Multifractal Analysis Of Complex Data And Its Application On Genomics Data

In recent years,time series and complex networks have been widely investigated in many fields,and their multifractal characteristics have become one of the hot issues even more.This thesis proposes a class of randomized version of multifractal analysis algorithm to make existing methods suitable for investigating longer time series.In order to verify the performance of this class of randomized version algorithm,we use the typical method — randomized version of multifractal temporally weighted detrended cross-correlation analysis(RMFTWXDFA)as an example to simulated series and real series.Numerical simulation experiments show that randomized version algorithms are significantly effective and time-saving on long series with statistically comparable accuracy.The application of real series shows that the results obtained by the randomized method can also explain the phylogenetic relationship between species.Then,for the research on fractality and multifractality of complex networks,we propose a modified version of multifractal analysis method,the modified version of the fixed size method(m FSM)and the modified version of the fixed mass method(m FMM)are taken as representatives.Finally,the same attempt is performed on weighted complex network.We first apply the corresponding method to the deterministic model network to measure the feasibility,and then investigate the multifractal properties of the mitochondrial genome.On deterministic model networks,numerical simulation experiments show that our modified version of the method is feasible on networks with greater heterogeneity.Namely,the relative standard error(RSE)on the(7)u,v(8)-flower network has decreased from 0.1465 to 0.0176.On the real network obtained from mitochondrial genome data,our modified version of the method can be considered an alternative method to study the phylogenetic relationship of species.