scholarly journals Calibration schemes with O(N log N) scaling for large-N radio interferometers built on a regular grid

2020 ◽  
Vol 500 (1) ◽  
pp. 66-81 ◽  
Author(s):  
Deepthi B Gorthi ◽  
Aaron R Parsons ◽  
Joshua S Dillon
Keyword(s):  
Cross Correlation ◽  
Future Generations ◽  
Regular Grid ◽  
Resource Requirement ◽  
Traditional Architecture ◽  
Large N ◽  
Time Calibration ◽  
Cross Correlations ◽  
Computational Resources ◽  
Redundant Arrays

ABSTRACT Future generations of radio interferometers targeting the 21 cm signal at cosmological distances with N ≫ 1000 antennas could face a significant computational challenge in building correlators with the traditional architecture, whose computational resource requirement scales as $\mathcal {O}(N^2)$ with array size. The fundamental output of such correlators is the cross-correlation products of all antenna pairs in the array. The FFT-correlator architecture reduces the computational resources scaling to $\mathcal {O}(N\log {N})$ by computing cross-correlation products through a spatial Fourier transform. However, the output of the FFT-correlator is meaningful only when the input antenna voltages are gain- and phase-calibrated. Traditionally, interferometric calibration has used the $\mathcal {O}(N^2)$ cross-correlations produced by a standard correlator. This paper proposes two real-time calibration schemes that could work in parallel with an FFT-correlator as a self-contained $\mathcal {O}(N\log {N})$ correlator system that can be scaled to large-N redundant arrays. We compare the performance and scalability of these two calibration schemes and find that they result in antenna gains whose variance decreases as 1/log N with increase in the size of the array.

scholarly journals Detrended Multiple Cross-Correlation Coefficient applied to solar radiation, air temperature and relative humidity

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Andrea de Almeida Brito ◽  
Heráclio Alves de Araújo ◽  
Gilney Figueira Zebende
Keyword(s):  
Relative Humidity ◽  
Solar Radiation ◽  
Solar Energy ◽  
Correlation Coefficient ◽  
Air Temperature ◽  
Cross Correlation ◽  
Global Solar Radiation ◽  
Meteorological Variables ◽  
Hourly Data ◽  
Cross Correlations

AbstractDue to the importance of generating energy sustainably, with the Sun being a large solar power plant for the Earth, we study the cross-correlations between the main meteorological variables (global solar radiation, air temperature, and relative air humidity) from a global cross-correlation perspective to efficiently capture solar energy. This is done initially between pairs of these variables, with the Detrended Cross-Correlation Coefficient, ρDCCA, and subsequently with the recently developed Multiple Detrended Cross-Correlation Coefficient, $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2. We use the hourly data from three meteorological stations of the Brazilian Institute of Meteorology located in the state of Bahia (Brazil). Initially, with the original data, we set up a color map for each variable to show the time dynamics. After, ρDCCA was calculated, thus obtaining a positive value between the global solar radiation and air temperature, and a negative value between the global solar radiation and air relative humidity, for all time scales. Finally, for the first time, was applied $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2 to analyze cross-correlations between three meteorological variables at the same time. On taking the global radiation as the dependent variable, and assuming that $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}={\bf{1}}$$DMCx2=1 (which varies from 0 to 1) is the ideal value for the capture of solar energy, our analysis finds some patterns (differences) involving these meteorological stations with a high intensity of annual solar radiation.

Auto and Cross Correlation Measurements in a Turbine Cascade Using a Digital Correlator

1982 ◽  
Author(s):  
P. J. Bryanston-Cross ◽  
J. J. Camus
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Cross Correlation ◽  
Turbine Blades ◽  
Image Plane ◽  
Strongly Correlated ◽  
Trailing Edge ◽  
Number Range ◽  
Cross Correlations ◽  
Digital Correlator

A simple technique has been developed which samples the dynamic image plane information of a schlieren system using a digital correlator. Measurements have been made in the passages and in the wakes of transonic turbine blades in a linear cascade. The wind tunnel runs continuously and has independently variable Reynolds and Mach number. As expected, strongly correlated vortices were found in the wake and trailing edge region at 50 KHz. Although these are strongly coherent we show that there is only limited cross-correlation from wake to wake over a Mach no. range M = 0.5 to 1.25 and variation of Reynolds number from 3 × 105 to 106. The trailing edge fluctuation cross correlations were extended both upstream and downstream and preliminary measurements indicate that this technique can be used to obtain information on wake velocity. The vortex frequency has also been measured over the same Mach number range for two different cascades. The results have been compared with high speed schlieren photographs.

