Topology visualization

The isotropic chord length distribution (CLD) is of limited practical value if soft matter with only short-range order is studied. Nevertheless, the related notions have been fruitful for the development of new methods for topology visualization from SAXS data. 

This is the topology visualized for hypothetical matter-free space-time. The proposition is neither in conflict with general relativity nor with Einstein s strict interpretation of Mach s principle. Superimposed on the uniform curvature of the real projective plane is the local gravitational field that... 

Xue L, Agarwal US, Zhang M, Staal BBP, Muller AHE, Badly CME, Lemstra PJ (2005) Synthesis and direct topology visualization of high-molecular-weight star PMMA. Macromolecules 38 2093-2100... 

The Kohonen network or self-organizing map (SOM) was developed by Teuvo Kohonen [11]. It can be used to classify a set of input vectors according to their similarity. The result of such a network is usually a two-dimensional map. Thus, the Kohonen network is a method for projecting objects from a multidimensional space into a two-dimensional space. This projection keeps the topology of the multidimensional space, i.e., points which are close to one another in the multidimensional space are neighbors in the two-dimensional space as well. An advantage of this method is that the results of such a mapping can easily be visualized. 

The presented scheme offers several extensions. For example, the model gives a clear route for an additional inclusion of entanglement constraints and packing effects [15]. Again, this can be realized with the successful mean field models based on the conformational tube picture [7,9] where the chains do not have free access to the total space between the cross-links but are trapped in a cage due to the additional topological restrictions, as visualized in the cartoon. 

These pharmacophore techniques are different in format from the traditional pharmacophore definitions. They can not be easily visualized and mapped to the molecular structures rather, they are encoded as keys or topological/topographical descriptors. Nonetheless, they capture the same idea as the classic pharmacophore concept. Furthermore, this formalism is quite useful in building quantitative predictive models that can be used to classify and predict biological activities. 

Visualization of Domain Topology from SAXS Data... 

A CDF is interpreted in the same way as a CLD or an IDF. All these functions exhibit the probability distributions of domain size and arrangement. Clearer than a CLD is the IDF, because it does not contain an orientation average but exhibits the topology in a selected direction. Clearer than an IDF is the CDF, because it visualizes the nanodomain topology in space, i.e., in more than one direction. 

The quantitative analysis of a multiphase topology comprises the formulation of structure models and the fitting of measured data. Fitting is discussed in Chap. 11. In this section the setup of topological models is discussed. The problem arises from the fact that most structural models of particle correlation are anisotropic and the visualization of structure in anisotropic materials by means of the CDF shows that suitable models must be rather complex. Thus a direct fit of anisotropic data would require fitting of a measured 3D or 2D function by a complex model. Both the effort to setup such models, and the computational effort to fit the data are very high. 

The microscopic world of atoms is difficult to imagine, let alone visualize in detail. Chemists and chemical engineers employ different molecular modelling tools to study the structure, properties, and reactivity of atoms, and the way they bond to one another. Richard Bader, a chemistry professor at McMaster University, has invented an interpretative theory that is gaining acceptance as an accurate method to describe molecular behaviour and predict molecular properties. According to Dr. Bader, shown below, small molecules are best represented using topological maps, where contour lines (which are commonly used to represent elevation on maps) represent the electron density of molecules. 

A method for visualizing recurrent topological substmctures in sets of active molecules./. Chem. Inf. Comput. Sci. 1998, 38, 915-924. 

Recently, the DAE-0 and DAO-E lattices have been constructed (E. Winfree et al., 1998). With both it is possible to ligate the strands together to get very long reporter strands. The most effective characterization of these arrays has been achieved without ligating them, merely by visualizing them in the atomic force microscope (AFM). It is possible to include a DAO+J or DAE+J motif in these arrays where the J hairpin points up, sometimes DAO+2J or DAE+2J, with one hairpin pointing up and one down these hairpins have no effect on the topology of the array, just as... 

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