scholarly journals Statistical Reliability of Neighboring Range Bin Estimates of Coherent Fractional Contributions to Radar Backscattered Power

2011 ◽  
Vol 50 (3) ◽  
pp. 745-749 ◽  
Author(s):  
A. R. Jameson
Keyword(s):  
Correlation Function ◽  
Standard Deviation ◽  
Angular Velocity ◽  
Cross Correlation ◽  
Constant Angular Velocity ◽  
The Other ◽  
Incoherent Scatter ◽  
Statistical Reliability ◽  
Cross Correlations ◽  
Coherent Backscatter

Abstract It was recently demonstrated that magnitudes of the power-normalized cross-correlation functions of complex amplitudes in neighboring range bins are identical to the fractional contributions made by radar coherent backscatter in the direction of propagation to the total backscattered power in rain and snow. Here, a theoretical framework is presented for calculating the noise associated with estimates of these normalized cross correlations. This noise is identical to the statistical uncertainties in . Radar signals consist of two components: the usual incoherent backscatter often modeled by a Gaussian process and a coherent component modeled for the purposes of these calculations by a phasor C of fixed magnitude that rotates at a constant angular velocity ωC. Using the representation of the cross-correlation function as the average over the real part of the phasor dot products, it is found that the noise in this function comes from the dot products of C with the incoherent-scatter phasors in each range bin as well as the dot product between the two incoherent phasors. Furthermore, as long as ωC ≠ 0 and the number of statistically independent realizations (samples) k is sufficiently large, the noise is represented well by a normal distribution with mean 0 and with a variance that goes as 1/(2k). It is then shown that as the magnitude of C increases it acts to suppress the variance of . A formula is derived that gives the standard deviation of as a function of the number of statistically independent samples in the observation and the observed value of . Two examples, one in rain and the other in snow, are also presented.

scholarly journals On a Periodic Solution of the 4-Body Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-3 ◽  
Author(s):  
Jian Chen ◽  
Bingyu Li
Keyword(s):  
Periodic Solution ◽  
Angular Velocity ◽  
Periodic Motion ◽  
Equilateral Triangle ◽  
Sufficient Conditions ◽  
Constant Angular Velocity ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
The Masses ◽  
Necessary And Sufficient

We study the necessary and sufficient conditions on the masses for the periodic solution of planar 4-body problems, where three particles locate at the vertices of an equilateral triangle and rotate with constant angular velocity about a resting particle. We prove that the above periodic motion is a solution of Newtonian 4-body problems if and only if the resting particle is at the origin and the masses of the other three particles are equal and their angular velocity satisfies a special condition.

scholarly journals The role of galaxies and AGN in reionizing the IGM – III. IGM–galaxy cross-correlations at z ∼ 6 from eight quasar fields with DEIMOS and MUSE

2020 ◽  
Vol 494 (2) ◽  
pp. 1560-1578
Author(s):  
Romain A Meyer ◽  
Koki Kakiichi ◽  
Sarah E I Bosman ◽  
Richard S Ellis ◽  
Nicolas Laporte ◽  
...  
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Mean Free Path ◽  
Lyman Break Galaxies ◽  
The Galaxy ◽  
Cross Correlations ◽  
The Mean ◽  
Improved Model ◽  
First Time

ABSTRACT We present improved results of the measurement of the correlation between galaxies and the intergalactic medium transmission at the end of reionization. We have gathered a sample of 13 spectroscopically confirmed Lyman-break galaxies (LBGs) and 21 Lyman-α emitters (LAEs) at angular separations 20 arcsec ≲ θ ≲ 10 arcmin (∼0.1–4 pMpc at z ∼ 6) from the sightlines to eight background z ≳ 6 quasars. We report for the first time the detection of an excess of Lyman-α transmission spikes at ∼10–60 cMpc from LAEs (3.2σ) and LBGs (1.9σ). We interpret the data with an improved model of the galaxy–Lyman-α transmission and two-point cross-correlations, which includes the enhanced photoionization due to clustered faint sources, enhanced gas densities around the central bright objects and spatial variations of the mean free path. The observed LAE(LBG)–Lyman-α transmission spike two-point cross-correlation function (2PCCF) constrains the luminosity-averaged escape fraction of all galaxies contributing to reionization to $\langle f_{\rm esc} \rangle _{M_{\rm UV}\lt -12} = 0.14_{-0.05}^{+0.28}\, (0.23_{-0.12}^{+0.46})$. We investigate if the 2PCCF measurement can determine whether bright or faint galaxies are the dominant contributors to reionization. Our results show that a contribution from faint galaxies ($M_{\rm UV} \gt -20 \, (2\sigma)$) is necessary to reproduce the observed 2PCCF and that reionization might be driven by different sub-populations around LBGs and LAEs at z ∼ 6.

