## 4 Conclusions  
We studied the influence of a recommendation system on the formation of originally nonexisting communities in a simulated social media system with collaborative filtering. In our model, people are modeled as simple linear perceptrons, and are characterized by a set of factors, i.e., preferences or tastes. A message is similarly formed by a set of components, and the opinion about a message is given by the match between factors and components. The message emitted by an individual is formed by a subset of his/her weights. The recommendation system delivers messages only to those people that are expected to express a positive judgment according to the database of past opinions. People then have a certain probability of evolving their weights accordingly. We always start by assigning random weights to people, so there is no initial community structure. When the recommendation system is initialized with a limited number of random posts, apparent communities may appear due to fluctuations in the sampling. When the recommendation system is asked to deliver messages only to people that are expected to express a highly positive opinion, those messages are sent only to those belonging to the fake community, which is therefore strengthened in the database. However, in this case the final state of the community structure reflects the real user overlap. However, as already suggested for different systems [31] the clustering effect, i.e., bubble formation, becomes real when people are let free to evolve their factors in the \"direction\" of the incoming messages. In this case, real communities form and stabilize due to the interplay between the initial fluctuations and the recommendation system, and therefore real isolation bubbles are formed. The community structure is strongly dependent on the sequences of messages, and does not depend uniquely on the initial distribution of user factors, i.e., if one could repeat the experience with limited changes (in this case, the order of users selected to send messages), as in the movie \"sliding doors\", one could get a completely different structure of final user \"tastes\". Once a user is connected to other users via the recommendation system, their factors evolve, leading to the formation of communities that were not present in the original distribution of factors. The velocity of the bubble formation depends mainly on the value of the factor evolution parameter that models the memory, while the numbers of community increases when the selection threshold of the recommendation system decreases. Recommendation systems do indeed have an influence on our lives. Probably, the fear for the \"inevitable\" formation of filter bubbles or echo chambers is exaggerated or not universally applicable, but there is indeed an influence at least in the formation of communities. The result is that the very first interactions in a social network with a recommendation system may determine an isolation bubble not univocally determined by the initial opinion  
Figure 7: Histograms of replica simulations made starting from same set of random users, \(R=10\) repetitions and \(M_{0}=200\), \(\tau=0.4\), \(f=0.4\), \(\epsilon=0.3\), \(M=20\),\(000\). For each of these simulations, we varied number of users and number of internal factors (opinions). (**a**) \(N=100\), \(L=40\); (**b**) \(N=100\), \(L=20\); (**c**) \(N=200\), \(L=40\). On x-axes, there is distance between users in replica 1 and same users in other other replicas. of the users, and even promote the formation of communities only based on the random sampling of messages. The consequence is that the first \"posts\" on a social group determine the final community structure. The current model is extremely simplified, which makes the interpretation of results simpler and clearer, with the risks of losing information related to the interaction of a much larger number of users or users with many more internal parameters.