핵심 개념
Compressing the chronology of a temporal network while preserving the underlying epidemic dynamics by quantifying the error induced by aggregating consecutive network snapshots.
초록
The content discusses a method to compress the chronology of a temporal network while preserving the underlying epidemic dynamics. The key points are:
Temporal interaction data is often represented as a series of "snapshots" - static networks active for short durations of time. Aggregating these snapshots can reduce analytical complexity, but it is nontrivial to determine when and how to do so without losing critical information about the dynamics.
The authors propose a method to compress network chronologies by progressively combining pairs of snapshots whose matrix commutators have the smallest dynamical effect on an epidemic spreading model. This quantifies the importance of chronology by considering its effects on the dynamics.
The method involves linearizing the susceptible-infected (SI) epidemic model and using the matrix commutator between consecutive snapshots as a measure of the error induced by aggregation. This error is used to greedily combine snapshots while preserving changes that significantly affect the dynamical process.
The authors apply this method to synthetic networks and real contact tracing data, showing that it can achieve significant compression while remaining faithful to the epidemic dynamics, outperforming even-width aggregation and an information-theoretic compression approach.
The error measure and compression algorithm have several potential applications, including bounding the accuracy of dynamics on temporal networks, compressing large temporal network datasets, estimating the quality of data collection, and comparing the structure of different networks.
통계
The content does not provide specific numerical data or statistics. The key figures and equations are:
Eq. (2): Linearized SI model dynamics
Eq. (3): Time-ordered exponential solution for SI dynamics on a series of snapshots
Eq. (6): Baker-Campbell-Hausdorff formula for aggregating snapshots
Eq. (7) and (8): Error measures for aggregating snapshots
Eq. (9): Combined error measure used in the compression algorithm
인용구
The content does not contain any direct quotes that are particularly striking or supportive of the key arguments.