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Abstract This paper addresses, for the first time, a key aspect of the phenomenology of compact symmetric objects (CSOs): the characteristics of their radio spectra. We present a radio-spectrum description of a complete sample of high-luminosity CSOs (CSO-2s), which shows that they exhibit the complete range of spectral types, including flat-spectrum sources (α≥ −0.5), steep-spectrum sources (α< −0.5), and peaked-spectrum sources. We show that there is no clear correlation between spectral type and size, but there is a correlation between the high-frequency spectral index and both object type and size. We also show that, to avoid biasing the data and to understand the various classes of active galactic nuclei (AGN) involved, the complete range of spectral types should be included in studying the general phenomenology of compact jetted AGN, and that complete samples must be used, selected over a wide range of frequencies. We discuss examples that demonstrate these points. We find that the high-frequency spectral indices of CSO-2s span −1.3 <α_hi< −0.3 and hence that radio spectral signatures cannot be used to discriminate definitively between CSO-2s, binary galactic nuclei, and millilensed objects, unless they haveα_hi> −0.3. 

Aims.Mrk 421 was in its most active state around early 2010, which led to the highest TeV gamma-ray flux ever recorded from any active galactic nuclei (AGN). We aim to characterize the multiwavelength behavior during this exceptional year for Mrk 421, and evaluate whether it is consistent with the picture derived with data from other less exceptional years. Methods.We investigated the period from November 5, 2009, (MJD 55140) until July 3, 2010, (MJD 55380) with extensive coverage from very-high-energy (VHE;E > 100 GeV) gamma rays to radio with MAGIC, VERITAS,Fermi-LAT,RXTE,Swift, GASP-WEBT, VLBA, and a variety of additional optical and radio telescopes. We characterized the variability by deriving fractional variabilities as well as power spectral densities (PSDs). In addition, we investigated images of the jet taken with VLBA and the correlation behavior among different energy bands. Results.Mrk 421 was in widely different states of activity throughout the campaign, ranging from a low-emission state to its highest VHE flux ever recorded. We find the strongest variability in X-rays and VHE gamma rays, and PSDs compatible with power-law functions with indices around 1.5. We observe strong correlations between X-rays and VHE gamma rays at zero time lag with varying characteristics depending on the exact energy band. We also report a marginally significant (∼3σ) positive correlation between high-energy (HE;E > 100 MeV) gamma rays and the ultraviolet band. We detected marginally significant (∼3σ) correlations between the HE and VHE gamma rays, and between HE gamma rays and the X-ray, that disappear when the large flare in February 2010 is excluded from the correlation study, hence indicating the exceptionality of this flaring event in comparison with the rest of the campaign. The 2010 violent activity of Mrk 421 also yielded the first ejection of features in the VLBA images of the jet of Mrk 421. Yet the large uncertainties in the ejection times of these unprecedented radio features prevent us from firmly associating them to the specific flares recorded during the 2010 campaign. We also show that the collected multi-instrument data are consistent with a scenario where the emission is dominated by two regions, a compact and extended zone, which could be considered as a simplified implementation of an energy-stratified jet as suggested by recentIXPEobservations.