Butterfly graph

Figure 1 illustrates a simple application of the Sachs algorithm to determine the spectrum of the four-vertex butterfly graph. The adjacency matrix of the butterfly graph (Figure la) is the following 4x4 matrix ... 

Sesqulvalent subgraphs of the butterfly graph with four vertices... 

Figure 1 (a) The four-vertex butterfly graph (b) the sesquivalent... 

An example will help to clear this point up. Fixing the value of y at 15, we can compute the cusp of fifth-order (or butterfly) singular points originating from the sixth-order singularity in the feasible region. When these points are plotted in the v-B plane, the result is the upper graph in Fig. 13. Choosing v and B to have the values 0.7520 and 930,000, the hysteresis variety projected... 

Draw two graphs. As the independent variable, use the ratio of Viceroy butterflies to Monarch butterflies. As the dependent variables, plot the expected population numbers of each kind of butterfly. Make the curves relative to the maximum population as the ratio varies. Justify why you drew the curves as you did. 

Currently available HX-MS software provides users with various options to visualize HX results (reviewed in Section 3.3.5). Some common options include deuterium uptake kinetic curves, heat maps [56], and butterfly plots [59]. The latter two present information such as the protein conformational dynamics and the differential deuterium uptake comparisons of full-length proteins in a single graph, making data interpretation more efficient. Anotha- informative way to interpret the HX results is to map the changes of deuterium uptake onto a known X-ray stracture of the antigen [41]. 

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