Parametric modeling defined

To investigate these two questions, a parametric model of the Jacobian of human erythrocytes was constructed, based on the earlier explicit kinetic model of Schuster and Holzhiitter [119]. The model consists of 30 metabolites and 31 reactions, thus representing a metabolic network of reasonable complexity. Parameters and intervals were defined as described in Section VIII, with approximately 90 saturation parameters encoding the (unknown) dependencies on substrates and products and 10 additional saturation parameters encoding the (unknown) allosteric regulation. The metabolic state is described by the concentration and fluxes given in Ref. [119] for standard conditions and is consistent with thermodynamic constraints. 

One widely used application of clinical MRS spectral simulation is the creation of prior information for spectral analysis and fitting routines. Well-defined metabolite prior information results in more consistent and complete estimations of the actual data. One example of a parametric model used to fit clinical MRS data is shown below. 

The Bank of England uses a variation of the Svensson yield curve model, a one-dimensional paranetric yield curve model. This is similar to the Nelson and Siegel model and defines the forward rate curve/(/n) as a function of a set of unknown parameters, which are related to the short-term interest rate and the slope of the yield curve. The model is summarised in Appendix B. Anderson and Sleath (1999) assess parametric models, including the Svensson model, against spline-based methods such as those described by Waggoner (1997), and we summarise their results later in this chapter. 

Dimension driven, parametric modeling is a relatively new achievement in FEM/FEA systems. Parameters defined for the geometry are completed by parameters defined for the FEM and FEA, such as material properties, force, temperature, and parameters of meshes. Two-way associativity can be established between shape... 

The term "parametric models" expresses the capability of certain CAD systems which allows the CAD system user to assign values to elementary data of some predefined type with the consequence that this will influence the CAD model in a certain way. A typical example is the length of some dimension in a model that is defined not as a constant but as a variable which has some value. Assignment of a new value to this length will cause a redefinition of all geometry that depends on this variable. The reference model allows the use of either constant values for predefined types, or references to entities of predefined type. 

The critical decisions in the modeling problem are related to the other three elements. The space G is most often defined as the linear span of a finite number, m, of basis functions, 0 ), each parametrized by a set of unknown coefficients w according to the formula... 

A second reason why AI is of value to scientists is that it offers powerful tools to cope with complexity. In favorable circumstances, the solutions to problems can be expressed by rules or by a well-defined, possibly trivial, model. If we want to know whether a compound contains a carbonyl group, we could record its infrared spectrum and check for a peak near 1760 cm1. The spectrum, paired with the rule that ketones generally show an absorption in this region, is all that we need. But other correlations are more difficult to express by rules or parametrically. What makes a good wine We may (or may not) be able to recognize a superior wine by its taste, but would have considerable difficulty in determining whether a wine is good, or even if it is palatable, if all we had to go on was a list of the chemicals of which it is comprised. 

Optimisation may be used, for example, to minimise the cost of reactor operation or to maximise conversion. Having set up a mathematical model of a reactor system, it is only necessary to define a cost or profit function and then to minimise or maximise this by variation of the operational parameters, such as temperature, feed flow rate or coolant flow rate. The extremum can then be found either manually by trial and error or by the use of numerical optimisation algorithms. The first method is easily applied with MADONNA, or with any other simulation software, if only one operational parameter is allowed to vary at any one time. If two or more parameters are to be optimised this method becomes extremely cumbersome. To handle such problems, MADONNA has a built-in optimisation algorithm for the minimisation of a user-defined objective function. This can be activated by the OPTIMIZE command from the Parameter menu. In MADONNA the use of parametric plots for a single variable optimisation is easy and straight-forward. It often suffices to identify optimal conditions, as shown in Case A below. 

The control points are defined by the basis set of points P. These control points define the parametric bicubic patches which form the surface model. Advantages of the parametric bicubic surface include continuity of position, slope, and curvature at the points where two patches meet. All the points on a bicubic surface are de by cubic equations of two parameters s and t, where s and t vary from 0 to 1. The equation for x s,t) is ... 

The major hurdle to overcome in the development of 3D-QSAR models using steric, electrostatic, or lipophilic fields is related to both conformation selection and subsequent suitable overlay (alignment) of compounds. Therefore, it is of some interest to provide a conformation-ally sensitive lipophilicity descriptor that is alignment-independent. In this chapter we describe the derivation and parametrization of a new descriptor called 3D-LogP and demonstrate both its conformational sensitivity and its effectiveness in QSAR analysis. The 3D-LogP descriptor provides such a representation in the form of a rapidly computable description of the local lipophilicity at points on a user-defined molecular surface. 

The exact nature of the axial field is irrelevant within this model — for example, it could be any of the distortions illustrated in Fig. 3 — and its effect is represented parametrically by a splitting between the orbital doublet and orbit singlet arising from the triplet 2 T2 term. The splitting, A in Fig. 4 (defined conventionally as positive if the singlet lies lowest), is thus defined, not in terms of the operator... 

---