Spatial Correlation Function Research Articles

Bayesian inference for group-level cortical surface image-on-scalar regression with Gaussian process priors.

In regression-based analyses of group-level neuroimage data, researchers typically fit a series of marginal general linear models to image outcomes at each spatially referenced pixel. Spatial regularization of effects of interest is usually induced indirectly by applying spatial smoothing to the data during preprocessing. While this procedure often works well, the resulting inference can be poorly calibrated. Spatial modeling of effects of interest leads to more powerful analyses; however, the number of locations in a typical neuroimage can preclude standard computing methods in this setting. Here, we contribute a Bayesian spatial regression model for group-level neuroimaging analyses. We induce regularization of spatially varying regression coefficient functions through Gaussian process priors. When combined with a simple non-stationary model for the error process, our prior hierarchy can lead to more data-adaptive smoothing than standard methods. We achieve computational tractability through a Vecchia-type approximation of our prior that retains full spatial rank and can be constructed for a wide class of spatial correlation functions. We outline several ways to work with our model in practice and compare performance against standard vertex-wise analyses and several alternatives. Finally, we illustrate our methods in an analysis of cortical surface functional magnetic resonance imaging task contrast data from a large cohort of children enrolled in the adolescent brain cognitive development study.

Dynamical critical behavior on the Nishimori point of frustrated Ising models.

By considering the quench dynamics of two-dimensional frustrated Ising models through numerical simulations, we investigate the dynamical critical behavior on the multicritical Nishimori point (NP). We calculate several dynamical critical exponents, namely, the relaxation exponent z_{c}, the autocorrelation exponent λ_{c}, and the persistence exponent θ_{c}, after a quench from the high temperature phase to the NP. We confirm their universality with respect to the lattice geometry and bond distribution. For a quench from a power-law correlated initial state to the NP, the aging dynamics are much slower. We also look up the issue of multifractality during the critical dynamics by investigating different moments of the spatial correlation function. We observe a single growth law for all the length scales extracted from different moments, indicating that the equilibrium multifractality at the NP does not affect the dynamics.

Mathematical Modeling of Refraction Characteristics of Electromagnetic Radiation at Stochastic Gravitational Field

Numerical-analytical modeling is used for estimation of gravitational noise influence on propagation of electromagnetic radiation at gravitational field of a group of astrophysical objects. The method bases on numerical integrate of system of light differential equations in the Euler’s form, added differential equations for calculation of statistic moments of side fluctuations of light at a picture plane of observer. The influence of gravitation was taken into account by introducing of the effective refraction index of vacuum, expressed through a gravitational potential. Visions about spatial correlation function of inhomogeneities of effective refraction index of vacuum are used as model. Calculating of gravitation effects of group astrophysical objects are performed under assumption additive contribution of field of every objects in general gravitational field. Modeling of the refraction characteristics of electromagnetic radiation is performed for a various configurations of gravitation field. Results of calculating are shown at a picture plane of observer. The blurring effects of gravitational lensing are investigated at dependence from position of localized area of gravitational noise and astrophysical objects. It’s showed that for case of single-component gravitational field full coverage of object by area of gravitational noise match maximum blurring of lensing effect. The features of gravitational focusing are determined at dependence from position of area noise for asymmetrical twocomponent gravitational field, where one of objects coverage by area of gravitational noise. Offered tool of modeling can be used for both investigation of gravitational lensing of multi-component gravitational field in presence variety of limited area of gravitational noise and under conditions uniform spatial distribution of stochastic gravitational inhomogeneities. Also it can use for recovering of gravitational potentials of non-radiating (hidden) objects by characteristics of received electromagnetic radiation of remote space sources.

Spatial Structure of the Radio‐Frequency Noise Field in a Large City

AbstractThe urban radio‐frequency (RF) noise generated by our cities continues to change with time. Although models exist to describe the RF noise as functions of frequency and urban land use types, very few models describe the spatial character or structure of the noise on the scales of city blocks (50–150 m). The goal of this work is to investigate the connection between urban morphology and the higher‐order spatial statistics of the noise field. To achieve this goal, a large measurement campaign was conducted in Boston, Massachusetts. Many spatial measurements allowed for calculation of spatial correlation functions of noise power in three different neighborhoods, which were used to quantify the spatial structure of the fields. A statistical point source model is then developed, with adjustable parameters relating to urban morphology. Good agreement between the model and the experimental correlation functions suggests the 25 MHz urban noise field is well described by a random network of fixed point sources, radiating with a 1/r power law behavior.

