Sentence examples for representation with the same from inspiring English sources

Then there exists a sublinear expectation (hat{mathbb{E}}) on (mathbb {D}_{0}(R^,R^{d})) such that the canonical process ((X_{t})_{tgeq 0}) is a G-Lévy process satisfying Levy-Khintchine representation with the same set (mathcal{U}).

On the left is the backbone representation and on the right is the surface representation with the same color scheme.

Mean and standard deviation were calculated for the number of partial reads across the targeted breakpoint region, and z-score for each base was calculated and used to detect breakpoint based on over-representation of tags with the same start/stop position.

Fourth, although our studies deal with images with 8-bit representation, the same conclusions are valuable for images with wider dynamic ranges, i.e., hyperspectral data [4].

The second fold is that in each matrix representation learning, different patterns represented with the same matrix representation can carry different information.

(d) The classical line plot representation of the same data with (c).

In comparing the results from the anatomically complex model with a more simplified representation of the same dataset, we provide a first glimpse into differences made by fine structural detail on the electrical activation dynamics as well as elucidate instances where global activation patterns are similar.

In Figure S3 in the Supporting Information all apparent Raman peak positions of CuO, Cu4O3, Cu2O, and crystalline anatase TiO2 were marked on an additional representation of the same data, shown there with no offset between the spectra, and on a logarithmic intensity scale.

We generated a table, in which products are grouped according to pharmacotherapeutic group and mechanism of action and the route of administration is shown, to provide a representation of all drugs with the same indication.

Representation is the same as Fig. 2.

Figure 5 is a graphical representation of the same data.