Cross-Correlations in the Brownian Motion of Colloidal Nanoparticles

2020 ◽  
Vol 65 (1-2) ◽  
pp. 27-34
Author(s):  
Sz. Kelemen ◽  
◽  
L. Varga ◽  
Z. Néda ◽  
◽  
...  
Keyword(s):  
Brownian Motion ◽  
Power Law ◽  
Cross Correlation ◽  
Colloidal Particles ◽  
Pearson Correlation ◽  
Transverse Component ◽  
Collective Effects ◽  
Colloidal Nanoparticles ◽  
Diffusive Motion ◽  
Cross Correlations

"The two-body cross-correlation for the diffusive motion of colloidal nano-spheres is experimentally investigated. Polystyrene nano-spheres were used in a very low concentration suspension in order to minimize the three- or more body collective effects. Beside the generally used longitudinal and transverse component correlations we investigate also the Pearson correlation in the magnitude of the displacements. In agreement with previous studies we find that the longitudinal and transverse component correlations decay as a function of the inter-particle distance following a power-law trend with an exponent around -2. The Pearson correlation in the magnitude of the displacements decay also as a power-law with an exponent around -1. Keywords: colloidal particles, Brownian motion, cross-correlation. "

Assessing Convergence in Predictions of Periodic-Unsteady Flowfields

2006 ◽  
Author(s):  
J. P. Clark ◽  
E. A. Grover
Keyword(s):  
Cross Correlation ◽  
Unsteady Flows ◽  
Digital Signal ◽  
Design Decisions ◽  
Time Resolved ◽  
Design Engineers ◽  
Cross Correlations ◽  
Parseval’S Theorem ◽  
Hot Streak

Predictions of time-resolved flowfields are now commonplace within the gas-turbine industry, and the results of such simulations are often used to make design decisions during the development of new products. Hence it is necessary for design engineers to have a robust method to determine the level of convergence in design predictions. Here we report on a method developed to determine the level of convergence in a predicted flowfield that is characterized by periodic-unsteadiness. The method relies on fundamental concepts from digital signal processing including the discrete Fourier transform, cross-correlation, and Parseval’s theorem. Often in predictions of vane-blade interaction in turbomachines, the period of the unsteady fluctuations is expected. In this method, the development of time-mean quantities. Fourier components (both magnitude and phase), cross-correlations, and integrated signal power are tracked at locations of interest from one period to the next as the solution progresses. Each of these separate quantities yields some relative measure of convergence that is subsequently processed to form a fuzzy set. Thus the overall level of convergence in the solution is given by the intersection of these sets. Examples of the application of this technique to several predictions of unsteady flows from two separate solvers are given. These include a prediction of hot-streak migration as well as more typical cases. It is shown that the method yields a robust determination of convergence. Also, the results of the technique can guide further analysis and/or post-processing of the flowfield. Finally, the method is useful for the detection of inherent unsteadiness in the flowfield, and as such it can be used to prevent design escapes.

scholarly journals Cross-Correlations in Meat Prices in Brazil: A Non-Linear Approach Using Different Time Scales

Economies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 133
Author(s):  
Derick Quintino ◽  
José Telo da Gama ◽  
Paulo Ferreira
Keyword(s):  
Time Scales ◽  
Cross Correlation ◽  
Positive Association ◽  
Recent Period ◽  
Linear Approach ◽  
Long Run ◽  
Short Run ◽  
Cross Correlations ◽  
Over Time ◽  
Different Time Scales

