Complex network approach for recurrence analysis of time series

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.     

Physical Explanation of Influence of Twin and Three Satellite Formation Mode on the Accuracy of Earth's Gravitational Field

The simulated results of the influence of twin and three satellite formation mode on the accuracy of GRACE Earth＇s gravitational field are interpreted from the viewpoint of physics. Because the effective satellite observation information of Earth＇s gravitational field recovery from three-satellite formation mode is only one time more than that of twin satellites, the improvement of the accuracy of Earth＇s gravitational field is far lower than one order of magnitude based on the simple two-times differences between three satellites. Three efficient ways of improving largely the accuracy of measurement of the Earth＇s gravitational field in the future international satellite gravity measurement programme, including proper decrease of satellite orbital altitude, the increase of accuracy from key payloads and an innovation of satellite observation mode are proposed.     

Multifractal analysis of the Yellow River flows

This paper deals with time series of the Yellow River daily flows at Tongguan hydrological station, from the year 2000 to 2005. Power spectrum analysis and statistical moment scaling function on a range of scales revealed scaling qualities of the data. The partition function, which displayed a convex curvature, and the generalized dimension function showed that multifractality is presented. The singularity spectrum, which is single-humped, has shown strong multifractality degree.     

Statistical methods and regression analysis of stratospheric ozone and meteorological variables in Isfahan

Data of seven meteorological variables (relative humidity, wet temperature, dry temperature, maximum temperature, minimum temperature, ground temperature and sun radiation time) and ozone values have been used for statistical analysis. Meteorological variables and ozone values were analyzed using both multiple linear regression and principal component methods. Data for the period 1999-2004 are analyzed jointly using both methods. For all periods, temperature dependent variables were highly correlated, but were all negatively correlated with relative humidity. Multiple regression analysis was used to fit the meteorological variables using the meteorological variables as predictors. A variable selection method based on high loading of varimax rotated principal components was used to obtain subsets of the predictor variables to be included in the linear regression model of the meteorological variables. In 1999, 2001 and 2002 one of the meteorological variables was weakly influenced predominantly by the ozone concentrations. However, the model did not predict that the meteorological variables for the year 2000 were not influenced predominantly by the ozone concentrations that point to variation in sun radiation. This could be due to other factors that were not explicitly considered in this study.     

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that qth-order generalized Hurst exponents h(q) and τ(q) change with the moments q. The nonlinear dependence of these scaling exponents and the singularity spectrum f(α) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.     

Multifractal analysis of ITO thin films prepared by electron beam deposition method

In this work, we developed the multifractality and its formalism to investigate the surface topographies of ITO thin films prepared by electron beam deposition method for various annealing temperatures from their atomic force microscopy (AFM) images. Multifractal analysis shows that the spectrum width, Δα (Δα = α_max − α_min), of the multifractal spectra, f(α), can be used to characterize the surface roughness of the ITO films quantitatively. Also, it is found that the f(α) shapes of the as-deposited and annealed films remained left hooked (that is Δf = f(α_min) − f(α_max) > 0), and falls within the range 0.149-0.677 depending upon the annealing temperatures.     

Multifractal analysis of human synchronous 12-lead ECG signals using multiple scale factors

Life is one of the most complex nonlinear systems and heart is the core of this lifecycle system. Electrocardiogram (ECG) signals taken from healthy adult subjects have been found to characterize multifractality. In this paper, multiscale analysis method was introduced to find the most effective parameters for expressing the complex dynamic characteristics during heart electrical activities. We then investigated the multifractal singularity spectrum area of synchronous 12-lead ECG signals from healthy human subjects and those with different clinical syndromes. The spectrum areas have spatial distribution along with scale factors, which is higher in the middle and lower on both sides and is not related to data length. The statistical results suggest the arithmetical mean value of the area of the 12 leads ECG signals is obviously small for myocardial infarction (MI) sufferer and large for healthy young, while the dispersing degree of the area of the 12 leads ECG signals is apparently large for MI sufferer and small for healthy young. As for the other crowds (e.g., the ischemia sufferer), these two values are almost of middle magnitude. Through those individual discrepancies, we can find some effective approaches to distinguish among healthy persons and the heart diseased.     

Multifractal analysis of the Korean agricultural market

We have studied the long-term memory effects of the Korean agricultural market using the detrended fluctuation analysis (DFA) method. In general, the return time series of various financial data, including stock indices, foreign exchange rates, and commodity prices, are uncorrelated in time, while the volatility time series are strongly correlated. However, we found that the return time series of Korean agricultural commodity prices are anti-correlated in time, while the volatility time series are correlated. The $n$-point correlations of time series were also examined, and it was found that a multifractal structure exists in Korean agricultural market prices.     

