Sentence examples for same computations as from inspiring English sources

It then follows that p ∈ T p. Setting x ∗ = p and following the same computations as in the proof of Theorem 3.1, we have from inequality (3.2) that lim ∥ x n − p ∥ exists.

Then, the same computations as in the Euclidean case allow to prove an (H^1) bound on the curves (x^tau ) (i.e. an (L^2) bound on the metric derivatives (|(x^tau )'|)) and prove equicontinuity.

The paper describes the characteristics of the three parallelizations mentioned and analyzes them from the point of view of their performance, because all of them perform the same computations as the sequential algorithm and thus produce the same results.

In order to be able to also account for temporal relationships, the same computations as above were repeated on sliding windows of variable length (1-hour, 4-hour and 1 day), producing second-order features that capture spatio-temporal relationships, thus preserving useful source data properties.

We note that although we propose that people interpret color-coding systems by solving decoding assignment problems, we do not claim that there is some part of the brain that performs the same computations as in Matlab's linprog function using the merit scores defined with Eq. 2.

In each control, we applied the exact same computations as the ones described in the text, and verified that the results remain statistically significant.

This suggests that the biophysical oscillatory behavior of neurons and synapses leads to selecting the corresponding frequency of the inputs and performing the same computation as for the Hebbian linear case of the previous section: computing the correlation of the (filtered) inputs.

We repeat the same computation as in Figure 5.

In this case, each node performs the same computation as every other node, but on a subset of data.

Let (p ρ,q ρ and (P ρ,Q ρ be, respectively, the solution of Eq. (15) and (16) with ((bar {x}(cdot),bar {y}(cdot),bar {z}(cdot),bar {u}(cdot))) replaced by (x ρ,y ρ,z ρ,u ρ, and all the coefficients endowed with the superscript ρ. Then, the same computation as for Theorem 1 leads to: y_{rho}^{varepsilon}(0 -y_{rho}(0 -y_{rho}{rho}(0)+o(varepsilon), (62).

This choice allows at the same time to ease the computations as well as to infer some conclusions about the framework outlined in "The setting" section, as both models can describe the G-setting.