Qualitative Theory for Lensed QSOs

We show that some characteristics of multiply-imaged QSO systems are very model-independent and can be deduced accurately by simply scrutinizing the relative positions of images and galaxy-lens center. These include the time-ordering of the images, the orientation of the lens potential, and the rough morphology of any ring. Other features can differ considerably between specific models; H_0 is an example. Surprisingly, properties inherited from a circularly symmetric lens system are model-dependent, whereas features that arise from the breaking of circular symmetry are model-independent. We first develop these results from some abstract geometrical ideas, then illustrate them for some well-known systems (the quads Q2237+030, H1413+117, HST14113+5211, PG1115+080, MG0414+0534, B1608+656, B1422+231, and RXJ0911+0551, and the ten-image system B1933+507), and finally remark on two systems (B1359+154 and PMN J0134-0931) where the lens properties are more complex. We also introduce a Java applet which produces simple lens systems, and helps further illustrate the concepts.Comment: 26 pages, incl. 15 figs; accepted to AJ; java applet available at http://ankh-morpork.maths.qmw.ac.uk/~saha/astron/lens

A New Estimate of the Hubble Time with Improved Modeling of Gravitational Lenses

This paper examines free-form modeling of gravitational lenses using Bayesian ensembles of pixelated mass maps. The priors and algorithms from previous work are clarified and significant technical improvements are made. Lens reconstruction and Hubble Time recovery are tested using mock data from simple analytic models and recent galaxy-formation simulations. Finally, using published data, the Hubble Time is inferred through the simultaneous reconstruction of eleven time-delay lenses. The result is H_0^{-1}=13.7^{+1.8}_{-1.0} Gyr.Comment: 24 pages, 9 figures. Accepted to Ap

Cosmological Parameter Determination in Free-Form Strong Gravitational Lens Modeling

We develop a novel statistical strong lensing approach to probe the cosmological parameters by exploiting multiple redshift image systems behind galaxies or galaxy clusters. The method relies on free-form mass inversion of strong lenses and does not need any additional information other than gravitational lensing. Since in free-form lensing the solution space is a high-dimensional convex polytope, we consider Bayesian model comparison analysis to infer the cosmological parameters. The volume of the solution space is taken as a tracer of the probability of the underlying cosmological assumption. In contrast to parametric mass inversions, our method accounts for the mass-sheet degeneracy, which implies a degeneracy between the steepness of the profile and the cosmological parameters. Parametric models typically break this degeneracy, introducing hidden priors to the analysis that contaminate the inference of the parameters. We test our method with synthetic lenses, showing that it is able to infer the assumed cosmological parameters. Applied to the CLASH clusters, the method might be competitive with other probes.Comment: 11 pages, 5 figures. Accepted for publication in MNRA

Look before you Hop: Conversational Question Answering over Knowledge Graphs Using Judicious Context Expansion

Fact-centric information needs are rarely one-shot; users typically ask follow-up questions to explore a topic. In such a conversational setting, the user's inputs are often incomplete, with entities or predicates left out, and ungrammatical phrases. This poses a huge challenge to question answering (QA) systems that typically rely on cues in full-fledged interrogative sentences. As a solution, we develop CONVEX: an unsupervised method that can answer incomplete questions over a knowledge graph (KG) by maintaining conversation context using entities and predicates seen so far and automatically inferring missing or ambiguous pieces for follow-up questions. The core of our method is a graph exploration algorithm that judiciously expands a frontier to find candidate answers for the current question. To evaluate CONVEX, we release ConvQuestions, a crowdsourced benchmark with 11,200 distinct conversations from five different domains. We show that CONVEX: (i) adds conversational support to any stand-alone QA system, and (ii) outperforms state-of-the-art baselines and question completion strategies

Radial density profiles of time-delay lensing galaxies

We present non-parametric radial mass profiles for ten QSO strong lensing galaxies. Five of the galaxies have profiles close to $\rho(r)\propto r^{-2}$, while the rest are closer to r^{-1}, consistent with an NFW profile. The former are all relatively isolated early-types and dominated by their stellar light. The latter --though the modeling code did not know this-- are either in clusters, or have very high mass-to-light, suggesting dark-matter dominant lenses (one is a actually pair of merging galaxies). The same models give H_0^{-1} = 15.2_{-1.7}^{+2.5}\Gyr (H_0 = 64_{-9}^{+8} \legacy), consistent with a previous determination. When tested on simulated lenses taken from a cosmological hydrodynamical simulation, our modeling pipeline recovers both H_0 and $\rho(r)$ within estimated uncertainties. Our result is contrary to some recent claims that lensing time delays imply either a low H_0 or galaxy profiles much steeper than r^{-2}. We diagnose these claims as resulting from an invalid modeling approximation: that small deviations from a power-law profile have a small effect on lensing time-delays. In fact, as we show using using both perturbation theory and numerical computation from a galaxy-formation simulation, a first-order perturbation of an isothermal lens can produce a zeroth-order change in the time delays.Comment: Replaced with final version accepted for publication in ApJ; very minor changes to text; high resolution figures may be obtained at justinread.ne

Second order perturbation theory for spin-orbit resonances

We implement Lie transform perturbation theory to second order for the planar spin-orbit problem. The perturbation parameter is the asphericity of the body, with the orbital eccentricity entering as an additional parameter. We study first and second order resonances for different values of these parameters. For nearly spherical bodies like Mercury and the Moon first order perturbation theory is adequate, whereas for highly aspherical bodies like Hyperion the spin is mostly chaotic and perturbation theory is of limited use. However, in between, we identify a parameter range where second order perturbation theory is useful and where as yet unidentified objects may be in second order resonances.Comment: To appear in A

Study of Phase Stability in NiPt Systems

We have studied the problem of phase stability in NiPt alloy system. We have used the augmented space recursion based on the TB-LMTO as the method for studying the electronic structure of the alloys. In particular, we have used the relativistic generalization of our earlier technique. We note that, in order to predict the proper ground state structures and energetics, in addition to relativistic effects, we have to take into account charge transfer effects with precision.Comment: 22 pages, 7 figures. Accepted for publication in JPC

Phase stability analysis in Fe-Pt and Co-Pt alloy systems: An augmented space study

We have studied the problem of phase stability in Fe-Pt and Co-Pt alloy systems. We have used the orbital peeling technique in the conjunction of augmented space recursion based on the tight binding linear orbital method as the method for the calculation of pair interaction energies. In particular, we have generalized our earlier technique to take into account of magnetic effects for the cases where the magnetic transition is higher than the order disorder chemical transition temperature as in the case of Co$_3$Pt. Our theoretical results obtained within this framework successfully reproduce the experimentally observed trends.Comment: 17 pages, 9 Figures. Accepted for publication in Journal of Physics : Condensed Matte