Relationships of exponents in multifractal detrended fluctuation analysis and conventional multifractal analysis

Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r（q） = qh（q） - 1 stipulating the relationship between the multifractal exponent T（q） and the generalized Hurst exponent h（q）. As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-（q） = qh（q） - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f（a）, are also derived according to this new relationship.

Predicting the subcellular location of apoptosis proteins based on recurrence quantification analysis and the Hilbert Huang transform

Apoptosis proteins play an important role in the development and homeostasis of an organism. The elucidation of the subcellular locations and functions of these proteins is helpful for understanding the mechanism of programmed cell death. In this paper, the recurrent quantification analysis, Hilbert-Huang transform methods, the maximum relevance and minimum redundancy method and support vector machine are used to predict the subcellular location of apoptosis proteins. The validation of the jackknife test suggests that the proposed method can improve the prediction accuracy of the subcellular location of apoptosis proteins and its application may be promising in other fields.