Stationary Correlation Research Articles

Stationary correlation pattern in highly non-stationary MEG recordings of healthy subjects and its relation to former EEG studies.

In this study, we analyze magnetoencephalographic (MEG) recordings from 48 clinically healthy subjects obtained from the Human Connectome Project (HCP) while they performed a working memory task and a motor task. Our results reveal a well-developed, stable interrelation pattern that spans the entire scalp and is nearly universal, being almost task- and subject-independent. Additionally, we demonstrate that this pattern closely resembles a stationary correlation pattern (SCP) observed in EEG signals under various physiological and pathological conditions (the distribution of Pearson correlations are centered at about 0.75). Furthermore, we identify the most effective EEG reference for studying the brain's functional network derived from lag-zero cross-correlations. We contextualize these findings within the theory of complex dynamical systems operating near a critical point of a phase transition.

An image-based nonparametric multivariate EWMA control chart for metal additive manufacturing process monitoring

Additive manufacturing offers considerable promise in terms of manufacturing flexibility, but print quality remains a major obstacle to its widespread adoption. Consequently, timely and accurate detection of process variations or anomalies is critical for implementing corrective actions. Melt pool characteristics are crucial to final product quality, and current state-of-the-art studies on melt pool image flow have primarily focused on in-situ sensing, feature extraction, and their relationship with process settings and material properties. This study aims to develop a statistical process control approach to detect process variations immediately using a predefined distribution of monitoring statistics. Two main challenges are addressed: 1) the unknown distribution of melt pool image features, rendering traditional parametric control charts unreliable and 2) the autocorrelation of melt pool image flow features, violating the traditional control chart assumption of independent and identically distributed monitoring data. To overcome these challenges, we propose a multivariate nonparametric Exponential Weighted Moving Average (EWMA) control chart that can appropriately accommodate stationary serial data correlation to monitor process stability by tracking physical features extracted from the original images. Key features of the proposed control chart include its ability to eliminate serial correlation effects and its distribution-free nature, requiring no prior information about the data distribution. Comparative analysis of simulated and real data demonstrates that the proposed approach outperforms baseline methods in anomaly detection accuracy. An actual case study in laser metal deposition (LMD) further validates the effectiveness of the proposed method.

Spatial correlation assessment of multiple earthquake intensity measures using physics-based simulated ground motions

Predictive models for spatial correlation play an effective role in the assessment of seismic risk associated with distributed infrastructure and building portfolios. However, existing models often rely on simplified approaches, assuming isotropy and stationarity. This paper verifies these assumptions by presenting a comprehensive study using a database of 3D physics-based simulated broadband ground motions for Istanbul, generated by the SPEED software. The results reveal significant event-to-event variability and nonstationary and anisotropic characteristics of spatial correlation influenced by source, path, and site effects. The development of nonstationary correlation models requires exploring influential metrics beyond spatial proximity and gaining a deep understanding of their impact, which is the focus of this study. Analysis of the spatial correlations of peak ground displacement, peak ground velocity, peak ground acceleration, and response spectral accelerations at different periods, employing both stationary and nonstationary correlation modelling methods and considering the finite fault model, indicates that the slip distribution pattern, direction and distance of station pairs relative to earthquake rupture, soil softness, and homogeneity of soil properties significantly influence the spatial correlations of near-field earthquake ground motions. Implementation of the introduced parameters in predictive spatial correlation models enhances the precision of regional seismic hazard assessments.

Generation of stationary entanglement and quantum discord in an optomechanical system through three-level atoms

In this paper, we investigate the stationary entanglement and quantum discord between the cavity and mechanical oscillator mode of an optomechanical system whose cavity contains three-level atoms. We examine how sharing entanglement and correlations would be affected by increasing the level of atoms injected into the cavity. In particular, using the appropriate preference of injected atoms to the cavity and optical cavity detuning, we found the impact of atoms and couplings on the degree of steady-state entanglement and quantum discord. Consequently, the stationary entanglement and quantum discord together rise to a certain range of normalized detuning and atom injection levels. Furthermore, both entanglement and Gaussian quantum discord are enhanced when three-level atoms are present, and the maximum entanglement manifests closest to the ringing case. Moreover, we are aware that the system’s physical parameters affect the generation of stationary entanglement and quantum correlation. Therefore, these results may provide a platform for a valuable asset in the practical realization of continuous variable entanglement and quantum information processing.

