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The result of average beam pattern is given by Theorem 3. Theorem 3: Using the presented PODB method, the average beam pattern, which is defined as P ̃ ≜ E [ P ] = E 1 K F 2. when ϕ ≠ ϕ0, can be approximated by P ̃ ≈ P ̃ a = 1 K + K - 1 K 2 J 1 ( α , 0 ) α , 0 2 + J 1 ( α , 0 ) α , 0 ∑ m = 1 M q m ς , m (26).
To represent the association between the RDM pattern and the EC sub-subclass, we define a reaction pattern profile for each RDM pattern, which is defined as x= x1, x2,…, x| EC |) T, where the k-th element is the number of reported reactions for the k-th EC sub-subclass.
We also analyzed the 'tissue specificity index' as a measure of expression pattern, which is defined as: where n is the number of tissues analyzed, E j the expression level of the gene in the jth tissue and Emax the maximum expression level of the gene across the n tissues (13 , 18.
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The PFC nanoparticles accumulated in all investigated mice in the shape of a hollow sphere at the rim of the edema pattern, which was defined by increased T2 values in comparison to surrounding muscle tissue (Fig. 3, Fig. 1B).
However, the distribution of mirror areas did not strictly follow a divergent pattern, which was defined as displaying more dissimilarity in sympatry than in allopatry for both taxa.
Then, we introduce the error pattern for each node, which is defined as {e_{Omega_{k}}(i)} triangleq { d_{k}(i }-{left[sumlimits_{li }-{left[sumlimits}(i) boldsymbolpsi_{lini)right]}^{H}{bOmega_{k} x_{k}(i)}.
Much less is known about the pattern of participation restriction, which is defined as "problems an individual may experience in involvement in life situations" and refers to the personal and societal consequences of health conditions [ 3].
In this paper we make an estimation of protein-protein interaction affinity derived from the law of mass action, i.e., a ij = x iu x iv There is another way to measure the co-expression pattern of the edges, which is defined by the absolute value of the difference between the two proteins, i.e., a ij = | x iu - x iv|.
The next step is to constrain the generated pattern spatially by multiplication with another Gaussian, which is defined on the plane P and chosen to be rotationally symmetric.
The calibration pattern plane is pasted on the wall, which is defined by 10×× 4 tags with 0.2 m × 0.2 m size of each tag and 0.2 m space between two tags.
In addition, we calculate a feature for each location which is defined by PROSITE patterns that are typical for this location.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com