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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