• Publications of The Korean Astronomical Society
• /
• v.7 no.1
• /
• pp.25-30
• /
• 1992

Recent redshift surveys suggest that most galaxies may be distributed on the surfaces of bubbles surrounding large voids. To investigate the quantitative consistency of this qualitative picture of large-scale structure, we study analytically the clustering properties of galaxies in a universe filled with spherical shells. In this paper, we report the results of the calculations for the spatial and angular two-point correlation functions of galaxies. With ${\sim}20%$ of galaxies in clusters and a power law distribution of shell sizes, $n_{sh}(R){\sim}R^{-{\alpha}}$, ${\alpha}\;{\simeq}\;4$, the observed slope and amplitude of the spatial two-point correlation function ${\xi}_{gg}(r)$ can be reproduced. (It has been shown that the same model parameters reproduce the enhanced cluster two-point correlation function, ${\xi}_{cc}(r)$). The corresponding angular two-point correlation function $w({\theta})$ is calculated using the relativistic form of Limber's equation and the Schecter-type luminosity function. The calculated w(${\theta}$) agrees with the observed one quite well on small separations (${\theta}{\lesssim}2deg$).

• Proceedings of the Optical Society of Korea Conference
• /
• 2008.07a
• /
• pp.187-189
• /
• 2008

The spatial coherence function of multy-mode beam was measured by using a Sagnac interferometer and self referencing technique. For leaner polarization laser beam passing through a multy-mode fiber, its change value of spatial mode and polarization from stress of faber and input coupling angle. And each spatial mode have each polarizations, when we simulation Wigner distribution function and Spatial Correlation function of spatial multi-mode beam by using Hermit Gaussian modes leaner sum. We measured spatial coherence function of using by multy-mode fiber. One can use this measurement method to study and characterize the property of multy-mode light field coming out of GRIN multy-mode fiber.

• Journal of Korea Water Resources Association
• /
• v.40 no.12
• /
• pp.943-956
• /
• 2007

Among various statistics, the spatial correlation function, that is "correlogram", is frequently used to evaluate or design the rain gauge network and to model the rainfall field. The spatial correlation structure of rainfall has the significant variation due to many factors. Thus, the variation of spatial correlation structure of rainfall causes serious problems when deciding the spatial correlation function of rainfall within the basin. In this study, the spatial rainfall structure was modeled using bivariate mixed distributions to derive monthly spatial correlograms, based on Gaussian and lognormal distributions. This study derived the correlograms using hourly data of 28 rain gauge stations in the Keum river basin. From the results, we concluded as following; (1) Among three cases (Case A, Case B, Case C) considered, the Case A(+,+) seems to be the most relevant as it is not distorted much by zero measurements. (2) The spatial correlograms based on the lognormal distribution, which is theoretically as well as practically adequate, is better than that based on the Gaussian distribution. (3) The spatial correlation in July exponentially decrease more obviously than those in other months. (4) The spatial correlograms should be derived considering the temporal resolution(hourly, daily, etc) of interest.

• International Journal of High-Rise Buildings
• /
• v.5 no.2
• /
• pp.95-103
• /
• 2016

One of the key problems in the design of high-rise commercial complex is how to guide reasonable pedestrian distribution in commercial space. In this study, pedestrian distribution in three high-rise commercial complexes in Shanghai and Hong Kong was studied using spatial configuration analysis software Space Syntax and quantification of physical elements in commercial spaces, such as functional attractiveness, entrances, escalators, level variations and passage width. Additionally, in an attempt to integrate functions with spatial integration and spatial depth, two combination variables, the spatial coefficient of function (IF) and spatial depth coefficient of function (F/D), were proposed. The results of the correlation analysis and multiple regression analyses reflected the following: (1) Regarding the influence on pedestrian distribution, there was a synergistic and complementary relationship between function and space; (2) The comprehensive flow distribution analytic model could successfully interpret flow distribution in high-rise commercial complexes and its R Square ranged up to about 70% in the three cases; (3) The spatial coefficient of function (IF) and spatial depth coefficient (F/D) could effectively integrate functions and spatial configuration, which could help close the gap between over-emphasis on function in commercial research and the lack of consideration of function in space-syntax analysis.

• Journal of Power System Engineering
• /
• v.4 no.2
• /
• pp.40-45
• /
• 2000

Some engineering materials are often known to have considerable spatial variation in their resisting strength and other properties. The objective of this study is to investigate the averaging effect and the applicability of extremal statistic for the statistical size effect. In the present study, it is assumed that the material property is a stationary random process in space. The theoretical autocorrelation function of the material strength are discussed for several correlation lengths. And, in order to investigate the statistical size effect, the material properties was simulated by using the non-Gaussian random process method. The material properties were plotted on the Weibull probability papers. The main results are summarized as follows: The autocorrelation function of the material properties are almost independent of the averaging length. The variance decreases with increasing the averaging length. As correlation length is smaller, the slope is larger. And also, it was found that Weibull statistics based on the weakest-link model could not explain the spatial variation of material properties with respect to the size effect satisfactory.

