Global sum

From the numerical results in the previous example we find that the global sum of squares of the concentrations of all trace elements in all wind directions amounts to ... 

Each eigenvector or contributes an amount X to the global sum of squares c of X. Hence, eigenvectors can be ranked according to their contributions to c. From now on we assume that the columns in U and V are arranged in decreasing order of their contributions. 

An important aspect of latent vectors analysis is the number of latent vectors that are retained. So far, we have assumed that all latent vectors are involved in the reconstruction of the data table (eq. (31.1)) and the matrices of cross-products (eq. (31.3)). In practical situations, however, we only retain the most significant latent vectors, i.e. those that contribute a significant part to the global sum of squares c (eq.(31.8)). 

A measure for the goodness of the reconstruction is provided by the relative contribution y of the retained latent vectors to the global sum of squares c (eq. (31.8)) ... 

Summation row-wise (horizontally) of the elements of a contingency table produces the vector of row-sums with elements Summation column-wise (vertically) yields the vector of column-sums with elements x j. The global sum is denoted by. These marginal sums are defined as follows ... 

The average or expected row-profile is obtained by dividing the marginal row in the original table by the global sum. The matrix F of deviations of row-closed profiles from their expected values is defined by ... 

In the case of the contingency Table 32.4 we obtained a chi-square of 15.3. Taking into account that the global sum equals 30, this produces a global interaction of 15.3/30 = 0.510. The square root of this value is the global distance of chi-square which is equal to 0.714. 

By storing a complete force array for the whole system, Newton s second law can be used which halves the force calculations that must be done during each time-step. But before the time-integration step the complete force array must be globally summed and then distributed to all nodes. When this has been done we can choose to integrate the whole system on each node and then go directly to the... 

Fig. 6 Decay-associated emission spectra (DAS) of Scenedesmus obL with open PS II reaction centers (F -state). Excitation at 630 nm. (see (19) for more details). The lifetimes are given in ps. (A) Results from the global sums-of-exponentials analysis. (B) Results from the global target analysis of the same data set.

Fig. 1.19 Demonstration of content addressable memory (CAM), (a) Global sum system realized by using an optical nano-fountain with three input-ports, (b) Broadcast system realized by using three nanophotonic switches...

One of the most important type of message passing operation is the global sum operation. This often occurs in molecular simulation where a... 

Figure 2. Example showing the paxailelisation of a simple force loop from a molecular d3mamics prt am. IDNODE ranges from 0 to NODES-1 and represents the processor number. Each step in the loop is taken by successive processors, eis shown for an eight processor system on the right of the figure. The call to the routine GDSUM at the end of the loop, will ensure a global sum for each one of the force vectors fi.

Figure 4- Results for parallel force evaluation (including anisotropic terms) for systems of Gay-Berne particles as described in reference [8]. The results use standard PVM calls on a Cray T3D. Improved performance over these results is possible by using cache-cache data transfers for the global sums at the end of the force evaluation.

A standard replicated data approach to parallelising this algorithm would involve each processor taking part in the energy evaluation, followed by a global sum operation (so that each processor could have the total energy... 

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