Multicountry Time-Varying Taylor Rule: Modeling Unconventional Monetary Policies and Bond Premiums

In the post-financial-crisis era, advanced economies have increasingly adopted unconventional monetary policies such as zero interest rate policy, negative interest rate policy, forward guidance communication, and international coordination policies. Consequently, the traditional Taylor rule has lost some of its explanatory power. This analysis extends the Taylor rule from a single-country to a multicountry analysis using cross-country panel data, incorporating nonmacro factors and stationary correlation in the diffusion matrix for a dynamic factor analysis, specifically covering the Group of Seven countries with datasets compiled by Bloomberg L.P. for the period 1999–2022. This approach comprehensively models these unconventional monetary policies, demonstrating greater statistical validity than existing models. Notably, the model extracts the impact of zero interest rate policy and negative interest rate policy as nonmacro factors and presents the high correlation of residuals as indicative of international coordination among central banks. Additionally, by interpreting the discrepancy between the Taylor rule and actual rate as unintended interest rate fluctuations by central banks, the study posits that interest rates will eventually return to the central bank’s intended fair value. The model’s estimation errors could be treated akin to bond value factors in global risk premia.

Stationary stable cross-correlation pattern and task specific deviations in unresponsive wakefulness syndrome as well as clinically healthy subjects.

Brain dynamics is highly non-stationary, permanently subject to ever-changing external conditions and continuously monitoring and adjusting internal control mechanisms. Finding stationary structures in this system, as has been done recently, is therefore of great importance for understanding fundamental dynamic trade relationships. Here we analyse electroencephalographic recordings (EEG) of 13 subjects with unresponsive wakefulness syndrome (UWS) during rest and while being influenced by different acoustic stimuli. We compare the results with a control group under the same experimental conditions and with clinically healthy subjects during overnight sleep. The main objective of this study is to investigate whether a stationary correlation pattern is also present in the UWS group, and if so, to what extent this structure resembles the one found in healthy subjects. Furthermore, we extract transient dynamical features via specific deviations from the stationary interrelation pattern. We find that (i) the UWS group is more heterogeneous than the two groups of healthy subjects, (ii) also the EEGs of the UWS group contain a stationary cross-correlation pattern, although it is less pronounced and shows less similarity to that found for healthy subjects and (iii) deviations from the stationary pattern are notably larger for the UWS than for the two groups of healthy subjects. The results suggest that the nervous system of subjects with UWS receive external stimuli but show an overreaching reaction to them, which may disturb opportune information processing.

Nonlocal correlations dynamics of two-qubit Heisenberg XYZ states with influence of intrinsic decoherence and y-component of Dzyaloshinskii-Moriya interaction

In this paper, we explore nonlocal correlation and Bell non-locality in a two-qubit Heisenberg XYZ model by using Bell-CHSH inequality and uncertainty induced nonlocality (UIN) as well as log-negativity. We consider the effects of spin-qubits XYZ-Heisenberg couplings, the y-component of DM interaction, and intrinsic decoherence. Our results show that spin-qubits Heisenberg couplings have a strong ability to create two-qubit nonlocal correlations, enhanced by combining with DM interactions. The generated Bell-CHSH nonlocality and entanglement conform to the hierarchy principle. The UIN correlation is more resistant to intrinsic decoherence compared to Bell-CHSH inequality and log-negativity. Intrinsic decoherence causes the disappearance of Bell-CHSH non-locality and log-negativity entanglement, while leading to the appearance of partial stationary spin-qubits UIN correlation.

Analysis Of The Effect Of Social Assistance And Capital Expenditure On Poverty

Abstract
 This study aims to determine the effect of social assistance spending and spending capital on poverty rates in districts/cities in South Sulawesi, which consists of 24 regencies, and takes samples from the last three years, namely 2018 – 2020. This research uses secondary data in the form of expenditure data. social assistance, capital spending and poverty rates. The data is taken from the government's official website, namely the Central Statistics Agency (BPS). For the purposes of analysis in this study, panel data were used from all regencies/cities in South Sulawesi Province. In processing the data that has been obtained, namely using the Eviws application. The method used in this study is the method of data analysis stationary test, correlation test and Granger causality test. The results of this study indicate that first, social assistance spending funds have no significant effect on poverty. Second, capital spending has no significant effect on poverty. Third, spending on social assistance and spending on capital do not mutually influence each other.

