In this paper, we investigate the asymptotical behavior for a partial sum sequence of independent random variables, and we derive a law of the iterated logarithm type.
D-PNN could create better long-time models based on a partial sum DE solution, than a standard ANN time-series prediction (based on entire pattern definitions too).
We define the function S k which is a partial sum of f ∈ A by S k ( z ) = z + ( a k k ) z k, k ≥ 2, a k ≠ 0. (2).
In such a case, the solution can be found approximately as a partial sum of the series, (u_{n} overline{x},t)=sum_{k=0}^{n}f _{k} overline{x}) t^{alpha k}) in some reasonable interval of t, and thus the overall errors can be made smaller by adding more new terms as shown in the following case.
Finally, in practice one wants to approximate the function with a finite number of terms, let's say with a Taylor polynomial or a partial sum of the trigonometric series, respectively.
Each such value is exactly S z, j) plus a partial sum of the values in v g.
In the k-mer counting example, the combiner emits a partial sum from the subset of 1s it evaluates, and the reduce function sums over the list of partial sums.
The C3 algorithm also uses a two-day guard band, but calculates a partial sum for the last three days of the positive deviation of the current value from the mean [ 6].
Its size- O(n) memory allocation (where n is the sum of all contingency table entries) could be avoided by reordering the calculation; it is only necessary to track a few partial sums.
While studying the software, we made two additional observations: Its size- O (n ) memory allocation (where n is the sum of all contingency table entries) could be avoided by reordering the calculation; it is only necessary to track a few partial sums.
