Dynamics of Two- and Four-Boson Interactions in Dressed Vacuum States

We analyze the spatial and temporal dynamics of virtual particles in the vacuum states of the one-dimensional ? ²- and ? ⁴-model systems. The properties of the vacuum state for the ? ²-system can be found analytically, which allows us to compute all spatial and temporal correlations exactly. For large spatial and temporal separations, the correlation functions approach a non-vanishing finite constant associated with the occurrence of multiple vacuum bubbles, in contradiction to lowest-order perturbation theory. Long-range inter-bubble correlations suggest that virtual particles can actually enhance the occurrence of another bubble due to stimulated emission. We argue that many of the vacuum’s properties can be explained in the usual particles terms.     

Ordinal pattern and statistical complexity analysis of daily stream flow time series

When calculating the Bandt and Pompe ordinal pattern distribution from given time series at depth D, some of the D! patterns might not appear. This could be a pure finite size effect (missing patterns) or due to dynamical properties of the observed system (forbidden patterns). For pure noise, no forbidden patterns occur, contrary to deterministic chaotic maps. We investigate long time series of river runoff for missing patterns and calculate two global properties of their pattern distributions: the Permutation Entropy and the Permutation Statistical Complexity. This is compared to purely stochastic but long-range correlated processes, the k-noise (noise with power spectrum f ^?k ), where k is a parameter determining the strength of the correlations. Although these processes closely resemble runoff series in their correlation behavior, the ordinal pattern statistics reveals qualitative differences, which can be phrased in terms of missing patterns behavior or the temporal asymmetry of the observed series. For the latter, an index is developed in the paper, which may be used to quantify the asymmetry of natural processes as opposed to artificially generated data.     

A Gibbs-Like Measure for Single-Time, Multi-Scale Energy Transfer in Stochastic Signals and Shell Model of Turbulence

A Gibbs-like approach for simultaneous multi-scale correlation functions in random, time-dependent, multiplicative processes for the turbulent energy cascade is investigated. We study the optimal log-normal Gibbs-like distribution able to describe the subtle effects induced by non-trivial time dependency on both single-scale (structure functions) and multi-scale correlation functions. We provide analytical expression for the general multi-scale correlation functions in terms of the two-point correlations between multipliers and we show that the log-normal distribution is already accurate enough to reproduce quantitatively many of the observed behavior. The main result is that non-trivial time effects renormalize the Gibbs-like effective potential necessary to describe single-time statistics. We also present a generalization of this approach to more general, non log-normal, potentials. In the latter case one obtains a formal expansion of both structure functions and multi-scale correlations in terms of cumulants of all orders.     

Transfert de chaleur au voisinage du point de recollement en aval d'une marche descendante

It has been noticed, although not yet explained, that in recirculating flows the heat transfer coefficient, which is maximum in the reattachment zone, does not correspond in position with the mean reattachment point. We propose an explanation based on impact (main component of velocity V < 0) and sweeping (main component of velocity U > 0) phenomena which are both induced by the vortical structures interacting with the heated wall. This approach uses information given by a numerical code based on the finite volume technique, as well as an analysis of the time evolution of the reattachment point X_r and the point of maximum heat transfer X_max. This analysis is supported by the time series and the profiles of the correlations relative to the velocities and temperature variables.     

Whitening as a Tool for Estimating Mutual Information in Spatiotemporal Data Sets

We address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites. The well-known problems resulting from correlations within and between the time series are addressed by explicit temporal and spatial modelling steps which aim at approximately removing all spatial and temporal correlations, i.e. at whitening the data, such that it is replaced by spatiotemporal innovations; this approach provides a link to the maximum-likelihood method and, for appropriately chosen models, removes the problem of estimating probability distributions of unknown, possibly complicated shape. A parsimonious multivariate autoregressive model based on nearest-neighbour interactions is employed. Mutual information can be reinterpreted in the framework of dynamical model comparison (i.e. likelihood ratio testing), since it is shown to be equivalent to the difference of the log-likelihoods of coupled and uncoupled models for a pair of sites, and a parametric estimator of mutual information can be derived. We also discuss, within the framework of model comparison, the relationship between the coefficient of linear correlation and mutual information. The practical application of this methodology is demonstrated for simulated multivariate time series generated by a stochastic coupled-map lattice. The parsimonious modelling approach is compared to general multivariate autoregressive modelling and to Independent Component Analysis (ICA).     

