Felipe Crispim

The image below shows the complexity of the global airport network. Suppose it is an undirected network with 9033 nodes, that shows the scale-free property, whose exponent degree (γ) changes over time. Considering that in 2022 January, the computed exponent degree (γ) was 2.8 and in February 3.0, please compute the average distances <d> between the airports in both months (round to 3 decimal places): Image extracted from  https://link.springer.com/article/10.1007/s42452-019-0702-2. A.  January <d>: 3.317, February <d>: 4.795 B. January <d>: 2.209 , February <d>: 4.123 C.  January <d>: 4.123 , February <d>: 2.209 D.  January <d>: 4.795, February <d>: 3.317 E. None of the above. Original idea by: Felipe Crispim da Rocha Salvagnini

 Consider that you work at a company that produces wooden boxes. A client requests a batch of 1000 boxes. However, he has some requirements: All boxes must have a  height  of  1 meter. All boxes must have a  volume  of  10000 liters. Using the data above choose the best box dimensions to spend the less amount of money possible on wood: (Consider a and b as the base dimensions of the  boxes ) A.  a = 3.162m b = 3.162m B.  a = 3.713m b = 3.162m C.  a = 3.713m b = 3.713m D.  a = 3.162m b = 3.713m E. None of the above. Original idea by: Felipe Crispim da Rocha Salvagnini

Considering that the evolution of a random network could be classified into four topologically distinct regimes, analyze the information below about a random network (N=1000) during different stages of its life. It evolved by changing its probability "p" (i.e., G(N, p)). Stage I: p = 0.01 Stage II: p = 0.0063 Stage III: p = 0.001 Stage IV: p = 0.0007 Stage V: p = 0.007 Please, select the option that better represents the stage's topological regime: A.    Stage I: Connected Stage II: Critical Stage III: Supercritical Stage IV: Critical  Stage V: Connected B.  Stage I: Connected Stage II: Connected Stage III: Critical Stage IV: Subcritical Stage V: Connected C.  Stage I: Connected Stage II: Critical Stage III: Subcritical Stage IV: Subcritical Stage V: Supercritical D.  Stage I: Connected Stage II: Supercritical Stage III: Critical Stage IV: Subcritical Stage V: Connected E. None of the above. Original idea by: Felipe Crispim da Rocha ...

One could use the DFS Algorithm to identify the safe order for tasks execution (i.e., for tasks that depend on previous ones), also known as topological sort. Please, select the option that shows which of the following directed graphs above could have its topological order extracted through DFS. I) II) III) Consider the usage of only the DFS algorithm, without additional algorithms to detect strongly connected components and deal with cyclic graphs. A. I. B. I, and III. C.  I, II, and III. D. III. E. None of the above. Original idea by: Felipe Crispim da Rocha Salvagnini