Competency models

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

Unfortunately the development of models is hindered by a lack of reliable experimental data. For example, the rates of ion-transfer reactions measured at different times and by different groups vary widely. Also, it has been suggested that the high interfacial capacities that are measured in certain systems are an experimental artifact [13]. While this is frustrating for the researcher who wants to decide between competing models, it can also be viewed as a sign that the electrochemistry of liquid-liquid interfaces is an active field, where fundamental issues are just being explored. 

The idea behind the computation of the Divergence only among adequate models in Step 2, is to base the decision for the next experiment on the models that are still competing. Models that have been found inadequate should not be included in the divergence computations. However, once the new data point becomes available it is good practice to update the parameter estimates for all models (adequate or inadequate ones). Practice has shown that under conditions of high experimental errors, as additional information becomes available some models may become adequate again ... 

Edgar The competing model will be that fancy promoters are not used to control cell cycle genes, but instead there is some kind of growth coupling mechanism. 

Among various model H(0) s that could be considered, the best such model is evidently that for which the perturbative corrections are most rapidly convergent, i.e., for which /7(perl) is in some sense smallest and the model Em> and < 0) are closest to the true E and T. Perturbation theory can therefore be used to guide selection of the best possible H(0) within a class of competing models, as well as to evaluate systematic corrections to this model. 

The structure of the condensed chromatin fiber is still under discussion [1,23,54], with two competing models the original solenoid model of Finch and Klug [16], and the straight-linker model [12,14,55]. Assessing the structure in vivo or in situ has proven impossible thus far, due to technical limitations. Chromatin fibers released from nuclei into solution by nuclease treatment have been widely used as models for fiber structure such fibers are extended at low ionic strength and condensed at ionic strengths believed to be close to those found in vivo ( 150 mM Na" " or 0.35 mM Mg " "). The salt-induced fiber compaction has been extensively studied in the past but is still poorly understood in terms not only of the details of the structure but also in terms of the molecular mechanisms of the compaction process. 

For theoreticians, such developments provide an opportunity to refine and test their more subtle inventions and to explain apparent correlations. I am quite sure they will seize this particular opportunity, given the exhavagant amount of data already accumulated, to choose amongst a crowd of competing models the one which best accounts for reality. 

Scientific inquiry demands a number of skills. The National Committee on Science Education Standards and Assessment and the National Research Council, in addition to other organizations such as the National Science Teachers Association, have stressed the training and development of these skills. Science students must learn how to raise important questions, design the tools or experiments necessary to answer these questions, apply models in explaining the results and revise the model as needed, be alert to alternative explanations, and construct and analyze arguments for and against competing models. 

At the outset it may also be advantageous to consider problems of structural identifiability and distinguishability. A model is not identifiable if in principle it is impossible to determine the desired parameters on the basis of proposed data to be obtained even if there is no experimental uncertainty or inadequacy in computer programming. Even when it is theoretically possible to determine the parameters for a given model, it may also be possible to compute those for a competing model from the same data and the models will then be indistinguishable. Resolution of these problems is often not simple. The subject is discussed in an advanced monograph by Walter (49) as well as in papers by Park and Himmelblau (49a) and Walter et al. (49b). 

One theory per phenomenon. The authors intend a teaching book, which acts as an introduction to graduate studies. They have tried to present, with due admission of the existing imperfections, a simple version of that model which seemed to them at the time of writing to reproduce the facts most consistently. They have for the most part refrained from presenting the detailed pros and cons of competing models in areas in which the theory is still quite mobile. 

The phase problem and the problem of arbitration. Fibrous structures are usually made up of linear polymers with helical conformations. Direct or experimental solution of the X-ray phase problem is not usually possible. However, the extensive symmetry of helical molecules means that the molecular asymmetric unit is commonly a relatively small chemical unit such as one nucleotide. It is therefore not difficult to fabricate a preliminary model (which incidently provides an approximate solution to the phase problem) and then to refine this model to provide a "best" solution. This process, however, provides no assurance that the solution is unique. Other stereochemically plausible models may have to be considered. Fortunately, the linked-atom least-squares approach provides a very good framework for objective arbitration independent refinements of competing models can provide the best models of each kind the final values of n or its components (eqn. xxiv) provide measures of the acceptability of various models these measures of relative acceptability can be compared using standard statistical tests (4) and the decision made whether or not a particular model is significantly superior to any other. 

Machinery now exists to permit, in many cases, very detailed analyses of fibrous structures using the under-appreciated X-ray diffraction data supplied by the polymers themselves. Some of this machinery can be adapted to tackle the problem of providing unique solutions statistical tests can be applied to (least-squares) optimised versions of competing models. However, additional or alternative tests of the creditability of different models should not be ignored. 

The major findings of the COMPETES model with regard to C02 cost pass-through are summarized in Table 2. They are compared to model results from the Integrated Planning Model (IPM), which are described in more detail by Neuhoff et al. (this issue). As results are very sensitive to the gas/coal shift, small differences in the assumptions about gas prices, available gas generation capacity and interconnection capacity can explain the differences between the results of both models for The Netherlands. 

France, Germany and The Netherlands, based on COMPETES model scenarios ... 

Table 4. Changes in profits of individual power companies operating in Belgium, France, Germany and The Netherlands, based on two COMPETES model scenarios (in M ) ...

Table 5. Changes in aggregated profits due to C02 emissions trading for the four largest power firms in The Netherlands (E.ON, Electrabel, ESSENT and NUON), based on COMPETES model scenarios...

The high estimate for The Netherlands (compared to a similar estimate by the COMPETES model) might be caused by the older nature of the IPM model, with coal having a stronger influence on power prices. 

A competing model called the chemiosmotic model was suggested by Mitchell in 1961 and won a Nobel prize. The physical events that which Mitchell s theory implies are less consistent with modem concepts of interfacial charge transfer than those of Williams, which do indicate interfacial charge transfer. 

In order to clearly explain the possibilities of describing nonequlibrium irreversible processes in terms of equilibrium it is certainly necessary to define quite accurately the notions of equilibrium and reversibility, nonequilibrium and irreversibility. It is clear that their interpretation, as well as the interpretation of other scientific notions, changes with the development of respective theories, models, and methods. Since the work touches upon the issues of interrelations between the competing models in a historical profile it is desirable that the appropriateness of various interpretations of the said notions be assessed in this profile. Making no pretence of the systematic presentation of the issue we will only touch upon some points that are important for understanding the text1 below. 

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