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There is still a limited number of high-redshift (z > 3) active galactic nuclei (AGNs) whose jet kinematics have been studied with very long baseline interferometry (VLBI). Without a dedicated proper motion survey, regularly conducted astrometric VLBI observations of bright radio-emitting AGN with sensitive arrays can be utilized to follow changes in the jets, by means of high-resolution imaging and brightness distribution modelling. Here, we present a first-time VLBI jet kinematic study of NVSS J080518 + 614423 (z = 3.033) and NVSS J165844 − 073918 (z = 3.742), two flat-spectrum radio quasars that display milliarcsecond-scale jet morphology. Archival astrometric observations carried out mainly with the Very Long Baseline Array, supplemented by recent data taken with the European VLBI Network, allowed us to monitor changes in their radio structure in the 7.6−8.6 GHz frequency band, covering almost two decades. By identifying individual jet components at each epoch, we were able to determine the apparent proper motion for multiple features in both sources. Apparent superluminal motions range $(1-14)\, c$, and are found to be consistent with studies of other high-redshift AGN targets. Using the physical parameters derived from the brightness distribution modelling, we estimate the Doppler-boosting factors (δ ≈ 11.2 and δ ≈ 2.7), the Lorentz factors (Γ ≈ 7.4 and Γ ≈ 36.6), and the jet viewing angles (θ ≈ 4.4° and θ ≈ 8.0°), for NVSS J080518 + 614423 and NVSS J165844 − 073918, respectively. The data revealed a stationary jet component with negligible apparent proper motion in NVSS J165844 − 073918.

NGC 4395 is a dwarf galaxy at a distance of about 4.3 Mpc (scale: ∼0.021 pc mas−1). It hosts an intermediate-mass black hole (IMBH) with a mass between ∼104 and ∼105 solar masses. The early radio observations of NGC 4395 with the very long baseline interferometry (VLBI) network, High Sensitivity Array (HSA), at 1.4 GHz in 2005 showed that its nucleus has a sub-mJy outflow-like feature (E) extending over 15 mas. To probe the possibility of the feature E as a continuous jet with a base physically coupled with the accretion disc, we performed deep VLBI observations with the European VLBI Network (EVN) at 5 GHz, and analysed the archival data obtained with the HSA at 1.4 GHz in 2008, NSF’s Karl G. Jansky Very Large Array (VLA) at 12–18 GHz and the Atacama Large Millimetre/submillimetre Array (ALMA) at 237 GHz. The feature E displays more diffuse structure in the HSA image of 2008 and has no compact substructure detected in the EVN image. Together with the optically thin steep spectrum and the extremely large angular offset (about 220 mas) from the accurate optical Gaia position, we explain the feature E as nuclear shocks likely formed by the IMBH’s episodic ejection or wide-angle outflow. The VLA and ALMA observations find a sub-mJy pc-scale diffuse feature, possibly tracing a thermal free–free emission region near the IMBH. There is no detection of a jet base at the IMBH position in the VLBI maps. The non-detections give an extremely low luminosity of ≤4.7 × 1033 erg s−1 at 5 GHz and indicate no evidence of a disc-jet coupling on sub-pc scales.

In the time domain, the radio sky in particular along the Galactic plane direction may vary significantly because of various energetic activities associated with stars, stellar, and supermassive black holes. Multi-epoch Very Large Array surveys of the Galactic plane at 5.0 GHz enabled the finding of a catalogue of 39 variable radio sources in the flux density range 1–70 mJy. To probe their radio structures and spectra, we observed 17 sources with the very-long-baseline interferometric (VLBI) imaging technique and collected additional multifrequency data from the literature. We detected all of the sources at 5 GHz with the Westerbork Synthesis Radio Telescope, but only G23.6644–0.0372 with the European VLBI Network (EVN). Together with its decadal variability and multifrequency radio spectrum, we interpret it as an extragalactic peaked-spectrum source with a size of ≲10 pc. The remaining sources were resolved out by the long baselines of the EVN because of either strong scatter broadening at the Galactic latitude < 1° or intrinsically very extended structures on centi-arcsec scales. According to their spectral and structural properties, we find that the sample has a diverse nature. We notice two young H ii regions and spot a radio star and a candidate planetary nebula. The rest of the sources are very likely associated with radio active galactic nuclei (AGNs). Two of them also display arcsec-scale faint jet activity. The sample study indicates that AGNs are common place even among variable radio sources in the Galactic plane.