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Background A common goal of scientific microscopic imaging is to determine if a spatial correlation exists between two imaged structures. This is generally accomplished by imaging fluorescently labeled structures and measuring their spatial correlation with a class of image analysis algorithms known as colocalization. However, the most commonly used methods of colocalization have strict limitations, such as requiring overlap in the fluorescent markers and reporting requirements for accurate interpretation of the data, that are often not met. Due to the development of novel super-resolution techniques, which reduce the overlap of the fluorescent signals, a new colocalization method is needed that does not have such strict requirements. Results In order to overcome the limitations of other colocalization algorithms, I developed a new ImageJ/Fiji plugin, Colocalization by cross-correlation (CCC). This method uses cross-correlation over space to identify spatial correlations as a function of distance, removing the overlap requirement and providing more comprehensive results. CCC is compatible with 3D and time-lapse images, and was designed to be easy to use. CCC also generates new images that only show the correlating labeled structures from the input images, a novel feature among the cross-correlating algorithms. Conclusions CCC is a versatile, powerful, and easy to use colocalization and spatial correlation tool that is available through the Fiji update sites. Full and up to date documentation can be found at https://imagej.net/plugins/colocalization-by-cross-correlation . CCC source code is available at https://github.com/andmccall/Colocalization_by_Cross_Correlation .

Several studies have been conducted on droughts, precipitation, and temperature, whereas none have addressed the underlying relationship between nonlinear dynamic properties and patterns of two main hydrological parameters, precipitation and temperature, and meteorological and hydrological droughts. Monthly datasets of Midlands in the UK between 1921 and 2019 were collected for analysis. Subsequent to apply a multifractal approach to attain the nonlinear features of the datasets, the relationship between two hydrological parameters and droughts was investigated through the cross-correlation technique. A similar process was performed to analyze the relationship between multifractal strength variations in time series of precipitation and temperature and droughts. The nonlinear dynamic results indicated that droughts (meteorological and hydrological) were substantially affected by precipitation than temperature. In other words, droughts were more sensitive to precipitation fluctuations than temperature fluctuations. Concerning temperature, meteorological, and hydrological droughts were dependent on the minimum and maximum temperatures (Tmin and Tmax), respectively. The correlation between precipitation and meteorological drought was more long-range persistence than precipitation and hydrological drought. Besides, the correlation between Tmax and droughts was more long-range persistence than Tmin and droughts. Analysis of nonlinear dynamic patterns proved that the multifractal strength of meteorological drought depended on the multifractal strength of precipitation and Tmax, whereas the multifractal strength of hydrological drought depended on the multifractal strength of the Tmin. The correlation between precipitation and drought indices exhibited more multifractal strength than temperature and drought indices. Finally, the pivotal role of maximum temperature on drought events was quite alerting due to global warming intensification.

Estimating time delays in event-based time-series is a crucial task in signal processing as it affects the data quality and is a prerequisite for many subsequent analyses. In particular, data acquired from wearable devices often suffer from a low timestamp precision or clock drift. Current state-of-the-art methods such as Pearson Cross-Correlation are sensitive to typical data quality issues, e.g. misdetected events, and Dynamic Time Warping is computationally expensive. To overcome these limitations, we propose Nearest Advocate, a novel event-based time delay estimation method for multi-sensor time-series data synchronisation. We evaluate its performance using three independent datasets acquired from wearable sensor systems, demonstrating its superior precision, particularly for short, noisy time-series with missing events. Additionally, we introduce a sparse variant that balances precision and runtime. Finally, we demonstrate how Nearest Advocate can be used to solve the problem of linear as well as non-linear clock drifts. Thus, Nearest Advocate offers a promising opportunity for time delay estimation and post-hoc synchronization for challenging datasets across various applications.

Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.

In this study the cross-correlations between the cryptocurrency market represented by the two most liquid and highest-capitalized cryptocurrencies: bitcoin and ethereum, on the one side, and the instruments representing the traditional financial markets: stock indices, Forex, commodities, on the other side, are measured in the period: January 2020–October 2022. Our purpose is to address the question whether the cryptocurrency market still preserves its autonomy with respect to the traditional financial markets or it has already aligned with them in expense of its independence. We are motivated by the fact that some previous related studies gave mixed results. By calculating the q-dependent detrended cross-correlation coefficient based on the high frequency 10 s data in the rolling window, the dependence on various time scales, different fluctuation magnitudes, and different market periods are examined. There is a strong indication that the dynamics of the bitcoin and ethereum price changes since the March 2020 COVID-19 panic is no longer independent. Instead, it is related to the dynamics of the traditional financial markets, which is especially evident now in 2022, when the bitcoin and ethereum coupling to the US tech stocks is observed during the market bear phase. It is also worth emphasizing that the cryptocurrencies have begun to react to the economic data such as the Consumer Price Index readings in a similar way as traditional instruments. Such a spontaneous coupling of the so far independent degrees of freedom can be interpreted as a kind of phase transition that resembles the collective phenomena typical for the complex systems. Our results indicate that the cryptocurrencies cannot be considered as a safe haven for the financial investments.