The Role of Functional Urban Areas in the Spread of COVID-19 Omicron (Northern Spain)

This study focuses on the space-time patterns of the COVID-19 Omicron wave at a regional scale, using municipal data. We analyze the Basque Country and Cantabria, two adjacent regions in the north of Spain, which between them numbered 491,816 confirmed cases in their 358 municipalities from 15th November 2021 to 31st March 2022. The study seeks to determine the role of functional urban areas (FUAs) in the spread of the Omicron variant of the virus, using ESRI Technology (ArcGIS Pro) and applying intelligence location methods such as 3D-bins and emerging hot spots. Those methods help identify trends and types of problem area, such as hot spots, at municipal level. The results demonstrate that FUAs do not contain an over-concentration of COVID-19 cases, as their location coefficient is under 1.0 in relation to population. Nevertheless, FUAs do have an important role as drivers of spread in the upward curve of the Omicron wave. Significant hot spot patterns are found in 85.0% of FUA area, where 98.9% of FUA cases occur. The distribution of cases shows a spatially stationary linear correlation linked to demographically progressive areas (densely populated, young profile, and with more children per woman) which are well connected by highways and railroads. Based on this research, the proposed GIS methodology can be adapted to other case studies. Considering geo-prevention and WHO Health in All Policies approaches, the research findings reveal spatial patterns that can help policymakers in tackling the pandemic in future waves as society learns to live with the virus.

Portfolio Construction in China’s Stock Market: Take Automobile Industry as Example

With the development of new energy vehicles, investors focus on the automobile subsidy in rural areas, and automobile section of China’s A share has been active recently. Based on ARMA model and Mean-Variance model, this paper hopes to give advice on portfolio construction. All the closing price of the stocks are download from AkShare database, from the 9th June, 2020 to the 9th June, 2022. After the stationary test and correlation test for time series, make predictions about return rates for the following 20 days based on ARMA model, construct a profitable portfolio based on Mean-Variance model, compare the accumulative returns and Sharp ratios of constructed portfolio and the one with equal weights. The result reveals that the constructed portfolio outperforms the latter portfolio obviously, so it can be considered that the construction is reasonable. This paper follows the current affairs about the policies on car subsidy in rural areas, uses statistical methods to provide suggestions of wealth allocation for investors, expands the application of the two models.

Correlations in nonequilibrium diffusive systems.

We study the behavior of stationary nonequilibrium two-body correlation functions for diffusive systems with equilibrium reference states (DSe). We describe a DSe at the mesoscopic level by M locally conserved continuum fields that evolve through coupled Langevin equationswith white noises. The dynamic is designed such that the system may reach equilibrium states for a set of boundary conditions. In this form, we make the system driven to a nonequilibrium stationary state by changing the equilibrium boundary conditions. We decompose the correlations in a known local equilibrium part and another one that contains the nonequilibrium behavior and that we call correlation's excess C[over ¯](x,z). We formally derive the differential equationsfor C[over ¯]. To solve them order by order, we define a perturbative expansion around the equilibrium state. We show that the C[over ¯]'s first-order expansion, C[over ¯]^{(1)}, is always zero for the unique field case, M=1. Moreover, C[over ¯]^{(1)} is always long range or zero when M>1. We obtain the surprising result that their associated fluctuations, the space integrals of C[over ¯]^{(1)}, are always zero. Therefore, fluctuations are dominated by local equilibrium up to second order in the perturbative expansion around the equilibrium. We derive the behaviors of C[over ¯]^{(1)} in real space for dimensions d=1 and 2 explicitly. Finally, we derive the two first perturbative orders of the correlation's excess for a generic M=2 case and a hydrodynamic model.

Disrupted seasonal cycle of the warm-adapted and main zooplankter of Lake Biwa, Japan

