Subset Volume

Figure 8 A joint principal coordinate projection of the occupied regions in the conformational spaces of linear (Ala) (triangles) and its conformational constraint counterpart, cyclic-CAla) (squares), onto the optimal 3D principal axes. The symbols indicate the projected conformations, and the ellipsoids engulf the volume occupied by the projected points. This projection shows that the conformational volume accessible to the cyclic analog is only a small subset of the conformational volume accessible to the linear peptide, (Adapted from Ref. 41.)...

This glossary lists all the acronyms referred to in the encyclopedia together with their meanings. The major technique acronyms are listed alphabetically. Alternatives to these acronyms are listed immediately below each of these entries, if they exist. Related acronyms (variations or subsets of techniques terminology used within the technique area) are grouped together below the major acronym and indented to the right. Most, but not all, of the techniques listed here are the subject of individual articles in this volume. 

Dissipative systems whether described as continuous flows or Poincare maps are characterized by the presence of some sort of internal friction that tends to contract phase space volume elements. They are roughly analogous to irreversible CA systems. Contraction in phase space allows such systems to approach a subset of the phase space, C P, called an attractor, as t — oo. Although there is no universally accepted definition of an attractor, it is intuitively reasonable to demand that it satisfy the following three properties ([ruelle71], [eckmanSl]) ... 

This approach did not seem to be as satisfactory for those sulfamates having heteroatom substituents (hetero-sulfamates). Spillane suggested that the various electronic effects of the hetero-atoms probably introduce an additional variable that is apparently absent, or constant, for the carbosulfamates. Because molecular connectivity correlates structure with molecular volume and electronic effects, Spillane included molecular connectivity, (computed for the entire molecule, RNHSOO to the four variables, x, y, z, and V, and applied the statistical technique of linear-discrimination analysis to 33 heterosulfamates (10 sweet, 23 not sweet). A correlation of >80% was obtained for the x, z, x subset 5 of the 33... 

The European Commission (EC) has sponsored four reports that evaluate a set of 553 substances selected by experts and stakeholders for assessment for endocrine disruption. Each report addresses a subset of the total set based on priorities such as whether the chemicals are persistent, bioaccumulating or High Production Volume chemicals and/or whether or not there is already regulatory control of the chemical. 

If we do not have any particular preference for a specific parameter or a particular subset of the parameter vector, we can minimize the variance of all parameters simultaneously by minimizing the volume of the joint 95% confidence region. Obviously a small joint confidence region is highly desirable. 

The non-degenerate ground state electron density p/(r) over any subset d of manifold S3, S3 zd d, where subset d has non-zero volume on S3, determines uniquely... 

The articles collected here represent only a subset of the advances that are being made in this rapidly developing area. Successive volumes will emphasize the progress being made in other areas of the subject. The editors are making a specific effort to include contributions from those relatively new to the field, who bring in new ideas and perspectives, as well as those more established in the field who also... 

Invasive hemodynamic monitoring should be considered in patients who are refractory to initial therapy, whose volume status is unclear, or who have clinically significant hypotension such as systolic BP <80 mm Hg. Such monitoring helps guide treatment and classify patients into four specific hemodynamic subsets based on cardiac index and pulmonary artery occlusion pressure (PAOP). Refer to textbook Chap. 16 (Heart Failure) for more information. 

A recently discovered subset of triple-stranded /l-helices from bacteriophage tail proteins (alternatively termed triple-stranded /1-solenoids ) represents another distinct group of /1-fibrous folds (Fig. 3B). In these structures, three identical chains related by threefold rotational symmetry wind around a common axis. These chains form unusual parallel /1-sheets with no intra- and only intermolecular -structural hydrogen bonding. Kajava and Steven (this volume) survey the distinguishing structural features of the known triple-stranded /1-solenoids, also documenting their notable diversity and differences in comparison to the single-stranded /1-solenoids. 

In practice, the scheme as explained above is not implemented. The consecutive generation of all possible chain conformations is a very expensive step. The reason for this is that there are of the order of ZN number of conformations, where Z is the lattice coordination number. A clever trick is to generate a subset of all possible conformations and to use this set in the SCF scheme. This approach is known in the literature as the single-chain mean-field theory, and has found many applications in surfactant and polymeric systems [96]. The important property of these calculations is that intramolecular excluded-volume correlations are rather accurately accounted for. The intermolecular excluded-volume correlations are of course treated on the mean-field level. The CPU time scales with the size of the set of conformations used. One of the obvious problems of this method is that one should make sure that the relevant conformations are included in the set. Typically, the set of conformations is very large, and, as a consequence, the method remains extremely CPU intensive. 

This does, however, raise a number of interesting questions about the way in which social skills relate to neocortex volume. There are, for example, at least three reasons why we might find a relationship between group size and neocortex size (assuming that the latter actually does measure computing power). One is that the animal has to remember all the other individuals with whom it interacts a second is that it has to be able to manipulate the information relating to these individuals in a complex cognitive hyperspace a third is that it has more to do with how the individual relates to a smaller subset of special allies. 

Not all frameworks built from tetrahedra as described above are considered to be zeolites. Dense phases are not considered to be zeolites, only those phases with some porosity. Generally, materials with pores accessible by windows defined by six T-atoms or less (six-rings) are not considered to be zeolites. In fact, the boundary between zeolites and dense phases is somewhat nebulous. lUPAC defines [1] zeolites as a subset of microporous or mesoporous materials containing voids arranged in an ordered manner and with a free volume larger than a 0.25 nm diameter sphere. The Structure Commission of the International Zeolite Association uses the criterion of framework density (T-atoms per lOOOA ) with the maximum framework density for zeolites ranging from 19 to 21. 

As a start to a tetralogy on dendrimers, the volumes Dendrimers and Den-drimers II have already appeared in print. This mini-series continues now with the latest volume Dendrimers III and will be completed by the fourth volume Dendrimers IV within the next few months. Volume III offers dendrimers based on novel design concepts leading to highly stiffened and shape persistent dendritic structures as well as to new families of rather soft and floppy dendrimers and focuses on new functional properties and materials aspects. As an example, the question of host-guest interactions with dendrimers, whose existence has been under intense debate for a long time, finds its final - and positive - answer in this volume. As a consequence, dendrimers clearly represent a subset of supramolecular chemistry. 

The need for a Greek key fold remains obscure. The apoproteins are clearly stable without metals there are examples other than immunoglobulins of Greek key folds. So far copper seems to be found in a very limited subset of structures other chapters in this volume show that zinc, for example, has a much wider variety of environments in proteins, as does iron. It may be that the copper-containing Greek key proteins represent a very small evolutionary niche. Structures of other copper proteins will undoubtedly reveal new surprises and help to clarify the essential role of copper in biological systems. 

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