The Real Space and Redshift Space Correlation Functions at Redshiftz= 1/3

1997 ◽  
Vol 479 (1) ◽  
pp. 82-89 ◽  
Author(s):  
C. W. Shepherd ◽  
R. G. Carlberg ◽  
H. K. C. Yee ◽  
E. Ellingson
Keyword(s):  
Correlation Functions ◽  
Real Space ◽  
Space Correlation ◽  
The Real

scholarly journals Statistical quality indicators for electron-density maps

2012 ◽  
Vol 68 (4) ◽  
pp. 454-467 ◽  
Author(s):  
Ian J. Tickle
Keyword(s):  
Electron Density ◽  
Statistical Significance ◽  
Significance Test ◽  
Real Space ◽  
Structure Model ◽  
Space Correlation ◽  
The Real ◽  
Difference Density ◽  
Density Maps ◽  
The Difference

The commonly used validation metrics for the local agreement of a structure model with the observed electron density, namely the real-space R (RSR) and the real-space correlation coefficient (RSCC), are reviewed. It is argued that the primary goal of all validation techniques is to verify the accuracy of the model, since precision is an inherent property of the crystal and the data. It is demonstrated that the principal weakness of both of the above metrics is their inability to distinguish the accuracy of the model from its precision. Furthermore, neither of these metrics in their usual implementation indicate the statistical significance of the result. The statistical properties of electron-density maps are reviewed and an improved alternative likelihood-based metric is suggested. This leads naturally to a χ2 significance test of the difference density using the real-space difference density Z score (RSZD). This is a metric purely of the local model accuracy, as required for effective model validation and structure optimization by practising crystallographers prior to submission of a structure model to the PDB. A new real-space observed density Z score (RSZO) is also proposed; this is a metric purely of the model precision, as a substitute for other precision metrics such as the B factor.

scholarly journals MAPPING THE REAL-SPACE DISTRIBUTIONS OF GALAXIES IN SDSS DR7. I. TWO-POINT CORRELATION FUNCTIONS

2016 ◽  
Vol 833 (2) ◽  
pp. 241 ◽  
Author(s):  
Feng Shi ◽  
Xiaohu Yang ◽  
Huiyuan Wang ◽  
Youcai Zhang ◽  
H. J. Mo ◽  
...  
Keyword(s):  
Correlation Functions ◽  
Real Space ◽  
The Real ◽  
Point Correlation

scholarly journals Evolution of the real-space correlation function from next generation cluster surveys

2017 ◽  
Vol 600 ◽  
pp. A32 ◽  
Author(s):  
Srivatsan Sridhar ◽  
Sophie Maurogordato ◽  
Christophe Benoist ◽  
Alberto Cappi ◽  
Federico Marulli
Keyword(s):  
Correlation Function ◽  
Real Space ◽  
Next Generation ◽  
Space Correlation ◽  
The Real

scholarly journals SIMULATIONS OF WIDE-FIELD WEAK-LENSING SURVEYS. II. COVARIANCE MATRIX OF REAL-SPACE CORRELATION FUNCTIONS

2011 ◽  
Vol 734 (2) ◽  
pp. 76 ◽  
Author(s):  
Masanori Sato ◽  
Masahiro Takada ◽  
Takashi Hamana ◽  
Takahiko Matsubara
Keyword(s):  
Covariance Matrix ◽  
Correlation Functions ◽  
Real Space ◽  
Weak Lensing ◽  
Wide Field ◽  
Space Correlation

scholarly journals Recovering the real-space correlation function from photometric redshift surveys

2009 ◽  
Vol 394 (3) ◽  
pp. 1631-1639 ◽  
Author(s):  
Pablo Arnalte-Mur ◽  
Alberto Fernández-Soto ◽  
Vicent J. Martínez ◽  
Enn Saar ◽  
Pekka Heinämäki ◽  
...  
Keyword(s):  
Correlation Function ◽  
Real Space ◽  
Space Correlation ◽  
The Real ◽  
Photometric Redshift ◽  
Redshift Surveys

scholarly journals Current Trends in Random Walks on Random Lattices

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1148
Author(s):  
Jewgeni H. Dshalalow ◽  
Ryan T. White
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Real Time ◽  
Real Space ◽  
Historical Background ◽  
Escape Time ◽  
The Real ◽  
Current Trends ◽  
One Step ◽  
Time Position

In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing.

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