scholarly journals Direct Observations of Coherent Backscatter of Radar Waves in Precipitation

2010 ◽  
Vol 67 (9) ◽  
pp. 3000-3005 ◽  
Author(s):  
A. R. Jameson ◽  
A. B. Kostinski
Keyword(s):  
Wave Propagation ◽  
Correlation Function ◽  
Cross Correlation ◽  
Nearest Neighbor ◽  
Cross Correlation Function ◽  
Coherent Scatter ◽  
Direct Observations ◽  
The Cross ◽  
Coherent Backscatter ◽  
Backscattered Signals

Abstract In previous work, it was argued that a source of radar coherent scatter occurs in the direction perpendicular to the direction of wave propagation because of the presence of grids of enhanced particle concentrations with spatial periodicities in resonance with the radar wavelength. While convincing, the evidence thus far has been indirect. In this work the authors now present direct observations of radar coherent backscattered signals in precipitation in the direction of wave propagation. The theory is developed for the cross-correlation function of the complex amplitudes in the direction of propagation calculated for nearest neighbor range bins. Data are analyzed in snow and in rain. The results agree with the earlier conclusions in the previous work, namely that coherent scatter occurs in both rain and snow, that it is larger in snow than it is in rain, and that it can be significant at times.

Causality-in-mean and causality-in-variance among Bitcoin, Litecoin, and Ethereum

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Eray Gemici ◽  
Müslüm Polat
Keyword(s):  
Correlation Function ◽  
Design Methodology ◽  
Cross Correlation ◽  
Structural Breaks ◽  
The Other ◽  
Short Term ◽  
Content Type ◽  
Volatility Spillovers ◽  
Daily Period

Purpose This study aims to examine the volatility spillovers between Bitcoin (BTC), Litecoin (LTC) and Ethereum (ETH) as they are related to structural breaks. Design/methodology/approach This study examines the daily period from August 7, 2015 to July 10, 2018 by conducting causality-in-mean and causality-in-variance tests among cryptocurrencies. Findings The findings showed that there was one-way causality-in-mean from BTC to LTC and ETH, but there was no causality-in-mean from LTC and ETH to BTC. On the other hand, considering the structural breaks included in the variance equations, the estimation results showed that there were short-term causality-in-variance from LTC to BTC and long-term causality-in-variance from BTC to LTC. Originality/value This study fills the gap by contributing in two ways. First, to the best of the authors’ knowledge, this is the first study that used the cross-correlation function (CCF) of causality to explore causality-in-variance among cryptocurrencies. Second, this study considers the structural breaks in variance in the return series.

scholarly journals Multivariate Downscaling Approach Preserving Cross Correlations across Climate Variables for Projecting Hydrologic Fluxes

2017 ◽  
Vol 18 (8) ◽  
pp. 2187-2205 ◽  
Author(s):  
Rajarshi Das Bhowmik ◽  
A. Sankarasubramanian ◽  
Tushar Sinha ◽  
Jason Patskoski ◽  
G. Mahinthakumar ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Cross Correlation ◽  
Global Climate Model ◽  
Surface Fluxes ◽  
Monthly Precipitation ◽  
Climate Variables ◽  
Quantile Mapping ◽  
Precipitation Temperature ◽  
Cross Correlations ◽  
Precipitation And Temperature

