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High-energy neutrinos are unique messengers of the high-energy universe, tracing the processes of cosmic-ray acceleration. This paper presents analyses focusing on time-dependent neutrino point-source searches. A scan of the whole sky, making no prior assumption about source candidates, is performed, looking for a space and time clustering of high-energy neutrinos in data collected by the IceCube Neutrino Observatory between 2012 and 2017. No statistically significant evidence for a time-dependent neutrino signal is found with this search during this period since all results are consistent with the background expectation. Within this study period, the blazar 3C 279, showed strong variability, inducing a very prominent gamma-ray flare observed in 2015 June. This event motivated a dedicated study of the blazar, which consists of searching for a time-dependent neutrino signal correlated with the gamma-ray emission. No evidence for a time-dependent signal is found. Hence, an upper limit on the neutrino fluence is derived, allowing us to constrain a hadronic emission model.