The phrase "associated to the difference" is not correct in standard written English.
The correct expression would be "associated with the difference."
Example: "The results were associated with the difference in temperature between the two samples."
Alternatives: "linked to the difference" or "related to the difference."
The swelling mechanism of PAH/PSS films is generally associated to the difference in charge density of polyelectrolyte chains induced by a change in the pH medium.
This technique consists of determining a stabilizing digital gain starting from a predetermined continuous-time controller, such that a performance criterion, associated to the difference between the continuous-time and discrete-time state trajectories, is minimized.
Note that difference equation (44) is not only theoretically but also practically solvable since the characteristic polynomial begin{aligned} p_{4}(lambda )=lambda ^{4}-a_{1}lambda ^{3}-b_{1} lambda ^{2}-c_{1}lambda -d_{1} end{aligned} (56) associated to the difference equation is of fourth order, which means that we can explicitly find its roots.
The gender effect was modelled to evaluate if any gene was associated to the difference in tumor growth observed between males and females.
As demonstrated in Table 4 and Figure 3, bias CItd-CIpc was most strongly associated to the difference CIpc-CItd(base) (rpart = -0.592 (evaluation-collective), rpart = -0.630 (validation-collective) and rpart = -0.606 (merged data); p < 0.001 for both collectives and merged data).
Based on the Dam methylation amplification results, a clear pattern was detected that could be associated to the differences between the two aphid variants.
To determine the metabolic signatures associated to the differences between age groups, loadings of the first predictive component of the OPLS-DA model were used, color coded according to the correlation coefficient of the variable [ 16] (Fig. S1).
Smoking is more prevalent among those with shorter education [ 7- 10], and this may associate to the difference in mortality rates between socioeconomic groups.
However, this is not the case since no significant differences were associated to the different type of medium.
The characteristic polynomial associated to the linear difference equation (58) is the following: P_{2}(lambda )=lambda ^{2}-alambda -c, from which it follows that the corresponding characteristic roots are given by the formulas in (39).
The same Cox proportional analysis was used to estimate the risk associated to the survival difference found by Kaplan-Meier curves in TNBC cohort.
