From: A robust information source estimator with sparse observations
Description | |
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q _{ uv } | The probability an infected node u infects its neighbor node v |
p _{ v } | The probability an infected node v recovers |
Y | The partial snapshot |
X_{ v }(t) | The state of node v at time t |
X(t) | The states of all nodes at time t |
X[ 0,t] | The sample path from 0 to t |
$\mathcal{X}\left(t\right)$ | The set of all valid sample paths from time slot 0 to t |
${\mathcal{I}}_{\mathbf{\text{Y}}}$ | The set of the observed infected nodes |
${\mathcal{\mathscr{H}}}_{\mathbf{\text{Y}}}$ | The set of the unobserved nodes |
$\stackrel{~}{e}(v,{\mathcal{I}}_{\mathbf{\text{Y}}})$ | The observed infection eccentricity of node v |
v ^{†} | The estimator of the information source |
v ^{∗} | The actual information source |
${t}_{v}^{\ast}$ | The time duration associated to the optimal sample path in which node v is the |
information source | |
$\mathcal{C}\left(v\right)$ | The set of children of v |
ϕ(v) | The parent of node v |
${\mathcal{Y}}^{k}$ | The set of infection topologies where the maximum distance from the source to |
an infected node is k | |
T _{ v } | The tree rooted in v |
${T}_{v}^{-u}$ | The tree rooted in v without the branch from its neighbor u |
$\mathbf{\text{X}}\left([\phantom{\rule{0.3em}{0ex}}0,t],{T}_{v}^{-u}\right)$ | The sample path restricted to topology ${T}_{v}^{-u}$ |
${t}_{v}^{I},{t}_{v}^{R}$ | The infection time and recovery time of node v |
d(v,u) | The length of the shortest path between node v and node u |