Independent feature formulation

Two main, quite different, approaches to the target cost function have been proposed. The first, described in this section is called the independent feature formulation (IFF) and was proposed in the original Hunt and Black paper. Since then, many variations of this have been put forward but all can be described in the same general form. The second, described in Section 16.4, is termed the acoustic space formulation (ASF) and shares many similarities with the HMM systems of Chapter 15. The fact that there are only two main target function formulations is probably more due to historical accidents of system development than because these are particularly salient solutions to the problem. As we shall see, we can consider a more general formulation which encompasses both these and many other potential formulations. 

The independent feature formulation (IFF) calculates a weighted sum of sub-costs, where each sub-costs concentrates on one or more features. 

Section 16.3. The Independent Feature Target Function Formulation... 

Pig producers mainly try to approach maximal rates of lean tissue deposition and carcass index values by providing diets formulated to meet all of the known requirements. In the growing period, protein accretion increases as the supply of limiting amino acids increases (Heger et al., 2002). The dose-effect ratio can be subdivided into the nutrition-dependent phase, which is substantially linear, and the plateau phase, which is independent of nutrition supply and whose maximum depends on features of the animals, primarily characterised by the genotype (Susenbeth, 2002). 

Remark. The essential feature of our composite process is that i is an independent process by itself, while the transition probabilities of r are governed by i. This situation can be formulated more generally. Take a Markov process Y(t), discrete or continuous, having an M-equation with kernel... 

Finally, let us briefly point out some essential features of the stability analysis for a more general transport problem. It can be exemplified by the moving a//9 phase boundary in the ternary system of Figure 11-12. Referring to Figure 11-7 and Eqn. (11.10), it was a single independent (vacancy) flux that caused the motion of the boundary. In the case of two or more independent components, we have to formulate the transport equation (Fick s second law) for each component, both in the a- and /9-phase. Each of the fluxes jf couples at the boundary b with jf, i = A,B,... (see, for example, Eqn. (11.2)). Furthermore, in the bulk, the fluxes are also coupled (e.g., by electroneutrality or site conservation). 

So far we have invoked the time-independent formulation to describe electronic transitions. In the same manner as described in Section 4.1 we can also derive the time-dependent picture of electronic transitions, using either the adiabatic or the diabatic representation. In the following we feature the latter which is more convenient for numerical applications (Coalson 1985, 1987, 1989 Coalson and Kinsey 1986 Heather and Metiu 1989 Jiang, Heather, and Metiu 1989 Manthe and Koppel 1990a,b Broeckhove et al. 1990 Schneider, Domcke, and Koppel 1990 Weide, Staemmler, and Schinke 1990 Manthe, Koppel, and Cederbaum 1991 Heumann, Weide, and Schinke 1992). 

Equation (10.6), formulated in the previous section, defines the relative permittivity tensor in terms of the mean orientation of certain uniformly distributed anisotropic elements, which we shall interpret here as the Kuhn segments of the model of the macromolecule described in Section 1.1. We shall now discuss the characteristic features of a polymer systems, in which the segments of the macromolecule are not independently distributed but are concentrated in macromolecular coils. 

In the Hamiltonian formulation generalized momenta are also independent variables at the same level as the generalized coordinates and should also feature in the transformation, which, more appropriately, should be formulated as... 

Formulating appropriate rate laws for CO adsorption, OH adsorption and the reaction between these two surface species, a set of four coupled ordinary differential equations is obtained, whereby the dependent variables are the average coverages of CO and OH, the concentration of CO in the reaction plane and the electrode potential. In accordance with the experiments, the model describes the S-shaped I/U curve and thus also bistability under potentiostatic control. However, neither oscillatory behavior is found for realistic parameter values (see the discussion above) nor can the nearly current-independent, fluctuating potential be reproduced, which is observed for slow galvanodynamic sweeps (c.f. Fig. 30b). As we shall discuss in Section 4.2.2, this feature might again be the result of a spatial instability. 

The yields of radiation-induced polymerizations can be very high. No additives are required, which makes it possible to synthesize very pure polymers. The initiation step is temperature independent giving rise to an easily controlled process at any desired temperature. These features account for the commercial interest in radiation polymerization. The very high speeds attainable within the layers of monomers subjected to powerful electron beams explain the wide use of this technique in radiation curing of adhesives, inks and coatings. The corresponding formulations are "solvent-free" and involve pre-polymers and monomers as reactive diluents. 

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