Long-term cross-correlational structures are examined for pairs of sea surface temperature anomalies (SSTAs) and advective forcing parameters and sea surface height anomalies (SSHAs) and current velocity anomalies (CVAs) in the East/Japan Sea (EJS); all these satellite datasets were collected between 1993 and 2023. By utilizing newly modified detrended cross-correlation analysis algorithms, incorporating local linear trend and local fluctuation level of an SSTA, the analyses were performed on timescales of 400–3000 days. Long-term cross-correlations between SSTAs and SSHAs are strongly persistent over nearly the entire EJS; the strength of persistence is stronger during rising trends and low fluctuations of SSTAs, while anti-persistent behavior appears during high fluctuations of SSTAs. SSTA-CVA pairs show high long-term persistence only along main current pathways: the zonal currents for the Subpolar Front and the meridional currents for the east coast of Korea. SSTA-CVA pairs also show negative long-term persistent behaviors in some spots located near the coasts of Korea and Japan: the zonal currents for the eastern coast of Korea and the meridional currents for the western coast of Japan; these behaviors seem to be related to the coastal upwelling phenomena. Further, these persistent characteristics are more conspicuous in the recent decades (2008~2023) rather than in the past (1993~2008).

A denoised complex network framework employing a detrended partial cross-correlation analysis-based coefficient for achieving the intrinsic scale-dependent correlations between each pair of variables is developed to explore the interrelatedness of multiple nonstationary variables in the real-world. In doing this, we start with introducing the detrended partial cross-correlation coefficient into random matrix theory, and executing a denoising process through correlation matrix reconfiguration, which is followed by utilizing the denoised correlation matrix to construct a planar maximally filtered graph network. It allows us assess the interactions among complex objects more accurately. The effectiveness of our proposed method is validated through the numerical experiments simulating the eigenvalue distribution, and the results show that our method accurately locates the maximum eigenvalue at a specific scale, but existing methods fail to achieve. As a practical application, we also apply the proposed denoising network framework to investigate the co-movement behavior of PM2.5 air pollution of North China and the linkage of commodity futures prices in China. The results show that the denoising process significantly enhances the information content of the network, revealing several interesting insights regarding network properties.

Passive surface-wave methods have been given increased attention from the near-surface geophysics community because of their advantages of being low-cost and environment-friendly, especially in urban environments. The traffic noise sources, however, are not randomly distributed in time and space in densely populated urban areas. Stacking of cross-correlations is unable to effectively attenuate the azimuthal effects due to noise source distribution, resulting in overestimated surface-wave phase velocities. To solve this problem, we proposed a beamforming-based segment (i.e., time window) selection scheme that applies a beamforming technique with a pseudo-linear array to capture the noise segments coming from the sources in the stationary-phase zone. The azimuthal range of in-line noise sources is determined by the Fresnel angle calculated from the measured shortest wavelength. The cross-correlation is applied to these selected stationary-phase segments. The causal parts of cross-correlations are stacked to obtain the final virtual shot gather, since the single directional in-line noise sources are known through beamforming analysis. We used a synthetic test and two real-world examples of traffic-induced noise data acquired in urban environments to verify the feasibility of the proposed scheme. Results demonstrated that the proposed selection scheme can obtain virtual shot gathers with higher signal-to-noise ratio, higher-resolution dispersion energy, and accurate phase velocities, which provides an alternative tool for the applications of using passive surface-wave methods in urban environments, especially for the case of changes in distribution of noise sources in a short time.

Search engine query data deliver insight into the behaviour of individuals who are the smallest possible scale of our economic life. Individuals are submitting several hundred million search engine queries around the world each day. We study weekly search volume data for various search terms from 2004 to 2010 that are offered by the search engine Google for scientific use, providing information about our economic life on an aggregated collective level. We ask the question whether there is a link between search volume data and financial market fluctuations on a weekly time scale. Both collective 'swarm intelligence' of Internet users and the group of financial market participants can be regarded as a complex system of many interacting subunits that react quickly to external changes. We find clear evidence that weekly transaction volumes of S&P 500 companies are correlated with weekly search volume of corresponding company names. Furthermore, we apply a recently introduced method for quantifying complex correlations in time series with which we find a clear tendency that search volume time series and transaction volume time series show recurring patterns.

Correlations in complex systems are often obscured by nonstationarity, long-range memory, and heavy-tailed fluctuations, which limit the usefulness of traditional covariance-based analyses. To address these challenges, we construct scale- and fluctuation-dependent correlation matrices using the multifractal detrended cross-correlation coefficient ρr that selectively emphasizes fluctuations of different amplitudes. We examine the spectral properties of these detrended correlation matrices and compare them to the spectral properties of the matrices calculated in the same way from synthetic Gaussian and -Gaussian signals. Our results show that detrending, heavy tails, and the fluctuation-order parameter jointly produce spectra, which substantially depart from the random case even under the absence of cross-correlations in time series. Applying this framework to one-minute returns of 140 major cryptocurrencies from 2021 to 2024 reveals robust collective modes, including a dominant market factor and several sectoral components whose strength depends on the analyzed scale and fluctuation order. After filtering out the market mode, the empirical eigenvalue bulk aligns closely with the limit of random detrended cross-correlations, enabling clear identification of structurally significant outliers. Overall, the study provides a refined spectral baseline for detrended cross-correlations and offers a promising tool for distinguishing genuine interdependencies from noise in complex, nonstationary, heavy-tailed systems.