Structural histogram

Examination of the cumulated histogram of localized AE sources for all monitoring intervals, in different operating conditions, suggests the conclusion that no structurally significant sources have been active in the monitored area of the SH header. 

Figure 4 Sample spatial restraint m Modeller. A restraint on a given C -C , distance, d, is expressed as a conditional probability density function that depends on two other equivalent distances (d = 17.0 and d" = 23.5) p(dld, d"). The restraint (continuous line) is obtained by least-squares fitting a sum of two Gaussian functions to the histogram, which in turn is derived from many triple alignments of protein structures. In practice, more complicated restraints are used that depend on additional information such as similarity between the proteins, solvent accessibility, and distance from a gap m the alignment.

Mixmre models have come up frequently in Bayesian statistical analysis in molecular and structural biology [16,28] as described below, so a description is useful here. Mixture models can be used when simple forms such as the exponential or Dirichlet function alone do not describe the data well. This is usually the case for a multimodal data distribution (as might be evident from a histogram of the data), when clearly a single Gaussian function will not suffice. A mixture is a sum of simple forms for the likelihood ... 

Figure 2.8 Adjacent antiparallel P strands are joined by hairpin loops. Such loops are frequently short and do not have regular secondary structure. Nevertheless, many loop regions in different proteins have similar structures, (a) Histogram showing the frequency of hairpin loops of different lengths in 62 different proteins, (b) The two most frequently occurring two-residue hairpin loops Type I turn to the left and Type II turn to the right. Bonds within the hairpin loop are green, [(a) Adapted from B.L. Sibanda and J.M. Thornton, Nature 316 170-174, 1985.]...

Critical points were obtained by inspection of histograms Pl N — Nb) of the number difference on different length scales L and analysis by the fourth-order cumulant (see Sec. IV A) obtained by subdivision of the simulation boxes of sizes and V2 (Ei + F2 = F) into smaller subsystems of size Lx L. For A < Ac the distributions are all singly peaked, for larger A a single-peak structure of Pl a b) results for large L and a double-peak structure for small L. An analysis of these histograms with the cumulants Ui = - ((V - - Nb) ) allows a determination of critical... 

Figure 8. A histogram of the energy distribution of the structures from Figure 7.

Figure 9. A histogram of the energy distribution of 1000 random structures which have been (a) minimized for 2000 steps, and (b) further subjected to 5 ps of dynamics at 600K and reminimized for 2000 steps.

Fig. 42.3. Time series of the observed queue lengths (n) in a department for structural analysis, with their corresponding histograms fitted with a Gaussian distribution.

Fig. 42.7. Histograms and cumulative distributions of the delays (waiting time + analysis time) in a department for structural analysis. (I) Observed values. ( ) Cumulative distribution. ( ) Fit with a theoretical model (not discussed in this chapter).

FIGURE 6.10 Three characteristic structures of pressure-treated casein micelles representative AFM images together with the associated size-histograms are shown. The solid lines are fit to Gauss distributions. (A) Intact micelles, P < SO MPa (B) compact reconstituted micelles, 120 MPa < P < 240 MPa (C) mini-micelles, P > 280 MPa. Reprinted with permission from Gebhardt et al. (2006). 

Fig. 26 (a) Structures of pyridine-, terpyridine-, and thiol-terminated PBI derivatives with different substituents at the bay positions X and X . The inset illustrates the alternation of optical properties of the PBIs with different bay-area substituents, (b) Plateau data-point histogram of Py-PBI in a mixture of mesitylene/THF (4 1). bias = 0.1 V, tip retraction rate was 60 nm s-1. The inset show the bias voltage dependence of the current through a molecular junction... 

Table 2 summarizes the numerical results on average intermolecular/interi-onic 0---0 and intramolecular/intra-ionic C-0 structural parameters for the [COOH]n---[COOH]n, [COOH]a---[COOH]a and [COOH]A---[COO]A inter-molecular interactions, together with those obtained for the [COOH] A- [COO ]A sample in the case of the hydrogen oxalate anion. Data were retrieved from the CSD with a cut-off distance on 0-"0 separations of 3.0 A. A visual prospect of the data listed in column III is provided in Fig. 6, where histograms of intramolecular C-0 distances within the protonated and deprotonated COOH/COO groups are presented. 

Figure 3.30. Analysis of the cP4-AuCu3 type structure. Coordination and interatomic (reduced) distances. The total number (n) of near-neighbour atoms around Au and Cu are plotted as a function of their reduced distances from the reference atom. The symbols of the surrounding atoms are indicated. Notice the similarity between the two histograms.

Considering then the phase composition as a significant parameter, we obtain the histogram shown in Fig. 7.1(a) for the distribution of the intermetallic phases according to the stoichiometry of binary prototypes. For instance, the binary Laves phases, the A1B2, Caln2, etc., type phases are all included in the number reported for the 66-67.99 stoichiometry range, even if the real stoichiometry of the specific phase is different, see Fig. 7.1(b). We may note the overall prevalence of phases and, to a certain extent, of structural types, which may be related to simple (1 2, 1 1, 1 3, 2 3, etc.) stoichiometric ratios. 

Figure 5. (Continued) different panels (e and f for HeLa, j and k for chicken erythrocyte, and o and p for yeast). A section profile obtained along X-Y line shows a typical granular structure in die nucleus (e, j, o), and the peak-to-peak distance between the granular structure was distributed from 60 nm to 120 nm (e). The diickness of the chromatin fibers released out of die nucleus varied possibly due to the assembly of diinner fibers (f, k, p). A section profile for the spread fibers was obtained along X-Y line (f, k, p). Isolated HeLa cell nucleus was treated widi (r, s) or without (q) RNase. The treatment releases SOnmfiber from the nucleus. The histogram of die fiber width is shown in an inset of (s). Bars, 250 nm. (See Colour Plate 2.)...

D. L. (2008) Solving the crystal structures of zeolites using electron diffraction data. 1. The use of potential-density histograms. Acta Crystallogr. A, A64, 284-294. 

Figure 9.3 A histogram of the final / mim values for 100 trial structures for 1JC4 was made by dividing the range of the values (0.158-0.315) into 15 intervals (buckets) and counting the number of trials whose / min values fell into each bucket. The 29 trials in the two left buckets with the lowest / y fj values are solutions, and the trials in the buckets at the right are non-solutions.

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