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Although Borel was not the first to define a conventional sum of a v series (a series of numbers that does not approach a certain number; see infinite series), he was the first to conceive and develop a systematic theory of such series (1899).
In the case of the real semiring, the final score for two sequences is the (conventional) sum of all possible paths generating those two sequences, where the weights in each path are (conventionally) multiplied.
Outfit is based on the conventional sum of squared standardized residuals.
The outfit statistic is a conventional sum of squared standardized residual.
One such approach will be evaluated in this study and compared with the conventional sum score.
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The cost functions investigated correspond to logistic regression, homoscedastic Gaussian (i.e. conventional sum-of-squares) regression and heteroscedastic Gaussian regression.
Different from the conventional sum-power constraint across all transmit antennas, we consider individual power constraints per antenna at the base station.
Again using a conventional sums of squares decomposition, the variability in weekly predictions was 19% spatial and 79% temporal, with the 2% remainder attributable to noise.
Using a conventional sums of squares decomposition, the variability in weekly predictions at the grid points shown in Figure S3 was 12% spatial and 87% temporal, with the remainder attributable to rounding error.
Higher PM10 concentrations near both major and minor roadways are evident (Supporting Information Figure S6), as is the importance of temporal compared to spatial variability: Using a conventional sums of squares decomposition, the variability in predicted values at these grid points was 7% spatial and 93% temporal.
To avoid "overfitting" problems, we chose an adequate regularisation method involving the modification of the conventional mean sum of the squares of the network errors by the addition of a term equal to the sum of the squares of the network synaptic weights and bias (Derras et al. 2012, 2014).
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