Representation communicative functions

Discussions of representation in the scientific literature devote too little attention to their communicative functions. Yet "representation" never takes place in a vacuum, and the issue of representation for what end is always relevant, even if masked. The context shapes the character and usage of the representations, as well as highlighting the social character of the scientific enterprise. An important exception to this general neglect is the intensive study of chemical language, particularly its symbolic components, by Mestrallet (1980 see also Hoffmann Laszlo, 1991 Laszlo, 1993 Weininger, 1998). 

Expert chemists constitute a community of practice which uses representations to make sense of the activities of the disciphne. Thus the conventions used in interpreting these representations are essential to the functioning of this community. 

Constraints in optimization arise because a process must describe the physical bounds on the variables, empirical relations, and physical laws that apply to a specific problem, as mentioned in Section 1.4. How to develop models that take into account these constraints is the main focus of this chapter. Mathematical models are employed in all areas of science, engineering, and business to solve problems, design equipment, interpret data, and communicate information. Eykhoff (1974) defined a mathematical model as a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in a usable form. For the purpose of optimization, we shall be concerned with developing quantitative expressions that will enable us to use mathematics and computer calculations to extract useful information. To optimize a process models may need to be developed for the objective function/, equality constraints g, and inequality constraints h. 

The importance of N-representability for pair-density functional theory was not fully appreciated probably because most research on pair-density theories has been performed by people from the density functional theory community, and there is no W-representability problem in conventional density functional theory. Perhaps this also explains why most work on the pair density has been performed in the first-quantized spatial representation (p2(xi,X2) = r2(xi,X2 xi,X2)) instead of the second-quantized orbital representation... 

Simply to look at the literature is to convince yourself of the importance that density functional theory (DFT) methods have attained in molecular calculations. But there is among the molecular physics community, it seems to me, a widespread sense of unease about their undoubted successes. To many it seems quite indecent that such a cheap and cheerful approach (to employ Peter Atkins s wonderful phrase) should work at all, let alone often work very well indeed. I think that no-one in the com-mimity any longer seriously doubts the Hohenberg-Kohn theo-rem(s) and anxiety about this is not the source of the unease. As Roy reminded us at the last meeting, the N— representability problem is still imsolved. This remains true and, even though the problem seems to be circumvented in DFT, it is done so by making use of a model system. He pointed out that the connection between the model system and the actual system remains obscure and in practice DFT, however successful, still appears to contain empirical elements And I think that is the source of our present unease. 

The mechanism by which the activated receptor talks to the G-protein is only partially understood. Generally, the switch function of the receptor is considered in terms of allosteric conformational changes of the 7-hehx membrane bimdle (review Bourne, 1997). According to this representation, changes in the structure of the transmembrane bimdle are passed on to the cytoplasmic loops of the receptor. Communication with the a-subunit of the heterotrimeric G-protein takes place via these loops. 

Assessment end points directly influence the type, characteristics, and interpretation of data and information used for analysis and the scale and character of the assessment. For example, an assessment end point such as fecundity of bivalves defines local population characteristics and requires very different types of data and ecosystem characterization compared with aquatic community structure and function. When concerns are on a local scale, the assessment end points should not focus on landscape concerns. But if ecosystem processes and landscape patterns are being considered, survival of a single species would provide inadequate representation of this larger scale. 

Thus molecular modeling can be defined as the generation, manipulation, calculation, and prediction of realistic molecular structures and associated physicochemical as well as biochemical properties by the use of a computer. It is primarily a mean of communication between scientist and computer, the imperative interface between human-comprehensive symbolism, and the mathematical description of the molecule. The endeavor is made to perceive and recognize a molecular structure from its symbolic representations with a computer. Thus functions of the molecular modeling include ... 

The tool-specific part of the implementation is done in the dedicated tool wrapper, which is an instance of the closed-form model representation component derived for the specific tool. Its function is the translation of commands and data between the tools specific interfaces and the generic interface of CHEOPS. This enables CHEOPS to communicate with the tools as if they were its own components and provides the technical and algorithmic solution for the tool integration. Currently, CHEOPS internally supports gPROMS [916] and MODELICA Equation Set Objects [655], and contains tool wrap-... 

If one compares the attempts reviewed in sec. 3.2 to base majiy-electron quantum mechanics on the two-particle density matrix, i.e. a 2-particle density matrix functional theory with the current density functional theory one realizes that for the former the functional is exactly known, while the full n-representability condition is unknown. For DFT on the other hand, the functional is unknown, but the n representability does not cause problems. Why should one take incomplete information on n-representability as more serious as lack of information on the exact functional Possibly there was just more reluctance in the two-particle-density matrix functional community to be satisfied with approximate n-representability conditions than in the density functional community to accept approximate density functionals, and that this different attitude was decisive for the historical development. 

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