Space-time Autocorrelation Function Research Articles

Development of the GSTARIMA(1,1,1) model order for climate data forecasting

The space-time model combines spatial and temporal elements. One example is the Generalized Space-Time Autoregressive (GSTAR) Model, which improves the Space-Time Autoregressive (STAR) model. The GSTAR model assumes that each location has heterogeneity characteristics, and that the data is stationary. In this research, the moving average component is calculated by involving the relationship between variable values at a certain time and residual values at a previous time, and it is assumed that the data is not stationary, so the model used is the Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) Model. The model order for GSTARIMA is determined through the Space-Time Autocorrelation Function (STACF) and Space-Time Partial Autocorrelation Function (STPACF) to ensure accurate forecasting. Previous research only discussed the GSTARIMA(1,1,1) model, so in this research, the GSTARIMA(3,1,1) model will be addressed as a form of development of the GSTARIMA(1,1,1) model and applied to climate data. The climate data used in this research is sourced from NASA POWER and consists of rainfall variables with large data sizes, requiring the use of the data analytics lifecycle method to analyse Big Data. The lifecycle includes six phases: discovery, data preparation, model planning, model building, communicating results, and operationalization. Based on the data processing results with Python software, the GSTARIMA(3,1,1) model has a MAPE value of 9% for out-sample data and 11% for in-sample data. In contrast, the GSTARIMA(1,1,1) model has a MAPE value of 11% for out-sample data and 12% for in-sample data. So the GSTARIMA(3,1,1) model provides more accurate forecasting results. Therefore, selecting the correct model order is crucial for accurate forecasting.

Numerical Study on the Validity of the Taylor Hypothesis in Space Plasmas

Abstract In situ heliospheric measurements allow us to resolve fluctuations as a function of frequency. A crucial point is to describe the power spectral density as a function of the wavenumber, in order to understand the energy cascade through the scales in terms of plasma turbulence theories. The most favorable situation occurs when the average wind speed is much higher than the phase speed of the plasma modes, equivalent to the fact that the fluctuations’ dynamical times are much longer than their typical crossing period through the spacecraft (frozen-in Taylor approximation). Using driven compressible Hall-magneothydrodynamics simulations, in which an “imaginary” spacecraft flies across a time-evolving turbulence, here we explore the limitations of the frozen-in assumption. We find that the Taylor hypothesis is robust down to sub-proton scales, especially for flows with mean velocities typical of the fast solar wind. For slow mean flows (i.e., speeds of the order of the Alfvèn speed) power spectra are subject to an amplitude shift throughout the scales. At small scales, when dispersive decorrelation mechanisms become significant, the frozen-in assumption is generally violated, in particular for k-vectors almost parallel to the average magnetic field. A discussion in terms of the spacetime autocorrelation function is proposed. These results might be relevant for the interpretation of the observations, in particular for existing and future space missions devoted to very high-resolution measurements.

Space–time correlation analysis of traffic flow on road network

Space–time correlation analysis has become a basic and critical work in the research on road traffic congestion. It plays an important role in improving traffic management quality. The aim of this research is to examine the space–time correlation of road networks to determine likely requirements for building a suitable space–time traffic model. In this paper, it is carried out using traffic flow data collected on Beijing’s road network. In the framework, the space–time autocorrelation function (ST-ACF) is introduced as global measure, and cross-correlation function (CCF) as local measure to reveal the change mechanism of space–time correlation. Through the use of both measures, the correlation is found to be dynamic and heterogeneous in space and time. The finding of seasonal pattern present in space–time correlation provides a theoretical assumption for traffic forecasting. Besides, combined with Simpson’s rule, the CCF is also applied to finding the critical sections in the road network, and the experiments prove that it is feasible in computability, rationality and practicality.

Static and dynamic properties of supercooled water in small nanotubes.

The static and dynamic properties of water in small silicon-carbide and carbon nanotubes have been studied over the temperature range 100 K-298 K, using extensive molecular dynamics simulations. The computed properties include the radial distribution function, the cage correlation function, the space-time autocorrelation function, the velocity autocorrelation function, and the self-diffusivity. They all indicate that, under the conditions that we study, water does not freeze in small nanotubes; the Stokes-Einstein relation breaks down, and the self-diffusivity exhibits a transition around 230 K, very close to 228 K, the temperature at which a fragile-to-strong dynamic crossover is supposed to happen. The cage correlation function C(t) decays according to a stretched-exponential function, C(t) ∼ exp[ - (t/τ)(β)], where τ is a relaxation time and β is a topological exponent.

Space-Time Velocity Correlation Function for Random Walks

Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. Here we adopt this concept for single-particle random walks and demonstrate that the corresponding space-time velocity autocorrelation functions reveal correlations which extend in time much longer than estimated with the commonly employed temporal correlation functions. A generic feature of considered random-walk processes is an effect of velocity echo identified by the existence of time-dependent regions where most of the walkers are moving in the direction opposite to their initial motion. We discuss the relevance of the space-time velocity correlation functions for the experimental studies of cold atom dynamics in an optical potential and charge transport on micro- and nanoscales.