Statistical Modeling of Right-Censored Spatial Data Using Gaussian Random Fields

Consider a fixed number of clustered areas identified by their geographical coordinates that are monitored for the occurrences of an event such as a pandemic, epidemic, or migration. Data collected on units at all areas include covariates and environmental factors. We apply a probit transformation to the time to event and embed an isotropic spatial correlation function into our models for better modeling as compared to existing methodologies that use frailty or copula. Composite likelihood technique is employed for the construction of a multivariate Gaussian random field that preserves the spatial correlation function. The data are analyzed using counting process and geostatistical formulation that led to a class of weighted pairwise semiparametric estimating functions. The estimators of model parameters are shown to be consistent and asymptotically normally distributed under infill-type asymptotic spatial statistics. Detailed small sample numerical studies that are in agreement with theoretical results are provided. The foregoing procedures are applied to the leukemia survival data in Northeast England. A comparison to existing methodologies provides improvement.

Effective Spatial Degrees of Freedom of Natural Temperature Variability as a Function of Frequency

Abstract A fundamental statistic of climate variability is its spatiotemporal correlation function. Its complex structure can be concisely summarized by a frequency-dependent measure of the effective spatial degrees of freedom (ESDOF). Here we present, for the first time, frequency-dependent ESDOF estimates of global natural surface temperature variability from purely instrumental measurements, using the HadCRUT4 dataset (1850–2014). The approach is based on a newly developed method for estimating the frequency-dependent spatial correlation function from gappy data fields. Results reveal a multicomponent structure of the spatial correlation function, including a large-amplitude short-distance component (with weak time scale dependence) and a small-amplitude long-distance component (with increasing relative amplitude toward the longer time scales). Two frequency-dependent ESDOF measures are applied, each responding mainly to either of the two components. Both measures exhibit a significant ESDOF reduction from monthly to multidecadal time scales, implying an increase of the effective spatial scale of natural surface temperature fluctuations. Moreover, it is found that a good approximation to the global number of equally spaced samples needed to estimate the variance of global mean temperature is given, at any frequency, by the greater one of the two ESDOF measures, decreasing from ∼130 at monthly to ∼30 at multidecadal time scales. Finally, the multicomponent structure of the correlation function together with the detected ESDOF scaling properties indicate that the ESDOF reduction toward the longer time scales cannot be explained simply by diffusion acting on stochastically driven anomalies, as it might be suggested from simple stochastic-diffusive energy balance models.

Time-dependent properties of run-and-tumble particles. II. Current fluctuations.

We investigate steady-state current fluctuations in two models of hardcore run-and-tumble particles (RTPs) on a periodic one-dimensional lattice of L sites, for arbitrary tumbling rate γ=τ_{p}^{-1} and density ρ; model I consists of standard hardcore RTPs, while model II is an analytically tractable variant of model I, called a long-ranged lattice gas (LLG). We show that, in the limit of L large, the fluctuation of cumulative current Q_{i}(T,L) across the ith bond in a time interval T≫1/D grows first subdiffusively and then diffusively (linearly) with T: 〈Q_{i}^{2}〉∼T^{α} with α=1/2 for 1/D≪T≪L^{2}/D and α=1 for T≫L^{2}/D, where D(ρ,γ) is the collective- or bulk-diffusion coefficient; at small times T≪1/D, exponent α depends on the details. Remarkably, regardless of the model details, the scaled bond-current fluctuations D〈Q_{i}^{2}(T,L)〉/2χL≡W(y) as a function of scaled variable y=DT/L^{2} collapse onto a universal scaling curve W(y), where χ(ρ,γ) is the collective particle mobility. In the limit of small density and tumbling rate, ρ,γ→0, with ψ=ρ/γ fixed, there exists a scaling law: The scaled mobility γ^{a}χ(ρ,γ)/χ^{(0)}≡H(ψ) as a function of ψ collapses onto a scaling curve H(ψ), where a=1 and 2 in models I and II, respectively, and χ^{(0)} is the mobility in the limiting case of a symmetric simple exclusion process; notably, the scaling function H(ψ) is model dependent. For model II (LLG), we calculate exactly, within a truncation scheme, both the scaling functions, W(y) and H(ψ). We also calculate spatial correlation functions for the current and compare our theory with simulation results of model I; for both models, the correlation functions decay exponentially, with correlation length ξ∼τ_{p}^{1/2} diverging with persistence time τ_{p}≫1. Overall, our theory is in excellent agreement with simulations and complements the prior findings [T. Chakraborty and P. Pradhan, Phys. Rev. E 109, 024124 (2024)1539-375510.1103/PhysRevE.109.024124].