Brazil is one of the world’s largest producers and exporters of cattle, chicken and swine. Therefore, co-movements of Brazilian meat prices are important for both domestic and foreign stakeholders. We propose to analyse the cross-correlation between meat prices in Brazil, namely, cattle, swine and chicken, including also in the analysis information from some commodities, namely maize, soya beans, oil, and the Brazilian exchange rate. Our sample covers the recent period which coincided with extensive macroeconomic and institutional changes in Brazil, from 2011 to 2020, and is divided in two periods: (i) presidential pre-impeachment (P1), occurring in August 2016, and; (ii) post-impeachment (P2). Our results indicate that in P1, only the prices of swine and chicken showed a positive and strong correlation over time, and that cattle showed some positive correlation with chicken only in the short run. In P2, there was also a positive and consistent correlation between swine and chicken, and only a positive association with swine and cattle in the long run. For more spaced time scales (days), the changes in the degree of correlation were significant only in the long run for swine and cattle.

scholarly journals Assessing the Wet Deposition Mechanism of Benzo(a)pyrene in the Atmosphere by MF-DCCA

Atmosphere ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 331 ◽  
Author(s):  
Chunqiong Liu ◽  
Kai Shi ◽  
Jian Liang ◽  
Hongliang Huang
Keyword(s):  
Time Scale ◽  
Wet Deposition ◽  
Cross Correlation ◽  
Coefficient Of Determination ◽  
Scaling Properties ◽  
Temporal Scaling ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
One Year

Based on the 19 year observation from 1998 to 2016 at the Tsuan Wan and Central/Western District monitoring stations in Hong Kong, the aim of this paper was to assess the wet deposition pathway of Benzo(a)pyrene (BaP) on a large time-scale. In order to achieve this goal, multi-fractal detrended cross-correlation analysis (MF-DCCA) was used to characterize the long-term cross-correlations behaviors and multi-fractal temporal scaling properties between BaP (or PM2.5) and precipitation. The results showed that the relationships between BaP and precipitation (or PM2.5) displayed long-term cross-correlation at the time-scale ranging from one month to one year; no cross-correlation between each other was observed in longer temporal scaling regimes (greater than one year). These results correspond to the atmospheric circulation of the Asian monsoon system and are explained in detail. Similar dynamic processes of the wet deposition of BaP and PM2.5 suggested that the main removal process of atmospheric BaP was rainfall deposits of PM2.5-bound BaP. Furthermore, cross-correlations between BaP (or PM2.5) and precipitation at the long time-scale have a multi-fractal nature and long-term persistent power-law decaying behavior. The temporal evolutions of the multi-fractality were investigated by the approach of a sliding window. Based on the evolution curves of multi-fractal parameters, the wet deposition pathway of PM2.5-bound BaP is discussed. Finally, the contribution degree of wet deposition to PM2.5-bound BaP was derived from the coefficient of determination. It was demonstrated that about 45% and 60% of atmospheric BaP removal can be attributed to the wet deposition pathway of PM2.5-bound BaP for the Tsuan Wan and Central/Western District areas, respectively. The findings in this paper are of great significance for further study on the removal mechanism of atmospheric BaP in the future. The MF-DCCA method provides a novel approach to assessing the geochemical cycle dynamics of BaP.

scholarly journals Modeling Complex System Correlation Using Detrended Cross-Correlation Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Keqiang Dong ◽  
Hong Zhang ◽  
You Gao
Keyword(s):  
Complex System ◽  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Correlation Property ◽  
Traffic Time Series ◽  
Cross Correlations ◽  
The Cross ◽  
Active Research

The understanding of complex systems has become an area of active research for physicists because such systems exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails, and fractality. We here focus on traffic dynamic as an example of a complex system. By applying the detrended cross-correlation coefficient method to traffic time series, we find that the traffic fluctuation time series may exhibit cross-correlation characteristic. Further, we show that two traffic speed time series derived from adjacent sections exhibit much stronger cross-correlations than the two speed series derived from adjacent lanes. Similarly, we also demonstrate that the cross-correlation property between the traffic volume variables from two adjacent sections is stronger than the cross-correlation property between the volume variables of adjacent lanes.