• Journal of Internet of Things and Convergence
• /
• v.8 no.2
• /
• pp.79-84
• /
• 2022

This paper presents an enhancement method of document restoration capability which is robust for security, loss, and contamination, It is based on two methods, that is, encryption and DnCNN(DeNoise Convolution Neural Network). In order to implement this encryption method, a mathematical model is applied as a spatial frequency transfer function used in optics of 2D image information. Then a method is proposed with optical interference patterns as encryption using spatial frequency transfer functions and using mathematical variables of spatial frequency transfer functions as ciphers. In addition, by applying the DnCNN method which is bsed on deep learning technique, the restoration capability is enhanced by removing noise. With an experimental evaluation, with 65% information loss, by applying Pre-Training DnCNN Deep Learning, the peak signal-to-noise ratio (PSNR) shows 11% or more superior in compared to that of the spatial frequency transfer function only. In addition, it is confirmed that the characteristic of CC(Correlation Coefficient) is enhanced by 16% or more.

• Geomechanics and Engineering
• /
• v.17 no.6
• /
• pp.565-572
• /
• 2019

Spatial variability is an inherent characteristic of soil, and auto-correlation length (ACL) is a very important parameter in the reliability or probabilistic analyses of geotechnical engineering that consider the spatial variability of soils. Current methods for estimating the ACL need a large amount of laboratory or in-situ experiments, which is a great obstacle to the application of random field theory to geotechnical reliability analysis and design. To estimate the ACL reasonably and efficiently, we propose a micro-structure based numerical simulation method. The quartet structure generation set algorithm is used to generate stochastic numerical micro-structure of soils, and scanning electron microscope test of soil samples combined with digital image processing technique is adopted to obtain parameters needed in the QSGS algorithm. Then, 2-point correlation function is adopted to calculate the ACL based on the generated numerical micro-structure of soils. Results of a case study shows that the ACL can be estimated efficiently using the proposed method. Sensitivity analysis demonstrates that the ACL will become stable with the increase of mesh density and model size. A model size of $300{\times}300$ with a grid size of $1{\times}1$ is suitable for the calculation of the ACL of clayey soils.

• Steel and Composite Structures
• /
• v.11 no.2
• /
• pp.115-130
• /
• 2011

Considering the randomness of material parameters in the laminated composite plate, a scheme of stochastic finite element method to analyze the displacement response variability is suggested. In the formulation we adopted the concept of the weighted integral where the random variable is defined as integration of stochastic field function multiplied by a deterministic function over a finite element. In general the elastic modulus of composite materials has distinct value along an individual axis. Accordingly, we need to assume 5 material parameters as random. The correlations between these random parameters are modeled by means of correlation functions, and the degree of correlation is defined in terms of correlation coefficients. For the verification of the proposed scheme, we employ an independent analysis of Monte Carlo simulation with which statistical results can be obtained. Comparison is made between the proposed scheme and Monte Carlo simulation.

• ETRI Journal
• /
• v.30 no.3
• /
• pp.355-364
• /
• 2008

Multiple-input multiple-output (MIMO) systems can provide significant increments in capacity; however, the capacity of MIMO systems degrades severely when spatial correlation among multipath channels is present. This paper demonstrates that the influence of shadowing on the channel capacity is more substantial than that of multipath fading; therefore, the shadowing effect is actually the dominant impairment. To overcome the composite fading effects, we propose combining macroscopic selection diversity (MSD) schemes with MIMO technology. To analyze the system performance, the capacity outage expression of MIMO-based MSD (MSD-MIMO) systems using a characteristic function is applied. The analytic results show that there are significant improvements when MSD schemes are applied, even for the two-base-station diversity case. It is also observed that the effect of spatial correlation due to multipath fading is almost negligible when multiple base stations cooperatively participate in the mobile communication topology.

• The Bulletin of The Korean Astronomical Society
• /
• v.46 no.2
• /
• pp.72.3-73
• /
• 2021

Baryon Acoustic Oscillations (BAO) are caused by acoustic density waves in the early universe and act as a standard ruler in the clustering pattern of galaxies in the late Universe. Measuring the BAO feature in the 2-point correlation function of a sample of galaxies allows us to estimate cosmological distances to the galaxies mean redshift, , which is important for testing and constraining the cosmology model. The BAO feature is also expected to appear in the higher order statistics. In this work we measure the generalized spatial N-point point correlation functions up to 4th order. We made measurements of the 2, 3, and 4-point correlation functions in the SDSS-III DR12 CMASS data, comprising of 777,202 galaxies. The errors and covariances matrices were estimated from 500 mock catalogues. We created a theoretical model for these statistics by measuring the N-point functions in halo catalogues produced by the approximate Lagrangian perturbation theory based simulation code, PINOCCHIO. We created simulations using initial conditions with and without the BAO feature. We find that the BAO is detected to high significance up to the 4-point correlation function.