Asymmetric cosine-Gaussian Schell-model sources

We introduce a new class of Schell-model source whose spatial correlation function carries a finite series of nontrivial phases and is modulated by cosine function. The propagating formula for the cross-spectral density (CSD) function of the beams generated by this new source in free space is derived and used to investigate the characteristics of the light fields for different modulation parameters. The results show that the appearance of the modulating function and the nontrivial phase sequence cause the radiated fields with extraordinary characteristics during propagation, such as self-splitting and self-interfering in an asymmetric manner. This method of jointly controlling the magnitude and phase of the source complex coherence state provides a new approach for achieving beam shaping.

Optical momentum distributions in monochromatic, isotropic random vector fields

Abstract We investigate the decomposition of the electromagnetic Poynting momentum density in three-dimensional random monochromatic fields into orbital and spin parts, using analytical and numerical methods. In sharp contrast with the paraxial case, the orbital and spin momenta in isotropic random fields are found to be identically distributed in magnitude, increasing the discrepancy between the Poynting and orbital pictures of energy flow. Spatial correlation functions reveal differences in the generic organization of the optical momenta in complex natural light fields, with the orbital current typically forming broad channels of unidirectional flow, and the spin current manifesting larger vorticity and changing direction over subwavelength distances. These results are extended to random fields with pure helicity, in relation to the inclusion of electric-magnetic democracy in the definition of optical momenta.

Three-Dimensional Spatial Atmospheric Turbulence Generation Method for Aerial Refueling Flight Simulation

Traditional flight simulation models often operate on the premise of a steady atmosphere, overlooking the complexities of actual atmospheric dynamics and the flight safety risks posed by wind disturbances, such as turbulence. To Address this oversight, the present study introduces a method for generating three-dimensional atmospheric turbulence based on spatial correlation functions. This method, rigorously validated against correlation and spectral benchmarks, guarantees isotropic properties in the synthesized turbulence fields. Through interpolation techniques, the model integrates the spatial atmospheric turbulence into the flight simulation framework effectively. The paper highlights the application of this model by examining the impact of atmospheric turbulence on the precise flight dynamics of quadcopter UAVs during aerial refueling operations. The findings demonstrate the model’s pertinence not only to UAVs but also to the broader spectrum of aircraft and their operational procedures.

Revealing void anisotropies in vertically-vibrated granular sphere packings with various structural characterizations

We utilize magnetic resonance imaging (MRI) techniques to study granular sphere packings prepared with vertical vibration, and reveal the extremely slight global anisotropies of the void phase with systematic analyses on Delaunay pores and chords. Unexpectedly, the global orientational orders of the eigenvectors of tensors quantifying (i) pore throats, (ii) chords going through individual pores, (iii) shape of Voronoi cells and (iv) contact fabrics have consistent evolution laws when packing fraction changes, but the orientational order of the eigenvectors of a pore volume tensor exhibits a peculiarly different trend. With an orientation-dependent spatial correlation function, we attribute their different behaviors to the fact that different anisotropy variables probe the void phase at different length scales, so that their dependences on packing fraction are different. The segmentation of the void region into pores sensitively captures a unique and intricate structural anisotropy at an intermediate length scale.

Microstructure reconstruction of 2D/3D random materials via diffusion-based deep generative models

Microstructure reconstruction serves as a crucial foundation for establishing process–structure–property (PSP) relationship in material design. Confronting the limitations of variational autoencoder and generative adversarial network within generative models, this study adopted the denoising diffusion probabilistic model (DDPM) to learn the probability distribution of high-dimensional raw data and successfully reconstructed the microstructures of various composite materials, such as inclusion materials, spinodal decomposition materials, chessboard materials, fractal noise materials, and so on. The quality of generated microstructure was evaluated using quantitative measures like spatial correlation functions and Fourier descriptor. On this basis, this study also achieved the regulation of microstructure randomness and the generation of gradient materials through continuous interpolation in latent space using denoising diffusion implicit model (DDIM). Furthermore, the two-dimensional microstructure reconstruction was extended to three-dimensional framework and integrated permeability as a feature encoding embedding. This enables the conditional generation of three-dimensional microstructures for random porous materials within a defined permeability range. The permeabilities of these generated microstructures were further validated through the application of the lattice Boltzmann method. The above methods provide new ideas and references for material reverse design.

