Formal methods

While many methods for parameter estimation have been proposed, experience has shown some to be more effective than others. Since most phenomenological models are nonlinear in their adjustable parameters, the best estimates of these parameters can be obtained from a formalized method which properly treats the statistical behavior of the errors associated with all experimental observations. For reliable process-design calculations, we require not only estimates of the parameters but also a measure of the errors in the parameters and an indication of the accuracy of the data. 

Safety analysis. A formal method of assessment should be used. Each component within the system should be considered in turn. The likely types of failure and their consequences for the system should be taken into account. This should include consideration of the reliability of operating procedures, where safety depends upon them, and should encompass both inadvertent and deliberate failure to follow procedures. 

Definition of competence assessment methods. The definition of formal methods of assessing competence is a neglected area in many training programs. It is obviously necessary to ensure that trainees possess the necessary skills to do the job at the end of the training program. 

Decision Theory Formalism in the Behavioral Sciences.46—A formal method for examining decisions is developed through the use of a utility matrix [ tj] similar to the payoff matrix of game theory. In this matrix the rows correspond to the various possible acts of a decision-maker (e.g., to invest money in enterprises AltA2, -, Am) and the columns to various states, i.e., circumstances (e.g., possible levels of development of each enterprise) under which the acts are performed. The element y gives the utility (return or value) for using act At when state sf prevails. 

These is no formal method of categorizing the types of chiral stationary phases available for liquid chromatography (784). This diversity is both a strength, in providing a wide range of possibilities to solve a particular problem, and a weakness in that it is often difficult to predict which phase will be most useful for solving a particular problem. Compilations of commercially available chiral stationary phases and their proven applications are available (780-785). As new phases continue to be introduced at a hectic pace only a brief overview of their properties will be attempted here. 

What if analysis This less formal method of identifying hazards applies the words what if to a number of areas of investigation. For instance, the question might be, What if the flow stops The analysis team then decides what the potential consequences might be and how to solve any problems. 

This chapter introduces additional central concepts of thermodynamics and gives an overview of the formal methods that are used to describe single-component systems. The thermodynamic relationships between different phases of a single-component system are described and the basics of phase transitions and phase diagrams are discussed. Formal mathematical descriptions of the properties of ideal and real gases are given in the second part of the chapter, while the last part is devoted to the thermodynamic description of condensed phases. 

Forecasting revenues fundamentally rests on models plus judgment. More formal methods project the trends of past revenues into the future adjusting for known or expected fluctuations. Typical models employed are... 

Quoting action specs is described in [Wills91] and elsewhere. The distinction between spec types and design types has long been known in formal methods our highlighting it, and factoring effects to specification types, is somewhat unique among 00 and CBD methods. 

Almost every method, from the most dense and formal ones to those based on the most loosely defined sketches and drawings, stakes a claim to being abstract. The formal ones have a precise idea of what kinds of things are omitted in the abstraction and exactly what it means to correctly implement that abstraction they also share our idea of a conformance relation with a justification Refinement is a well-established technique in the formal methods community. The ideas of protocol refinement and data reification (model or state refinement) have been separately but quite thoroughly worked out elsewhere. 

Wills91] Wills, A. C. 1991. Application of Formal Methods to OO Programming Ph.D. thesis. See http //www.trireme.com/catalysis/fresco/specific.pdf. 

The sensitivity of IHC has been improved by developing formal methods of antigen retrieval and signal amplification (Kim et al., 2003). Knowledge of the exact localization of an antigen in tissue is critical to... 

The purpose of this research was to explore the representation, manipulation, and utilization of strategic knowledge in organic synthesis planning. The method we decided to explore was to create an axiomatic theory to replace our intuitive theory about chemical synthesis. This formal method of reasoning is very powerful in that it completely eliminates any questions about the method used to reach a conclusion. Since any conclusions reached would be theorems of the axiomatic theory, the acceptability of the conclusions rests completely on the acceptability of the postulates and not upon the method of reasoning. We are then free to focus on the chemical principles which are provided as postulates. 

