Maximum simplicity

Theoretically it has been shown (Thayse, 1988) that the DDP formalism is closely related to a simpler form of horn clause logic, i.e., the propositional calculus. This would suggest that we could use the horn clause form to express some of the types of knowledge we are required to manipulate in combinatorial optimization problems. The explicit inclusion of state information into the representation, necessitates the shift from the simpler propositional form, to the first-order form, since we wish to parsimoniously represent properties that can be true, or take different values, in different states. By limiting the form to horn clauses, we are striving to retain the maximum simplicity of representation, whilst admitting the necessary expressive power. 

Rotated axes are characterized by their position in the original space, given by the vectors = [cos0 -sin0] and F = [sin0 cos0] (see Fig. 34.8). In PCA or FA, these axes fulfil specific constraints (see Chapter 17). For instance, in PCA the direction of k is the direction of the maximum variance of all points projected on this axis. A possible constraint in FA is maximum simplicity of k, which is explained in Section 34.2.3. The new axes (k,l) define another basis of the same space. The position of the vector [x,- y,] is now [fc, /,] relative to these axes. 

In the first section of this work, in order to obtain maximum simplicity of interpretation, we chose to impose the strong orthogonality constraint on our model wave functions any two separate-group functions will be constrained by Eq. (11) ... 

A particularly simple type of chirality function is a polynomial in one or more ligand parameters, such as the two functions of Eq. (III-I). Maximum simplicity is obtained if one requires each component of the qualitatively complete x to be a polynomial of lowest possible order in the parameter(s). We first consider the case <3 = <3 . 

Carbon skeleton, functional group manipulation and stereochemical control. Rule of maximum simplicity... 

Although the three aspects are not strictly independent, sometimes, from a didactic point of view, and to simplify the synthetic analysis, they may be considered separately. However, their mutual interaction must be allowed for in some further stage of the analysis, in order to introduce the pertinent modifications into the process and to arrive at the simplest possible solution (see Diagram 1.1) this means that the maximum correlation must exist among the different individual synthetic operations, so that each one of them allows, facilitates or simplifies, in some way, all the other ones ("rule of maximum simplicity"). 

In terms of complexity, the "rule of maximum simplicity" means that the complexity of the intermediates throughout the synthetic sequence must be kept as near as possible to the complexity of the starting materials, Cg, and to that of the... 

Since maximum simplicity would be attained in the "ideal" case of a one-step synthesis,... 

The problem of creating the carbon-carbon (or carbon-heteroatom) bonds is not strictly separable from the problem of functional group manipulations. In fact, as has been stated by Ireland [2] "Synthetic planning, then, is a balance between the problem of framework constmction through the use of carbon-carbon bond-forming reactions and the problem of subsequent functional group manipulations" (Cf. the "rule of maximum simplicity"). 

The usefulness of FGI operations is easily understood considering a very simple example. 1,3-Butanediol, notwithstanding being a 1,3-C system, does not offer a reasonable disconnection mechanism. However, if the primary hydroxyl group is converted to a carbonyl group, the resulting product can be then disconnected into two stable identical molecules of acetaldehyde, according to a reasonable retro-aldol mechanism, and the whole process represents a simple solution in accordance with the criterium of maximum simplicity. 

In contrast to "illogical disconnections", in "plausible disconnections" a reasonable or, at least, plausible mechanism exists which involves the motion of electron pairs and leads to stable fragments, either ions or molecules. In any case, however, the "principle of maximum simplicity" does not hold here, since one of the resulting fragments is always a dissonant three-membered ring. 

This methodology, as in the cases of rearrangements and of plausible disconnections, does not meet the criterium of maximum simplicity, since the reconnection represents an increase of the "cyclic order" and therefore of the complexity of the molecule. 

Although this synthesis provides the most direct entry into the twistane polycyclic structure, the adequate balance between the problem of framework construction and the subsequent functional group manipulations, required by the "principle of maximum simplicity", is missed. However, the synthesis represents without doubt an outstanding contribution to the synthesis of polycyclic non-natural products. 

Extensive use of flowcharts is made as a means of illustrating the various processes and to show the main reactors and the paths of the feedstocks and products. However, no effort is made to include all of the valves and ancillary equipment that might appear in a true industrial setting. Thus, the flowcharts used here have been reduced to maximum simplicity and are designed to show principles rather than details. 

As we can see, it is far too early to draw reliable conclusions about eukaryotic genomes, but once again we can appreciate how important it is to distinguish between simple and primitive properties. The streamlining strategy did succeed in producing cells that combined maximum efficiency and maximum simplicity, but when all that was erasable was in fact erased, it become impossible to go further, and bacterial evolution reached a sort of stationary state. Other cells, instead, went on with primitive cargoes and junk molecules, and their evolution remained open, free, creative and unpredictable. 

Maximum simplicity. So let us return to the simplest version of the Huckel method. We have not as yet mentioned still another simplifying assumption of this method most of the matrix elements in Eq. (6) are assumed... 

Today, cyding and disposal by re-injedion offers a promising alternative to avoid sulfur production and reduce CO2 emissions to the atmosphere simultaneously. To this end, technologies of choice are those that offer maximum simplicity and require least downstream processing intensity and power for re-injection. 

There are, of course, an infinite number of stacking sequences possible within the definition of close packing, all of them, naturally, having the same packing density. The hep and ccp sequences are those of maximum simplicity and symmetry. Some of the more complex sequences are actually encountered in Nature, though far less often than the two just described. 

HBr][HBrOg] oc [H+j EBriEBrOg-], whence the overall order of the change. Here, incidentally, we have an example of the resolution of a reaction into a series of stages, each of maximum simplicity— a principle the importance of which will become increasingly evident. 

Maximum simplicity of the plant design based on a single circuit scheme of the power unit to reduce construction and operating costs in this, an additional barrier to radioactive substance propagation is provided by application of a special scheme for the separation of phases inside the reactor ... 

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