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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.08594 |
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| _version_ | 1866911915557519360 |
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| author | Agarwal, Khushboo |
| author_facet | Agarwal, Khushboo |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08594 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limiting behaviour of Branching Processes and Online Social Networks Agarwal, Khushboo Probability Social and Information Networks Physics and Society 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). |
| title | Limiting behaviour of Branching Processes and Online Social Networks |
| topic | Probability Social and Information Networks Physics and Society |
| url | https://arxiv.org/abs/2406.08594 |