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For σ > σ c, robustness to both noise and mutation evolved.
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To sum up, the changeability of each gene expression level by noise and mutation was correlated, for a robust evolved system.
However, GRNs that have achieved robustness to noise and mutation through evolution may have some constraints among expressions of different genes.
When the system has achieved robustness to noise and mutation through evolution, the fitness level changes only to a small degree (i.e., remains almost neutral) against a considerable amount of change in the GRNs due to mutation [ 21].
Indeed, the evolved robust GRN has some constraint on the errors by noise and mutation, as plotted in Figure 4. To achieve higher robustness, there needs to be some correlation between the changes in the expression statuses of genes.
A technique called "sliding windows" addresses both noise and delay.
We assumed that the observed (log) data for each probe consisted of either noise or both noise and signal, plus an array-specific noise.
The necessity of fluctuation for evolution to increase robustness to noise and to mutation needs theoretical examination.
Indeed, this relationship was confirmed by the evolutionary stability theory and numerical simulations [ 14, 16], which imply that robustness to noise and to mutation are correlated.
Both measurement noise and cellular variation contribute to this distribution.
> As ABR threshold shifts in mutants were stable with age, attempts were made to test whether interactions between environmental noise and the mutations were a cause of the progressive hearing loss reported in human subjects.
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