Planting Synchronisation Trees for Discovering Interaction Patterns Among Brain Regions The proposed data mining method is designed to analyse the synchronisation behaviour of multiple time series with the Kuramoto model which we use to construct synchronisation trees. By transforming time series data with the Hilbert transform, the initial phases of multiple time series can be provided to the model and subsequently the synchronisation process is represented by a tree structure, which can then further be analysed, e.g., by comparing tree edit distances. The proposed analysis might be interesting in the context of neuroscience as brain activity of a subject is often represented by time series corresponding to different brain regions. Discovering certain synchronisation patterns is then useful, when alterations of those patterns can be observed in different pathologies or brain states.

Discovering Periodic Patterns in Irregular Time Series Finding (partial) periodic patterns in time series data is a challenging problem of great importance in many applications. Due to computational reasons, most previous studies in this area have focused on the efficient discovery of periodic patterns in regular time series data. Unfortunately, these studies have limited applicability because realworld data naturally exists as an irregular time series. This paper proposes a more flexible model of periodic pattern that may be present in irregular time series. Two measures, period and periodsupport, were employed to determine the interestingness of a pattern in a series. The former measure captures the interarrival times of a pattern in a series, while the latter captures the number of periodic occurrences of a pattern in a series. A novel tree structure, called Periodic Pattern tree (PPtree), has been introduced to record the irregular occurrences of items within the series. A patterngrowth algorithm has also been presented to find all periodic patterns from PPtree. Experimental results demonstrate that the proposed model can find useful information, and the algorithm is efficient.