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This paper proposes a novel partial discharge (PD) identification and location method based on cross-correlation. The technique aims to solve the problem of weak signal identification and interference suppression. Taking advantage of the characteristics that the time axis of PD pulses at both ends of the cable is symmetrical and the interference signal is asymmetric, the cross-correlation computation is carried out through the alignment of reference pulses to suppress the interference effects such as corona. In calculating the basis PD pulse time difference, the synchronous pulse that is actively injected is used to shorten the data time window and reduce the influence of noise. The accurate time difference is extracted through generalized cross-correlation (GCC). In this paper, the above methods are verified by simulation and experiment. Simulation and computer analysis have been used to test the suggested approach for identifying power cable attenuation. By enhancing the signal-to-noise ratio (SNR) from 28dB to 47dB, the technique reduces the impacts of cable attenuation. Its ability to precisely locate PD sources within a 5m error margin, improve weak PD signal detection, and reduce pulse interference makes it a dependable option for practical uses. The analysis results show that the interference can be suppressed and the weak signal recognition ability can be improved through multiple correlation operations, which lays the foundation for accurate PD location.

In recent years, climate change and its impacts on human health have been the subject of intense discussions in the scientific literature worldwide. Although there is evidence relating climate variations to the occurrence of some pathologies, identification of diseases mostly due to fluctuations in climate variables over time, is still a gap to be filled. In this study, we measured the association between the variables: precipitation, air temperature, relative humidity and radiation and the incidence of the following diseases: dengue, viral hepatitis, leptospirosis, malaria, meningitis, hepatitis and tuberculosis in Salvador-BA through the cross-correlation coefficient and Granger’s causality test. Results found indicated the existence of a cross-correlation in large temporal and causality between the time series analyzed.

Neurons extracted from specific areas of the Central Nervous System (CNS), such as the hippocampus, the cortex and the spinal cord, can be cultured in vitro and coupled with a micro-electrode array (MEA) for months. After a few days, neurons connect each other with functionally active synapses, forming a random network and displaying spontaneous electrophysiological activity. In spite of their simplified level of organization, they represent an useful framework to study general information processing properties and specific basic learning mechanisms in the nervous system. These experimental preparations show patterns of collective rhythmic activity characterized by burst and spike firing. The patterns of electrophysiological activity may change as a consequence of external stimulation (i.e., chemical and/or electrical inputs) and by partly modifying the "randomness" of the network architecture (i.e., confining neuronal sub-populations in clusters with micro-machined barriers). In particular we investigated how the spontaneous rhythmic and synchronous activity can be modulated or drastically changed by focal electrical stimulation, pharmacological manipulation and network segregation. Our results show that burst firing and global synchronization can be enhanced or reduced; and that the degree of synchronous activity in the network can be characterized by simple parameters such as cross-correlation on burst events.

We investigate and quantify the multifractal detrended cross-correlation of return interval series for Chinese stock markets and a proposed price model, the price model is established by oriented percolation. The return interval describes the waiting time between two successive price volatilities which are above some threshold, the present work is an attempt to quantify the level of multifractal detrended cross-correlation for the return intervals. Further, the concept of MF-DCCA coefficient of return intervals is introduced, and the corresponding empirical research is performed. The empirical results show that the return intervals of SSE and SZSE are weakly positive multifractal power-law cross-correlated, and exhibit the fluctuation patterns of MF-DCCA coefficients. The similar behaviors of return intervals for the price model is also demonstrated.

A single-mode laser noise model driven by quadratic pump noise is proposed. The approximation Fokker–Planck equation (AFPE) and steady probability distribution of the laser intensity for the model are derived. It is found that the AFPE is symmetrical with respect to the sign of λ. This point leads to some symmetrical features for the statistical properties of the system. As an important application of the above-mentioned results, the normalized intensity variance NIV is derived. It is found that the NIV is controlled intensively by the cross-correlation between the real and imaginary parts of pump noise. For the NIV versus a curves an interest cross-correlation effect, the two directions of the NIV versus a curves, is found.

