56 lines
3.0 KiB
Plaintext
56 lines
3.0 KiB
Plaintext
---
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title: "Relationship between the flagship server and others over time"
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resource-path:
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- "../"
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---
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## Competition Among Servers in Attracting Newcomers
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_How does mastodon.social factor into the aggregate Mastodon onboarding process?_
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{fig-env="figure" width=6cm height=6cm}
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: The main page of mastodon.social as viewed by a logged out web browser on November 1, 2020. The sign-up form is blurred out and instead there is a message suggesting to either sign up on mastodon.online or see a list of servers accepting new accounts at joinmastodon.org.
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Throughout its history, Mastodon's flagship server, mastodon.social, has allowed and disallowed open sign-ups at various times. When the website did not allow sign-ups, it displayed a message redirecting those interested in signing up for an account to mastodon.social or alternatively to a list of potential servers at joinmastodon.com.
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We found three main periods during which mastodon.social did not accept new signups by first noting the times in @fig-account-timeline where the proportion of new accounts on mastodon.social drops to zero. We then used the Internet Archive to verify that signups were disabled during these periods.
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1. An extended period of through the end of October 2020.
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2. A temporary issue when the email host limited the server in mid-2022.
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3. Two periods in late 2022 and early 2023.
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We construct an interrupted time series using an autoregressive integrated moving average (ARIMA) model for sign-ups on mastodon.social, the servers linked in joinmastodon.org, and all other servers. For the first period, we also include mastodon.online since mastodon.social linked to it directly during that time.
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$$
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\begin{aligned}
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y_t &= \beta_0 + \beta_1 \text{open}_t + \beta_2 \text{day}_t + \beta_3 (\text{open} \times \text{day})_t \\
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&\quad + \beta_4 \sin\left(\frac{2\pi t}{7}\right) + \beta_5 \cos\left(\frac{2\pi t}{7}\right) \\
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&\quad + \beta_6 \sin\left(\frac{4\pi t}{7}\right) + \beta_7 \cos\left(\frac{4\pi t}{7}\right) \\
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&\quad + \phi_1 y_{t-1} + \phi_2 y_{t-2} + \epsilon_t
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\end{aligned}
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$$
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where $y_t$ is the number of new accounts on a server at time $t$, $\text{open}_t$ is a binary variable indicating if the server is open to new sign-ups, $\text{day}_t$ is an increasing integer represnting the date, and $\epsilon_t$ is a white noise error term. We use the sine and cosine terms to account for weekly seasonality.
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| Period | Setting | Significant |
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|------------|:----------------|:----|
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| 2020-2021 | mastodon.online | Yes |
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| | JoinMastodon | No |
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| | Other | No |
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| Mid 2022 | JoinMastodon | No |
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| | Other | No |
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| Early 2022 | JoinMastodon | No |
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| | Other | No |
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: Results from ARIMA models for the number of new accounts on mastodon.social, mastodon.online, servers linked in joinmastodon.org, and all other servers.
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# Appendix {#appendix .appendix}
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## Push and Pull Model
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{{< include _push_pull.qmd >}}
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