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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. Using multi-epoch Very Large Array surveys of the Galactic plane at 5.0 GHz, Becker et al. (2010) presented 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 multi-frequency 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 multi-frequency 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 deg 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 (AGN). Two of them also displays arcsec-scale faint jet activity. The sample study indicates that AGN are commonplace even among variable radio sources in the Galactic plane., Comment: 15 pages, 18 figures, accepted for publication in MNRAS

The jet in active galactic nuclei (AGN) is a key ingredient in understanding the co-evolution of galaxies and their central supermassive black holes (SMBHs). Unfortunately, the mechanism of jet launching and collimation is still elusive. The observational evidence of decreasing radio loudness with increasing Eddington ratio implies that the jet should be coupled with the accretion process. To further explore the relationship between the jet and accretion, it is necessary to extend our knowledge of the jet to an extreme end of the Eddington ratio distribution of AGN. Using Very Long Baseline Array (VLBA), we report the detection of the parsec-scale radio structure in Mrk 335, a radio-quiet narrow-line Seyfert 1 galaxy with an Eddington ratio close to/above unity. The VLBA image at 1.5 GHz reveals an elongated structure extending $\sim20$ parsec in north-south direction with a peak flux density of $1.98\pm0.05$ mJy/beam and radio brightness temperatures as high as $6\times10^{7}$ K. This feature provides a strong evidence of a parsec-scale (bipolar) jet launched from a highly accreting SMBH. We discuss the result by comparing Mrk 335 with other highly accreting systems, e.g. Galactic black holes and tidal disruption events, and recall the discovery of collimated corona in the vicinity of SMBH in Mrk 335 by previous X-ray observations, whose relation to the parsec-scale radio jet should be explored by future simultaneous X-ray spectroscopy and high resolution radio observations., Comment: Published in MNRAS, 9 pages, 2 figures

Cloud networks are difficult to monitor because they grow rapidly and the budgets for monitoring them are limited. We propose a framework for estimating network metrics, such as latency and packet loss, with guarantees on estimation errors for a fixed monitoring budget. Our proposed algorithms produce a distribution of probes across network paths, which we then monitor; and are based on A- and E-optimal experimental designs in statistics. Unfortunately, these designs are too computationally costly to use at production scale. We propose their scalable and near-optimal approximations based on the Frank-Wolfe algorithm. We validate our approaches in simulation on real network topologies, and also using a production probing system in a real cloud network. We show major gains in reducing the probing budget compared to both production and academic baselines, while maintaining low estimation errors, even with very low probing budgets.

In this paper, we give a complete study on the existence and non-existence of normalized solutions for Schr\"{o}dinger system with quadratic and cubic interactions. In the one dimension case, the energy functional is bounded from below on the product of $L^2$-spheres, normalized ground states exist and are obtained as global minimizers. When $N=2$, the energy functional is not always bounded on the product of $L^2$-spheres. We give a classification of the existence and nonexistence of global minimizers. Then under suitable conditions on $b_1$ and $b_2$, we prove the existence of normalized solutions. When $N=3$, the energy functional is always unbounded on the product of $L^2$-spheres. We show that under suitable conditions on $b_1$ and $b_2$, at least two normalized solutions exist, one is a ground state and the other is an excited state. Furthermore, by refining the upper bound of the ground state energy, we provide a precise mass collapse behavior of the ground state and a precise limit behavior of the excited state as $\beta\rightarrow 0$. Finally, we deal with the high dimensional cases $N\geq 4$. Several non-existence results are obtained if $\beta<0$. When $N=4$, $\beta>0$, the system is a mass-energy double critical problem, we obtain the existence of a normalized ground state and its synchronized mass collapse behavior. Comparing with the well studied homogeneous case $\beta=0$, our main results indicate that the quadratic interaction term not only enriches the set of solutions to the above Schr\"{o}dinger system but also leads to a stabilization of the related evolution system., Comment: 59 pages

Jets of high-redshift active galactic nuclei (AGNs) can be used to directly probe the activity of the black holes in the early Universe. Radio sources with jets misaligned with respect to the line of sight are expected to dominate the high-redshift AGN population. In this paper, we present the high-resolution imaging results of a z=4.57 AGN J2102+6015 by analyzing its multi-epoch dual-frequency very long baseline interferometry (VLBI) data. The 8.4-GHz VLBI images reveal two major features along the east-west direction separated by $\sim$ 10 milli-arcsec (mas). From the spectral index map, both features show flat/inverted spectra. The separation between the two features remains almost unchanged over an observation period of $\sim$ 13 years, placing an upper limit of the separation speed as about 0.04 mas year$^{-1}$. Previous studies have classified the source as a GHz-peaked spectrum quasar. Our results indicate that J2102+6015 is most likely a young, compact symmetric object rather than a blazar-type core-jet source., Comment: 11 pages, 5 figures, accepted by MNRAS

In this paper, we consider the existence and asymptotic behavior on mass of the positive solutions to the following system: \begin{equation}\label{eqA0.1}\nonumber \begin{cases} -\Delta u+\lambda_1u=\mu_1u^3+\alpha_1|u|^{p-2}u+\beta v^2u\quad&\hbox{in}~\R^4,\\ -\Delta v+\lambda_2v=\mu_2v^3+\alpha_2|v|^{p-2}v+\beta u^2v\quad&\hbox{in}~\R^4,\\ \end{cases} \end{equation} under the mass constraint $$\int_{\R^4}u^2=a_1^2\quad\text{and}\quad\int_{\R^4}v^2=a_2^2,$$ where $a_1,a_2$ are prescribed, $\mu_1,\mu_2,\beta>0$; $\alpha_1,\alpha_2\in \R$, $p\!\in\! (2,4)$ and $\lambda_1,\lambda_2\!\in\!\R$ appear as Lagrange multipliers. Firstly, we establish a non-existence result for the repulsive interaction case, i.e., $\alpha_i<0(i=1,2)$. Then turning to the case of $\alpha_i>0 (i=1,2)$, if $2