][1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], young adult image [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], middle-aged adult image [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], and senior adult image (> 50) based on correlation fractal dimension value of a facial edge image (21...…”

Section: Introductionmentioning

confidence: 99%

“…In case of fractal analysis and modeling of DNA walk, almost all reported works in literatures focused on proving the multi fractal nature of DNA walk (22)(23)(24)(25)(26). In a different work on employing fractal theory for analysis of DNA walk, we analyzed the complexity of DNA walk in case of healthy subjects and subjects with skin cancer using fractal theory.…”

Section: Introductionmentioning

confidence: 99%