Analyzing the Impact of COVID-19 on the Cross-Correlations between Financial Search Engine Data and Movie Box Office

2020 ◽  
pp. 2150021
Author(s):  
Renyu Wang ◽  
Yujie Xie ◽  
Hong Chen ◽  
Guozhu Jia
Keyword(s):  
Financial Market ◽  
Cross Correlation ◽  
Multifractal Spectrum ◽  
Movie Industry ◽  
Box Office ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
The Cross ◽  
Google Search ◽  
The Impact

This paper explores the COVID-19 influences on the cross-correlation between the movie market and the financial market. The nonlinear cross-correlations between movie box office data and Google search volumes of financial terms such as Dow Jones Industrial Average (DJIA), NASDAQ and PMI are investigated based on multifractal detrended cross-correlation analysis (MF-DCCA). The empirical results show there are nonlinear cross-correlations between movie market and financial market. Metrics such as Hurst exponents, singular exponents and multifractal spectrum demonstrate that the cross-correlation between movie market and financial market is persistent, and the cross-correlation in long term is more stable than that in short term. In the COVID-19 period, the multifractal features of cross-correlation become stronger implying that COVID-19 enhanced the complexity between the movie industry and the financial market. Furthermore, through the rolling window analysis, the Hurst exponent dynamic trends indicate that COVID-19 has a clear influence on the cross-correlation between movie market and financial market.

scholarly journals Investigations of Broad Line Region Structure and Kinematics Using Variability

1989 ◽  
Vol 134 ◽  
pp. 93-95
Author(s):  
C. Martin Gaskell ◽  
Anuradha P. Koratkar ◽  
Linda S. Sparke
Keyword(s):  
Time Series ◽  
Cross Correlation ◽  
Sampling Interval ◽  
Broad Line ◽  
Line Flux ◽  
Line Region ◽  
Cross Correlations ◽  
The Mean ◽  
The Cross ◽  
The Continuum

Gaskell and Sparke (1986) showed that one can determine the sizes of BLRs more accurately that the mean sampling interval by cross-correlating the continuum flux time series with a line flux time series. The position of the peak in the cross-correlation function (CCF) and its shape give an indication of the BLR size. The technique is explained in detail in Gaskell and Peterson (1987). The widely propagated misunderstanding is that the method involves simply interpolating both time series and cross-correlating them (in which case the CCF is dominated by the cross-correlations of “made-up” data). Actually the method involves cross correlating the observed points in one time series (continuum, say) with the linear interpolations of the other series (line flux). The line flux time series must always be smoother than the continuum time series it is derived from. We have usually employed the method with the interpolation done both ways round and averaged them (to reduce errors due to the interpolation) and we can intercompare the two results (to investigate errors).

Time-Series and Dynamic Cross-Correlations Analysis on Unexpected Information: Evidence from Media News and Online Postings

2019 ◽  
Vol 19 (02) ◽  
pp. 2050011
Author(s):  
Yan Li ◽  
Xiangyu Kong ◽  
Xiao Li ◽  
Zuochao Zhang
Keyword(s):  
Mass Media ◽  
New Media ◽  
Trading Volume ◽  
Cross Correlation ◽  
Short Term ◽  
Cross Correlations ◽  
The Cross ◽  
The One ◽  
The Relationship

In this paper, we investigate the relationship between unexpected information from postings and news, and the unexpected information is measured by the residual of regressions of trading volume on numbers of news or postings. We mainly find that (i) There are significant positive contemporaneous correlations between the unexpected information coming from postings and different kinds of news; the correlation between the unexpected information coming from postings and new media news is stronger than that between the unexpected information coming from postings and mass media news; (ii) The unexpected information coming from postings could cause the unexpected information coming from news, but only the unexpected information coming from the mass media news could cause that coming from postings; (iii) There are persistent power-law cross-correlations between the unexpected information coming from postings and that coming from mass media news and new media news. The cross-correlation between the unexpected information coming from postings and new media news is more persistent than the one between the unexpected information coming from postings and mass media news. The cross-correlations are all more stable in long term than in short term. We attribute our findings above to the dissemination speed of the information on the Internet.

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