We study the effects of cross-correlations between the real and imaginary parts of quantum noise on the intensity fluctuation of a saturation laser model. By virtue of the locked phase method,we derived an approximate Fokker–Planck equation and analytic expressions of the stationary probability distribution function (SPD) of the laser system. Based on the SPD, the mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that the correlation strength of the cross-correlations between the real and imaginary parts of quantum noise increases the intensity fluctuations.

This paper presents a method for estimating vehicle speed using two roadside passive infrared (PIR) sensors whose optical axes are parallel to each other and perpendicular to the moving direction of vehicles. The vehicle speed was calculated based on the time lag between the two signals received by the PIR sensors, which was evaluated by using cross-correlation analysis. The experiments show that the method has an error of less than 5 km/h over a speed range of 20–60 km/h.

This paper presents a method of measuring transportation vehicle’s speed via analog signals of a couple of pyroelectric infrared sensors. The measuring system is located along the roadside with the assumption that optical axes of the sensors are parallel to each other and perpendicular to the moving direction of vehicles. A cross-correlation method combined with interpolation has been used in order to determine the time delay between two output signals, thus defining the traveling speed of the target. The experiment results show that the proposed method has an error of less than 5 km/h over the speed range of 20–90 km/h.

Movement of different strains in Drosophila melanogaster was continuously observed by using computer interfacing techniques and was analyzed by permutation entropy (PE) after exposure to toxic chemicals, toluene (0.1 mg/m³) and formaldehyde (0.01 mg/m³). The PE values based on one-dimensional time series position (vertical) data were variable according to internal constraint (i.e. strains) and accordingly increased in response to external constraint (i.e. chemicals) by reflecting diversity in movement patterns from both normal and intoxicated states. Cross-correlation function revealed temporal associations between the PE values and between the component movement patterns in different chemicals and strains through the period of intoxication. The entropy based on the order of position data could be a useful means for complexity measure in behavioral changes and for monitoring the impact of stressors in environment.

Based on the daily price data of Shanghai and London gold spot markets, we applied detrended cross-correlation analysis (DCCA) and detrended moving average cross-correlation analysis (DMCA) methods to quantify power-law cross-correlation between domestic and international gold markets. Results show that the cross-correlations between the Chinese domestic and international gold spot markets are multifractal. Furthermore, forward DMCA and backward DMCA seems to outperform DCCA and centered DMCA for short-range gold series, which confirms the comparison results of short-range artificial data in L. Y. He and S. P. Chen [Physica A 390 (2011) 3806–3814]. Finally, we analyzed the local multifractal characteristics of the cross-correlation between Chinese domestic and international gold markets. We show that multifractal characteristics of the cross-correlation between the Chinese domestic and international gold markets are time-varying and that multifractal characteristics were strengthened by the financial crisis in 2007–2008.

Long range or multistep-ahead time series forecasting is an important issue in various fields of business, science and technology. In this paper, we have proposed a modified nearest neighbor based algorithm that can be used for long range time series forecasting. In the original time series, optimal selection of embedding dimension that can unfold the dynamics of the system is improved by using upsampling of the time series. Zeroth order cross-correlation and Euclidian distance criterion are used to select the nearest neighbor from up-sampled time series. Embedding dimension size and number of candidate vectors for nearest neighbor selection play an important role in forecasting. The size of embedding is optimized by using auto-correlation function (ACF) plot of the time series. It is observed that proposed algorithm outperforms the standard nearest neighbor algorithm. The cross-correlation based criteria shows better performance than Euclidean distance criteria.

Multistep ahead time series forecasting has become an important activity in various fields of science and technology due to its usefulness in future events management. Nearest neighbor search is a pattern matching algorithm for forecasting, and the accuracy of the method considerably depends on the similarity of the pattern found in the database with the reference pattern. Original time series is embedded into optimal dimension. The optimal dimension is determined by using autocorrelation function plot. The last vector in the embedded matrix is taken as the reference vector and all the previous vectors as candidate vectors. In nearest neighbor algorithm, the reference vector is matched with all the candidate vectors in terms of Euclidean distance and the best matched pattern is used for forecasting. In this paper, we have proposed a hybrid distance measure to improve the search of the nearest neighbor. The proposed method is based on cross-correlation and Euclidean distance. The candidate patterns are shortlisted by using cross-correlation and then Euclidean distance is used to select the best matched pattern. Moreover, in multistep ahead forecasting, standard nearest neighbor method introduces a bias in the search which results in higher forecasting errors. We have modified the search methodology to remove the bias by ignoring the latest forecasted value during the search of the nearest neighbor in the subsequent iteration. The proposed algorithm is evaluated on two benchmark time series as well as two real life time series.

