scholarly journals Weakly non-Gaussian formula for the Minkowski functionals in general dimensions

2021 ◽  
Vol 104 (10) ◽  
Author(s):  
Takahiko Matsubara ◽  
Satoshi Kuriki
Keyword(s):  
Minkowski Functionals ◽  
Non Gaussian ◽  
Gaussian Formula

scholarly journals MINKOWSKI FUNCTIONALS AND CLUSTER ANALYSIS FOR CMB MAPS

1999 ◽  
Vol 08 (03) ◽  
pp. 291-306 ◽  
Author(s):  
D. NOVIKOV ◽  
HUME A. FELDMAN ◽  
SERGEI F. SHANDARIN
Keyword(s):  
Large Data ◽  
Threshold Level ◽  
Distribution Functions ◽  
Large Data Sets ◽  
Cumulative Distribution ◽  
Temperature Threshold ◽  
Data Sets ◽  
Minkowski Functionals ◽  
And Cluster Analysis ◽  
Non Gaussian

We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the cumulative distribution function and genus. We compute the distribution functions of the Partial Minkowski Functionals for the excursion set above or bellow a constant temperature threshold. Minkowski Functionals are additive and are translationally and rotationally invariant. Thus, they can be used for patchy and/or incomplete coverage. The technique is highly efficient computationally (it requires only O(N) operations, where N is the number of pixels per one threshold level). Further, the procedure makes it possible to split large data sets into smaller subsets. The full advantage of these statistics can be obtained only on very large data sets. We apply it to the 4-year DMR COBE data corrected for the Galaxy contamination as an illustration of the technique.

scholarly journals Non Gaussian Minkowski functionals and extrema counts for CMB maps

2014 ◽  
Vol 11 (S308) ◽  
pp. 61-66 ◽  
Author(s):  
Dmitri Pogosyan ◽  
Sandrine Codis ◽  
Christophe Pichon
Keyword(s):  
Cosmic Microwave Background ◽  
Orthogonal Polynomials ◽  
Gaussian Fields ◽  
Spherical Space ◽  
Matter Distribution ◽  
Microwave Background ◽  
Minkowski Functionals ◽  
Second Derivatives ◽  
Non Gaussian ◽  
The Universe

AbstractIn the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating the effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime example.

scholarly journals Non-Gaussian Minkowski functionals and extrema counts in redshift space

2013 ◽  
Vol 435 (1) ◽  
pp. 531-564 ◽  
Author(s):  
S. Codis ◽  
C. Pichon ◽  
D. Pogosyan ◽  
F. Bernardeau ◽  
T. Matsubara
Keyword(s):  
Minkowski Functionals ◽  
Non Gaussian

scholarly journals Non-Gaussian morphology on large scales: Minkowski functionals of the REFLEX cluster catalogue

2001 ◽  
Vol 377 (1) ◽  
pp. 1-16 ◽  
Author(s):  
M. Kerscher ◽  
K. Mecke ◽  
P. Schuecker ◽  
H. Böhringer ◽  
L. Guzzo ◽  
...  
Keyword(s):  
Minkowski Functionals ◽  
Non Gaussian

STATEMENT OF THE PROBLEM ON SYNTHESIS OF OPTIMAL EVALUATION OF SIGNAL PARAMETERS IN NON-GAUSSIAN NOISE

2012 ◽  
Vol 71 (17) ◽  
pp. 1541-1555
Author(s):  
V. A. Baranov ◽  
S. V. Baranov ◽  
A. V. Nozdrachev ◽  
A. A. Rogov
Keyword(s):  
Gaussian Noise ◽  
Signal Parameters ◽  
Non Gaussian ◽  
Optimal Evaluation

NONPARAMETRIC DECODING OF BLOCK CODES IN CHANNELS WITH NON-GAUSSIAN NOISE

2013 ◽  
Vol 72 (11) ◽  
pp. 1029-1038
Author(s):  
M. Yu. Konyshev ◽  
S. V. Shinakov ◽  
A. V. Pankratov ◽  
S. V. Baranov
Keyword(s):  
Gaussian Noise ◽  
Block Codes ◽  
Non Gaussian
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