STICCS Reveals Matrix-Dependent Adhesion Slipping and Gripping in Migrating Cells

Two-color spatio-temporal image cross-correlation spectroscopy (STICCS) is a new, to our knowledge, image analysis method that calculates space-time autocorrelation and cross-correlation functions from fluorescence intensity fluctuations. STICCS generates cellular flow and diffusion maps that reveal interactions and cotransport of two distinct molecular species labeled with different fluorophores. Here we use computer simulations to map the capabilities and limitations of STICCS for measurements in complex heterogeneous environments containing micro- and macrostructures. We then use STICCS to analyze the co-flux of adhesion components in migrating cells imaged using total internal reflection fluorescence microscopy. The data reveal a robust, time-dependent co-fluxing of certain integrins and paxillin in adhesions in protrusions when they pause, and in adhesions that are sliding and disassembling, demonstrating that the molecules in these adhesions move as a complex. In these regions, both α6β1- or αLβ2-integrins, expressed in CHO.B2 cells, co-flux with paxillin; an analogous cotransport was seen for α6β1-integrin and α-actinin in U2OS. This contrasts with the behavior of the α5β1-integrin and paxillin, which do not co-flux. Our results clearly show that integrins can move in complexes with adhesion proteins in protrusions that are retracting.

Space-time autocorrelation function for reverberation propagation in a dispersive medium

We obtain the space-time autocorrelation function for a reverberation model that is constructed by the superposition of elementary signals. This is done by defining a four-dimensional Wigner spectrum which is a function of space, wavenumber, position and frequency.

Some space-time statistics of the turbulent point-spread function

We consider the point-spread function (PSF) of an imaging system looking through weak optical turbulence along a horizontal path through the atmospheric surface layer. From this PSF we derive a scalar total irradiance field and a center-of-mass vector field. Theoretical values are found for the space-time autocorrelation and cross-correlation functions for these fields, which are then compared with the observed correlation functions obtained from data taken at the Validation Measurements on Propagation in the Infrared and Radar (VAMPIRA) measurement trial. We discuss the meaning of these results and possible directions for future work.

Intensity fluctuations in a moving random medium

We consider the intensity fluctuations arising when a point source of radiation moves in a randomly inhomogeneous scattering medium. The medium itself can also move with a velocity whose component normal to the direction of propagation can have an arbitrary distribution. We derive an expression for the space–time autocorrelation function of the intensity fluctuations transverse to the direction of propagation. The result is analysed for some particular cases and it is shown how the resulting information can be useful in examining the behaviour of random media in situations of practical interest.

Intensity fluctuations in a moving random medium

We consider the intensity fluctuations arising when a point source of radiation moves in a randomly inhomogeneous scattering medium. The medium itself can also move with a velocity whose component normal to the direction of propagation can have an arbitrary distribution. We derive an expression for the space–time autocorrelation function of the intensity fluctuations transverse to the direction of propagation. The result is analysed for some particular cases and it is shown how the resulting information can be useful in examining the behaviour of random media in situations of practical interest.

An analytical and statistical examination of the low-wave-number region of the turbulent boundary layer wall pressure

The underlying physical mechanisms that generate the low-wave-number pressure components of the turbulent boundary layer wall pressure are examined based on a solution of linearized Navier-Stokes equations in the viscous sublayer with no-slip wall condition. The result indicates that the predominant low-wave-number pressure components are generated by viscous diffusion of shear stress fluctuations at the no-slip wall. These random pressure components have a wave-number spectrum spanning from zero wave number to well beyond the convective wave number. However, their contribution to the convective ridge of the wall pressure spectrum is negligible compared to those of other sources. In the low-wave-number limit, we reach the same conclusion reached by Chase [J. Fluid Mech. 225, 545–555 (1991)], i.e., the wave number spectral density does not vanish as the streamwise wave number approaches zero. The reasons for nonvanishing wave-number spectral density as k→0, for both shear stress and wall pressure, are established analytically. A statistical model is derived based on a probabilistic area-averaging on an assumed random process which is capable of producing the measured two-point correlation functions. The result is a space-time autocorrelation function that yields the experimental low-wave-number data. [Work supported by NSWC ILIR Program and ONR.]

