Redundancy, removal

The unnecessary parts would not be incorrect, only redundant. Removing them leaves a much simpler operation specification ... 

The redundancy removal based on the CRC32 matching eliminated the most obvious redundancy from TrEMBL. However tens of thousands of cases of potential (not easily detectable) redundancy, still need to be eliminated ... 

Forward- or backward adaptive predictors can be used to increase the redundancy removal capability of an audio coding scheme. In the case of high resolution filter banks backward adaptive predictors of low order have been used with success [Fuchs, 1995],... 

Removing redundant anchors - It is often the case that not all anchors in the anchor set are needed to compute the start time of an operation. This is due to the cascading effect of anchors that make some redundant in computing the start time. For a well-posed graph, we identify and remove the redundant anchors. Through redundancy removal, it is possible to obtain a smaller and faster control implementation because the start time depends on fewer offsets, and hence fewer synchronizations. 

The approach to heat exchanger network design discussed so far is based on the creation of an irreducible structure. No redundant features were included. Of course, when the network is optimized, some of the features might be removed by the optimization. The scope for the optimization to remove features results from the assumptions made during the creation of the initial structure. However, no attempt was made to deliberately include redundant features. 

An alternative approach is to create a reducible structure that deliberately includes redundant features and then subject this to optimization. Redundant features are then removed by the optimization. 

Once the quality of the dataset is defined, the next task is to improve it. Again, one has to remove outliers, find out and remove redundant objects (as they deliver no additional information), and finally, select the optimal subset of descriptors. 

We have already mentioned that real-world data have drawbacks which must be detected and removed. We have also mentioned outliers and redundancy. So far, only intuitive definitions have been given. Now, aimed with information theory, we are going firom the verbal model to an algebraic one. 

Although the problem of compilation of training and test datasets is crucial, unfortunately no de-faao standard technique has been introduced. Nevertheless, we discuss here a method that was designed within our group, and that is used quite successfully in our studies. The method is mainly addressed to the task of finding and removing redundancy. 

This scheme has all circuit breakers linked in a closed loop, with connections entering at the junction between breakers. This way, any connection may be isolated or any single circuit breaker removed without interrupting the other connections. This provides a higher level of redundancy than the systems mentioned above. Control and protective relaying issues are somewhat more complicated for this arrangement. 

Use of deoxy- in combination with an established trivial name (see Charts I and II) is straightforward if the formal deoxygenation does not affect the configuration at any asymmetric centre. However if deoxy removes a centre of chirality, the resulting names contain stereochemical redundancy. In such cases, systematic names are preferred, especially for the naming of derivatives. 

The values 1/V(dj dj) are for the atoms i and j, which make up this bond, and the connectivity index, x, is obtained as the sum of the bond connectivities. In molecules containing heteroatoms, the d values were considered to be equal to the difference between the number of valence electrons (E") and the number of hydrogen atoms (hi). Thus, for an alcoholic oxygen atom, d = 1, and d = 5. The valence connectivity-index, y can then be calculated the use of removes redundancies that can occur through the use of y alone. The calculation of connectivity indices and for the case of two isomeric heptanols is as follows. 

Filters are designed to remove unwanted information, but do not address the fact that processes involve few events monitored by many measurements. Many chemical processes are well instrumented and are capable of producing many process measurements. However, there are far fewer independent physical phenomena occurring than there are measured variables. This means that many of the process variables must be highly correlated because they are reflections of a limited number of physical events. Eliminating this redundancy in the measured variables decreases the contribution of noise and reduces the dimensionality of the data. Model robustness and predictive performance also require that the dimensionality of the data be reduced. 

The slow decay of the signal counter, unless it is boosted by fresh wins, serves a second purpose. While a large counter indicates a suitable region of the map for the insertion of a new unit, a very small value indicates the opposite. The unit may be of so little value to the network that it is a candidate for deletion (section 4.5). Unlike the SOM, not only can units be added in the GCS, they can also be removed, so the signal counter can be used to identify redundant areas of the network where pruning of a unit may enhance efficiency. 

Selection of the best sequences and removal of worst and redundant sequences so that the size of population stays constant. 

Currently, a good LP solver running on a fast (> 500 mHz) PC with substantial memory, solves a small LP in less than a second, a medium-size LP in minutes to tens of minutes, and a large LP in an hour or so. These codes hardly ever fail, even if the LP is badly formulated or scaled. They include preprocessing procedures that detect and remove redundant constraints, fixed variables, variables that must be at bounds in any optimal solution, and so on. Preprocessors produce an equivalent LP, usually of reduced size. A postprocessor then determines values of any removed variables and Lagrange multipliers for removed constraints. Automatic scaling of variables and constraints is also an option. Armed with such tools, an analyst can solve virtually any LP that can be formulated. 

The process has four separate subsystems for the degree-of-freedom analysis. Redundant variables and redundant constraints are removed to obtain the net degrees of freedom for the overall process. The 2 added to Nsp refers to the conditions of temperature and pressure in a stream +1 represents the heat transfer Q. 

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