The resulting symmetric value of similarity between any two articles is rooted in the invariance of the hypergeometric distribution in Eq. (2) under permutation of the pair i and j, i.e., of the two quantities (d_{i}), (d_{j}).
In particular, we update the corresponding elements of points p s k ∈ ℬ p by suitably increasing the probability values: for each point p i ∈ P, the new probability value S p ′ ( p i, p s k ) (and its symmetric value S ′ p ( p s k, p i ) ) is evaluated as S p ′ ( p i, p s k ) = S p ( p i, p s k ) ⋅ exp ( ν ⋅ f QLCP ( T, δ ) ), (15).
Therefore we analytically derive a unique and symmetric value of error for each region of the UBP and this determined the sensitivity of peak detection in two ways (Methods S1).
Unfortunately, implementing quadrature circuits brings always a challenge of matching the in-phase (I) and quadrature (Q) rails, which should ideally have symmetric component values.
The distribution of the symmetric difference values for the original non-swapped data is depicted on Figure 2B.
In accordance with the hypothesis of symmetric gait, values of opposite foot strike (not expressed in percentage of gait cycle, i.e., 0.501 ± 0.008) were not found significantly different from 0.5 (P = 0.476).
The overall distribution of probabilities of these two groups of genes is roughly bimodal in both driver lists, which allowed us to choose these symmetric cutoff values (Fig. 2 and Supplementary Fig. S2) such as 0.3 and 0.7 for LoF and Act genes, respectively.
The Tau value reached was 0.653 (p < 0.001) for the dependent variable, with a symmetric "Cu" value of 0.836 (p = 0.048), a value that implied that the knowledge of one variable reduced 83%% of the error when forecasting the values of the other.
After the obtained p-values were transformed in minus log scale with base 10, the symmetric p-value matrix was visualized as a heat map (Figure 9).
Symmetric boundary value problems (BVPs) are commonplace in electromagnetics and generally in science and engineering.
