This paper presents an efficient probability analysis method using Fast Fourier transform taking into account that (1) a probability density function and its characteristic function are a pair of Fourier transforms, and (2) the characteristic function of the sum of statistically independent random variables is given by the product of the characteristic functions of each random variable.
Therefore, miRNAs, which are not upregulated, reduce their efficient probability to regulate their corresponding targets.
In the second step, exact graph isomorphism identification based on circuit simulation [ 27] is modified to make efficient probability graph isomorphic decision.
This approximation is then integrated in the design of an optimal polynomial controller, allowing for the efficient estimation of statistics and probability density functions of quantities of interest.
Thus, the efficient computation of marginal genotype probabilities using equation 4 requires an efficient algorithm to compute the likelihood.
A numerical strategy for the efficient estimation of set-valued failure probabilities, coupling Monte Carlo with optimization methods, is presented in this paper.
We have found in [ 1] that this method, there denoted by classRF, is far less efficient at probability estimation, and the consistency of the probability estimates thus produced has not been demonstrated in the literature.
We illustrate an additional tension between efficient and equilibrium states; the probability of contributing to the public good decreases with respect to out-degree in equilibrium, whereas it increases in the efficient state.
Previous work on the functional categories of putative transferred genes resulted in the complexity theory, which contemplates the negative correlation between the probability of efficient acquisition and participation of the transferred genes in complex interactions [ 5].
There is a large recent literature on analysis of two-stage case control designs using more efficient inverse probability weighted estimation procedures and semiparametric efficiency procedures [ 116].
