Implicit knowledge

Second, neural networks that may store knowledge implicitly and find appropriate answers after presentation of training patterns or structures (cf Section 8.2) are exploited. Neural networks are built at present by using conventional programming languages. In the future, however, parallel operating computers or transputers will be applied. 

In 1972, however, Mori [15] showed that if a fixed (finite) basis is used, i.e., a basis which is independent of b, then the R and S matrices defined above are independent of the value of b used. If, of course, the finite basis is changed to satisfy the log derivative b.c. s at Anj then the results do depend on b. However, no regular procedure for improving the results by varying the basis and b has ever been established (to my knowledge). Implicit in Mori s work, however, is the idea that one should use basis "functions which are defined in a wider region than the internal region" [15]. 

There are also approaches [, and M] to control that have had marked success and which do not rely on quantum mechanical coherence. These approaches typically rely explicitly on a knowledge of the internal molecular dynamics, both in the design of the experiment and in the achievement of control. So far, these approaches have exploited only implicitly the very simplest types of bifiircation phenomena, such as the transition from local to nonnal stretch modes. If fiittlier success is achieved along these lines m larger molecules, it seems likely that deliberate knowledge and exploitation of more complicated bifiircation phenomena will be a matter of necessity. 

Neural networks have the following advantages (/) once trained, their response to input data is extremely fast (2) they are tolerant of noisy and incomplete input data (J) they do not require knowledge engineering and can be built direcdy from example data (4) they do not require either domain models or models of problem solving and (5) they can store large amounts of information implicitly. 

Both the.se methods have weaknesses. The historical data, implicit in both, may not be appropriate for the component in the assumed environment for the particular circumslances considered and may be irrelevant because of design rectification based on knowledge of previous failure. The broad approach may then be unduly pessimistic. On the other hand, the fault tree may fail to identify a primary cause which may have been missed by the plant designer to underestimate the probability of failure. The fault tree approach also takes credit for the preventative measures which may not be present in practice. The broad approach is likely to overestimate the risks because of insufficient account of preventative measures. The PSA team used the broad approach, recognizing that more accuracy may be attained by detailed industry studies. 

This then provides a physical derivation of the finite-difference technique and shows how the solution to the differential equations can be propagated forward in time from a knowledge of the concentration profile at a series of mesh points. Algebraic derivations of the finite-difference equations can be found in most textbooks on numerical analysis. There are a variety of finite-difference approximations ranging from the fully explicit method (illustrated above) via Crank-Nicolson and other weighted implicit forward. schemes to the fully implicit backward method, which can be u.sed to solve the equations. The methods tend to increase in stability and accuracy in the order given. The difference scheme for the cylindrical geometry appropriate for a root is... 

The implicit LS, ML and Constrained LS (CLS) estimation methods are now used to synthesize a systematic approach for the parameter estimation problem when no prior knowledge regarding the adequacy of the thermodynamic model is available. Given the availability of methods to estimate the interaction parameters in equations of state there is a need to follow a systematic and computationally efficient approach to deal with all possible cases that could be encountered during the regression of binary VLE data. The following step by step systematic approach is proposed (Englezos et al. 1993)... 

As discussed and illustrated in the introduction, data analysis can be conveniently viewed in terms of two categories of numeric-numeric manipulation, input and input-output, both of which transform numeric data into more valuable forms of numeric data. Input manipulations map from input data without knowledge of the output variables, generally to transform the input data to a more convenient representation that has unnecessary information removed while retaining the essential information. As presented in Section IV, input-output manipulations relate input variables to numeric output variables for the purpose of predictive modeling and may include an implicit or explicit input transformation step for reducing input dimensionality. When applied to data interpretation, the primary emphasis of input and input-output manipulation is on feature extraction, driving extracted features from the process data toward useful numeric information on plant behaviors. 

McFarland et al. recently [1] published the results of studies carried out on 22 crystalline compounds. Their water solubilities were determined using pSOL [21], an automated instrument employing the pH-metric method described by Avdeef and coworkers [22]. This technique assures that it is the thermodynamic equilibrium solubility that is measured. While only ionizable compounds can be determined by this method, their solubilities are expressed as the molarity of the unionized molecular species, the intrinsic solubility, SQ. This avoids confusion about a compound s overall solubility dependence on pH. Thus, S0, is analogous to P, the octanol/water partition coefficient in both situations, the ionized species are implicitly factored out. In order to use pSOL, one must have knowledge of the various pKas involved therefore, in principle, one can compute the total solubility of a compound over an entire pH range. However, the intrinsic solubility will be our focus here. There was one zwitterionic compound in this dataset. To obtain best results, this compound was formulated as the zwitterion rather than the neutral form in the HYBOT [23] calculations. 

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