The seasonal cycle is an important feature of life, leading to the succession of different species and allowing them to share a common environment. Disruption in the seasonal cycle of many species has been reported, but the source of disruption varies from species to species. Lacustrine zooplankton species are widely acknowledged to respond to climate-induced, thermal and trophic variations. Here, we discuss the case of a warm-adapted copepod in Lake Biwa (i.e., Eodiaptomus japonicus), which experienced changes in trophic status and thermal regime over four decades (1966–2010). We investigated the phenological response of E. japonicus to these changes over this period and aimed to identify the sources of the observed variations. The combined results of wavelet analysis and cluster analysis indicated that E. japonicus exhibited different seasonal cycles during the study period. The common unimodal seasonal cycle of the copepod was disrupted on several occasions during which it presented sometimes two or three modes. Wavelet coherence analysis revealed a strong stationary correlation with lake temperature for the total abundance, the clutch size, and the birth rate, but a transient correlation with the body size of females at the annual scale. No coherence was found with food proxies. Discriminant analysis between unimodal and plurimodal seasonal cycles highlighted the effect of low temperature and high predation in leading to plurimodal cycles. Our study emphasizes the need for considering the seasonality of both lower and higher trophic levels for understanding zooplankton phenology.

Within‐event spatial correlation of peak ground acceleration and spectral pseudo‐acceleration ordinates in the Chilean subduction zone

AbstractA regional seismic risk assessment requires the estimation of ground‐motion intensities at multiple locations for a given event simultaneously. In this context, the spatial correlation of ground‐motion residuals plays an important role in characterizing the probability distribution of the field of shaking intensities. Over the last 20 years, the spatial correlation of ground‐motions has been widely studied and different models have been developed. In general, these models vary from each other depending on the ground‐motion database used to generate them, on the adopted intensity measure, on the selected ground‐motion model, and on the estimation methods, among others. This paper proposes a spatial correlation model for within‐event residuals of peak ground acceleration and spectral pseudo‐acceleration ordinates in the Chilean subduction zone. Although the database considered for this study has only a few well‐recorded earthquakes, it contains a large number of station pairs sharing several common events. Therefore, we compute non‐stationary correlations between station pairs and then fit a stationary spatial correlation model. Results of this paper are compared with previous models, concluding that, in general, subduction models show higher spatial correlations than those for active shallow crust events for long‐period spectral ordinates. Moreover, no evidence was found for a systematic effect of earthquake magnitude or site conditions on spatial correlation. Finally, the proposed model is compared with a model obtained assuming stationarity in spatial correlations, showing more reliable estimates when using the proposed model.

Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation.

Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction.

Crucial Events and Biology

In the last years of the 20th century, the attention of physicists working in statistical physics moved from equilibrium processes characterized by stationary correlation functions and Poisson dynamics to biological processes exhibiting ergodicity breaking. The discovery of these processes raised a debate on whether basic properties such as the Onsager principle had to be abandoned or properly revisited. 1 The discovery of Levy processes led many researchers to replace the conventional central limit theorem with the generalized central limit theorem, responsible for a striking departure from the ordinary Gaussian statistics. The discovery of the processes of self-organization made the study of avalanches become very popular. 2 The observation of turbulent processes led to the discovery of new waiting time distribution densities, characterized by inverse power laws 3 and a new stochastic central limit theorem was invented to explain the emergence of Mittag-Leffler function, which is now widely used for the foundation of fractional derivatives. 4 The traditional Linear Response Theory of Kubo was replaced by a new form of linear response, compatible with the ergodic breakdown of complex systems, and this new form of linear response was used for the foundation of Complexity Matching (CM). 5 I plan to prove that crucial events are responsible for ergodicity breaking and that the CM phenomenon is a manifestation of crucial events. One problem still open in this field of research is the origin of [Formula: see text] noise that is traditionally interpreted as a manifestation of the Mandelbrot Fractional Brownian Motion (FBM). 6 I plan to show that the [Formula: see text] noise proposed in 5 for the foundation of the CM phenomenon has a completely different nature, involving crucial events rather than the FBM infinite memory. A recent result of my research group 7 proved that the progress of autonomic neuropathy makes the heartbeats of healthy individuals, dominated by crucial events, turn into FBM. Quite surprisingly, the same phenomenon of transition from the crucial event to the FBM regime was observed in the germination process of lentils 8 in the absence of light. The transition from Levy to Gauss statistics is supposed to be generated by environmental fluctuations and I will illustrate the experimental and theoretical research works that will shed light into their nature.

