Vectors domain pattern

Tax, D., Duin, E., 1999. Support vector domain description. Pattern Recognit. Lett. 20, 1191-1199. 

A similarity assessment of the shapes encoded by these vectors can be carried out on various levels. For two molecules (or conformers) Mj and M2, the number of matches along their C(M ) and C(M2) vectors, divided by the dimension (3 x 861), provides a simple, numerical similarity measure [262]. The comparison of the first 2 x 861 components [i.e., the comparison of vectors C( )(Mi) and C(2)(Mi) to C( )(M2) and C(2)(M2), respectively] appears the most important for a crude shape analysis, since these vectors store the information on the number and type of shape domains occurring for various a and b parameter values. By contrast, a direct comparison of vectors C<3)(M ) and C(3)(M2) gives information on the similarities of the patterns of different shape domains on the two families of molecular surfaces. 

Here, Pcz>/ P>gd/ o are constant for the whole pattern (taken at zero value of the wave vector Sq of the first peak). The integral breaths found from the experimental diffraction profiles allow calculation of the surface-weighted (Ds) and volume-weighted (Dy) domain size and a mean-square (Gaussian) strain, s, which is the total strain averaged over infinite distance ... 

Stationary domain walls. For the sake of simplicity, let us consider a plane domain wall perpendicular to the axis X, which separates two semi-infinite roll systems with wave vectors ki and lc2 [51], as shown in Fig. 15a. Because the Lyapunov functional densities of both roll patterns are equal, there is no reason for a motion of the domain wall, hence it is motionless [52]. The problem is governed by the following system of ordinary differential equations ... 

Using a vector carrying a splice acceptor sequence placed upstream of a reporter gene (such as lacZ or GFP [green fluorescent protein]), different types of regulatory or gene sequences can be trapped (31-33). ES cell-chimeric embryos are stained for the histochemical marker to reveal expression domains of the tr jped elements (31-33). On the basis of the expression pattern information... 

The circularly averaged intensity of the patterns at lOQ C monotonicaUy decreases with scattering vector q (Fig. 7.7). The increase in intensity with time can be associated with the increases in the number and/or the anisotropy of the domains. In Fig. 7.8, the shape of the log-log plots of scattering profiles indicates that the domains are fractal objects. Kratky plots in Fig. 7.9 indicate that these domains are diffuse. For, the intensity profiles at high q region (if q I, where a the length scale of the scattering objects,) can be fitted to the Porod form [52-54] ... 

---