Gaussian Correlation Research Articles

ON IMPROVED GAUSSIAN CORRELATION INEQUALITIES FOR SYMMETRICAL -RECTANGLES EXTENDED TO CERTAIN MULTIVARIATE GAMMA DISTRIBUTIONS AND SOME FURTHER PROBABILITY INEQUALITIES

The Gaussian correlation inequality (GCI) for symmetrical n-rectangles is improved if the absolute components have a joint cumulative distribution function (cdf), which is MTP2 (multivariate totally positive of order 2). Inequalities of the given type hold at least for all MTP2-cdfs on or with everywhere positive smooth densities. In particular, at least some infinitely divisible multivariate chi-square distributions (gamma distributions in the sense of Krishnamoorthy and Parthasarathy) with any positive real “degree of freedom” are shown to be MTP2. Moreover, further numerically calculable probability inequalities for a broader class of multivariate gamma distributions are derived. A different improvement for inequalities of the GCI-type, and of a similar type with three instead of two groups of components with more special correlation structures is also obtained. The main idea behind these inequalities is to find for a given correlation matrix with positive correlations, a further correlation matrix with smaller correlations whose inverse is an M-matrix and where the corresponding multivariate gamma distribution function is numerically available.

The asymmetric correlation and causality between the European Union carbon market and fossil energy markets caused by COVID-19

The carbon and fossil energy markets have been significantly affected by the COVID-19 pandemic. This article examines the nonlinear correlation and the spillover effect between the global fossil energy markets and the European Union carbon market prior to and following COVID-19. The nonlinear correlation is captured by the localized Gaussian correlation approach, and the spillover effect is evaluated using a quantile-based Granger causality analysis method. Empirical evidence demonstrates that COVID-19 strengthens the correlation between the carbon and oil markets. Conversely, the correlation between the carbon and coal markets is weakened by COVID-19. Furthermore, COVID-19 only resulted in the contagion between the carbon and Texas gas markets. Finally, the spillover effect between the European Union carbon market and fossil energy markets changes from unidirectional to bidirectional. This article provides inspiration for investors to adjust their portfolios to reduce investment risks and meaningful information for policymakers to maintain market stability.

Testing for time‐varying nonlinear dependence structures: Regime‐switching and local Gaussian correlation

AbstractThis paper examines nonlinear and time‐varying dependence structures between a pair of stochastic variables, using a novel approach which combines regime‐switching models and local Gaussian correlation (LGC). We propose an LGC‐based bootstrap test for examining whether the dependence structure between two variables is equal across different regimes. We examine this test in a Monte Carlo study, where it shows good level and power properties. We argue that this approach is more intuitive than competing approaches, typically combining regime‐switching models with copula theory. Furthermore, LGC is a semi‐parametric approach, hence avoids any parametric specification of the dependence structure. We illustrate our approach using financial returns from the US–UK stock markets and the US stock and government bond markets, and provide detailed insight into their dependence structures.

Demonstrating a Quartz Crystal Microbalance with Dissipation (QCMD) to Enhance the Monitoring and Mechanistic Understanding of Iron Carbonate Crystalline Films.

This paper reports the real time monitoring of siderite deposition, on both Au- and Fe-coated surfaces, using the changes in frequency and dissipation of quartz crystal microbalance with dissipation (QCMD). In an iron chloride solution saturated with carbon dioxide, buffered with sodium bicarbonate to pH 6.8, roughly spherical particles of siderite formed within 15 min, which subsequently deposited on the QCMD crystal surface. Imaging of the surface showed a layer formed from particles ca. < 0.5 μm in diameter. Larger particles are clearly deposited on top of the lower layer; these larger particles are >1 μm in diameter. Monitoring of the frequency clearly differentiates the formation of the lower layer from the larger crystals deposited on top at later times. The elastic moduli calculated from QCMD data showed a progressive dissipation increase; the modeling of the solid-liquid interface using a flat approximation resulted in a poor estimation of elastic and storage moduli. Rather, the impedance modeled as a viscoelastic layer in contact with a semi-infinite liquid, where a random bumpy surface with a Gaussian correlator is used, is much more accurate in determining the elastic and storage moduli as losses from the uneven interface are considered. A further step considers that the film is in fact a composite consisting of hard spherical particles of siderite with water in the vacant spaces. This is treated by considering the individual contributions of the phases to the losses measured, thereby further improving the accuracy of the description of the film and the QCMD data. Collectively, this work presents a new framework for the use of QCMD, paired with traditional approaches, to enhance the understanding of crystal deposition and film formation as well as quantify the often evolving mechanical properties.