Detecting long-range correlations in fire sequences with Detrended fluctuation analysis

The spatial-temporal power-law distributions are found in many natural systems, which have self-similarity and fractal behavior. By analyzing the time series of such systems, we could expect to explore and understand the underlying mechanisms. In this paper, the Detrended fluctuation analysis (DFA) is used to analyze the long-range correlations of forest and urban fires in Japan and China. It is found that the interevent time series of both forest and urban fires have the persistent long-range power-law correlations, and they all have two scaling exponents, α₁ and α₂, which are both bigger than 0.5 and smaller than 1.0, despite the different regions and countries. For forest fires, 0.61<α₁<0.73,0.87<α₂<0.98 and for urban fires, 0.52<α₁<0.61,0.59<α₂<0.88. The result suggests that fires have self-similarity characteristics. The occurrence of forest fires may have connection with the weather fluctuations, which have significant effects on the ignition and have the similar temporal correlations. It is shown that the interval sequences of urban fires closely resemble that of white noise in small timescale, and the correlations are weaker than that of forest fires. Human behavior and human density may affect the long-range correlation in some way. This seems to be helpful to understand the complexity of fire system in temporal aspect.     

A new treatment of correlations in reaction theory

The problem of correlations in reaction theory is treated making use of relationships between theS-matrix and appropriate correlation functions. The correlation functions are calculated from the resolvent matrix with the help of Feshbach's projection operator technique, generalized in such a way that correlations can be incorporated. A perturbation procedure in terms of a continued fraction expansion can be defined which avoids the well known divergence problems of the Born series. As a byproduct a conceptually and numerically simple treatment of single particle resonances is obtained and worked out in an example.     

Selfconsistent approximations in Mori's theory

The constitutive quantities in Mori's theory, the residual forces, are expanded in terms of time-dependent correlation functions and products of operators at t = 0, where it is assumed that the time derivatives of the observables are given by products of them. As a first consequence the Heisenberg dynamics of the observables are obtained as an expansion of the same type. The dynamic equations for correlation functions result to be selfconsistent nonlinear equations of the type known from mode-mode coupling approximations. The approach yields a necessary condition for the validity of the presented equations. As a third consequence the static correlations can be calculated from fluctuation-dissipation theorems, if the observables obey a Lie algebra. For a simple spin model the convergence of the expansion is studied. As a further test, dynamic and static correlations are calculated for a Heisenberg ferromagnet at low temperatures, where the results are compared to those of a Holstein-Primakoff treatment.     

Long-range dependence in tree-ring width time series of Austrocedrus Chilensis revealed by means of the detrended fluctuation analysis

By using the detrended fluctuation analysis and detrended moving average method, 823 time series of tree-ring widths in Austrocedrus Chilensis in Patagonia were analyzed. The tree-ring widths of A. Chilensis have been widely used for climatological studies. The results point out to the presence of significant scaling in the temporal fluctuations of tree-ring, which is not due to singular probability density function of the widths but due to the presence of long-range correlations. Such results are in good agreement with those concerning the evidence of long-range dependencies in weather time series.     

GTAD: Graph and Temporal Neural Network for Multivariate Time Series Anomaly Detection

The rapid development of smart factories, combined with the increasing complexity of production equipment, has resulted in a large number of multivariate time series that can be recorded using sensors during the manufacturing process. The anomalous patterns of industrial production may be hidden by these time series. Previous LSTM-based and machine-learning-based approaches have made fruitful progress in anomaly detection. However, these multivariate time series anomaly detection algorithms do not take into account the correlation and time dependence between the sequences. In this study, we proposed a new algorithm framework, namely, graph attention network and temporal convolutional network for multivariate time series anomaly detection (GTAD), to address this problem. Specifically, we first utilized temporal convolutional networks, including causal convolution and dilated convolution, to capture temporal dependencies, and then used graph neural networks to obtain correlations between sensors. Finally, we conducted sufficient experiments on three public benchmark datasets, and the results showed that the proposed method outperformed the baseline method, achieving detection results with F1 scores higher than 95% on all datasets.     

Correlation inequalities for Ising spin lattices

A change of spin representation is used to present expectation inequalities on Ising lattices directly as sums of terms of like sign. The technique is extended to correlation inequalities by introducing replica variables which convert correlations into expectations on a larger space. Second order correlations are analyzed in full from this viewpoint, recovering the FKG set, among others. Third order correlations are examined in some detail, and the sign of the multi-site Ursell correlationsF ₃,F ₄,F ₆ established under appropriate restrictions.     

Assessment of long-range correlation in animal behavior time series: The temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

Detrended Fluctuation Analysis (DFA) is a method that has been frequently used to determine the presence of long-range correlations in human and animal behaviors. However, according to previous authors using statistical model systems, in order to correctly use DFA different aspects should be taken into account such as: (1) the establishment by hypothesis testing of the absence of short term correlation, (2) an accurate estimation of a straight line in the log–log plot of the fluctuation function, (3) the elimination of artificial crossovers in the fluctuation function, and (4) the length of the time series. Taking into consideration these factors, herein we evaluated the presence of long-range correlation in the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus  ). In our study, modeling the data with the general autoregressive integrated moving average (ARFIMA) model, we rejected the hypothesis of short-range correlations (d=0)$(d=0)$ in all cases. We also observed that DFA was able to distinguish between the artificial crossover observed in the temporal pattern of locomotion of Japanese quail and the crossovers in the correlation behavior observed in mosquito larvae locomotion. Although the test duration can slightly influence the parameter estimation, no qualitative differences were observed between different test durations.     