Multifractal analysis of the software evolution in software networks

As the scale and complexity have been increased in software systems, developers place more emphases on software engineering and system designs. Software architecture is evolved with update of softwares, and it plays a fundamental role in determining quality of software systems. Multifractal characteristics of software networks can reflect software quality. In this paper, we construct a software network from the dependencies between object classes, and gain a deep understanding of software through network analysis. To be specific, multifractal analysis of the software network is performed based on a modified box-covering algorithm that yields fewer boxes. We verify that software with different functions and dependencies is multifractal. Further, different versions of the software are compared to discover the evolution of the software architecture. The results show that the singularity of class dependencies decreases as the software is updated. This trend leads to a more specific division of functions between software modules. One of the visible advantages of our work is that it allows the characterization of software structures at the code level. The methodology and results of this paper provide new insights into the evaluation and design of large-scale software systems.     

Investigation of scaling properties in monthly streamflow and Standardized Streamflow Index (SSI) time series in the Ebro basin (Spain)

Scaling behaviors in monthly streamflow and Standardized Streamflow Index (SSI) of 11 gauging stations in Ebro basin (Spain) were analyzed: four located in the mainstream and seven in tributaries. The time span is from 1950 to 2005. The methods used are the power spectrum and the detrended fluctuation analysis. All the streamflows are signaled by the presence of the yearly oscillation, which also plays the role of crossover between two regions: for frequencies smaller than the yearly cycle (or timescales higher than 1 year) the dynamics is approximately random, while for frequencies higher than the yearly frequency (or timescales smaller than 1 year) the dynamics is persistently correlated. The SSI shows approximately similar characteristics, although the annual oscillation is not evidenced. Except for a few peculiar features, the power spectrum and the detrended fluctuation analysis (DFA) have shown similar results for all the streamflow and SSI time series, indicating a universal scaling behavior over the Ebro basin.     

Multifractal detrended fluctuation analysis of derivative and spot markets

We investigate the multifractal properties of price increments in the cases of derivative and spot markets. Through the multifractal detrended fluctuation analysis, we estimate the generalized Hurst and the Renyi exponents for price fluctuations. By deriving the singularity spectrum from the above exponents, we quantify the multifractality of a financial time series and compare the multifractal properties of two different markets. The different behavior of each agent-group in transactions is also discussed. In order to identify the nature of the underlying multifractality, we apply the method of surrogate data to both sets of financial data. It is shown that multifractality due to a fat-tailed distribution is significant.     

A brief description to different multi-fractal behaviors of daily wind speed records over China

Scaling behaviors of the long daily wind speed records of four selected weather stations over China were analyzed by using Multi-Fractal Detrended Fluctuation Analysis (MF-DFA). The results indicated that all these four stations are characterized by long-range power-law correlations, but MF-DFA results showed non-universal multi-fractal behaviors over China. We fitted generalized Hurst exponent h(q) via a modified generalized binomial multiplicative cascade model, and different widths of the multi-fractal spectrum are estimated.     

Multifractal detrended fluctuation analysis of the Chinese stock index futures market

Based on the multifractal detrended fluctuation analysis (MF-DFA) and multifractal spectrum analysis, this paper empirically studies the multifractal properties of the Chinese stock index futures market. Using a total of 2942 ten-minute closing prices, we find that the Chinese stock index futures returns exhibit long-range correlations and multifractality, making the single-scale index insufficient to describe the futures price fluctuations. Further, by comparing the original time series with the transformed time series through shuffling procedure and phase randomization procedure, we show the existence of two different sources of the multifractality for the Chinese stock index futures market. Our results suggest that the multifractality is mainly due to long-range correlations, although the fat-tailed probability distributions also contribute to such multifractal behaviour.     

On the detection of trends in long-term correlated records

We use the Detrended Fluctuation Analysis (DFA) to quantify underlying trends in long-term correlated records. Our approach is based on the fact that different orders of DFA are affected differently by trends. For a given instrumental record of length N, we compare the fluctuation exponent α₀ of DFA0 where trends are not being eliminated, with the fluctuation exponent α₂ of DFA2 where possible linear trends in the instrumental record are being eliminated. From this we deduce numerically the probability density p(A) that in the considered long-term correlated record, a linear trend with a slope between A and occurs. Without loss of generality we focus on Gaussian distributed data. As an example, we apply our analysis to several long temperature records (Melbourne, Oxford, Prague, Pusan, Uppsala, and Vienna), where we discuss the trends within the last 90 years, which may originate from both, urban and global warming.     