A Copula Based Unsupervised Domain Adaptation for Image Classification

In this paper, we present an unsupervised domain adaptation algorithm for image classification using principal component analysis (PCA) and Gaussian copula function alignment. The motivation of the proposed algorithm stems from the idea of CORAL algorithm which extracts domain invariant features by aligning the correlation structure between a source and a target domain. However, it suffers from the fact that highly skewed marginal distributions happen to distort the correlation structure so that it may cause a negative transfer. Therefore we utilize a copula function that enables us to analyze separately the dependency structure and the marginals by Sklar’s theorem. In particular, we propose to align the Gaussian copula correlations in the copula feature spaces instead of aligning the correlation matrices in the original space. Considering the extremely skewed distribution of SURF image features in Office-Caltech10 data set we apply PCA first in order to extract some skewness-mitigated principal features and then derive copula features to align for domain adaptation by using CORAL idea with Gaussian copula correlation matrices. The proposed method showed a good classification accuracy when applied to image classification problem in an unsupervised domain adaptation setting.

Surrogate Model of Solved Poisson Kriging Method for Radiation Field Reconstruction

Reverse reconstruction methods for the radiation field do not require information on the radioactive source and are capable of constructing the radiation field using a small amount of monitoring data, showing huge significance for radiation protection. However, in previous studies, inverse reconstruction methods have given less consideration to variations in the time dimension. Herein, the principle of the Poisson Kriging method solved by the surrogate model has been analyzed, and the Poisson Kriging method has been applied to the inverse reconstruction of two-dimensional radiation fields at different moments. On this basis, this work also investigated the effects of the principal function and correlation coefficient model on the objective function, the results of which demonstrate that the quadratic polynomial principal function and the Gaussian model correlation coefficient have good stability and convergence. Compared with the inverse distance weighting methods and the radial basis function methods, the Poisson Kriging method has smaller errors, showing that it is more suitable for reconstructing complex radiation fields. Finally, the Poisson Kriging method was applied to the Fukushima nuclear accident radiation field calculation. The Pearson correlation coefficient of its results was r = 0.49, reflecting the validity of this method. Our work provides a calculation method for the spatial distribution and trend of the radiation field in the early stages of a nuclear accident, which is helpful for furthering radiation protection and emergency responses to nuclear accidents.

Decoherence and entropy generation at one loop in the inflationary de Sitter spacetime for Yukawa interaction

Abstract The decoherence mechanism is believed to be possibly connected to the quantum to classical transition of the primordial cosmological perturbations in the early universe. In this paper, we extend our previous analysis on decoherence in a fermion and scalar quantum field theory coupled via the Yukawa interaction in the Minkowski spacetime, to the inflationary de Sitter background. We treat the scalar field as the system and the fermions as the environment, and both the fields are taken to be massless. We utilise a non-equilibrium effective field theory formalism, suitable for open quantum systems such as this. We assume that an observer measures only the Gaussian 2-point correlator for the scalar field, as the simplest realistic scenario. In order to compute the von Neumann entropy generated at late times as a measure of the decoherence, we construct the one loop renormalised Kadanoff-Baym equation, which is the equation of motion satisfied by the 2-point correlators in the closed time path Schwinger-Keldysh formalism. These equations account to the self energy corrections. Using this, we next construct the one loop corrected statistical propagator for the scalar, which is related to its phase space area, to compute the von Neumann entropy. We also compute the variation of the von Neumann entropy with respect to relevant parameters. We note the qualitative similarity between our findings and the scenario where both the system and the environment are scalars. Our result is also qualitatively similar to an earlier one found by using the influence functional technique for a massive Yukawa theory.