Stationary EEG pattern relates to large-scale resting state networks – An EEG-fMRI study connecting brain networks across time-scales

Relating brain dynamics acting on time scales that differ by at least an order of magnitude is a fundamental issue in brain research. The same is true for the observation of stable dynamical structures in otherwise highly non-stationary signals. The present study addresses both problems by the analysis of simultaneous resting state EEG-fMRI recordings of 53 patients with epilepsy. Confirming previous findings, we observe a generic and temporally stable average correlation pattern in EEG recordings. We design a predictor for the General Linear Model describing fluctuations around the stationary EEG correlation pattern and detect resting state networks in fMRI data. The acquired statistical maps are contrasted to several surrogate tests and compared with maps derived by spatial Independent Component Analysis of the fMRI data. By means of the proposed EEG-predictor we observe core nodes of known fMRI resting state networks with high specificity in the default mode, the executive control and the salience network. Our results suggest that both, the stationary EEG pattern as well as resting state fMRI networks are different expressions of the same brain activity. This activity is interpreted as the dynamics on (or close to) a stable attractor in phase space that is necessary to maintain the brain in an efficient operational mode. We discuss that this interpretation is congruent with the theoretical framework of complex systems as well as with the brain’s energy balance.

Biophotons and Emergence of Quantum Coherence-A Diffusion Entropy Analysis.

We study the emission of photons from germinating seeds using an experimental technique designed to detect light of extremely small intensity. We analyze the dark count signal without germinating seeds as well as the photon emission during the germination process. The technique of analysis adopted here, called diffusion entropy analysis (DEA) and originally designed to measure the temporal complexity of astrophysical, sociological and physiological processes, rests on Kolmogorov complexity. The updated version of DEA used in this paper is designed to determine if the signal complexity is generated either by non-ergodic crucial events with a non-stationary correlation function or by the infinite memory of a stationary but non-integrable correlation function or by a mixture of both processes. We find that dark count yields the ordinary scaling, thereby showing that no complexity of either kinds may occur without any seeds in the chamber. In the presence of seeds in the chamber anomalous scaling emerges, reminiscent of that found in neuro-physiological processes. However, this is a mixture of both processes and with the progress of germination the non-ergodic component tends to vanish and complexity becomes dominated by the stationary infinite memory. We illustrate some conjectures ranging from stress induced annihilation of crucial events to the emergence of quantum coherence.

Design variable-sampling control charts using covariate information

Statistical Process Control (SPC) charts are widely used in manufacturing industry for monitoring the performance of sequential production processes over time. A common practice in using a control chart is to first collect samples and take measurements of certain quality variables from them at equally-spaced sampling times, and then make decisions about the process status by the chart based on the observed data. In some applications, however, the quality variables are associated with certain covariates, and it should improve the performance of an SPC chart if the covariate information can be used properly. Intuitively, if the covariate information indicates that the process under monitoring is likely to have a distributional shift soon based on the established relationship between the quality variables and the covariates, then it should benefit the process monitoring by collecting the next process observation sooner than usual. Motivated by this idea, we propose a general framework to design a variable-sampling control chart by using covariate information. Our proposed chart is self-starting and can well accommodate stationary short-range serial data correlation. It should be the first variable-sampling control chart in the literature that the sampling intervals are determined by the covariate information. Numerical studies show that the proposed method performs well in different cases considered.

A dynamic Bayesian approach for probability of default and stress test

Obligor defaults are cross-sectionally correlated as obligors share common economic conditions; in addition obligors are longitudinally correlated so that an economic shock like the IMF crisis in 1998 lasts for a period of time. A longitudinal correlation should be used to construct statistical scenarios of stress test with which we replace a type of artificial scenario that the banks have used. We propose a Bayesian model to accommodate such correlation structures. Using 402 obligors to a domestic bank in Korea, our model with a dynamic correlation is compared to a Bayesian model with a stationary longitudinal correlation and the classical logistic regression model. Our model generates statistical financial statement under a stress situation on individual obligor basis so that the genearted financial statement produces a similar distribution of credit grades to when the IMF crisis occurred and complies with Basel IV (Basel Committee on Banking Supervision, 2017) requirement that the credit grades under a stress situation are not sensitive to the business cycle.

Fractional oscillator noise and its applications

It is shown that a fractional oscillator (FO) noise, which is a generalization of the ordinary overdamped linear oscillator driven by the white noise may be ‘applied to diverse systems; its stationary correlation function presentspower-law-like function, exponential-like function, exponential function, and oscillatory decays. The model may be employed to describe the fluctuation of the distance between a fluorescein–tyrosine pair within a single protein complex and the internal dynamics of a lysozyme molecule in solution. It also has the possibility of describing a Brownian particle in an oscillatory viscoelastic shear flow.