Sentence examples for methods thus we from inspiring English sources

Note that even without including the higher-order stochastic integrals the Strang splitting integrator given by Eq. (24) performs considerably better in our numerical simulations than the Lie Trotter methods, thus we recommend to use this type of integrator.

However, it is almost impossible to obtain Bernoulli numbers by the ordinary recursive methods thus we hardly know the values of (zeta (2n)), if the argument is large enough.

One drawback of using radio-transmitters is that we could not obtain exact altitudes for the birds and had to estimate them (see methods); thus, we could only approximate atmospheric conditions during the flights.

The main purpose of the EGF/NRG1 example network is to illustrate the presented methods; thus, we tried to keep the network simple while still being biologically plausible.

For the hydrolysis of monosaccharides in S. cerevisiae, we estimate λ ∼ 3 ('Materials and methods'); thus we expect the success of invertase production to be strongly affected by colony geometry.

However, note that these qualitative aspects have not been included in the objective function (SSE) used by the optimization methods: thus, we cannot objectively and fairly compare the methods along this dimension.

We modify the proximal-gradient algorithm based on the viscosity proximation method; thus, we obtain strong convergence of results in [11].

Firstly, causal relationship between process variables is constructed based on the time delay estimation method, thus we can determine the alarms propagation path and then select the optimized variables.

This is the first large study which adapted comorbidity adjusted method, thus we decided to include relatively homogenous groups.

In contrast, the wAnaITG samples had varying genome coverage throughout the genome making CNVnator an unsuitable method; thus, we used experimental methods to directly quantify the differences in the genome coverage (see below).

It is well known, however, that these techniques are not well suited for assessing agreement between different analytical methods, and thus, we also analyzed our data according to the method by Bland and Altman [ 22, 23]: the differences between the two methods (bias = mGFR – eGFR) are plotted against the common mean values.