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05.06.2026 | Spreading phenomena

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An epidemiologist observed the behavior of a new disease that emerged in southern Brazil 3 years ago. The data shows that 15% of a city's population always has the active virus at any time of the year. The figure below demonstrates the fraction of infected individuals over time. Which endemic model does the new disease follow? A. It is a disease following the SIR model, where, although part of the population builds resistance, in this model there is a transmission resistance to the outside of the city and it will always be present, even if the entire population is affected. B. It is a disease following the SIS model, in which individuals recover from the illness but do not develop permanent immunity, returning to the susceptible state. This continuous cycle allows the virus to circulate indefinitely, balancing the infection and recovery rates to maintain a stable endemic state of 15%.  C. It follows the SI model, given that the virus remains active year-round. In this scenario, the...
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15.05.2026 | Network Robustness

A cybersecurity expert is evaluating the vulnerabilities of a communication grid mapped as a scale-free network. He observes that while the grid survives random router failures effortlessly, it collapses quickly when a very small fraction of specific high-degree routers is targeted. What explains this behavior? A) Targeted attacks uniquely decrease the minimum degree of the network, causing a cascading failure among low-degree nodes. B) Targeted attacks on scale-free networks automatically convert their topology into a random Erdos-Renyi network, which cannot sustain a giant component . C) The attack threshold ( $f_c$ ) for scale-free networks is theoretically proven to be higher than the threshold for random failures . D) Removing a fraction of the hubs significantly lowers the maximum degree of the network and alters the degree distribution, meaning that even removing a tiny fraction of hubs can destroy the network . E) None of the above. Original idea by: Yuri S. Costa
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10.04.2026 | Network Flow

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 In the study of Network Flow, the Ford-Fulkerson algorithm relies on constructing a Residual Network $R_f$ from an original flow network $G$ and a valid flow $f$ . Below is the Residual Graph ( $R_f$ ) generated from an unknown flow network. Which of the following pairs of Original Network $G$ (left) and Flow $f$ (right) correctly generated the Residual Graph above? Pair I: Pair II: Pair III: Pair IV: The alternative that represents the correct statement is: a) Only pair II is correct. b) Only pairs I and III are correct. c) Only pairs II and IV are correct. d) Only pair I is correct. e) None of the above. Original idea by: Yuri S. Costa
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27.03.2026 | SCCs | Graph Algorithms

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Which of the following directed graphs represents a scenario where every single node is its own distinct Strongly Connected Component (SCC)? I.  II. III. IV. The alternative that contains the correct graph(s) is: a) Only graphs I and II. b) Only graphs I, III, and IV. c) Only graph II. d) Only graphs II and IV. e) None of the above. Original idea by: Yuri S. Costa
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13.03.2026 | BFS

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Consider the following statements regarding a Breadth-First Search (BFS) traversal of the graph. Assume that whenever multiple neighbor nodes are available for expansion, they are selected in ascending numerical order : I. The BFS traversal path when starting from node 1 is: 2-4-6-3-7-9-10-5-8.  II. Nodes 5 and 8 are the furthest from node 1, just as node 1 is the furthest node when the search is initiated from either node 5 or 8. III. Adding an edge between nodes 9 and 8 alters the path when expanding from node 1, causing node 8 to be discovered before node 5. IV. Adding a new edge between nodes 2 and 7 makes no difference to the generated path when starting the expansion from node 1. The alternative that represents the correct statements is: a) Only statements I and II are correct. b) Only statements I, III, and IV are correct. c) Only statements II and IV are correct. d) Only statements IIII and IV are correct. e) None of the above. Original idea by: Yuri S. Costa
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06.03.2026 | Graph Theory

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Observe the graph below and choose the correct alternative. Consider the following statements:   I. There are two bridges and two strongly connected components. II. Removing node A results in a graph with no strongly connected components. III. Creating the link HE results in a new strongly connected component. IV. Removing the link IA transforms the graph into a disconnected graph. The alternative that represents the correct statements is: a) Only statements I and II are correct. b) Only statements II and IV are correct. c) Only statements II, III, and IV are correct. d) Only statements I, III, and IV are correct. e) None of the above. Original idea by: Yuri S. Costa
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