Correlations of nearby levels induced by a random potential

We consider a Hamiltonian H which is the sum of a deterministic part H₀ and of a random potential V. For finite N x N matrices, following a method introduced by Kazakov, we derive a representation of the correlation functions in terms of contour integrals over a finite number of variables. This allows one to analyse the level correlations, whereas the standard methods of random matrix theory, such as the method of orthogonal polynomials, are not available for such cases. At short distance we recover, for an arbitrary H₀ an oscillating behavior for the connected two-level correlation.     

Correlations and variability in electrical signals related to earthquake activity

Evaluating complex fluctuations in geoelectric time series is an important task not only for earthquake prediction but also for understanding complex processes related to earthquake preparation. Previous studies have reported alterations, such as the emergence of correlated dynamics in geoelectric potentials prior to an important earthquake (EQ). However, the presence of correlations and its relation with variability has not been widely explored. In this work we apply the detrended fluctuation analysis and the multiscale entropy methods to analyze the fluctuations of geoelectric time series monitored in two sites located in Mexico. We systematically calculate the correlation exponents and the sample entropy (S_E) of geoelectric time series. Important differences in the scaling exponents and entropy profiles for several time scales are observed. In particular, a complex behavior, characterized by a high entropy across several scales and crossover in the correlation exponents, is observed in the vicinity of an that occurred on Sept. 14, 1995. Moreover, we compare the changes in the entropy of the original data with their corresponding shuffled version to see whether correlations in the original data are related to variability.     

Second moment of multiple-quantum NMR and a time-dependent growth of the number of multispin correlations in solids

The time evolution of multispin correlations (the growth of the number of correlated spins as a function of time) can be observed directly using the multiple-quantum nuclear magnetic resonance spectroscopy of solids. A quantity related to this number, namely, the second moment 〈n ²(t)〉 of the intensity distribution of coherences of different orders in the multiple-quantum spectrum can be calculated using the theory proposed in this work. An approach to the calculation of the four-spin time correlation function through which this moment is expressed is developed. The main sequences of contributions in the expansion of this function into a time power series are summed using the approximation of a large number of neighbors both for systems with a secular dipole-dipole interaction and for systems with a nonsecular effective interaction. An exponential dependence of 〈n ²(t)〉 is obtained. The value of 〈n ²(t)〉 is additionally calculated using an expansion in terms of orthogonal operators for three model examples corresponding to different limiting realizations of spin systems. It is shown that the results of the microscopic theory at least qualitatively agree with both the results obtained for model examples and experimental results obtained recently for adamantane.     

A Novel Time-Sensitive Composite Similarity Model for Multivariate Time-Series Correlation Analysis

Finding the correlation between stocks is an effective method for screening and adjusting investment portfolios for investors. One single temporal feature or static nontemporal features are generally used in most studies to measure the similarity between stocks. However, these features are not sufficient to explore phenomena such as price fluctuations similar in shape but unequal in length which may be caused by multiple temporal features. To research stock price volatilities entirely, mining the correlation between stocks should be considered from the point view of multiple features described as time series, including closing price, etc. In this paper, a time-sensitive composite similarity model designed for multivariate time-series correlation analysis based on dynamic time warping is proposed. First, a stock is chosen as the benchmark, and the multivariate time series are segmented by the peaks and troughs time-series segmentation (PTS) algorithm. Second, similar stocks are screened out by similarity. Finally, the rate of rising or falling together between stock pairs is used to verify the proposed model’s effectiveness. Compared with other models, the composite similarity model brings in multiple temporal features and is generalizable for numerical multivariate time series in different fields. The results show that the proposed model is very promising.     

High dimensional model representation method for fuzzy structural dynamics

Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.     

Tests of the reduced width amplitude distribution with proton resonance data

The assumption that the distribution of reduced partial-width amplitudes is multivariate Gaussian is tested by separate measurement of width and amplitude correlations. Two approaches to the analysis are employed:1) analyzing the data sets separately and then averaging the results;2) combining the data sets and then performing the analysis. Although the latter procedure provides a nuclear width ensemble (1117 widths), several tests suggest that it is preferable to analyze the individual data sets and then average the results. When the data are transformed to a representation in which the amplitude correlation is zero, the average width correlation for 21 data sets is ¯r _w =?0.01+0.03, consistent with the Gaussian assumption.