Summing up perturbation series around superintegrable point

We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on the example of a single Miwa variable. The ordinary Gaussian model is superintegrable, i.e. the average of the Schur functions SQ is an explicit function of the Young diagram Q. The question is what happens to this property after perturbation. We show that the entire perturbation series can be nicely summed up into a kind of Borel transform of a universal exponential function, while the dependence on R enters through a polynomial factor in front of this exponential. Moreover, these polynomials can be described explicitly through a single additional structure, which we call “truncation” of the Young diagram Q. It is unclear if one can call this an extended superintegrability, but at least it is a tremendously simple deformation of it. Moreover, the vanishing Gaussian correlators remain vanishing and, hence, are not deformed at all.

Modeling groundwater flow with random hydraulic conductivity using radial basis function partition of unity method

Simulating groundwater flows in heterogeneous aquifers is one of the most widely studied problems. The heterogeneity is modeled through random hydraulic conductivity fields log-normally distributed. In this paper, we aim to generate the realization of the log-normal hydraulic conductivity by summing up a finite number of random periodic modes with the Kraichnan algorithm. To address Neumann conditions, we propose a change of variables that results in Dirichlet boundary conditions along all boundaries of the computational domain. Then, we suggest using the radial basis function partition of unity method (RBFPUM) and RBFPUM with QR factorization (RBFPUM-QR) to analyze groundwater flow in the heterogeneous porous medium. We evaluate the performance of the proposed methods by increasing the number of random modes and the variance of the log-hydraulic conductivity fields using Gaussian and exponential correlation. In addition, we verify the effectiveness of the presented approaches in one and two dimensions using the method of manufactured solutions. Furthermore, we provide statistical inferences through Monte Carlo simulations. Numerical results demonstrate that RBFPUM-QR performs well in handling higher heterogeneity in both single realizations and Monte Carlo simulations.

On heavy-tailed risks under Gaussian copula: The effects of marginal transformation

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a few interesting consequences. First, as the threshold increases, we note that the rate of decay of probabilities of tail sets varies depending on the type of tail sets considered and the Gaussian correlation matrix. Second, we discover that although any multivariate model with a Gaussian copula admits the so-called asymptotic tail independence property, the joint tail behavior under heavier tailed marginal variables is structurally distinct from that under Gaussian marginal variables. The results obtained are illustrated using examples and simulations.

How would the war and the pandemic affect the stock and cryptocurrency cross-market linkages?

This paper studies the cross-market linkages between six international stock markets and the two major cryptocurrency markets during the Covid-19 pandemic and the Russian invasion of Ukraine. By employing the local (partial) Gaussian correlation approach, we find that during the Covid-19 pandemic period, both cryptocurrency markets possess limited diversification and safe haven properties, which further diminish during the war. Bootstrap tests for contagion suggest that during the Covid-19 pandemic, the East Asian markets lead the transmission of contagion towards the two cryptocurrency markets. During the Russian invasion, the US stock market emerges as the principal transmitter of contagion. Uncovering the role of pandemic (Infectious Disease EMV Index) and geopolitical risk (GPR index) induced uncertainties, we find that under conditions of high uncertainty and falling prices, the dependency between the US and UK stock markets with both cryptocurrency markets increases considerably. The latter is more profound during the Russian–Ukrainian conflict. Our findings are useful for investors in their search for understanding the differences in asymmetric connectedness between markets during extreme events.