Abstract Most of the currently employed procedures for bias correction and statistical downscaling primarily consider a univariate approach by developing a statistical relationship between large-scale precipitation/temperature with the local-scale precipitation/temperature, ignoring the interdependency between the two variables. In this study, a multivariate approach, asynchronous canonical correlation analysis (ACCA), is proposed and applied to global climate model (GCM) historic simulations and hindcasts from phase 5 of the Coupled Model Intercomparison Project (CMIP5) to downscale monthly precipitation and temperature over the conterminous United States. ACCA is first applied to the CNRM-CM5 GCM historical simulations for the period 1950–99 and compared with the bias-corrected dataset based on quantile mapping from the Bureau of Reclamation. ACCA is also applied to CNRM-CM5 hindcasts and compared with univariate asynchronous regression (ASR), which applies regular regression to sorted GCM and observed variables. ACCA performs better than ASR and quantile mapping in preserving the cross correlation at grid points where the observed cross correlations are significant while reducing fractional biases in mean and standard deviation. Results also show that preservation of cross correlation increases the bias in standard deviation slightly, but estimates observed precipitation and temperature with increased likelihood, particularly for months exhibiting significant cross correlation. ACCA also better estimates the joint likelihood of observed precipitation and temperature under hindcasts since hindcasts estimate the observed variability in precipitation better. Implications of preserving cross correlations across climate variables for projecting runoff and other land surface fluxes are also discussed.

scholarly journals X-ray cross-correlation analysis of the low-mass X-ray binary 4U 1636-53

2014 ◽  
Vol 10 (S306) ◽  
pp. 397-399
Author(s):  
Ya-Juan Lei
Keyword(s):  
Correlation Function ◽  
Correlation Analysis ◽  
Cross Correlation ◽  
X Rays ◽  
X Ray ◽  
Cross Correlation Analysis ◽  
Low Mass ◽  
Cross Correlations ◽  
The Cross ◽  
Positive Correlations

AbstractWe analyze the cross-correlation function of the soft and hard X-rays of the atoll source 4U 1636-53 with RXTE data. The results show that the cross-correlations evolve along the different branches of the color-color diagram. At the lower left banana states, we have both positive and ambiguous correlations, and positive correlations are dominant for the lower banana and the upper banana states. The anti-correlation is detected at the top of the upper banana states. The cross-correlations of two atoll sources 4U 1735-44 and 4U 1608-52 have been studied in previous work, and the anti-correlations are detected at the lower left banana or the top of the upper banana states. Our results show that, in the 4U 1636-53, the distribution of the cross-correlations in the color-color diagram is similar to those of 4U 1735-44 and 4U 1608-52, and confirm further that the distribution of cross-correlations in color-color diagram could be correlated with the luminosity of the source.

Analyzing kinesin and cytoplasmic-dynein driven movement with nanometer precision

1989 ◽  
Vol 47 ◽  
pp. 833-833
Author(s):  
B.J. Schnapp ◽  
J. Gelles ◽  
E. Steuer ◽  
M. P. Sheetz
Keyword(s):  
Correlation Function ◽  
Standard Deviation ◽  
Relative Position ◽  
Glass Surface ◽  
Cross Correlation ◽  
Video Sequence ◽  
Cytoplasmic Dynein ◽  
Bidirectional Transport ◽  
Dic Microscopy

Kinesin and cytoplasmic dynein are microtubule-based, force-generating ATPases thought to be involved in the bidirectional transport of vesicular organelles along microtubules. In vitro, kinesin and dynein promote movement of 0.1 - 0.2μm plastic beads toward the plus and minus ends, respectively, of microtubules. In these systems, the proteins are thought to remain fixed, by nonspecific absorption, to the bead surface. The motion of the bead on the microtubule is detected by video enhanced, DIC microscopy, and reflects the movement of the motor protein along the microtubule.To quantitate bead motion, a method was devised for tracking the position of kinesin or dynein coated beads moving along microtubules. The method involves 1) cross-correlation of a template bead image (the kernal) with each of the frames in a video sequence, followed by 2) calculation of the centroid of the cross-correlation function for each of the frames in the sequence. The centroid provides a measure of bead position. Application of this method to the measurement of the relative position of two stationary beads adsorbed nonspecifically to the glass surface indicates that the standard deviation of the measured horizontal and vertical coordinates can be less than 0.5 nm. More recently, we have determined that centroid calculation of the unprocessed bead image (i.e. without cross-correlation) can provide a measure of bead position with standard deviations in the horizontal and vertical directions of less than 2 nm. The latter method is faster, but more sensitive to the contrast and magnification of the video image.

