Forward pass

Square nodes in the ANFIS structure denote parameter sets of the membership functions of the TSK fuzzy system. Circular nodes are static/non-modifiable and perform operations such as product or max/min calculations. A hybrid learning rule is used to accelerate parameter adaption. This uses sequential least squares in the forward pass to identify consequent parameters, and back-propagation in the backward pass to establish the premise parameters. 

The learning procedure consists of two stages. In the forward pass training input data go forward the ANFIS architecture, and in the backward pass the error rates propagate backward, being the both the consequent and the membership parameters updated by gradient descent. 

Father Julius Arthur Nieuwland (1878-1936) did much of the early work on the polymerization of ethyne. He was born in Belgium and settled with his parents in South Bend, Indiana, two years later. He became a priest and a professor of botany and chemistry at the University of Notre Dame, where Knute Rockne—the inventor of the forward pass—worked for him as a research assistant. Rockne also taught chemistry at Notre Dame, but when he received an offer to coach the football team, he switched fields, in spite of Father Nieuwland s attempts to convince him to continue his work as a scientist. 

Several isotopomer separations have been reported for packed capillary FCCE. Deuterium-substituted phenylalanine showing no resolution during the first forward pass was almost baseline resolved after an 11 h separation time. Figure 24.17 shows a packed capillary FCCE separation of bromine-79 and bromine-81 using UV absorbance detection. After 6 h of ran time (Figure 24.17b), a distinct notch is seen in the bromide ion peak. The separation was maintained for over 60 forward passes requiring over 1100 min, and clear separation of the isotopes can easily be seen. > ... 

Figure 15.2 Each stage in Figure 15.3 has a pump to drive it, and the forward passing soiids stream is simpiy piumbed in together with the returning wash stream into the pump feed...

The Gaussian elimination procedure can therefore be considered as two operations, a forward pass and a backward pass. The objective of the forward pass is to transform the original matrix into an upper-triangular matrix. The backward pass calculates the unknown variables using the back substitution procedure. 

The forward pass of Gaussian elimination results in an upper triangular matrix, U, which has the general form... 

The right hand side of these equations is just the n column vectors of the identity matrix. Since A has been decomposed into U and L, then these n solutions for to o can be solved using the forward pass and backward pass equations given by (2.2.19) to (2.2.22). Finally A is synthesized by... 

On the other hand, the presupposed statistical independence diminishes with decreasing layer thickness, for the quality characteristics of adjacent raw material layers stacked in the blending bed tend to be correlated with one another. This phenomenon can most easily be visualized at the reversal points of the stacking operation. At the end of each forward pass and the beginning of each return pass of the stacker, material possessing the same properties is stacked in two successive layers. Thus the condition that the material must be stacked in discrete quantities At[t] is fulfilled only after every second layer, i.e., only every second layer contributes to the homogenization achieved in the blending bed. 

The second, forward pass, using the known value, is then identical with that for equal intervals, see Sect. 5.2, Eq. 5.43. Programming details can be seen in the program VARX in the final chapter. 

NOW THE SECOND, FORWARD PASS, STARTING WITH THE KNOWN CO... 

Steps 1-3 are known as the forward pass, while Steps 4-8 are known as the backward pass. 

The forward pass yields Earliest Start Times and Earliest Finish Times for each... 

Continuing the above process from Start to Stop and including all tasks yields on EFT for the entire project of 23 weeks. This is called the forward pass, that is, going from Start to Stop and determining ESTs and EFTs. We have accomplished one of our two purposes Determining the minimum time in which the project can be completed. 

This is called the backward pass, that is, going from Stop to Start and determining all the LFTs and LSTs. Having completed the forward pass and backward pass, we can identify the CP provided that we use this nomenclature ... 

The updating process is simply a matter of showing the new information on the network and then performing a new forward pass and backward pass. As a result of the update, the absolute completion time and/or the location of the CP are likely to change. Let s illustrate the updating process. Assume that you, as project manager, have periodically assessed the status of each task and the project is at the end of the week 10. The status of tasks is shown in Table 6.2. 

How long will it take The CPM answers this question in that the forward pass provides the EFT for the entire project. 

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