Topological features

The D matrix plays an important role in the forthcoming theory because it contains all topological features of an electronic manifold in a region surrounded by a contour F as will be explained next. 

Gelemter and Rose [25] used machine learning techniques Chapter IX, Section 1.1 of the Handbook) to analyze the reaction center. Based on the functionalities attached to the reaction center, the method of conceptual clustering derived the features a reaction needed to possess for it to be assigned to a certain reaction type. A drawback of this approach was that it only used topological features, the functional groups at the reaction center, and its immediate environment, and did not consider the physicochemical effects which are so important for determining a reaction mechanism and thus a reaction type. 

Inclusions of Other Grown Analogues. A variety of crown analogues and hybrid modifications (24—28) with other topological features (lariat ethers (31,32), octopus molecules (33), spherands (eg, (12) (34), torands (35)) including chiral derivatives (36) have been prepared and demonstrated to show particular inclusion properties such as chiroselective inclusion (Fig. 4) (37) or formation of extremely stable complexes (K ">(LR) for (12)... 

Below, we give a sampling of the sorts of dynamical behaviors that can immediately be deduced from basic topological features of . 

The chemical bonding and the possible existence of non-nuclear maxima (NNM) in the EDDs of simple metals has recently been much debated [13,27-31]. The question of NNM in simple metals is a diverse topic, and the research on the topic has basically addressed three issues. First, what are the topological features of simple metals This question is interesting from a purely mathematical point of view because the number and types of critical points in the EDD have to satisfy the constraints of the crystal symmetry [32], In the case of the hexagonal-close-packed (hep) structure, a critical point network has not yet been theoretically established [28]. The second topic of interest is that if NNM exist in metals what do they mean, and are they important for the physical properties of the material The third and most heavily debated issue is about numerical methods used in the experimental determination of EDDs from Bragg X-ray diffraction data. It is in this respect that the presence of NNM in metals has been intimately tied to the reliability of MEM densities. 

All three proteins were analyzed at 3.0 A resolution. Experiments were performed on a portion of the relative density map containing an entire connected protein. In order to discern effects of topological features just outside the boundaries of this volume, our analysis was extended 5.0 A outside the boundaries on all sides of this volume. 

In contrast to common ANNs, Kohonen networks produce self-organized topological feature maps (Kohonen [1982, 1984]). The basic idea of Kohonen mapping is that information in data usually contains not only an algebraic but also a topological aspect. These double aspect is shown schematically in Fig. 8.25 where the data and the structure of them are composed. 

McAllister, M. A., A. Perczel, P. Csaszar, and I. G. Csizmadia. 1993a. Peptide Models 5. Topological Features of Molecular Mechanics and Ab Initio 4D-Ramachandran Maps. Conformational Data for Ac-L-Ala-L-Ala-NHMe and For-L-Ala-L-Ala-NH2. J. Mol. Struct. (Theochem) 288,181-198. 

McAllister, M. A., Perczel, P. Csaszar, W. Viviani, J.-L. Rivail, and I. G. Csizmadia. 1993b. Peptide Models 4. Topological Features of Molecular Mechanics and Ab Initio 2D-Ramachandran Maps. Conformational Data for For-Gly-NH2, For-L-Ala-NH2, Ac-l-Ala-NHMe and For-L-Val-NH2. J. Mol. Struct. (Theochem) 288, 161-179. Mehrotra, P. K., M. Mezei, and D. L. Beveridge. 1984. Monte Carlo Determination of the Internal Energies of Hydration for the Ala Dipeptide in the C7, C5, aR, and Pn Conformations. Int. J. Quantum Chem. Quantum Biol. Symp. 11, 301-308. 

Using the more advanced quantum chemical computational methods it is now possible to determine the fundamental electronic properties of zeolite structural units. The quantum chemical basis of Loewenstein s "aluminum avoidance" rule is explored, and the topological features of energy expectation value functionals within an abstract "nuclear charge space" model yield quick estimates for energy relations for zeolite structural units. 

The applicability of Eq. (45) to a broad range of biological (i.e., toxic, geno-toxic) structure-activity relationships has been demonstrated convincingly by Hansch and associates and many others in the years since 1964 [60-62, 80, 120-122, 160, 161, 195, 204-208, 281-285, 289, 296-298]. The success of this model led to its generalization to include additional parameters in attempts to minimize residual variance in such correlations, a wide variety of physicochemical parameters and properties, structural and topological features, molecular orbital indices, and for constant but for theoretically unaccountable features, indicator or dummy variables (1 or 0) have been employed. A widespread use of Eq. (45) has provided an important stimulus for the review and extension of established scales of substituent effects, and even for the development of new ones. It should be cautioned here, however, that the general validity or indeed the need for these latter scales has not been established. 

Figure 2. General topological feature of PS translocation and decarboxylation in mammalian cells. PS is synthesized by PSS I and II in endoplasmic reticulum (ER) or mitochondria-associated membrane (MAM). The nascent PS is transported other membranes such as plasma membrane, nucleus, and mitochondria. The PS transported to the mitochondrial outer membrane is then translocated to the inner membrane, in which PS is converted to PE by PS decarboxylase (PSD). The PE formed in mitochondria is dynamic and can be exported to other organelles for membrane biogenesis.

Strategies based on some special topological features, such as the presence of "strategic bonds" and/or "common atoms" which apply preferentially to sesquiterpene compounds (as, for instance, longifolene, patchouli alcohol, seychellene, sativene, etc.) and non-natural compounds with a high degree of internal connectivity as, for example, twistane, bullvalene, etc. 

Further distinct topological features of the jet vorticity dynamics are expected for larger AR (e.g., for AR > 4), for which vortex-ring bifurcation has been observed [8, 22, 25, 26]. 

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