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Numerical evidence showing that the mean of  S = 1 ( n − 1 ) 2 ∑ i = 2 n ∑ j = 2 n ( − 1 λ i + λ j ) is well approximated by 1 / ( 2 p n ), for the Erdös Rényi ensemble with p ≥ 0.3.

For a given value of p, the colored asterisks show the sample mean of S as a function of n over 10 realizations (with error bars showing the standard deviation) and the black curve is 1 / ( 2 p n ).

The mean of S l ¯ b is large when l ¯ b → l b but close to zero when l ¯ b → l b + M / 2. However, S l ¯ b + M / 2 has the least impact on S l ¯ b, that is l ^ b least likely equals to l b   +  M/2.

For the Erdös Rényi ensemble with n nodes and edge probability p, we have E [ S ] → 1 / ( n C ) for C = 2 p. Figure 5 shows that the sample mean of S over 10 realizations (i.e. 10 different Erdös Rényi random graph configurations with the same parameters) rapidly approaches 1 / ( 2 p n ), as n increases, for values of p ranging from 0.3 to 0.9.

The bootstrap estimated mean of S mp in A. mellifera was significantly greater than the bootstrap estimated mean of S mp in Bombus spp. The rest of the comparisons (A. mellifera and lepidopterans; Bombus spp. and lepidopterans) were not statistically different.

From the above result, we conclude that for two positive numbers s and t, the geometric mean of Γ k ( s ) and Γ k ( t ) is greater than or equal to Γ k (arithmetic mean of s and t).

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The geometric mean of s-FSH was 10.9 (Table 1).

The distance between the means of S i and Si + 1 is μi + 1− μ i = Δi,1 + Δi + 1,0.

The half-life of the S100A4 protein was estimated by means of S-incorporation.

Since (U_{s}=chi (overline {mathcal {G}}_{s})), the above value is the mean of U s.

Distribution of mean of K s of Xanthomonas citri pv.

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