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Social networks can be a very successful tool to engage users to discuss relevant topics for society. However, there are also some dangers that are associated with them, such as the emergence of polarization in online discussions. Recently, there has been a growing interest to try to understand this phenomenon, as some consider that this can be harmful concerning the building of a healthy society in which citizens get used to polite discussions and even listening to opinions that may be different from theirs. In this work, we face the problem of defining a precise measure that can quantify in a meaningful way the level of polarization present in an online discussion. We focus on the Reddit social network, given that its primary focus is to foster discussions, in contrast to other social networks that have some other uses. Our measure is based on two different characteristics of an online discussion: the existence of a balanced bipartition of the users of the discussion, where one partition contains mainly users in agreement (regarding the topic of the discussion) and the other users in disagreement, and the degree of negativity of the sentiment of the interactions between these two groups of users. We discuss how different characteristics of the discussions affect the value of our polarization measure, and we finally perform an empirical evaluation over different sets of Reddit discussions about diverse classes of topics. Our results seem to indicate that our measure can capture differences in the polarization level of different discussions, which can be further understood when analyzing the values of the different factors used to define the measure. [ABSTRACT FROM AUTHOR]

The social distancing imposed by the novel coronavirus, SARS-CoV-2, has affected people's everyday lives and has resulted in companies changing the way they conduct business. The airline industry has been continually adapting since the novel coronavirus appeared. A series of airlines have changed their airplane boarding and passenger seat allocation process to increase their passengers' safety. Many suggest a minimum social distance among passengers in the aisle while boarding. Some airlines have reduced their airplanes' capacities by keeping the middle seats empty. Recent literature indicates that the Reverse Pyramid boarding method provides favorable values for boarding time and passenger health metrics when compared to other boarding methods. This paper analyses the extent to which aisle social distancing, the quantity of carry-on luggage, and an airline's relative preferences for different performance metrics influence the optimal number of passengers to board the airplane in each of three boarding groups when the Reverse Pyramid method is used and the middle seats are empty. We also investigate the resulting impact on the average boarding time and health risks to boarding passengers. We use an agent-based model and stochastic simulation approach to evaluate various levels of aisle social distancing among passengers and the quantity of luggage carried aboard the airplane. When minimizing boarding time is the primary objective of an airline, for a given value of aisle social distance, decreasing the carry-on luggage volumes increases the optimal number of boarding group 1 passengers and decreases the optimal number of group 2 passengers with aisle seats; for a given volume of luggage, an increase in aisle social distance is associated with more passengers in group 1 and more aisle seat passengers in group 2. When minimizing the health risk to aisle seat passengers or to window seat passengers, the optimal solution results from assigning an equal number of window seat passengers to groups 1 and 2 and an equal number of aisle seat passengers to groups 2 and 3. This solution is robust to changes in luggage volume and the magnitude of aisle social distance. Furthermore, across all luggage and aisle social distancing scenarios, the solution reduces the health risk to aisle seat passengers between 22.76% and 35.31% while increasing average boarding time by less than 3% in each scenario. [ABSTRACT FROM AUTHOR]

The onset of the novel coronavirus SARS-CoV2 has changed many aspects of people's economic and social activities. For many airlines, social distancing has reduced airplane capacity by one third as a result of keeping the middle seats empty. Additionally, social distancing between passengers traversing the aisle slows the boarding process. Recent literature has suggested that the reverse pyramid boarding method provides favorable values for boarding time and passenger health metrics when compared to other boarding methods with social distancing. Assuming reverse pyramid boarding with the middle seats unoccupied, we determined the number of passengers to include in each of three boarding groups. We assumed that passengers use a jet-bridge that connects the airport terminal to the airplane's front door. We used agent-based modeling and a stochastic simulation to evaluate solutions. A full grid search found an initial good solution, and then local search optimization determined the best solution based upon the airline's relative preference for minimizing average boarding time and minimizing risks to previously seated passengers from later-boarding, potentially contagious passengers breathing near them. The resulting solution contained the number of passengers to place into each of the three boarding groups. If an airline is most concerned about the health risk to seated passengers from later boarding passengers walking near them, the best three-group reverse pyramid method adapted for social distancing will first board passengers with window seats in the rear half of the airplane, then will board passengers with window seats in the front half of the airplane and those with aisle seats in the rear half of the airplane, and finally will board the passengers with aisle seats in the front half of the airplane. The resulting solution takes about 2% longer to board than the three-group solution that minimizes boarding time while providing a 25% decrease in health risk to aisle seat passengers from later boarding passengers. [ABSTRACT FROM AUTHOR]