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On the estimation variance for the specific Euler–Poincaré characteristic of random networks
Author(s) -
Tscheschel A.,
Stoyan D.
Publication year - 2003
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1046/j.1365-2818.2003.01194.x
Subject(s) - estimator , simple (philosophy) , poisson distribution , variance (accounting) , euler's formula , mathematics , topology (electrical circuits) , euler characteristic , computer science , statistical physics , mathematical analysis , statistics , physics , combinatorics , philosophy , accounting , epistemology , business
Summary The specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.