A computable quantification of multi-mode Gaussian coherence and complete monogamy relation

We propose a quantification CνGn of n-mode Gaussian coherence. The value of CνGn only depends on the covariance matrices and displacement vectors of continuous-variable states without any optimization procedures, and thus is easily calculated. For n=1, CνG1 is a proper Gaussian coherence measure of single-mode CV system. For n≥2, CνGn is invariant under any permutation of submodes, nonincreasing under any n-mode local incoherent Gaussian channels, vanishes at incoherent Gaussian states, and, satisfies the unification condition and the hierarchy condition that a multi-partite quantum correlation measure should obey. Thus CνGn is a multi-partite Gaussian correlation measure, which reveals, though the quantum coherence lives in single-partite systems, that the multi-mode coherence for continuous-variable systems can be regarded as a multipartite Gaussian correlation between modes, and such multi-partite Gaussian correlation is also a quantum resource. Moreover, we show that CνGn is completely monogamous as a multipartite Gaussian correlation measure. This means that the n-mode Gaussian coherence subjects to the principles of resource allocation. In addition, CνGn is an upper bound of the geometric-based single-mode Gaussian coherence measure CBu by the Bures distance at pure Gaussian states of mode ≤2 and can be used to detect coherence in any n-mode Gaussian states more efficiently.

The implications of non‐synchronous trading in G‐7 financial markets

AbstractWe investigate the effects of non‐synchronous trading on volatility spillover for the G‐7 equity markets during the Eurozone sovereign debt crisis (ESDC) and the Covid‐19 pandemic crisis. For data synchronisation we utilise ΜΑ(1) adjusted return series to estimate the Baba‐Engle‐Kraft‐Kroner (BEKK) and the dynamic conditional correlation (DCC) models. We also consider the use of realised kernels as explanatory variables in the variance equation. In this set up, the contagion effects during crises periods are more perceptible, as the spikes are easier to interpret. We also check the robustness of our main results by applying, wavelet coherence analysis to G‐7 major equity indices with realised kernels, as well as local Gaussian correlations (LGC). Our findings suggest the empirical significance of the synchronisation effects for the US and the other G‐7 equity markets. We also conclude that realised kernels is an effective tool for mitigating non‐synchronous effects. These results underline the significance of quantifying the synchronisation effects in equity markets as well as international portfolio diversification strategies.

Modeling and tracking control of underwater unmanned underwater vehicles for deep-sea marine environment detection

Abstract This paper focuses on enhancing target tracking techniques for unmanned underwater vehicles (UUVs) used for deep-sea exploration, especially for the latest advances in digital technology. The article begins with an innovative UUV target tracking algorithm improvement based on the correlation filtering algorithm. Introducing the spatio-temporal regularization method and penalty function optimizes the filter parameters and enhances the algorithm’s performance. Then, a new objective function is constructed by combining the optimal feature weights and baseline function calculated by the dynamic feature weighting method, which effectively excludes the influence of interference peaks in the algorithm. In addition, by applying the Gaussian correlation method, the article further improves the algorithm’s robustness. When the obstacle avoidance ability of the algorithm is analyzed, it is found that the control error of the obstacle avoidance speed in both X and Y directions is less than 0.1 m/s, and the difference between the actual angle and the desired angle of the attitude angle is less than 0.5 degrees. This indicates that the algorithm can effectively avoid all obstacles and accurately track the target. The target tracking experiments show that the tracking performance scores of the algorithm are generally higher than 9, and the tracking accuracy is more than 95%, which is significantly better than other existing algorithms. The optimized tracking algorithm proposed in this paper not only provides essential technical support for the development of unmanned underwater vehicle technology, but also provides valuable reference for the future application and practice of the algorithm.

Exponential vs Gaussian Correlation Functions in the Characterization of Block Copolymer Grain Structure by Depolarized Light Scattering.

Block copolymer (BCP) grain structure affects the mechanical, optical, and electrical properties of BCP materials, making the accurate characterization of this grain structure an important goal. In this study, improved BCP grain parameters were obtained by employing an exponentially decaying correlation function within the ellipsoidal grain model, instead of the Gaussian correlation function that was used in previous work. The exponential correlation function provides a better fit to the experimental depolarized light scattering data, which outweighs the disadvantage that it requires numerical integration to obtain the model scattered intensity.

