First maps

Step 11. At this point a computer program refines the atomic parameters of the atoms that were assigned labels. The atomic parameters consist of the three position parameters x,j, and for each atom. Also one or six atomic displacement parameters that describe how the atom is "smeared" (due to thermal motion or disorder) are refined for each atom. The atomic parameters are varied so that the calculated reflection intensities are made to be as nearly equal as possible to the observed intensities. During this process, estimated phase angles are obtained for all of the reflections whose intensities were measured. A new three-dimensional electron density map is calculated using these calculated phase angles and the observed intensities. There is less false detail in this map than in the first map. 

The second experiment covers the velocity range between the minimum measurable velocity and the minimum velocity detected by the first experiment. It is distorted because of back-folding of high velocities into the spectrum, but it shows the small velocities properly. All voxels from the first map that show zero velocity can now be compared with the corresponding (undistorted) voxels of the second map. If those show a finite velocity, the value can be transferred to the first map. 

Familial hypocalciuric hypercalcemia is inherited in an antosomal dominant manner with almost 100% penetrance but variable expressivity. The FHH locus was first mapped to 3q21-24 by linkage analysis (47). Most FHH families map to the long arm of chromosome 3, but one clearly maps to another locns, 19pl3.3 (44). 

Figure 10.6 Histogram matching. In (a) are shown a histogram from a first map in phase refinement (dashed line) and a theoretical protein histogram (solid line). In (b), the protein histogram (dashed line) and a sharp solvent histogram (solid line) are shown.

A first map of this kind is shown in Fig. 5.8. The X-N deformation density is thermally averaged, and has limited resolution as the summation in Eq. (5.17) is truncated at the limit of the experimental observations. Since both Fobs and Fcalc are complex for an acentric structure, the structure factor phases are continuously variable, and must be considered. Expression (5.17) can be rewritten as... 

The mapping of a watermark message m onto a sequence of watermark letter depends on the coded modulation technique. However, in all schemes considered, the message m is first mapped onto a binary sequence b, with one element hn G 0,1 for each host-data element. Fig. 8 depicts the block diagrams for the encoding of b into d for 4-aiy-CC-TCM,... 

In the proof of Lemma 3.8 it is shown that the first map is zero. ... 

The first map in this sequence corresponds to the incidence relation on Pr, which is the diagonal... 

In the model calculations, the aircraft effluents are put into the models as follows. The gridded fuel bum data (kg fuel/day) are first mapped into the model grid. The amount of material emitted into each grid box is given by the product of the fuel bum and the... 

I will consider the latter case, in which the first map defines a molecular envelope, with perhaps a little additional detail. If more detail can be discerned, the crystallographer can jump ahead to later stages of the map-improvement process I am about to describe. If the molecular envelope cannot be discerned, then more data collection is required. 

The crude molecular image seen in the F0 map, which is obtained from the original indexed intensity data (IFobsI) and the first phase estimates (a calc), serves now as a model of the desired structure. A crude electron density function is devised to describe the unit-cell contents as well as they can be observed in the first map. Then the function is modified to make it more realistic in the light of known properties of proteins and water in crystals. This process is called, depending on the exact details of procedure, density modification, solvent leveling, or solvent flattening. 

Support Vector Machine (SVM) is a classification and regression method developed by Vapnik.30 In support vector regression (SVR), the input variables are first mapped into a higher dimensional feature space by the use of a kernel function, and then a linear model is constructed in this feature space. The kernel functions often used in SVM include linear, polynomial, radial basis function (RBF), and sigmoid function. The generalization performance of SVM depends on the selection of several internal parameters of the algorithm (C and e), the type of kernel, and the parameters of the kernel.31... 

In most insects, pheromones are synthesized in specialized cells or tissues associated with the epidermis (Tillman et al., 1999). Biochemical analyses traced the localization of Scolytid pheromone accumulation to portions of the alimentary canal, particularly the hindgut (e.g. Borden et al., 1969 Byers, 1983), but the actual tissue source of pheromone components was unknown. Fortunately, the tight correlation of HMG-R gene expression with pheromone component biosynthesis meant that hybridization techniques could be used to map the location of pheromone biosynthesis. Northern blots provided the first maps, while in situ hybridizations definitively showed which tissues were elevating HMG-R mRNA in response to feeding or JH III treatment. As with endocrine regulation studies, the molecular and biochemical data complemented each other. 

The equation expresses that the space of all genotypes, the sequence space I, is a discrete space with the Hamming distance as metric. It is mapped onto a discrete space of structures called shape space with the structure distance as metric (We use I rather than 4 in order to indicate different numbering schemes used for sequences and structures). The evolutionarily relevant quantity, the fitness value fk as shown in Fig. 2.3, is derived from the phenotype Sk through evaluation, which can be understood as another mapping, a map from shape space into the positive real numbers including zero, fk = f(Sk). Both maps need not be invertible in the sense that more than one phenotype may have the same fitness value, and more than one sequence may lead to the same structure. We shall study here neutrality induced by the first map, (// in Eq. (6). 

Fig. 2.7 shows the graph of T in A. The shape of the graph explains the mapping s name. All points with x < 0 are mapped monotonically to —oo. Points with x > 1 are first mapped to 3(1 — x) < 0 and then also to —oo. Thus, none of the points outside A will ever be mapped into A. This is an important property. It implies that whenever a point of A is mapped outside A this point will never return to A. Thus, this property is called the never-come-hackpiopeTty. It facilitates appreciably the analysis of the tent map. 

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