Aiming at problems of multipoint leakage source detection and low positioning accuracy in urban gas pipelines, a multipoint leak location method base on improved variational mode decomposition (VMD) was proposed. By improving the VMD decomposition of the original leakage signal, the parameters of the VMD were optimized to reduce the influence of noise and weak correlation signals on the leak location. Then the multi-point leakage location model of pipeline was established, and the sensitive modal component Intrinsic mode function (IMF) with the most leakage information was selected by multiscale entropy. According to the characteristics of the blind source separation method, the relevant time delays of the simultaneous leakage of multiple points on the pipeline and the frequency of the signal are extracted. Finally, The location of the leak source is determined according to the principle of cross-correlation. The experimental results show that compared with the direct cross-correlation method and the VMD-based method, the proposed multipoint leak diagnosis method has less error, the minimum relative error is 1.61%, and the positioning accuracy is higher.

The Hopfield model for associative recall in a massively connected binary network is reviewed. The problems involved in representation are pointed out. Learning of cross-correlations is introduced, and results of computer simulations are displayed. The relationship with least mean squares learning in feed-forward layered networks is pointed out, leading to the analogue of unlearning. Simulation results show the performance of such a system.

The study of diverse natural and nonstationary signals has recently become an area of active research for physicists. This is because these signals exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails and fractality. The focus of the present paper is on the intriguing power-law autocorrelations and cross-correlations in traffic series. Detrended Cross-Correlation Analysis (DCCA) is used to study the traffic flow fluctuations. It is demonstrated that the time series, observed on the Anhua-Bridge highway in the Beijing Third Ring Road (BTRR), may exhibit power-law cross-correlations when they come from two adjacent sections or lanes. This indicates that a large increment in one traffic variable is more likely to be followed by large increment in the other traffic variable. However, for traffic time series derived from nonadjacent sections or lanes, we find that even though they are power-law autocorrelated, there is no cross-correlation between them with a unique exponent. Our results show that DCCA techniques based on Detrended Fluctuation Analysis (DFA) can be used to analyze and interpret the traffic flow.

We establish a financial price process by continuum percolation system, in which we attribute price fluctuations to the investors’ attitudes towards the financial market, and consider the clusters in continuum percolation as the investors share the same investment opinion. We investigate the cross-correlations in two return time series, and analyze the multifractal behaviors in this relationship. Further, we study the corresponding behaviors for the real stock indexes of SSE and HSI as well as the liquid stocks pair of SPD and PAB by comparison. To quantify the multifractality in cross-correlation relationship, we employ multifractal detrended cross-correlation analysis method to perform an empirical research for the simulation data and the real markets data.

In this study, we apply multifractal detrended cross-correlation analysis (MF-DCCA) to examine the nonlinear cross-correlations between bacterial foodborne diseases (FBDs) and meteorological factors in South Korea. The results demonstrate that power-law cross-correlations between bacterial FBD and meteorological factors exist; and that multifractal characteristics are significant. In addition, the cross-correlation between bacterial FBD and temperature is more persistent than that between bacterial FBD and humidity. Comparison of the strengths of multifractal spectra showed that the degree of multifractality of the Humidity/FBD time series pair is greater than that of Temperature/FBD pair; this indicates that the monthly number of outpatient FBD cases is more sensitive to humidity. Furthermore, to document the major source of multifractality, we shuffle the original series. We conclude that both the long-range correlations and fat-tail distribution contribute to the multifractality of the Temperature/FBD time series pair. The long-range correlations are also an important source that contributes to the multifractality between bacterial FBD and humidity time series.