There have been attempts to apply formal methods to the representation of organic compounds [1],[2], some attempts to apply artificial intelligence to organic synthesis [3],[4], and numerous attempts to apply the use of molecular orbital calculations to the verification of the validity of compounds in the synthesis route. This effort was a moderate attempt to examine the representation issues involved in writing production rules for Diels-Alder disconnections. 

In the opening segment the facilitator should discuss the importance of and methods for choosing the top event and any preestablished and existing boundaries of the investigation. If multiple events are involved, it is best to start with the last event in the time sequence. It may be appropriate, depending on the nature of the occurrence, to formally review the rules and symbols used in logic tree or fault tree development or whichever other formal method will be used. 

In the time that has elapsed since the previous edition of this book, it has been the authors impression that enthusiasm for formal methods of causality assessment has decreased to the extent that few, if any, pharmaceutical companies still use them. Nevertheless, brief comments on methods that have been developed over the years are needed to complete the picture. 

The number of sampling iterations must be sufficient to give stable results for output distributions, especially for the tails. There are no simple rules, because the necessary number of runs depends on the number of variables entered as distributions, model complexity (mathematical structure), sampling technique (random or Latin hypercube), and the percentile of interest in the output distribution. There are formal methods to establish the number of iterations (Cullen and Frey 1999) however, the simulation iterations could simply be increased to a reasonable point of convergence. 

Ideally, define the assessment endpoint so that it relates directly to the management goal. If this is not practical, (e.g., if the management goal refers to population sustainability but the assessment endpoint refers to individual mortality), define in advance how the assessment endpoint will be interpreted. If this involves subjective judgments then consider the use of formal methods. 

Several examples of applicable formal methods were discussed. Nonhierarchical quantitative models can be applied several times based on plausible scenarios emerging from a qnalitative informed opinion. Expanding on the example above, a Monte Carlo simulation of pesticide ingestion rates may be conducted with and without consideration of water sources. Hierarchical Monte Carlo methods can be used in a similar manner. 

Regardless of the method used, the basis of the final risk characterization must be explicit. All components and sources of evidence should be described. The explicit linkage between the analysis results and the assessment endpoints must be clearly but adequately stated. Tandem presentation of conventional methods (e.g., ad hoc weight of evidence) and formal methods (e.g., Bayesian, meta-anal-ysis) are recommended to enhance understanding. This is intended to facilitate acceptance of unfamiliar approaches, not to imply that the conventional methods are a touchstone. 

An extremely useful addition to the formal method for combining the studies is to represent the data from the individual studies, together with the combination, in a meta-analysis plot. 

Although the formal method of describing orbitals is to use mathematical expressions, much understanding of orbital properties may be gained by the use of pictorial representations. The most useful pictorial representations of atomic orbitals are similar to boundary surfaces (which are based on V /2), but are based upon the distribution of jf values, with the sign of / being indicated in the various parts of the diagram. The shapes of these distributions are based upon the contours of jf within... 

There is a formal method of converting a reducible representation to a sum of irreducible representations, but commonly the outcome is either obvious or may be arrived at by a few guesses. The formal method is described in Appendix 2. 

In the text, when the character of a set of orbitals is deduced to give a reducible representation, the reduction to a sum of irreducible representations has been carried out by inspection of the appropriate character table. In some instances this procedure can be lengthy and unreliable. The formal method can also be lengthy, but it is highly reliable, although not to be recommended for simple cases where inspection of the character table is usually sufficient. The formal method will be explained by doing an example. 

Different approaches may be used to validate the sample preparation component of the dissolution test. However, it is important to understand that the objective of validation is to demonstrate that the procedure is suitable for its intended purpose. For example, one of the strategies will demonstrate the validity of different aspects of sample preparation during method development (prior to the formal method validation exercise). As a result, the final validation experiments will confirm the work done during method development. The strategy that will be followed for the method development and validation process will depend on the culture, expertise, and strategy of the analytical laboratory. 

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