Time series model based on global structure of complete genome

A time series model based on the global structure of the complete genome is proposed. Three kinds of length sequences of the complete genome are considered. The correlation dimensions and Hurst exponents of the length sequences are calculated. Using these two exponents, some interesting results related to the problem of classification and evolution relationship of bacteria are obtained.Comment: 11 pages with 3 figures and 2 tables, Chaos, Solitons and Fractals (Accepted for publications

Fractal Analysis for Cancer Research: Case Study and Simulation of Fractals

2010 Mathematics Subject Classification: 65D18.This paper discusses the possibilities of application of fractal geometry for cancer research. Fractal geometry is a new tool that can be extremely useful for many problems in almost every scientific field. The studies recently done in medicine show fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Cancer diagnosis can be done via determination of fractal dimension. A likelihood ratio test for the Hausdorff dimension is employed in [7] We empirically checked the obtained tests on Sierpinski Carpet and on cancer data. However, several issues arisen, especially those related to simulation of fractals which may mimic tissues. These are discussed in the present paper

Understanding Genomic Evolution of Olfactory Receptors through Fractal and Mathematical Morphology

Fractals and Mathematical Morphology are immensely used to study many problems in different branches of science and technology including the domain of Biology. There are many more unrevealed facts and figures of genes and genome in Computational Biology. In this paper, our objective is to explore how the evolutionary network is associated among Human, Chimpanzee and Mouse with regards to their genomic information. We are about to explore their genomic evolution through the quantitative measures of fractals and morphology. We have considered olfactory receptors for our case study. These olfactory receptors do function in different species with subtle differences in the structures of DNA sequences. Those subtle differences can be exposed through intricate details of Fractals and Mathematical Morphology

Multifractal characterisation of length sequences of coding and noncoding segments in a complete genome

The coding and noncoding length sequences constructed from a complete genome are characterised by multifractal analysis. The dimension spectrum $D_{q}$ and its derivative, the 'analogous' specific heat $C_{q}$, are calculated for the coding and noncoding length sequences of bacteria, where $q$ is the moment order of the partition sum of the sequences. From the shape of the $$ and $C_{q}$ curves, it is seen that there exists a clear difference between the coding/noncoding length sequences of all organisms considered and a completely random sequence. The complexity of noncoding length sequences is higher than that of coding length sequences for bacteria. Almost all $D_{q}$ curves for coding length sequences are flat, so their multifractality is small whereas almost all $D_{q}$ curves for noncoding length sequences are multifractal-like. We propose to characterise the bacteria according to the types of the $C_{q}$ curves of their noncoding length sequences.Comment: 15 pages with 5 figures, Latex, Accepted for publication in Physica