Estimate of Stochastic Process Frequency-Time Parameters

2017 ◽  
pp. 521-582
Author(s):  
Vyacheslav Tuzlukov
Keyword(s):  
Stochastic Process ◽  
Time Parameters

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Cleavage of Human Embryos: Options and Diversity

Acta Naturae ◽  
2016 ◽  
Vol 8 (3) ◽  
pp. 88-96
Author(s):  
Yu. K. Doronin ◽  
I. V. Senechkin ◽  
L. V. Hilkevich ◽  
M. A. Kurcer
Keyword(s):  
Time Lapse ◽  
Reproductive Technologies ◽  
Human Embryos ◽  
Imaging Data ◽  
Noninvasive Methods ◽  
Topographic Features ◽  
Time Parameters ◽  
Embryo Cleavage ◽  
Time Lapse Imaging ◽  
Developmental Dynamics

In order to estimate the diversity of embryo cleavage relatives to embryo progress (blastocyst formation), time-lapse imaging data of preimplantation human embryo development were used. This retrospective study is focused on the topographic features and time parameters of the cleavages, with particular emphasis on the lengths of cleavage cycles and the genealogy of blastomeres in 2- to 8-cell human embryos. We have found that all 4-cell human embryos have four developmental variants that are based on the sequence of appearance and orientation of cleavage planes during embryo cleavage from 2 to 4 blastomeres. Each variant of cleavage shows a strong correlation with further developmental dynamics of the embryos (different cleavage cycle characteristics as well as lengths of blastomere cycles). An analysis of the sequence of human blastomere divisions allowed us to postulate that the effects of zygotic determinants are eliminated as a result of cleavage, and that, thereafter, blastomeres acquire the ability of own syntheses, regulation, polarization, formation of functional contacts, and, finally, of specific differentiation. This data on the early development of human embryos obtained using noninvasive methods complements and extend our understanding of the embryogenesis of eutherian mammals and may be applied in the practice of reproductive technologies.

Matching as a Stochastic Process

2013 ◽  
Author(s):  
Friedel Bolle ◽  
Philipp E. Otto
Keyword(s):  
Stochastic Process
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