Geometric versus Entropic Gaussian Correlations in an Open Quantum System of Two Bosonic Modes

Different types of geometric and entropic quantum correlation quantifiers are studied for a system composed of two resonant bosonic modes embedded in a thermal bath. The description of the evolution of the correlation measures is formulated in the framework of the theory of open systems, based on completely positive quantum dynamical semigroups, by using both a geometric and entropic quantification of total nonclassical correlations of Gaussian states. We consider the special case when the initial squeezed thermal state of the system preserves its form in time. We show that time evolution of the measures strongly depends on the parameters characterising the initial state of the system (squeezing parameter and average thermal photon numbers of the two modes) and of the thermal environment (temperature of the thermal bath and dissipation rate). In the limit of large times all the considered measures asymptotically tend to zero value, corresponding to an asymptotic bimodal uncorrelated product state. We make a comparison between the behaviour of the evolution in time of the Gaussian geometric quantum correlations and Gaussian entropic quantum correlations.

Endogeneity of marketing variables in multicategory choice models

A regressor is endogenous if it is correlated with the unobserved residual of a model. Ignoring endogeneity may lead to biased coefficients. We deal with the omitted variable bias that arises if firms set marketing variables considering factors (demand shocks) that researchers do not observe. Whereas publications on sales response or brand choice models frequently take the potential endogeneity of marketing variables into account, multicategory choice models provide a different picture. To consider endogeneity in multicategory choice models, we follow a two-step Gaussian copula approach. The first step corresponds to an individual-level random coefficient version of the multivariate logit model. We analyze yearly shopping data for one specific grocery store, referring to 29 product categories. If the assumption of a Gaussian correlation structure is met, the copula approach indicates the endogeneity of a category-specific marketing variable in about 31% of the categories. The majority of marketing variables rated as endogenous are positively correlated with the omitted variable, implying that ignoring endogeneity leads to an overestimation of the coefficients of the respective marketing variable. Finally, we investigate whether taking endogeneity into account by the copula approach leads to different managerial implications. In this regard, we demonstrate that for our data ignoring endogeneity often suggests a level of marketing activity that is too high.

The Poetry and Music of Science: Comparing Creativity in Science and Art

The Poetry and Music of Science: Comparing Creativity in Science and Art

Does COVID-19 impact the dependence between oil and stock markets? Evidence from RCEP countries

This paper studies the dependence between crude oil and RCEP stock markets before and after COVID-19 by using local Gaussian correlations, contagion tests, and time-frequency domain causality tests. Empirical results show that the lower tail dependence considerably enhanced except in China, while the higher tail dependence significantly increased in Australia, New Zealand, Japan, and Thailand. Contagion is detected from the WTI oil to New Zealand and Thailand stocks. The crude oil market has a short-term (0–32 day frequency) effect on RCEP stock markets, whereas the RCEP stock markets have a relatively stronger, long-term (64–128 day frequency) impact on crude oil markets. RCEP public panic disrupted the oil and stock markets during the Delta and Omicron spread. These findings may help the RCEP governments, institutions, and investors boost energy cooperation, capital flow, and cross-border investments under different market states and investment horizons.

Time evolution of quantum correlations induced by atomic state superpositions

In this article, we study the time evolution of Gaussian quantum correlations induced by the superposition of atomic states. Photon-based quantum information and communication are powerful and suitable because the relevant physical mechanisms, the high combination rate of photons, and the sources of coherence can be understood and easily modeled. To this end, coupled photon pairs produced by coherent superposition of atomic states in an atomic laser and influences of spontaneous atomic decay due to vacuum field fluctuations have been considered. The dynamics of the quantum system leads to temporal quantum correlations such as quantum discord, quantum entanglement, and quantum steering, which are treated by the density operator approach. It was found that the generated photon pairs are completely in a separable state in the initial phase of the dynamical processes. The quantum coherences must be given sufficient time to generate quantum correlations that saturate after very short time scales. The strength of these quantum correlations has been improved by increasing the number of superposed atoms per unit of time. In particular, two-way quantum steering, which is a guarantee for the existence of quantum discord and quantum entanglement, can be achieved by increasing the atom injection rate from 10 kHz to 100 kHz when the probability of finding atoms in the excited state is 45%.