If we denote the average transmit power, required to satisfy target SINRs at K s users selected through NUS from a pool of K users, by pN(K s, K), this can be obtained by computing the expectations in the following expression: p N ( K s, K ) ≤ γ ∑ i = 1 K s E F ∥ h ∥ 2 ( M, K s + 1 - i, K ; x ) 1 x E F sin 2 θ ( i - 1 ) ( M ; x ) 1 x.
Hence, with optimal ordering (the weaker user gets decoded with no interference), the lower bound on the average transmit power can be obtained by computing the expectations in the following expression: p L ( 2, K ) = γ E F ∥ h ∥ 2 ( M, 2, K ; x ) 1 x + E F ∥ h ∥ 2 ( M, 1, K ; x ) 1 x E F sin 2 θ 1 ( M, 1, K - 1 ; x ) 1 x (53).
Further, we calculated the average time needed for reprogramming by computing the expectation of time arriving in state n (n=4) on the condition that the cell is still alive: Expectation (cell cycles needed for reprogramming |can be reprogrammed) = 8.72 cell cycles.
When (mathcal{Y}(t)) is commutative, i.e., (y(t)) is a classical measurement process (by the spectral theorem [32], Theorem 3.3), the optimal filter in the least squares sense is obtained by computing the conditional expectation onto (mathcal{Y}(t)) [5, 32].
One might select the model order K by arg max p(K| x, y) with K ∈{0,1,…, Kmax} and also can perform parameter estimation by computing the conditional expectation E(θ K | x, y) based on (10) shown subsequently.
We tested this expectation by computing the Spearman rank correlation between the length of each ORF in the genome and the quantile of its true mRNA folding energy compared with the null distribution.
In the case of a single flow (i.e., ) we can easily carry out value iteration numerically, by discretizing the argument and values of and computing the expectation and maximization numerically.
Random genome-wide expectation for eQTL was calculated by computing the number of eQTL associated with a random set of 537 genes (the number of genes which overlap CNV regions).
Parameters were estimated by computing the maximum likelihood estimation of the parameters without any approximation of the model (that is, no linearization) using the stochastic approximation expectation maximization algorithm combined with a Markov chain Monte Carlo procedure.
Statistical physics suggests to compute the expectation with respect to this Gibbs measure (the posterior mean in the synchronization problem), by minimizing the so-called Thouless-Anderson-Palmer (TAP) free energy, instead of the mean field (MF) free energy.
