Prestige for all edge cases

Pn={P(n1)×min(ΔK,c) if ΔK1P(n1)×max(ΔK,p) if ΔK<1\displaystyle\mathfrak{P}{\tiny n} = \begin{cases} \mathfrak{P}{\tiny (n-1)} \times min(\sum \Delta K, c) \text{ if } \sum \Delta K \ge 1 \\ \\ \mathfrak{P}{\tiny(n-1)} \times max(\sum \Delta K, p{\tiny \ominus}) \text{ if } \sum \Delta K < 1\end{cases}

Where:

  • Pn\mathfrak {P}_{n} is the Prestige of a community in the given period.

  • P(n1)\mathfrak {P}_{(n-1)} is the Prestige of a community in the previous period.

  • c: constraint factor, just like in the PS framework, c controls the slope in P\mathfrak{P}’s rate of change. It’s initially fixed at to 1.4 (40% growth), later customizable by the Hub itself.

  • pp_{\tiny \ominus} is the penalty factor for Hubs inactive in a specific period. Same as in Participation Score.

  • ΔK\sum \Delta K is the sum of the rates of change of each individual parameter, between the current and the previous intervals.

Relationship between Participation Score & Prestige

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