These results are based on new upper and lower bounds for these domains whose asymptotic expansions coincide up to the orders mentioned.
When applied to sequences of functionals of a general Gaussian field, our results can be combined with the Carbery Wright inequality in order to yield multidimensional entropic rates of convergence that coincide, up to a logarithmic factor, with those achievable in smooth distances (such as the 1-Wasserstein distance).
If it turned out that \ \textbf{P} = \textbf{NP}\), then the difficulty of these two tasks would coincide (up to a polynomial factor) for all problems in \ \textbf{NP}\).
In general, the parameters obtained with CAKE, gmkin, KinGUII and OpenModel coincided up to three significant digits when degradation was truly biphasic, i.e. when it became slower towards the end of the data series.
The sectional curvature K on (M^{n}) is defined by [3] (see also [18, 19]) begin{aligned} K Xwedge Y =frac{1}{ 2}[g R X,Y X,Y +g(R^ X,Y X,Y ], end{aligned}for any orthonormal vectors (X,Yin T_{p}M^{n},) (pin M^{n}.) In the case of the Levi-Civita connection, the above definition coincides (up to the sign) to the standard definition of the sectional curvature.
H3K4me3 and AcH3 signals coincided up to 1000 bp upstream and 500 bp downstream showing almost complete overlap on both sides of the transcriptional start sites.
Nevertheless, increases and decreases in copy number coincide with up- and downregulation in a number of cases.
Note that, for, the Hausdorff measure coincides, up to a positive multiplicative constant, with the Lebesgue measure in.
This result extends Theorem 1, where aggregation is done on the set of probability measures coinciding up to time t, i.e. exactly sharing the same view on all measurable sets up to time t.
In fact the set of possible distortion functions of subgroups of (F_2times F_2) coincides, up to a natural equivalence, with the set of Dehn functions of finitely presented groups [47].
This implies that the torsion tensor (mathrm{T}) is defined completely by its value on (T_e G), which is a linear map begin{aligned} T_e Gotimes T_e Grightarrow T_e G. end{aligned}This map coincides, up to sign, with the Lie bracket on (T_e G).
