Correlation Function Parameters Research Articles

Very short-term irradiance forecasting at unobserved locations using spatio-temporal kriging

Several variants of spatio-temporal kriging are used to perform very short-term solar irradiance forecasting by utilizing data from a sensor network. Kriging can produce forecasts not only at the locations of the irradiance monitoring stations, but also at locations where sensors are not installed. Leave-one-out cross-validation is used to test the kriging performance at unobserved locations. Kriging weights are determined either empirically or using a correlation function. Four parametric correlation functions (correlograms) are herein considered, namely, separable, fully symmetric, and two polynomial-adjusted correlation functions. A dense 1km×1.2km network of 17 stations located on Oahu island, Hawaii, is used in this paper.We find that kriging based on a polynomial-adjusted correlation function (the best among the parametric models) is able to obtain forecast skill up to 0.43 and 0.36 for observed and unobserved locations respectively, for a forecast horizon of 50s. It is also found that empirical kriging performs better than parametric models at small forecast horizons (such as 30s). However, it loses accuracy for forecast horizons longer than 100s.

Clustering of the AKARI NEP deep field 24μm selected galaxies

We present a method of selection of 24~$\mu$m galaxies from the AKARI North Ecliptic Pole (NEP) Deep Field down to $150 \mbox{ }\mu$Jy and measurements of their two-point correlation function. We aim to associate various 24 $\mu$m selected galaxy populations with present day galaxies and to investigate the impact of their environment on the direction of their subsequent evolution. We discuss using of Support Vector Machines (SVM) algorithm applied to infrared photometric data to perform star-galaxy separation, in which we achieve an accuracy higher than 80\%. The photometric redshift information, obtained through the CIGALE code, is used to explore the redshift dependence of the correlation function parameter ($r_{0}$) as well as the linear bias evolution. This parameter relates galaxy distribution to the one of the underlying dark matter. We connect the investigated sources to their potential local descendants through a simplified model of the clustering evolution without interactions. We observe two different populations of star-forming galaxies, at $z_{med}\sim 0.25$, $z_{med}\sim 0.9$. Measurements of total infrared luminosities ($L_{TIR}$) show that the sample at $z_{med}\sim 0.25$ is composed mostly of local star-forming galaxies, while the sample at $z_{med}\sim0.9$ is composed of luminous infrared galaxies (LIRGs) with $L_{TIR}\sim 10^{11.62}L_{\odot}$. We find that dark halo mass is not necessarily correlated with the $L_{TIR}$: for subsamples with $L_{TIR}= 10^{11.15} L_{\odot}$ at $z_{med}\sim 0.7$ we observe a higher clustering length ($r_{0}=6.21\pm0.78$ $[h^{-1} \mbox{Mpc}]$) than for a subsample with mean $L_{TIR}=10^{11.84} L_{\odot}$ at $z_{med}\sim1.1$ ($r_{0}=5.86\pm0.69$ $h^{-1} \mbox{Mpc}$). We find that galaxies at $z_{med}\sim 0.9$ can be ancestors of present day $L_{*}$ early type galaxies, which exhibit a very high $r_{0}\sim 8$~$h^{-1} \mbox{Mpc}$.

ΛΛ Correlation function in Au+Au collisions at √[S(NN)]=200 GeV.

We present ΛΛ correlation measurements in heavy-ion collisions for Au+Au collisions at sqrt[s_{NN}]=200 GeV using the STAR experiment at the Relativistic Heavy-Ion Collider. The Lednický-Lyuboshitz analytical model has been used to fit the data to obtain a source size, a scattering length and an effective range. Implications of the measurement of the ΛΛ correlation function and interaction parameters for dihyperon searches are discussed.

Sensitivity of polarization fluctuations to the nature of protein-water interactions: study of biological water in four different protein-water systems.