On the Expected Structure of Extreme Waves in a Gaussian Sea. Part II: SWADE Scanning Radar Altimeter Measurements

Abstract In a previous paper (Phillips et al.) an approximate theory was developed that predicted that the expected configuration of extreme waves in a random sea (or the average configuration of an ensemble of extreme waves) is proportional to the space-time autocorrelation function of the surface displacement of the wave field as a whole. This result is tested by examination of scanning radar altimeter measurements made during SWADE in four different sea states, including a unimodal mature wave field, a short fetch, a wind-generated sea crossing swell, a very broad directional spectrum, and a fetch-limited wind sea with opposing swell. In each of these, the spatial autocorrelation function was found directly from the SRA data. The highest waves in each dataset were selected and their configurations averaged with respect to the crest. These averaged configurations were in each case found to be consistent with the autocorrelation function.

Expected Structure of Extreme Waves in a Gaussian Sea. Part I: Theory and SWADE Buoy Measurements

This paper is concerned with the expected configuration in space and time surrounding extremely high crests in a random wave field, or, equivalently, the mean configuration averaged over realizations of extreme events. A simple, approximate theory is presented that predicts that the mean configuration ζ¯(x + r, t + τ) surrounding a crest at (x, t) that is higher than γσ (where σ is the overall rms surface displacement and γ ≫ 1), when normalized by ζ¯(x,t) for ζ > γσ, is the space-time autocorrelation function ρ(r, t) = ¯ζ(x, t)ζ(x + r, t + τ)/ ζ¯2 for the entire wave field. This extends and simplifies an earlier result due to Boccotti and is consistent with a precise calculation of the one-dimensional case with r = 0, involving the time history of measurements at a single point. The results are compared with buoy data obtained during the Surface Wave Dynamics Experiment and the agreement is found to be remarkably good.

Space–time correlation properties of dynamic laser speckle in the near diffraction field of a longitudinally moving diffuse object

The space–time autocorrelation function of detected speckle-intensity fluctuation is derived for a quite general case in which both the diffuse object and the photodetector move along the axis of an illuminating Gaussian beam. Correlation properties of some particular cases of this general arrangement are then analyzed. The considerations presented here are limited to the near diffraction field in which the speckle complex amplitude is assumed to obey circular Gaussian statistics. New time-stationary processes are revealed, and the possibility of their application in speckle velocimetry is discussed.

Amendments and Corrections: Moments of the Sampled Space-Time Autocovariance and Autocorrelation Function

Amendments and Corrections: Moments of the Sampled Space-Time Autocovariance and Autocorrelation Function

‘Moments of the sampled space-time autocovariance and autocorrelation function’

On page 692, the expression for var {γ^00(s)} for s>1 should be σ4N2(T-s)[tr{Γ2(0)}+(2-1T-s)tr{Γ2(1)}]

Moments of the Sampled Space-Time Autocovariance and Autocorrelation Function

Moments of the Sampled Space-Time Autocovariance and Autocorrelation Function

Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering.

A quantum theory of stimulated Raman scattering is presented that takes into account three-dimensional propagation and collisional dephasing, allowing the study of the spatial and temporal coherence properties of the generated Stokes light. Maxwell-Bloch equations for the Stokes field operator and the collective atomic operators are solved analytically under low-signal-gain conditions, where the laser field and the atomic ground states remain undepleted. The intensity and the space-time autocorrelation function of the Stokes field are calculated. The Stokes field is expanded into a set of statistically independent ``coherence modes,'' which are determined explicitly for the case of a cylindrically shaped pumped volume. The Stokes pulse energy W is found to fluctuate from pulse to pulse. The probability distribution function for pulse energies P(W) is calculated for a range of Fresnel numbers of the excited volume and collisional dephasing rates. For small values of Fresnel number and dephasing rate, P(W) is a negative exponential distribution. For large values of either, P(W) narrows and approaches a Gaussian-shaped distribution. This occurs because many independent modes contribute to the Stokes emission, making it spatially and/or temporally incoherent.

Moments of the sampled space-time autocovariance and autocorrelation function

SUMMARY Pfeifer & Deutsch (1981) have derived expressions for the means and variances of the sampled autocovariances and autocorrelations, in the case of a white-noise space-time process. This note shows how their work can be extended to general space-time autoregressive moving average processes. The results are useful for testing the significance of observed space-time autocorrelations, given a hypothesized space-time

A model of dynamic scattering by microemulsions

A model previously developed for the statistical thermodynamics of microemulsion phase equilibria is used to treat the static and dynamic scattering by such systems. The random internal oil/water geometry is represented as resulting from a Voronoi tessellation, and temporal fluctuations are introduced by allowing the generating Poisson nuclei to perform independent Brownian motions. This dynamic model maintains the stationary statistics required of an equilibrium system and also allows representation of a continuous set of structures from oil-in-water to water-in-oil geometries including the bicontinuous geometries expected when oil and water are present in comparable amounts. Comparison of calculated scattering functions with experiment shows quantitative agreement with Rayleigh scattering data and at least qualitative agreement with measured space-time autocorrelation functions. Calculations of a k-dependent diffusion coefficient also are compared with experimental results.