scholarly journals The clustering of critical points in the evolving cosmic web

2021 ◽  
Vol 502 (3) ◽  
pp. 3885-3910
Author(s):  
J Shim ◽  
S Codis ◽  
C Pichon ◽  
D Pogosyan ◽  
C Cadiou
Keyword(s):  
Critical Points ◽  
Acoustic Oscillation ◽  
Gaussian Random Fields ◽  
Exclusion Zone ◽  
Qualitative Comparison ◽  
Baryonic Acoustic Oscillation ◽  
Non Linear ◽  
Cross Correlations ◽  
The Cross ◽  
Small Separation

ABSTRACT Focusing on both small separations and baryonic acoustic oscillation scales, the cosmic evolution of the clustering properties of peak, void, wall, and filament-type critical points is measured using two-point correlation functions in ΛCDM dark matter simulations as a function of their relative rarity. A qualitative comparison to the corresponding theory for Gaussian random fields allows us to understand the following observed features: (i) the appearance of an exclusion zone at small separation, whose size depends both on rarity and signature (i.e. the number of negative eigenvalues) of the critical points involved; (ii) the amplification of the baryonic acoustic oscillation bump with rarity and its reversal for cross-correlations involving negatively biased critical points; (iii) the orientation-dependent small-separation divergence of the cross-correlations of peaks and filaments (respectively voids and walls) that reflects the relative loci of such points in the filament’s (respectively wall’s) eigenframe. The (cross-) correlations involving the most non-linear critical points (peaks, voids) display significant variation with redshift, while those involving less non-linear critical points seem mostly insensitive to redshift evolution, which should prove advantageous to model. The ratios of distances to the maxima of the peak-to-wall and peak-to-void over that of the peak-to-filament cross-correlation are ${\sim} \sqrt{2}$ and ${\sim} \sqrt{3}$, respectively, which could be interpreted as the cosmic crystal being on average close to a cubic lattice. The insensitivity to redshift evolution suggests that the absolute and relative clustering of critical points could become a topologically robust alternative to standard clustering techniques when analysing upcoming surveys such as Euclid or Large Synoptic Survey Telescope (LSST).

scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

scholarly journals Non-central limit theorems for functionals of random fields on hypersurfaces

2020 ◽  
Vol 24 ◽  
pp. 315-340
Author(s):  
Andriy Olenko ◽  
Volodymyr Vaskovych
Keyword(s):  
Rate Of Convergence ◽  
Central Limit ◽  
Random Fields ◽  
Limit Theorems ◽  
Gaussian Random Fields ◽  
Central Limit Theorems ◽  
Integral Functionals ◽  
Asymptotic Results ◽  
Non Linear ◽  
Linear Integral

This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in ℝd. We obtain the rate of convergence for these functionals. The results extend recent findings for solid figures. We apply the obtained results to the case of sojourn measures and demonstrate different limit situations.

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 Disentangling interstellar plasma screens with pulsar VLBI: combining auto- and cross-correlations

2019 ◽  
Vol 488 (4) ◽  
pp. 4963-4971 ◽  
Author(s):  
D Simard ◽  
U-L Pen ◽  
V R Marthi ◽  
W Brisken
Keyword(s):  
Angular Position ◽  
Angular Separation ◽  
Pulsar Emission ◽  
Scattering Geometry ◽  
Interstellar Plasma ◽  
Single Station ◽  
Cross Correlations ◽  
The Mean ◽  
The Cross ◽  
Scattering Systems

Abstract Current methods of measuring distances to pulsar scattering screens rely on a single screen dominating the scintillation pattern. We present a novel technique to reconstruct the scattered flux of a pulsar and solve for the scattering geometry in cases where the scattering environment along the line of sight to the pulsar is complex and may be composed of multiple scattering screens. This technique combines interferometric visibilities with cross-correlations of single-station intensities. It takes advantage of the fact that if one considers the interference of radiation from two points in the scattered image in delay–delay rate space, the visibilities are sensitive to the mean angular position of the points, while the cross-correlated intensities are sensitive to their angular separation. By combining the visibilities and the cross-correlated intensities, it is possible to measure the angular locations of both points in the pair. We show that this technique is able to reconstruct the published scattering geometry of PSR B0834+06. We then apply this technique to one-dimensional simulations of more complicated scattering systems, where we find that it can distinguish features from different scattering screens. This technique holds promise for studies of the interstellar medium and pulsars themselves: It will allow the application of scintillometry techniques, such as resolving pulsar emission regions using interstellar scattering, to sources for which a current lack of understanding of the scattering environment has precluded their use.

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.

Multiscale Multifractal Detrended Cross-Correlation Analysis of High-Frequency Financial Time Series

2019 ◽  
Vol 18 (03) ◽  
pp. 1950014 ◽  
Author(s):  
Jingjing Huang ◽  
Danlei Gu
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
High Frequency ◽  
Cross Correlation ◽  
Financial Time Series ◽  
Chinese Market ◽  
Change Of Scale ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
The Cross

In order to obtain richer information on the cross-correlation properties between two time series, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA). This method is based on the Hurst surface and can be used to study the non-linear relationship between two time series. By sweeping through all the scale ranges of the multifractal structure of the complex system, it can present more information than the multifractal detrended cross-correlation analysis (MF-DCCA). In this paper, we use the MM-DCCA method to study the cross-correlations between two sets of artificial data and two sets of 5[Formula: see text]min high-frequency stock data from home and abroad. They are SZSE and SSEC in the Chinese market, and DJI and NASDAQ in the US market. We use Hurst surface and Hurst exponential distribution histogram to analyze the research objects and find that SSEC, SZSE and DJI, NASDAQ all show multifractal properties and long-range cross-correlations. We find that the fluctuation of the Hurst surface is related to the positive and negative of [Formula: see text], the change of scale range, the difference of national system, and the length of time series. The results show that the MM-DCCA method can give more abundant information and more detailed dynamic processes.

scholarly journals OBSERVATIONAL H(z) DATA AS A COMPLEMENTARITY TO OTHER COSMOLOGICAL PROBES

2009 ◽  
Vol 24 (21) ◽  
pp. 1699-1709 ◽  
Author(s):  
HUI LIN ◽  
CHENG HAO ◽  
XIAO WANG ◽  
QIANG YUAN ◽  
ZE-LONG YI ◽  
...  
Keyword(s):  
Cosmic Microwave Background ◽  
Acoustic Oscillation ◽  
Microwave Background ◽  
Shift Parameter ◽  
Data Set ◽  
Flat Universe ◽  
Baryonic Acoustic Oscillation ◽  
Cosmological Observations

In this paper, we use a set of observational H(z) data (OHD) to constrain the ΛCDM cosmology. This data set can be derived from the differential ages of the passively evolving galaxies. Meanwhile, the [Formula: see text]-parameter, which describes the Baryonic Acoustic Oscillation (BAO) peak, and the newly measured value of the Cosmic Microwave Background (CMB) shift parameter [Formula: see text] are used to present combinational constraints on the same cosmology. The combinational constraints favor an accelerating flat universe while the flat ΛCDM cosmology is also analyzed in the same way. We obtain a result compatible with that by many other independent cosmological observations. We find that the observational H(z) data set is a complementarity to other cosmological probes.

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