Since the time of Kirkwood, observed deviations in magnitude of the dielectric constant of aqueous protein solution from that of neat water (∼80) and slower decay of polarization have been subjects of enormous interest, controversy, and debate. Most of the common proteins have large permanent dipole moments (often more than 100 D) that can influence structure and dynamics of even distant water molecules, thereby affecting collective polarization fluctuation of the solution, which in turn can significantly alter solution's dielectric constant. Therefore, distance dependence of polarization fluctuation can provide important insight into the nature of biological water. We explore these aspects by studying aqueous solutions of four different proteins of different characteristics and varying sizes, chicken villin headpiece subdomain (HP-36), immunoglobulin binding domain protein G (GB1), hen-egg white lysozyme (LYS), and Myoglobin (MYO). We simulate fairly large systems consisting of single protein molecule and 20000-30000 water molecules (varied according to the protein size), providing a concentration in the range of ∼2-3 mM. We find that the calculated dielectric constant of the system shows a noticeable increment in all the cases compared to that of neat water. Total dipole moment auto time correlation function of water ⟨δMW(0)δMW(t)⟩ is found to be sensitive to the nature of the protein. Surprisingly, dipole moment of the protein and total dipole moment of the water molecules are found to be only weakly coupled. Shellwise decomposition of water molecules around protein reveals higher density of first layer compared to the succeeding ones. We also calculate heuristic effective dielectric constant of successive layers and find that the layer adjacent to protein has much lower value (∼50). However, progressive layers exhibit successive increment of dielectric constant, finally reaching a value close to that of bulk 4-5 layers away. We also calculate shellwise orientational correlation function and tetrahedral order parameter to understand the local dynamics and structural re-arrangement of water. Theoretical analysis providing simple method for calculation of shellwise local dielectric constant and implication of these findings are elaborately discussed in the present work.

Selecting a separable parametric spatiotemporal covariance structure for longitudinal imaging data.

Longitudinal imaging studies allow great insight into how the structure and function of a subject's internal anatomy changes over time. Unfortunately, the analysis of longitudinal imaging data is complicated by inherent spatial and temporal correlation: the temporal from the repeated measures and the spatial from the outcomes of interest being observed at multiple points in a patient's body. We propose the use of a linear model with a separable parametric spatiotemporal error structure for the analysis of repeated imaging data. The model makes use of spatial (exponential, spherical, and Matérn) and temporal (compound symmetric, autoregressive-1, Toeplitz, and unstructured) parametric correlation functions. A simulation study, inspired by a longitudinal cardiac imaging study on mitral regurgitation patients, compared different information criteria for selecting a particular separable parametric spatiotemporal correlation structure as well as the effects on types I and II error rates for inference on fixed effects when the specified model is incorrect. Information criteria were found to be highly accurate at choosing between separable parametric spatiotemporal correlation structures. Misspecification of the covariance structure was found to have the ability to inflate the type I error or have an overly conservative test size, which corresponded to decreased power. An example with clinical data is given illustrating how the covariance structure procedure can be performed in practice, as well as how covariance structure choice can change inferences about fixed effects.

Locally Homogeneous and Isotropic Gaussian Fields in Kriging

The paper deals with the application of the theory of locally homogeneous and isotropic Gaussian fields (LHIGF) to probabilistic modelling of multivariate data structures. An asymptotic model is also studied, when the correlation function parameter of the Gaussian field tends to infinity. The kriging procedure is developed which presents a simple extrapolator by means of a matrix of degrees of the distances between pairs of the points of measurement. The resulting model is rather simple and can be defined only by the mean and variance parameters, efficiently evaluated by maximal likelihood method. The results of application of the extrapolation method developed for two analytically computed surfaces and estimation of the position of the spacecraft re-entering the atmosphere are given.

Galaxy And Mass Assembly (GAMA): colour- and luminosity-dependent clustering from calibrated photometric redshifts