Multifractal analysis of the fracture surfaces of foamed polypropylene/polyethylene blends

The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene (PP/PE) blends at different temperatures. Nice power-law scaling relationship between the detrended fluctuation function F_q and the scale s is observed for different orders q and the scaling exponent h(q) is found to be a nonlinear function of q, confirming the presence of multifractality in the fracture surfaces. The multifractal spectra f(α) are obtained numerically through Legendre transform. The shape of the multifractal spectrum of singularities can be well captured by the width of spectrum and the difference of dimension . With the increase of the PE content, the fracture surface becomes more irregular and complex, as is manifested by the facts that increases and decreases from positive to negative. A qualitative interpretation is provided based on the foaming process.     

Multifractal analysis of fracture morphology of poly(ethylene-co-vinyl acetate)/carbon black conductive composite

In this paper, based on scanning electron microscope (SEM), the fracture morphology of poly(ethylene-co-vinyl acetate)/carbon black (EVA/CB) conductive composite with various cross-linkers 2,4-di(2-phenylisopropyl) phenol (DCP) contents were analysed by multifractal analysis. The relationship among the multifractal spectrum, cross-linker DCP content, the fracture morphology, fracture process and some mechanical property were discussed. The results showed that the larger the width Δα (Δα = α_max − α_min) of the multifractal spectra f(α), the more nonuniform the fracture surface morphology, in other words, the more the roughness. Moreover, the width Δα (Δα = α_max − α_min) of the multifractal spectra f(α) is the result of competition between ductile fracture and brittle fracture. Also, some mechanical property will correspondingly change when various cross-linker DCP contents were added. Multifractal analysis showed that the spectrum width Δα (Δα = α_max − α_min) of the multifractal spectra f(α) could be used to characterize the surface morphology and mechanical property of EVA/CB conductive composite, quantitatively.     

Geographic coarse graining analysis of the railway network of China

We investigate the detailed, empirical analysis of the statistical properties of the Railway Network of China (RNC) in space L and space G, constructed by geographic coarse graining process. The RNC exhibits similar properties in the cumulative distributions of degree and strength in two spaces, and it presents the hierarchical structure, small-world behavior and assortativity, areciprocal connection both in space L and space G. We also investigate the path length that every train runs, the distribution of the railroad length per degree and the optimal distribution of stations.     

中国东部海域叶绿素时空变化经验正交分析及探讨

利用经验正交函数(EOF)分析了中国东部海域SeaWiFS叶绿素a(1998—2007年)时空变化主要模态,对前3个模态进行了功率谱分析。气候平均结果表明,叶绿素a空间总体分布特征为近海高、外海低,季节变化为春季3—4月最高,夏季6—7月最低。EOF前3个模态所占的贡献率分别为84.89%,3.38%,1.06%。第一模态权重占绝对优势,空间分布与气候平均场基本一致,时间序列表明1998年和2000年为叶绿素a浓度典型低值年,2007年为叶绿素a浓度典型高值年,线性拟合表明总体叶绿素a浓度呈缓慢增加趋势。第二模态主要体现为季节变化,功率谱显著周期为12个月,空间上呈长江口、杭州湾及浙江沿岸海域为正,离岸海域为负的反位相分布特征。第三模态功率谱显著周期为12个月和6个月,以122.9°E,32.2°N为中心的区域呈负相位,黄海和浙江外海区域呈正相位分布,这可能受沿岸流、长江径流转向路径和台湾暖流变化所影响。     

Isotopic fingerprint of the middle Olt River basin,Romania

One of the most important tributaries of the Danube River in Romania, the Olt River, was characterized in its middle catchment in terms of the isotopic composition using continuous flow–isotope ratio mass spectrometry (CF–IRMS). Throughout a period of 10 months, from November 2010 to August 2011, water samples from the Olt River and its more important tributaries were collected in order to investigate the seasonal and spatial isotope patterns of the basin waters. The results revealed a significant difference between the Olt River and its tributaries, by the fact that the Olt River waters show smaller seasonal variations in the stable isotopic composition and are more depleted in ¹⁸O and ²H. The waters present an overall enrichment in heavy isotopes during the warm seasons.     

Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields

We report the effect of substitution of Cr by V and Mn in the spin- \frac12\frac{1}{2} 1 2 dimer compound Sr₃Cr₂O₈. In the pentavalent Cr site, V ion has zero effective moment, while Mn remains in the spin-1 state. For both V and Mn substitutions, the gap in the spin excitation spectra remains almost unchanged in the dilute doping regime. The low temperature Curie tail, expected to be originated from free or quasi-free magnetic ions, is found to be larger in case of V doped samples. However, inter-dimer interaction is found to be stronger in the Mn doped samples. The underlying magnetic behaviour of these doped samples is presumably related to the effect of broken dimers due to random substitutions.