scholarly journals The Cross-Correlation of Abell Clusters with the Lick Galaxy Counts

1988 ◽  
Vol 130 ◽  
pp. 550-550
Author(s):  
Per B. Lilje ◽  
G. Efstathiou
Keyword(s):  
Correlation Function ◽  
Luminosity Function ◽  
Cold Dark Matter ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Galactic Latitude ◽  
Abell Clusters ◽  
Theoretical Predictions ◽  
Cross Correlations ◽  
The Cross

We have analysed the cross-correlations between Abell clusters and the 10′ × 10′ Lick galaxy counts. The main new features of our analysis are as follows: (a) we correct for gradients in the Lick counts that depend only on galactic latitude; (b) we check the effects of applying a filter to remove (likely artificial) gradients on scales >20°; (c) redshifts for Abell clusters are used to compute a cross-correlation function wcg(σ), where σ = vϑ/Ho is the projected separation between a cluster with recession speed v and a galaxy at angular distance ν from the cluster centre; (d) the amplitude of the spatial cross-correlation function ξcg(r) is estimated using modern determinations of the galaxy luminosity function. Our results show that the shape of ξcg is reasonably well determined on scales r ≲20h−1 Mpc. On larger scales, the results depend sensitively on the corrections for large-scale gradients in the Lick counts. The results based on wcg(σ) are well described by a power-law model ξcg(r)≃(r/8.8h−1 Mpc)−2.2, while the angular cross-correlations for Abell clusters in distance class D=5 are better described by the model ξcg(r)=(r/6h−1 Mpc)−2.3 + (r/7h−1 Mpc)−1.7. Seldner and Peebles (1977) derived a larger amplitude for ξcg because they assumed a different luminosity function. We compare these results with theoretical predictions of ξcg in the Ω=1 biased cold dark matter (CDM) model. On scales 1 h−1 Mpc ≲ r ≲ 10 h−1 Mpc, the theoretical predictions for ξcg are in surprisingly good agreement with our observational estimates. On smaller scales, the CDM model gives too high an amplitude whereas on larger scales the predicted amplitude is too low. Neither of these discrepancies is particularly serious.

scholarly journals Segment Stock Market, Foreign Investors, and Cross-Correlation: Evidence from MF-DCCA and Spillover Index

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Nan Xu ◽  
Songsong Li
Keyword(s):  
Stock Market ◽  
Stock Markets ◽  
Multifractal Analysis ◽  
Cross Correlation ◽  
Spillover Effects ◽  
The Other ◽  
Foreign Investors ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
The Cross

Employing the tools of multifractal detrended cross-correlation analysis (MF-DCCA) and Diebold–Yilmaz spillover index (D.Y. spillover index), we examine the effect that the foreign investors have on the cross-correlations between the two-segment stock markets, that are the accessible and the inaccessible stock markets, and the other ten respective stock markets. The shares cross-listed by the same corporates on both the A-share and H-share stock markets of China serve as the best sample to compile the two stock indices, which stands for the inaccessible stock market (AHA) and the accessible stock market (AHH), respectively. Empirical results show that the cross-correlations between the two-segment stock markets and the other ten pairs are multifractal, the multifractal strength of cross-correlations is stronger in AHH than AHA, and the intensified growth of the multifractal cross-correlations in AHA can be seen as the increasing of the openness in the inaccessible market. The empirical result of D.Y. spillover index is consistent with the multifractal analysis above, and another interesting finding is that among the selected markets, the three markets with the strongest spillover effects with AHA and AHH are Taiwan, South Korea, and Singapore, respectively, and the weakest one is Australia during the sample scenarios.

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