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Spreading Question

  Consider a pathogen spreading on a highly heterogeneous contact network whose degree distribution follows a power law with exponent 2 < γ < 3 2 < \gamma < 3 .  Based on network epidemic theory and immunization strategies, which of the statements below is correct ? A) In networks with 2 < γ < 3 2 < \gamma < 3 , the epidemic threshold λ c \lambda_c ​ is positive. Therefore, random immunization is sufficient to stop the epidemic if at least 30% of the population is vaccinated. B) Strategies that immunize the acquaintances of randomly selected individuals tend to target high-degree nodes, increasing the epidemic threshold. C) The strategy of immunizing acquaintances of random individuals does not improve epidemic control in real networks, because there is no correlation between the degree of a node and the degree of its neighbors. D) For networks with ⟨ k 2 ⟩ → ∞ \langle k^2 \rangle \to \inf , SI and SIS models have the same epidemic threshold, sinc...
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TSP question

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  Considering that ties are decided in alphabetical order, select the alternative with the correct heuristic and the initial state used to obtain the following Traveling Salesperson Problem solution: A. Closest neighbor, starting at vertex  a . B. Cheapest insertion, starting with a cycle with vertices  a, b and c . C.  Closest neighbor, starting at vertex  b . D. Farthest insertion,  starting with a cycle with vertices  a, b  and  c . E. None of the above. Original idea by: Pedro Zaffalon.  
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Degree Correlations Question

Which of the following statements about degree correlations is true: A. In n eutral networks, hubs tend to link with low degrees nodes. B. In  assortative networks, e ⱼₖ tends to be lower for similar values of j and k . C. In disassortative networks, the average degree of the nearest  neighbors is inversely proportional to  a node’s degree. D. In perfectly assortative  networks,  nodes connect to each  other with the expected  random probabilities. E.  None of the above. Original idea by: Pedro Zaffalon.   k n n k n n k n n k n n k n n
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Network Flow Question

Which of the following alternatives contains a false statement regarding network flow? a) The residual network is obtained by subtracting the flow’s edge weights from their corresponding edges in the original network. b) Residual networks obtained from maximum flows have no augmenting path. c) To push flow into an edge, the original vertex needs to have excess flow and the same height as the destination vertex. d) The sum of the weights of all edges of a single vertex in a flow is always zero, except for the source and the sink. e) None of the above. Original idea by: Pedro Zaffalon da Silva
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Which of the following alternatives contains a graph with only one Strongly Connected Component (SCC)?  a) b) c)  d)   e) None of the above Original idea by: Pedro Zaffalon da Silva  
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BFS Question

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A BFS was performed on an unknown graph, producing the following visitation order: a-c-d-b-f-g-e-h There are four candidate graphs: I) II) III) IV)  Assuming that neighbors are always visited in  ascending order , which of the graphs are valid candidates for the original graph? a) I and II b) I and III b) II and IV d)  III and IV e) None of the above Original idea by: Pedro Zaffalon da Silva
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