2024/06/12 by Khushboo Agarwal, Agarwal, Khushboo
Computer Science · Mathematics · #Cellular Automata and Applications #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Probability (math.PR) #Social and Information Networks (cs.SI) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2406.08594
openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The literature considers multi-type Markov branching processes (BPs), where the offspring distribution depends only on the living (current) population. We analyse the total-current population-dependent BPs where the offspring distribution can also depend on the total (dead and living) population. Such a generalization is inspired by the need to accurately model content propagation over online social networks (OSNs). The key question investigated is the time-asymptotic proportion of the populations, which translates to the proportional visibility of the posts on the OSN. We provide the answer using a stochastic approximation (SA) technique, which has not been used in the existing BP literature. The analysis is derived using a non-trivial autonomous measurable ODE. Interestingly, we prove the possibility of a new limiting behaviour for the stochastic trajectory, named as hovering around. Such a result is not just new to the theory of BPs but also to the SA based literature. Later, we explore three new variants of BPs: (i) any living individual of a population can attack and acquire the living individuals of the other population, in addition to producing its offspring; (ii) the individuals can die due to abnormal circumstances, and not just at the completion of their lifetimes; (iii) the expected number of offspring decreases as the total-population increases, leading to the saturation of the total-population. Such variants aid in analysing unexplored aspects of content propagation over OSNs: (i) competition in advertisement posts for similar products; (ii) controlling fake-post propagation, while not affecting the sharing of real-post; (iii) impact of re-forwarding the posts. We also designed and analysed a participation (mean-field) game where the OSN lures the users with a reward-based scheme to provide their opinion about the actuality of the post (fake or real).