Drug-target interaction (DTI) is the basis of drug discovery and design. It is time consuming and costly to determine DTI experimentally. Hence, it is necessary to develop computational methods for the prediction of potential DTI. Based on complex network theory, three supervised inference methods were developed here to predict DTI and used for drug repositioning, namely drug-based similarity inference (DBSI), target-based similarity inference (TBSI) and network-based inference (NBI). Among them, NBI performed best on four benchmark data sets. Then a drug-target network was created with NBI based on 12,483 FDA-approved and experimental drug-target binary links, and some new DTIs were further predicted. In vitro assays confirmed that five old drugs, namely montelukast, diclofenac, simvastatin, ketoconazole, and itraconazole, showed polypharmacological features on estrogen receptors or dipeptidyl peptidase-IV with half maximal inhibitory or effective concentration ranged from 0.2 to 10 µM. Moreover, simvastatin and ketoconazole showed potent antiproliferative activities on human MDA-MB-231 breast cancer cell line in MTT assays. The results indicated that these methods could be powerful tools in prediction of DTIs and drug repositioning. Study of drug-target interaction is an important topic toward elucidation of protein functions and understanding of molecular mechanisms inside cells. Traditional methods to predict new targets for known drugs were based on small molecules, protein targets or phenotype features. Here, we proposed a network-based inference (NBI) method which only used drug-target bipartite network topology similarity to infer new targets for known drugs. The performance of NBI outperformed the drug-based similarity inference and target-based similarity inference methods as well as other published methods. Via the NBI method five old drugs, namely montelukast, diclofenac, simvastatin, ketoconazole, and itraconazole, were identified to have polypharmacological effects on human estrogen receptors or dipeptidyl peptidase-IV with half maximal inhibitory or effective concentration from submicromolar to micromolar by in vitro assays. Moreover, simvastatin and ketoconazole showed potent antiproliferative activities on human MDA-MB-231 breast cancer cell line in MTT assays. The results indicated that the drug-target bipartite network-based inference method could be a useful tool for fishing novel drug-target interactions in molecular polypharmacological space.

We propose a method called multifractal detrended cross-correlation analysis to investigate the multifractal behaviors in the power-law cross-correlations between two time series or higher-dimensional quantities recorded simultaneously, which can be applied to diverse complex systems such as turbulence, finance, ecology, physiology, geophysics, and so on. The method is validated with cross-correlated one- and two-dimensional binomial measures and multifractal random walks. As an example, we illustrate the method by analyzing two financial time series.

The ‘social brain hypothesis’ for the evolution of large brains in primates has led to evidence for the coevolution of neocortical size and social group sizes, suggesting that there is a cognitive constraint on group size that depends, in some way, on the volume of neural material available for processing and synthesizing information on social relationships. More recently, work on both human and non–human primates has suggested that social groups are often hierarchically structured. We combine data on human grouping patterns in a comprehensive and systematic study. Using fractal analysis, we identify, with high statistical confidence, a discrete hierarchy of group sizes with a preferred scaling ratio close to three: rather than a single or a continuous spectrum of group sizes, humans spontaneously form groups of preferred sizes organized in a geometrical series approximating 3–5, 9–15, 30–45, etc. Such discrete scale invariance could be related to that identified in signatures of herding behaviour in financial markets and might reflect a hierarchical processing of social nearness by human brains.

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter $\theta${} determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward ($\theta${}=0), centered ($\theta${}=0.5), and forward ($\theta${}=1) detrending windows. We find that the estimated multifractal scaling exponent $\tau${}(q) and the singularity spectrum f($\alpha${}) are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.

For stationary time series, the cross-covariance and the cross-correlation as functions of time lag n serve to quantify the similarity of two time series. The latter measure is also used to assess whether the cross-correlations are statistically significant. For nonstationary time series, the analogous measures are detrended cross-correlations analysis (DCCA) and the recently proposed detrended cross-correlation coefficient, $\rho${}DCCA(T,n), where T is the total length of the time series and n the window size. For $\rho${}DCCA(T,n), we numerically calculated the Cauchy inequality $-${}1$\le${}$\rho${}DCCA(T,n)$\le${}1. Here we derive $-${}1$\le${}$\rho${}DCCA(T,n)$\le${}1 for a standard variance-covariance approach and for a detrending approach. For overlapping windows, we find the range of $\rho${}DCCA within which the cross-correlations become statistically significant. For overlapping windows we numerically determine\char22{}and for nonoverlapping windows we derive\char22{}that the standard deviation of $\rho${}DCCA(T,n) tends with increasing T to 1/T. Using $\rho${}DCCA(T,n) we show that the Chinese financial market's tendency to follow the U.S. market is extremely weak. We also propose an additional statistical test that can be used to quantify the existence of cross-correlations between two power-law correlated time series.

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.