Sentence examples for methods we derive from inspiring English sources

However, in this section, by using different methods, we derive the Kakutani fixed point theorem.

First of all, applying the harmonic balance methods, we derive the corresponding harmonic balance equations for networks of identical nonlinear systems with delay couplings.

Through an in-depth analysis of the interaction of the two filtering methods, we derive a tight bound that reduces the number of tuples retrieved during query processing while guaranteeing the correct query results.

Applying the developed missing data methods, we derive the estimation procedures for Poisson regression model with missing outcomes based on auxiliary outcomes and a validated sample for true outcomes.

By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions.

Thus, in Methods, we derive again the main results of MCA without relying on such an assumption.

Using GLIMMIX based on these linearization methods, we derived formulas for power and sample size calculations for longitudinal designs with attrition over time.

For both methods, we derived their features on our dataset and applied their techniques.

Using curve fitting (described in detail in methods), we derived IC50 values for each inhibitor in the presence of the three different activators.

Using the procedure described in Materials and Methods, we derived 525 sequence profiles from the archaeal proteomes (complete list is given in Additional File 4) and matched them to the sequences of the arCOGs.

Methods: We derived and compared apparent temperature (AT) and heat wave days (with heat waves defined as ≥ 2 days of daily mean AT ≥ 95th percentile of warm-season average) from weather observations and six different forecast products.