Controlling Fake News by Collective Tagging: A Branching Process Analysis

Kapsikar, Suyog; Saha, Indrajit; Agarwal, Khushboo; Kavitha, Veeraruna; Zhu, Quanyan

doi:10.23919/acc50511.2021.9483257

Cited by 2 publications

(5 citation statements)

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“…Accordingly, the number of forwards (Γ(A(τ − ))) can be viewed as the offsprings of the population. Further, when the post is shared by a user, the current shares reduce by 1 (see ( 1)); this is exactly like a death in a BP (see [1], [5], [7] for similar details).…”

Section: A Saturated Content Propagation and Branching Processmentioning

confidence: 99%

“…To facilitate the study of STP-BP, we analyse the embedded chain corresponding to the underlying continuous-time process, as in [5], [7]. In general, it is a standard technique to use embedded chains, when transience, recurrence, extinction and similar properties of continuous-time jump process are studied.…”

Section: Dynamics and Ode Approximationmentioning

confidence: 99%

“…As in [5], [7], we use stochastic approximation (SA) approach to study the embedded chain. Towards this, define the following fractions of current and total shares respectively, Ψ c n := Cn /n and Ψ a n := An /n for n ≥ 1, with…”

Section: Dynamics and Ode Approximationmentioning

confidence: 99%

“…Thus, we have two operators which are converging towards each other; the first operator including ε n in (7) provides the BP trajectory, while the second operator without ε n in (7) provides the ODE solution. Further, using Maximum theorem, we show that the difference between the two solutions of the operators (7) with and without ε n is small, when ||ε n || is small. Formally, we state the result as follows:…”

Section: Dynamics and Ode Approximationmentioning

confidence: 99%

“…At last, we validate our theory through detailed simulations on the SNAP Twitter dataset, which illustrate a good fit. Recently, we analysed many new variants of BPs, using a new approach based on stochastic approximation techniques, e.g., attack and acquisition BP (competing viral markets [5]), and proportion dependent BP (fake news on OSNs [7]). Further modifying the said approach to address the required finite horizon analysis, we are able to analyse saturation resulting from total population dependency.…”

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Saturated total-population dependent branching process and viral markets

Agarwal¹,

Kavitha²

2022

Preprint

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The universal prevalence of online social networks (OSNs) is unquestionable today; the interesting posts/contents are forwarded repeatedly by the users of the OSN. Such propagation leads to the re-forwarding of the post to a subset of previous recipients, which increases as the post gets viral (reaches a large number of the users). Consequently, the effective forwards (after deleting the re-forwards) reduce, eventually leading to the saturation of the total number of copies. We study such a process using a new variant of the branching process and named it as 'Saturated total-population-dependent branching process'.We analyse the new variant using the stochastic approximation technique and derive an ODE, dependent on the expected effective forwards. Finally, we obtain deterministic trajectories which approximate the total and unread copies of the post 'asymptotically and almost surely' over any finite time window; this trajectory is entirely described by four parameters related to the network characteristics. Further, we provide theoretical expressions for the peak unread copies, maximum outreach and the life span of the post. We again observe well-known exponential growth, however, with time-varying rates. At last, we validate our theory through detailed simulations on the SNAP Twitter dataset, which illustrate a good fit. Recently, we analysed many new variants of BPs, using a new approach based on stochastic approximation techniques, e.g., attack and acquisition BP (competing viral markets [5]), and proportion dependent BP (fake news on OSNs [7]).Further modifying the said approach to address the required finite horizon analysis, we are able to analyse saturation resulting from total population dependency. Key contributions: The contribution of this paper is two fold: first, we formally analyse the STP-BP. We derive an appropriate ordinary differential equation (ODE) and its solution which (time asymptotically) almost surely approx-

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Section: A Saturated Content Propagation and Branching Processmentioning

confidence: 99%

Section: Dynamics and Ode Approximationmentioning

confidence: 99%

Section: Dynamics and Ode Approximationmentioning

confidence: 99%

Section: Dynamics and Ode Approximationmentioning

confidence: 99%

mentioning

confidence: 99%

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Saturated total-population dependent branching process and viral markets

Agarwal¹,

Kavitha²

2022

Preprint

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Stochastic Growth Models for the Spreading of Fake News

Di Crescenzo,

Paraggio,

Spina

2023

Mathematics

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The propagation of fake news in online social networks nowadays is becoming a critical issue. Consequently, many mathematical models have been proposed to mimic the related time evolution. In this work, we first consider a deterministic model that describes rumor propagation and can be viewed as an extended logistic model. In particular, we analyze the main features of the growth curve, such as the limit behavior, the inflection point, and the threshold-crossing-time, through fixed boundaries. Then, in order to study the stochastic counterparts of the model, we consider two different stochastic processes: a time non-homogeneous linear pure birth process and a lognormal diffusion process. The conditions under which the means of the processes are identical to the deterministic curve are discussed. The first-passage-time problem is also investigated both for the birth process and the lognormal diffusion process. Finally, in order to study the variability of the stochastic processes introduced so far, we perform a comparison between their variances.

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Controlling Fake News by Collective Tagging: A Branching Process Analysis

Cited by 2 publications

References 14 publications

Saturated total-population dependent branching process and viral markets

Saturated total-population dependent branching process and viral markets

Stochastic Growth Models for the Spreading of Fake News

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