We measure the two-point angular correlation function of a sample of 4,289,223 galaxies with r < 19.4 mag from the Sloan Digital Sky Survey as a function of photometric redshift, absolute magnitude and colour down to M_r - 5log h = -14 mag. Photometric redshifts are estimated from ugriz model magnitudes and two Petrosian radii using the artificial neural network package ANNz, taking advantage of the Galaxy and Mass Assembly (GAMA) spectroscopic sample as our training set. The photometric redshifts are then used to determine absolute magnitudes and colours. For all our samples, we estimate the underlying redshift and absolute magnitude distributions using Monte-Carlo resampling. These redshift distributions are used in Limber's equation to obtain spatial correlation function parameters from power law fits to the angular correlation function. We confirm an increase in clustering strength for sub-L* red galaxies compared with ~L* red galaxies at small scales in all redshift bins, whereas for the blue population the correlation length is almost independent of luminosity for ~L* galaxies and fainter. A linear relation between relative bias and log luminosity is found to hold down to luminosities L~0.03L*. We find that the redshift dependence of the bias of the L* population can be described by the passive evolution model of Tegmark & Peebles (1998). A visual inspection of a random sample of our r < 19.4 sample of SDSS galaxies reveals that about 10 per cent are spurious, with a higher contamination rate towards very faint absolute magnitudes due to over-deblended nearby galaxies. We correct for this contamination in our clustering analysis.

The effect of the nugget on Gaussian process emulators of computer models

The effect of a Gaussian process parameter known as the nugget, on the development of computer model emulators is investigated. The presence of the nugget results in an emulator that does not interpolate the data and attaches a non-zero uncertainty bound around them. The limits of this approximation are investigated theoretically, and it is shown that they can be as large as those of a least squares model with the same regression functions as the emulator, regardless of the nugget’s value. The likelihood of the correlation function parameters is also studied and two mode types are identified. Type I modes are characterised by an approximation error that is a function of the nugget and can therefore become arbitrarily small, effectively yielding an interpolating emulator. Type II modes result in emulators with a constant approximation error. Apart from a theoretical investigation of the limits of the approximation error, a practical method for automatically imposing restrictions on its extent is introduced. This is achieved by means of a penalty term that is added to the likelihood function, and controls the amount of unexplainable variability in the computer model. The main findings are illustrated on data from an Energy Balance climate model.

IMPROVING CORRELATION FUNCTION FITTING WITH RIDGE REGRESSION: APPLICATION TO CROSS-CORRELATION RECONSTRUCTION

Cross-correlation techniques provide a promising avenue for calibrating photometric redshifts and determining redshift distributions using spectroscopy which is systematically incomplete (e.g., current deep spectroscopic surveys fail to obtain secure redshifts for 30-50% or more of the galaxies targeted). In this paper we improve on the redshift distribution reconstruction methods presented in Matthews & Newman (2010) by incorporating full covariance information into our correlation function fits. Correlation function measurements are strongly covariant between angular or spatial bins, and accounting for this in fitting can yield substantial reduction in errors. However, frequently the covariance matrices used in these calculations are determined from a relatively small set (dozens rather than hundreds) of subsamples or mock catalogs, resulting in noisy covariance matrices whose inversion is ill-conditioned and numerically unstable. We present here a method of conditioning the covariance matrix known as ridge regression which results in a more well behaved inversion than other techniques common in large-scale structure studies. We demonstrate that ridge regression significantly improves the determination of correlation function parameters. We then apply these improved techniques to the problem of reconstructing redshift distributions. By incorporating full covariance information, applying ridge regression, and changing the weighting of fields in obtaining average correlation functions, we obtain reductions in the mean redshift distribution reconstruction error of as much as ~40% compared to previous methods. In an appendix, we provide a description of POWERFIT, an IDL code for performing power-law fits to correlation functions with ridge regression conditioning that we are making publicly available.

Parameter-dependent spectral statistics of chaotic quantum graphs: Neumann versus circular orthogonal ensemble boundary conditions

The parameter-dependent spectral statistics of totally connected quantum graphs with n = 4-30 vertices, such as the parametric velocities correlation functions and the distribution of curvatures, are studied. The inverse participation ratio (IPR), an important measure of localization effects, was also numerically investigated. In the calculations, we successfully used two different theoretical approaches. The first approach was based on the graphs' eigenenergies and wave functions calculations, while the second one used the eigenphases and the eigenvectors of the bond scattering matrix S(k). We considered graphs with Neumann and circular orthogonal ensemble (COE) boundary conditions. We show that in contrast to large Neumann graphs, for which the departure of many parameter-dependent spectral statistics from the random matrix theory (RMT) predictions is observed, for large COE graphs, the spectral statistics and IPR are in good agreement with the RMT predictions.

