Table 1 An overview of the mathematical symbols
From: Self-regulatory information sharing in participatory social sensing
Symbol | Interpretation |
|---|---|
i | An agent index |
e | An epoch index |
t | A time index within an epoch |
T | Epoch duration |
\(R_{i, e}\) | Sequence of raw data |
\(r_{i, e, t}\) | A record of raw data |
\(S_{i, e}\) | Sequence of summarized data |
\(s_{i, e, t}\) | A record of summarized data |
\(f_{\mathsf {s}}()\) | Summarization function |
j | An index for a possible summarization value |
\(c_{i, e, j}\) | A possible summarization value |
\(k_{i, e}\) | The number of possible summarization values |
l | Number of epochs |
\(\alpha _{i, e}\) | Summarization metric |
\(D_{i, e}\) | Sequence of raw or summarization data |
\(H(D_{i, e})\) | Entropy |
\(p_{i, e, j}\) | Probability of a possible value occurring in an epoch |
\(n_{t}\) | Occurrence or not of possible value at time t |
\(\beta _{i, e}\) | Diversity |
\(m_{t}\) | Change or not between two consecutive time periods t and t + 1 |
\(\epsilon _{i, e, t}\) | Local error |
\(\varepsilon _{i, e}{ t}\) | Global error |
n | Number of participating citizens |
\(\epsilon _{e, t}\) | Average local error among citizens |
\(\gamma _{e}\) | Total rewards that data aggregators are willing to provide |
\(P_{\mathsf {r}}()\) | Probability density function for rewards |
z | Number of discrete participation levels |
\(P_{\mathsf {s}}()\) | Probability density function for summarization |
\(\gamma _{i, e}\) | Rewards provided to agent i |