Interpretive algorithms

The Stratonovich SDEs for either generalized or Cartesian coordinates could be numerically simulated by implementing the midstep algorithm of Eq. (2.238). Evaluation of the required drift velocities would, however, require the evaluation of sums of derivatives of B or whose values will depend on the decomposition of the mobility used to dehne these quantities. This provides a worse starting point for numerical simulation than the forward Euler algorithm interpretation. 

Hopgood, F.F., N. Woodcock, N.J. HaUam, and P.D. Picton, Interpreting ultrasonic images using rules, algorithms and neural networks , European Journal of NDT, Vol. 2, No. 4, April 1993, pp. 135-149. 

The interpretated value of crack depth hi is calculated by means of the algorithm of solving inverse task, the parameters I or T have limit values correspondingly. 

The preferable theoretical tools for the description of dynamical processes in systems of a few atoms are certainly quantum mechanical calculations. There is a large arsenal of powerful, well established methods for quantum mechanical computations of processes such as photoexcitation, photodissociation, inelastic scattering and reactive collisions for systems having, in the present state-of-the-art, up to three or four atoms, typically. " Both time-dependent and time-independent numerically exact algorithms are available for many of the processes, so in cases where potential surfaces of good accuracy are available, excellent quantitative agreement with experiment is generally obtained. In addition to the full quantum-mechanical methods, sophisticated semiclassical approximations have been developed that for many cases are essentially of near-quantitative accuracy and certainly at a level sufficient for the interpretation of most experiments.These methods also are com-... 

Other methods consist of algorithms based on multivariate classification techniques or neural networks they are constructed for automatic recognition of structural properties from spectral data, or for simulation of spectra from structural properties [83]. Multivariate data analysis for spectrum interpretation is based on the characterization of spectra by a set of spectral features. A spectrum can be considered as a point in a multidimensional space with the coordinates defined by spectral features. Exploratory data analysis and cluster analysis are used to investigate the multidimensional space and to evaluate rules to distinguish structure classes. 

Analysts The above is a formidable barrier. Analysts must use limited and uncertain measurements to operate and control the plant and understand the internal process. Multiple interpretations can result from analyzing hmited, sparse, suboptimal data. Both intuitive and complex algorithmic analysis methods add bias. Expert and artificial iutefligence systems may ultimately be developed to recognize and handle all of these hmitations during the model development. However, the current state-of-the-art requires the intervention of skilled analysts to draw accurate conclusions about plant operation. 

A common use of statistics in structural biology is as a tool for deriving predictive distributions of strucmral parameters based on sequence. The simplest of these are predictions of secondary structure and side-chain surface accessibility. Various algorithms that can learn from data and then make predictions have been used to predict secondary structure and surface accessibility, including ordinary statistics [79], infonnation theory [80], neural networks [81-86], and Bayesian methods [87-89]. A disadvantage of some neural network methods is that the parameters of the network sometimes have no physical meaning and are difficult to interpret. 

ANOVA) if the standard deviations are indistinguishable, an ANOVA test can be carried out (simple ANOVA, one parameter additivity model) to detect the presence of significant differences in data set means. The interpretation of the F-test is given (the critical F-value for p = 0.05, one-sided test, is calculated using the algorithm from Section 5.1.3). 

The partial differential equations used to model the dynamic behavior of physicochemical processes often exhibit complicated, non-recurrent dynamic behavior. Simple simulation is often not capable of correlating and interpreting such results. We present two illustrative cases in which the computation of unstable, saddle-type solutions and their stable and unstable manifolds is critical to the understanding of the system dynamics. Implementation characteristics of algorithms that perform such computations are also discussed. 

The ideas presented in Section III are used to develop a concise and efficient methodology for the compression of process data, which is presented in Section IV. Of particular importance here is the conceptual foundation of the data compression algorithm instead of seeking noninterpretable, numerical compaction of data, it strives for an explicit retention of distinguished features in a signal. It is shown that this approach is both numerically efficient and amenable to explicit interpretations of historical process trends. 

In summary, the branch-and-bound algorithm as defined in this chapter assumes that the semantics of objective function, feasibility, and branching operation are fixed with respect to the problem class. As long as their interpretations are not changed, the derived equivalence and dominance rules would remain valid. 

Optimal control theory, as discussed in Sections II-IV, involves the algorithmic design of laser pulses to achieve a specified control objective. However, through the application of certain approximations, analytic methods can be formulated and then utilized within the optimal control theory framework to predict and interpret the laser fields required. These analytic approaches will be discussed in Section VI. 

To perform the maximization over (X,t), we need an algorithm such as the Nelder-Mead simplex search (14). An alternative that is adequate in many cases is a simple search over a (X,t) grid. The critical value XX has an interpretation of its own. It is the upper bound on a simultaneous prediction interval for ng as yet unobserved observations from the background population. 

The aim of factor analysis is to calculate a rotation matrix R which rotates the abstract factors (V) (principal components) into interpretable factors. The various algorithms for factor analysis differ in the criterion to calculate the rotation matrix R. Two classes of rotation methods can be distinguished (i) rotation procedures based on general criteria which are not specific for the domain of the data and (ii) rotation procedures which use specific properties of the factors (e.g. non-negativity). 

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