On the Use of Anisotropic Covariance Models in Estimating Atmospheric DInSAR Contributions

Stochastic models are often used to describe the spatial structure of atmospheric phase delays in differential interferometric synthetic aperture radar (DInSAR) data. Synthetic aperture radar interferograms often exhibit anisotropic atmospheric signals. In view of this, the use of anisotropic models for atmospheric phase estimation is increasingly advocated. However, anisotropic models lead to increased computational complexity in estimating the correlation function parameters with respect to the isotropic case. Moreover, the performance is degraded when dealing with DInSAR techniques involving only a few sparse points usable for computations, as in the case of persistent scatterer interferometry applications, particularly when this estimation has to be done in an automated way on many interferograms. In the present work, we propose some observations about the actual advantage given by anisotropic modeling of atmospheric phase in the case of sparse-grid point-target DInSAR applications. Through analysis of simulated data, we observe that an improvement in the performances of kriging reconstruction approaches can be obtained only when sufficient sampling densities are available. In critical sampling conditions, automated methods with reasonable computational cost may improve their performance if external information on the atmospheric phase screen field is available.

Nonparametric Bayesian models for a spatial covariance

A crucial step in the analysis of spatial data is to estimate the spatial correlation function that determines the relationship between a spatial process at two locations. The standard approach to selecting the appropriate correlation function is to use prior knowledge or exploratory analysis, such as a variogram analysis, to select the correct parametric correlation function. Rather that selecting a particular parametric correlation function, we treat the covariance function as an unknown function to be estimated from the data. We propose a flexible prior for the correlation function to provide robustness to the choice of correlation function. We specify the prior for the correlation function using spectral methods and the Dirichlet process prior, which is a common prior for an unknown distribution function. Our model does not require Gaussian data or spatial locations on a regular grid. The approach is demonstrated using a simulation study as well as an analysis of California air pollution data.

Analysis of 2D CS Spectra for Systems with Non-Gaussian Dynamics

We investigate how accurate different methods of the spectral line shape analysis work in two-dimensional correlation spectroscopy (2D CS) for systems with non-gaussian dynamics. A direct link is established between the frequency dependent correlation functions and a number of line shape metrics. Two model systems are constructed mimicking a typical molecular system with conventional gaussian and non-gaussian spectral dynamics. The frequency dependent correlation function and several line shape parameters extracted from the 2D CS spectra at different waiting times reveal dissimilar dynamics in different frequency domains in the non-gaussian case and similar dynamics in all domains in the gaussian case. The extracted frequency dependent correlation times agree well with the local dynamics in the underlying model for all analysis methods. We also find an extension of the existing line shape analysis methods that allows the extraction of the third-order correlation function.

Quasar correlation function and redshift space distortion from SDSS DR5 data

For z = 0.8–2.2 redshift interval, quasar pair correlation function parameters and β redshift space distortion parameter (connected to large-scale potential flows) values are estimated. We base them on the Main QSO Sample from SDSS Data Release 5. Standard correlation function form ξ(r) = (r 0/r)γ is used for comoving distances r = 2–50 Mpc between quasars. We fix the parameters of the cosmological model: ΩΛ = 1 − Ω M = 0.726 and H 0 = 70.5 km/(s Mpc). We come to the best-fit parameter values of γ = 1.77 ± 0.20, r 0 = 5.52 ± 0.95 Mpc/h for r in the range 2–30 Mpc, γ = 1.91 ± 0.11, r 0 = 5.82 ± 0.61 Mpc for r in the range 2–50 Mpc. The mean β value is β = 0.43 ± 0.22.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on 1/6/2010orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Efficient diagrammatic computation method for higher order correlation functions of local type primordial curvature perturbations

We present a new efficient method for computing the non-linearity parameters of thehigher order correlation functions of local type curvature perturbations in inflation models having a \U0001d4a9-component scalar field, focusing on the non-Gaussianity generated during the evolution on super-horizon scales. In contrast to the naive expectation that the number of operations necessary to compute the n-point functions is proportional to \U0001d4a9n, it grows only linearly in \U0001d4a9 in our formalism. Hence, our formalism is particularly powerful for the inflation models composed of a multi-component scalar field, including the models in whichthe slow-roll conditions are violated after the horizon crossing time. Explicit formulas obtained by applying our method are provided for n = 2, 3, 4 and 5, which correspond to power-, bi-, tri- and quad-spectra, respectively. We also discuss how many parameters we need to parameterize the amplitude and the shapeof the higher order correlation functions of local type.

