Overlap distribution

These experiments use the product state distribution technique to allow a qualitative characterization of the competition between multiple electronic states. In contrast to the pathway competition in the molecular channel of formaldehyde (Section V.D), where the correlated product state distributions delineate the two channels quite cleanly, it will likely more often be the case that the product state distribution method allows only qualitative separation, due to overlapping distributions. Nevertheless, such experiments provide critical insight into pathway competition. 

Baldo B. A., Daniel R. A., Berridge C. W., Kelley A. E. (2003). Overlapping distributions of orexin/hypocretin- and dopamine-beta-hydroxylase immunoreactive fibers in rat brain regions mediating arousal, motivation, and stress. J. Comp. Neurol. 464, 220-37. 

The quantity PJS can then be regarded as the electronic population of the atomic overlap distribution < > < >. Diagonal terms such as P S give the net electronic charge re-... 

The overlap distribution method is more reliable than the direct averaging or single-direction FEP/NEW calculation. For example, it is capable of producing a good estimate of the chemical potential of dense fluids where the latter methods fail... 

The distribution function for globular clusters is somewhat more complicated, as there appear to be two (probably overlapping) distributions corresponding to the halo and the thick disk, respectively. These have been tentatively fitted in Fig. 8.20 with a Simple model truncated at [Fe/H] = —1.1 for the halo and a model for the thick disk clusters with an initial abundance [Fe/H] = —1.6 (the mean metallicity of the halo) and truncated at [Fe/H] = —0.35. The disk-like character of the more metal-rich clusters is supported by their spatial distribution (Zinn 1985). Furthermore, there is a marginally significant shortage of globular clusters in the lowest... 

Resolution, on the other hand, is a more technical term. It refers to the distance between adjacent bands relative to their bandwidths and acknowledges the fact that proteins are distributed in Gaussian profiles with overlapping distributions. The numerical expression for resolution is obtained by dividing the distance between the centers of adjacent bands by some measure of their average bandwidths. It expresses the distance between band centers in units of bandwidth and gives a measure of the overlap between two adjacent bands. For preparative applications, when maximal purity is desired, two proteins to be isolated should be separated by at least a bandwidth. In many applications it is sufficient to be able to simply discern that two bands are distinct. In this case bands can be less than a bandwidth apart. 

The situation is not so simple with K R). The overlap charge distribution is shown in Fig. 2.7 and is far from spherical. The upshot of the differences is that the k2 R) integral is the self-energy of the overlap distribution and is more dependent upon its charge than upon its size. In addition, at any distance there is in ki R) a portion of the distribution that surrotmds the point charge, and, again, the distance dependence is decreased. The overall effect is thus that shown in Fig. 2.4. 

Fig. 6. Distribution of Fe2+/Fe3+ reorganization energies found in the MD simulation of electron transfer in a hydrolyzing solution of Fe3+ (the Fe2+ could hydrolyze, but never does) at an apparent pH near 3.9. The strongly overlapping distributions show almost no shift in reorganization energy as a function of hydrolysis, indicating that the hydrolysis fluctuations lie on a continuum with all other solvent fluctuations.

Sherman et al. (1997) mention two models regarding how the detection of cues leads to acceptance of nestmates. These are similar to the earlier models proposed by Crazier and Dix (1979) and Getz (1982), yet explicitly on the phenotypic level. Under the desirable-present model (D-present), individuals are accepted when they possess desirable cues, i.e. cues that are possessed by nearly all desirable individuals (nestmates), but also by some undesirable individuals (non-nestmates), due to overlapping distribution of cues (Figure 11.2B). Under the undesirable-absent (U-absent) model, individuals are accepted when they lack undesirable cues, i.e. cues that are possessed by undesirable individuals, but also by some desirable individuals. These two fundamentally different models are implicitly also different in their... 

The magnitude of the charge in the overlap distribution, lsals, is S(R), and here again, the overall result is the difference between the energies of attractive and repulsive terms involving the same sized charges of different shaped distributions. The values are shown in Fig. (3), where we see that... 

M., Madden, D.T. et al.. Interaction of Slap2p s ANTH domain with PtdIns(4,5)P2 is important for actin-dependent endocytotic internalization, Mol. Biol. Cell 16, 717-730, 2005 Yao, P.J., Bushlin, I., and Petralia, R.S., Partially overlapping distribution of epsinl and HIPl at the synapse analysis by immunoelectron microscopy, J. Comp. Neurol. 494, 368-379, 2006. 

Figure 3.4 ROC curves for ideal and overlapping distributions of actives and decoys.

Overlap distribution in the bonding and aniibonding molecular ixbitals and the atomic orbitals... 

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