Efficient grain size evaluation based on single direction measurement of ultrasonic backscattering coefficient

<sec>GH4742 nickel-based superalloy exhibits excellent mechanical properties, and grain size is a key factor affecting its performance. A physical model-based ultrasonic backscattering method makes grain size measurement accurate and efficient. Nevertheless, it is constrained by complex models or multiple measurements taken from various beam angles. As a result, a backscattering coefficient method that requires only a single measurement for grain size evaluation is proposed. In contrast to the existing methods, the proposed method solely focuses on the backscattering coefficient component of the backscattering signal. It effectively eliminates the influence of unrelated factors, such as the measurement system and the acoustic field, through the utilization of reference signals.</sec><sec>The independent scattering model is employed to derive the backscattering coefficient, which solely pertains to the material itself. The relationship between grain size and backscattering coefficient is described by using a spatial correlation function. To consider the irrelevant factors, an experimental measurement method is developed by using the reference signals. Through numerical calculation and analysis, it has been observed that the backscattering coefficient is closely related to the frequency. When the product of the wavenumber and the grain size is significantly greater than 1 (<inline-formula><tex-math id="M1">\begin{document}$ ka\gg 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M1.png"/></alternatives></inline-formula>), a Stochastic scattering limit is reached. Conversely, when <inline-formula><tex-math id="M2">\begin{document}$ ka\ll 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M2.png"/></alternatives></inline-formula>, a Rayleigh scattering limit is observed. Furthermore, the backscattering coefficient is directly proportional to the grain size. As a general trend, larger grain sizes result in higher backscattering coefficient.</sec><sec>Three sets of GH4742 specimens with different grain sizes are prepared for phased array ultrasound experiments. It can be observed that the experimental backscattering coefficients, root mean square (RMS) values, and the amplitude trend of time domain signal are consistent. To perform grain size inversion, the backscattering coefficients in the effective bandwidth range of the probe are selected. By utilizing the least-square method, the theoretical backscattering coefficient is employed to fit the curves of the experimental backscattering coefficients. The evaluation results are compared with those obtained by metallographic analysis. The results show that the grain sizes obtained by the proposed method have a maximum relative error of –22.7% and a minimum relative error of –3.7%.</sec>

Multiscaling in the 3D critical site-diluted Ising ferromagnet

We study numerically the appearance of multiscaling behavior in the 3D ferromagnetic Ising site-diluted model, in the form of a multifractal distribution of the decay exponents for the spatial correlation functions at the critical temperature. We have computed the exponents of the long-distance decay of higher moments of the correlation function, up to the 10th power, by studying three different quantities: global susceptibilities, local susceptibilities and correlation functions. We have found very clear evidence of multiscaling behavior.

A three‐dimensional wideband mmWave multiple‐input multiple‐output channel model for aerial reconfigurable intelligent surface‐assisted communication systems

SummaryThis paper presents a wideband millimeter wave (mmWave) channel model for aerial reconfigurable intelligent surface (ARIS) communications, in which the reconfigurable intelligent surface (RIS) is attached to an unmanned aerial vehicle (UAV) to enable intelligent signal reflections in the air. The model is established according to standard 3GPP channel models and considers important propagation factors, for example, large‐scale fading, small‐scale fading, and radiation pattern of reflection units (RUs). In addition, the model assumes three‐dimensional (3D) rotations of RIS and can capture its effects on channel characteristics. Based on the model, we propose a design method for RIS reflection phases. Statistics including channel amplitude, spatial, temporal, and frequency correlation functions (CFs), and space‐Doppler power spectral density (SD‐PSD) are obtained. The impacts of RU number, UAV height and speed, and RIS rotation on channel statistics are investigated. Results suggest that the designed reflection phases can effectively mitigate multipath fading and Doppler effect. Compared to the yaw angle of the UAV platform, channel characteristics are more sensitive to the roll and pitch angles.

Exploring TEM Coherence Properties via Speckle Contrast Analysis in Coherent Electron Scattering of Amorphous Material

We investigate the coherence properties of a transmission electron microscope by analyzing nano-diffraction speckles originating from bulk metallic glass. The spatial correlation function of the coherent diffraction patterns, obtained in the transmission geometry, reveals the highly coherent nature of the electron probe beam and its spatial dimension incident on the sample. Quantitative agreement between the measured speckle contrast and an analytical model yields estimates for the transverse and longitudinal coherence lengths of the source. We also demonstrate that the coherence can be controlled by changing the beam convergence angle. Our findings underscore the preservation of electron beam coherence throughout the electron optics, as evidenced by the high-contrast speckles observed in the scattering patterns of the amorphous system. This study paves the way for the application of advanced coherent diffraction methodologies to investigate local structures and dynamics occurring at atomic-length scales across a diverse range of materials.