Differential identities for parametric correlation functions in disordered systems

We derive a family of differential identities for parametric correlation functions in disordered systems by casting them as first- or second-order Ward identities of an associated matrix model. We show that this approach allows for a systematic classification of such identities, and provides a template for deriving higher-order results. We also reestablish and generalize some identities of this type which had been derived previously using a different method.

Understanding the dynamics of biological colloids to elucidate cataract formation and develop a methodology for its early diagnosis

The eye lens is the most notable example of mammalian tissues exhibiting complex colloidal behavior. In this paper, we briefly describe how dynamics in colloidal suspensions can address selected aspects of cataracts, which is ultimately related to protein self-assembly under pathological conditions. Results from dynamic light-scattering of eye lens homogenates over a wide protein concentration were analyzed and the various relaxation modes were identified in terms of collective and self-diffusion processes. Using this information as an input, the complex relaxation pattern of the intact lens nucleus was rationalized. The model of cold cataract–a phase separation effect of the lens cytoplasm with cooling–was used to simulate a lens cataract under in vitro conditions to determine the correlation function parameters, which could be used as reliable indicators of cataract onset. The applicability of dynamic light scattering as a non-invasive, early diagnostic tool for ocular diseases is also demonstrated in light of these findings.

Comparações entre os valores genéticos para características de crescimento de bovinos da raça Nelore preditos com modelos de dimensão finita ou infinita

Foram utilizados 20.065 pesos de 3.016 animais da raça Nelore com o objetivo de comparar os valores genéticos para características de crescimento, preditos pelo modelo de regressão aleatória (RA) sobre polinômios de Legendre da idade (PL) e pelo modelo de regressão aleatória sobre polinômios de Legendre associada a uma estrutura de correlações paramétricas para modelar as correlações entre diferentes medidas do mesmo animal (FC). Análises bicaracterísticas (BC) para as idades-padrão também foram realizadas. Todos os modelos incluíram o efeito de grupo contemporâneo como fixo e a idade da mãe (efeitos linear e quadrático) como co-variável. Para as análises de RA, as tendências médias foram modeladas por uma regressão cúbica sobre polinômios ortogonais da idade do animal. As ordens dos polinômios foram 4, 4, 6 e 3 para os efeitos genéticos direto e materno, de ambiente permanente direto e materno, respectivamente. Alternativamente, correlações entre diferentes medidas do mesmo animal foram modeladas por uma função paramétrica não-estacionária. Para os resíduos, considerou-se uma função de variâncias ou classes de resíduos. Comparações dos valores genéticos preditos para as idades-padrão; por análises BC e por PL e FC, comprovaram que ocorreram diferenças importantes na classificação dos animais quando se passou de um modelo de dimensão finita para um de dimensão infinita. As correlações de posto entre os valores genéticos preditos usando PL e os preditos usando FC foram próximas da unidade.

Segmentation of isolated words based on dynamics of parameters of short correlation functions

In the paper, results of theoretical and experimental studies of dynamics of parameters of short correlation functions of speech signals are exposed. We present the results of the theoretical investigation of the dependence of the maxima of correlation functions of quasi-periodic signals in a general form on the characteristics defining the degree of their quasi-periodicity. Based on these dependences, estimates for the parameters of the quasi-periodicity degree, of the length of quasi-periodic intervals, of the main period, etc. are constructed. The obtained estimates are interpreted in the case of speech signals, and it is shown that many important parameters used in speech technologies can be calculated from them. Experimental results on segmentation of isolated words into separate phonemes are given as an example of efficiency of the approach based on the analysis of correlation functions. It is shown that the segmentation based on monitoring of singularities of dynamics of parameters of short correlation turns out to be stable and adequate to perception.