Understanding of its correlation to some relevant factors is of paramount importance for modeling and predication of the air pollution process. Compared with the traditional cross-correlation analysis, multifractal detrended cross-correlation analysis (MFDCCA) was argued to be a more suitable method to analyze air pollutant time series due to their non-stationarity nature. Multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA) was proposed to improve the shortcomings of MFDCCA. In this study, we apply MF-TWXDFA to investigate the cross-correlation between pollutants (${\mathrm{\text{PM}}}_{10}$ and ${\mathrm{\text{NO}}}_{\mathrm{\text{X}}}$) and meteorological factors (temperature, pressure, wind speed (WS) and relative humidity (RH)). The results on the dataset from 1 January 2005 to 31 December 2014 in urban and rural areas of Hong Kong show the existence of multifractal cross-correlation between all pairs of pollutants and meteorological factors in both urban and rural areas. Different from the previous MFDCCA results, we found that the multifractal degree of cross-correlation between ${\text{PM}}_{10}$ and (temperature, pressure) is more obvious in urban area. The multifractal strength of cross-correlation between ${\mathrm{\text{NO}}}_{\mathrm{\text{X}}}$ and WS is very weak in either urban or rural area. Furthermore, the MF-TWXDFA cross-correlation coefficient ${\rho }_{\mathrm{\text{MF-TWXDFA}}}$ can capture negative correlation between pollutants and meteorological factors. For ${\mathrm{\text{PM}}}_{10}$, ${\rho }_{\mathrm{\text{MF-TWXDFA}}}$ in urban area is less than or close to that in rural area with respect to these four meteorological factors. The ${\rho }_{\mathrm{\text{MF-TWXDFA}}}$ of ${\mathrm{\text{NO}}}_{\mathrm{\text{X}}}$ in urban and rural areas shows more complex patterns for varied meteorological factors. Compared with MFDCCA, MF-TWXDFA can provide much richer information about the relationships between pollutants and meteorological factors, which is beneficial to further modeling and prediction of the air pollution process.

Independent of science branch, scientists have a consensus that peoples lives are highly susceptible to risk, and effectively quantifying risk is a big challenge. This paper assesses the Multifractal Cross-Correlation Measure (MRCC) among West Texas Intermediate (WTI), seven fiat currencies and three foreign exchange rates. Therefore, we use the Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) to examine the volatility dynamics considering the pairs of these financial records. We discover that all these volatility time series pairs $({\alpha }_{xy}(0)>0.5)$ are characterized by overall persistent behavior based on the values of ${\alpha }_{xy}(0)$. The MRCC values exhibit that the pairs WTI versus MXN $(\mathrm{\Gamma }=0.821425)$, WTI versus JPY $(\mathrm{\Gamma }=0.796747)$ and WTI versus NOK $(\mathrm{\Gamma }=0.756545)$ are more complex and persistent than the other pairs. Otherwise, the pairs WTI versus AUD $(\mathrm{\Gamma }=0.580362)$, WTI versus CAD $(\mathrm{\Gamma }=0.667706)$ and WTI versus EMK $(\mathrm{\Gamma }=0.705446)$ are less complex and persistent. Thus, our empirical findings shed light on the problem of quantification risk based on a multifractal perspective.

We take the novel Twitter-based economic uncertainty (TEU) to examine if it has cross-correlation characteristics with four major cryptocurrencies i.e. Bitcoin, Ethereum, Litecoin, and Ripple. To conduct a more thorough analysis, we apply multifractal detrended cross-correlation analysis (MFDCCA) on seasonal-trend decomposition using Loess (STL) decomposed series as well as without decomposed series on the daily data, ranging from 1 June 2011 to 30 June 2021. The findings of this study indicate that: (i) all pairs of TEU with cryptocurrencies are multifractal and have power-law behavior; (ii) the pairs of Ethereum and Bitcoin with TEU are found to be the most multifractal while Litecoin with TEU has the lowest multifractal characteristics; (iii) all STL decomposed series of cryptocurrency have persistent cross-correlation with TEU with the exception of Ethereum which has anti-persistent cross-correlation with TEU; (iv) all without decomposed series of cryptocurrencies show significant persistent cross-correlation characteristics with TEU; (v) the highest linkage is found for the pair of Bitcoin with TEU. Moreover, to reveal the dynamic characteristics in the cross-correlation of TEU with cryptocurrencies, the rolling window is employed for MFDCCA. These findings have important managerial and academic implications for policymakers, investors, and market participants.