Ring-originated anisotropy of local structural ordering in amorphous and crystalline silicon dioxide

Rings comprising chemically bonded atoms are essential topological motifs for the structural ordering of network-forming materials. Quantification of such larger motifs beyond short-range pair correlation is essential for understanding the linkages between the orderings and macroscopic behaviors. Here, we propose two quantitative analysis methods based on rings. The first method quantifies rings by two geometric indicators: roundness and roughness. These indicators reveal the linkages between highly symmetric rings and crystal symmetry in silica and that the structure of amorphous silica mainly consists of distorted rings. The second method quantifies a spatial correlation function that describes three-dimensional atomic densities around rings. A comparative analysis among the functions for different degrees of ring symmetries reveals that symmetric rings contribute to the local structural order in amorphous silica. Another analysis of amorphous models with different orderings reveals anisotropy of the local structural ordering around rings; this contributes to building the intermediate-range ordering.

Flickering of a radio-signal due to an atmospheric turbulence

Background. Turbulent fluctuations of the refractive index in the atmosphere lead to distortions during the passage of the radio signal. This can lead to distortion of the transmitted information due to the resulting fluctuations of the amplitude, phase and intensity of the electromagnetic wave that transmits the radio signal. Fluctuations in the intensity of the radio signal lead to flickering of the radio signal on the receiving antenna due to turbulent phenomena in the atmosphere, which are a complex multifunctional physical phenomenon. Aim. The problem of fluctuation of the intensity of the radio signal at the receiving antenna due to atmospheric turbulence is considered the flicker of the radio signal. This problem is currently extremely actual, because there is a tendency of active, negative interference in the process of high-quality transmission of the radio signal on the background of naturally caused turbulent fluctuations. Methods. A theoretical analysis of the passage of a radio signal through a turbulent atmosphere is carried out. The spatial correlation function of fluctuations in the intensity of the received radio signal due to atmospheric turbulence is investigated. Results. The concept of the radio signal flicker characteristic is introduced as the average value of a random variable over the cross section of the receiving antenna the dispersion of the logarithm of the radio signal power. A model of the occurrence of fluctuations in the case of two regions in the cross section of the receiving antenna with different levels of radio signal intensity is calculated. The correlation function for this model is found. Conclusion. Based on the Fourier-spectrum expansion of the two-point spatial correlation function of turbulent fluctuations of the refractive index, the dependence of the flicker characteristic of the radio signal on the wave number of turbulent fluctuations of the atmosphere is found. It is shown that the turbulence of the atmosphere has the greatest effect on the radio signal when the length of the electromagnetic wave is comparable to the scale of turbulent fluctuations.

Scattering transform in microstructure reconstruction

AbstractDescriptor‐based microstructure characterization plays a crucial role in the field of reversed material engineering for random heterogeneous media. With the advent of differentiable microstructure characterization and reconstruction, there has been a growing interest in the development of differentiable formulations of descriptors. The search for effective descriptors becomes indispensable to adequately characterize a wide range of microstructures. This work proposes a novel approach to construct a descriptor by utilizing a wavelet‐based transformation called the scattering transformation on microstructure images. The characterization and reconstruction capabilities of this newly developed descriptor are compared to a benchmark descriptor based on spatial correlation functions using various 2D microstructure images. The comparative analysis aims to evaluate the effectiveness and potential advantages of the proposed wavelet‐based descriptor.

Spatial Channel Degrees of Freedom for Optimum Antenna Arrays

One of the ultimate goals of future wireless networks is to maximize data rates to accommodate bandwidth-hungry services and applications. Thus, extracting the maximum amount of information bits for given spatial constraints when designing wireless systems will be of great importance. In this paper, we present antenna array topologies that maximize the communication channel capacity for given number of array elements while occupying minimum space. Capacity is maximized via the development of an advanced particle swarm optimization (PSO) algorithm devising optimum standardized and arbitrarily-shaped antenna array topologies. Number of array elements and occupied space are informed by novel heuristic spatial degrees of freedom (SDoF) formulations which rigorously generalize existing SDoF formulas. Our generalized SDoF formulations rely on the differential entropy of three-dimensional (3D) angle of arrival (AOA) distributions and can associate the number of array elements and occupied space for any AOA distribution. The proposed analysis departs from novel closed-form spatial correlation functions (SCFs) of arbitrarily-positioned array elements for all classes of 3D multipath propagation channels, namely, isotropic, omnidirectional, and directional. Extensive simulation runs and comparisons with existing trivial solutions verify correctness of our SDoF formulations resulting in optimum antenna array topologies with maximum capacity performance and minimum space occupancy.