SDP Duals without Duality Gaps for a Class of Convex Minimax Programs

In this paper we introduce a new dual program, which is representable as a semi-definite linear programming problem, for a primal convex minimax programming model problem and show that there is no duality gap between the primal and the dual whenever the functions involved are SOS-convex polynomials. Under a suitable constraint qualification, we derive strong duality results for this class of minimax problems. Consequently, we present applications of our results to robust SOS-convex programming problems under data uncertainty and to minimax fractional programming problems with SOS-convex polynomials. We obtain these results by first establishing sum of squares polynomial representations of non-negativity of a convex max function over a system of SOS-convex constraints. The new class of SOS-convex polynomials is an important subclass of convex polynomials and it includes convex quadratic functions and separable convex polynomials. The SOS-convexity of polynomials can numerically be checked by solving semi-definite programming problems whereas numerically verifying convexity of polynomials is generally very hard

Compact steep-spectrum sources from the S4 sample

We present the results of 5-GHz observations with the VLA A-array of a sample of candidate Compact Steep Spectrum sources (CSSs) selected from the S4 survey. We also estimate the symmetry parameters of high-luminosity CSSs selected from different samples of radio sources, and compare these with the larger sources of similar luminosity to understand their evolution and the consistency of the CSSs with the unified scheme for radio galaxies and quasars. The majority of CSSs are likely to be young sources advancing outwards through a dense asymmetric environment. The radio properties of CSSs are found to be consistent with the unified scheme, in which the axes of the quasars are observed close to the line of sight, while radio galaxies are observed close to the plane of the sky.Comment: accepted for publication in mnras; 8 pages, figure 1 with 21 images, and two additional figures; 2 table

Collimation of extragalactic radio jets in compact steep spectrum and larger sources

We study the collimation of radio jets in the high-luminosity Fanaroff-Riley class II sources by examining the dependence of the sizes of hotspots and knots in the radio jets on the overall size of the objects for a sample of compact steep-spectrum or CSS and larger-sized objects. The objects span a wide range in overall size from about 50 pc to nearly 1 Mpc. The mean size of the hotspots increases with the source size during the CSS phase, which is typically taken to be about 20 kpc, and the relationship flattens for the larger sources. The sizes of the knots in the compact as well as the larger sources are consistent with this trend. We discuss possible implications of these trends. We find that the hotspot closer to the nucleus or core component tends to be more compact for the most asymmetric objects where the ratio of separations of the hotspots from the nucleus, r_d > 2. These highly asymmetric sources are invariably CSS objects, and their location in the hotspot size ratio - separation ratio diagram is possibly due to their evolution in an asymmetric environment. We also suggest that some soures, especially of lower luminosity, exhibit an asymmetry in the collimation of the oppositely-directed radio jets.Comment: MNRAS in press, 9 pages and 3 figures, MNRAS LaTe

ExplainIt! -- A declarative root-cause analysis engine for time series data (extended version)

We present ExplainIt!, a declarative, unsupervised root-cause analysis engine that uses time series monitoring data from large complex systems such as data centres. ExplainIt! empowers operators to succinctly specify a large number of causal hypotheses to search for causes of interesting events. ExplainIt! then ranks these hypotheses, reducing the number of causal dependencies from hundreds of thousands to a handful for human understanding. We show how a declarative language, such as SQL, can be effective in declaratively enumerating hypotheses that probe the structure of an unknown probabilistic graphical causal model of the underlying system. Our thesis is that databases are in a unique position to enable users to rapidly explore the possible causal mechanisms in data collected from diverse sources. We empirically demonstrate how ExplainIt! had helped us resolve over 30 performance issues in a commercial product since late 2014, of which we discuss a few cases in detail.Comment: SIGMOD Industry Track 201

Spectral ageing analysis of the double-double radio galaxy J1453+3308

We present new radio observations at frequencies ranging from 240 to 4860 MHz of the well-known, double-double radio galaxy (DDRG), J1453+3308, using both the Giant Metrewave Radio Telescope (GMRT) and the Very Large Array (VLA). These observations enable us to determine the spectra of the inner and outer lobes over a large frequency range and demonstrate that while the spectrum of the outer lobes exhibits significant curvature, that of the inner lobes appears practically straight. The break frequency, and hence the inferred synchrotron age of the outer structure, determined from 16$-$arcsec strips transverse to the source axis, increases with distance from the heads of the lobes. The maximum spectral ages for the northern and southern lobes are $\sim$47 and 58 Myr respectively. Because of the difference in the lengths of the lobes these ages imply a mean separation velocity of the heads of the lobes from the emitting plasma of 0.036c for both the northern and southern lobes. The synchrotron age of the inner double is about 2 Myr which implies an advance velocity of $\sim$0.1c, but these values have large uncertainties because the spectrum is practically straight.Comment: 10 pages, 10 figures, 5 tables, accepted for publication in MNRA

Jet propagation and the asymmetries of CSS radio sources

As Compact Steep Spectrum radio sources have been shown to be more asymmetrical than larger sources of similar powers, there is a high probability that they interact with an asymmetric medium in the central regions of the host elliptical galaxy. We consider a simple analytical model of the propagation of radio jets through a reasonable asymmetric environment and show that they can yield the range of arm-length and luminosity asymmetries that have been observed. We then generalize this to allow for the effects of orientation, and quantify the substantial enhancements of the asymmetries that can be produced in this fashion. We present two-dimensional and three-dimensional simulations of jets propagating through multi-phase media and note that the results from the simulations are also broadly consistent with the observations.Comment: 11 pages, 6 figures, 1 table, accepted for publication in A&