Trajectory Synthesis for Fisher Information Maximization

Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general, nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix. A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the Fisher information matrix by three orders of magnitude compared to the initial trajectory. Experimental results show that this optimized trajectory translates to an order of magnitude improvement in the parameter estimate error in practice.Comment: 12 page

The Born and Lens-Lens Corrections to Weak Gravitational Lensing Angular Power Spectra

We revisit the estimation of higher order corrections to the angular power spectra of weak gravitational lensing. Extending a previous calculation of Cooray and Hu, we find two additional terms to the fourth order in potential perturbations of large-scale structure corresponding to corrections associated with the Born approximation and the neglect of line-of-sight coupling of two foreground lenses in the standard first order result. These terms alter the convergence ($\kappa\kappa$), the lensing shear E-mode ($\epsilon\epsilon$), and their cross-correlation ($\kappa\epsilon$) power spectra on large angular scales, but leave the power spectra of the lensing shear B-mode ($\beta\beta$) and rotational ($\omega\omega$) component unchanged as compared to previous estimates. The new terms complete the calculation of corrections to weak lensing angular power spectra associated with both the Born approximation and the lens-lens coupling to an order in which the contributions are most significant. Taking these features together, we find that these corrections are unimportant for any weak lensing survey, including for a full sky survey limited by cosmic variance.Comment: Added references, minor changes to text. 9 pages, 2 figure

Analytic Time Delays and H_0 Estimates for Gravitational Lenses

We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay proportional to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H_0; the complicated Q 0957+561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H_0, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.Comment: 16 pages with 2 embedded figures; submitted to Ap

Simulations and cosmological inference: A statistical model for power spectra means and covariances

We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate Normal distribution for the power spectrum band powers, but takes full account of the (parameter dependent) power spectrum covariance. The model is calibrated using an extension of the framework in Habib et al. (2007) to train Gaussian processes for the power spectrum mean and covariance given a set of simulation runs over a hypercube in parameter space. We demonstrate the performance of this machinery by estimating the parameters of a power-law model for the power spectrum. Within this framework, our calibrated sample variance distribution is robust to errors in the estimated covariance and shows rapid convergence of the posterior parameter constraints with the number of training simulations.Comment: 14 pages, 3 figures, matches final version published in PR

Formalism for testing theories of gravity using lensing by compact objects. III: Braneworld gravity

Braneworld gravity is a model that endows physical space with an extra dimension. In the type II Randall-Sundrum braneworld gravity model, the extra dimension modifies the spacetime geometry around black holes, and changes predictions for the formation and survival of primordial black holes. We develop a comprehensive analytical formalism for far-field black hole lensing in this model, using invariant quantities to compute all geometric optics lensing observables. We then make the first analysis of wave optics in braneworld lensing, working in the semi-classical limit. We show that wave optics offers the only realistic way to observe braneworld effects in black hole lensing. We point out that if primordial braneworld black holes exist, have mass M, and contribute a fraction f of the dark matter, then roughly 3e5 x f (M/1e-18 Msun)^(-1) of them lie within our Solar System. These objects, which we call "attolenses," would produce interference fringes in the energy spectra of gamma-ray bursts at energies ~100 (M/1e-18 Msun)^(-1) MeV (which will soon be accessible with the GLAST satellite). Primordial braneworld black holes spread throughout the universe could produce similar interference effects; the probability for "attolensing" may be non-negligible. If interference fringes were observed, the fringe spacing would yield a simple upper limit on M. Detection of a primordial black hole with M <~ 1e-19 Msun would challenge general relativity and favor the braneworld model. Further work on lensing tests of braneworld gravity must proceed into the physical optics regime, which awaits a description of the full spacetime geometry around braneworld black holes.Comment: 13 pages, 3 figures; accepted in PRD; expanded discussion of prospects for observing attolensing with GLAS

Discovery of an 86 AU Radius Debris Ring Around HD 181327

HST/NICMOS PSF-subtracted coronagraphic observations of HD 181327 have revealed the presence of a ring-like disk of circumstellar debris seen in 1.1 micron light scattered by the disk grains, surrounded by a di use outer region of lower surface brightness. The annular disk appears to be inclined by 31.7 +/- 1.6 deg from face on with the disk major axis PA at 107 +/-2 deg . The total 1.1 micron flux density of the light scattered by the disk (at 1.2" < r < 5.0") of 9.6 mJy +/- 0.8 mJy is 0.17% +/- 0.015% of the starlight. Seventy percent of the light from the scattering grains appears to be confined in a 36 AU wide annulus centered on the peak of the radial surface brightness (SB) profile 86.3 +/- 3.9 AU from the star, well beyond the characteristic radius of thermal emission estimated from IRAS and Spitzer flux densities assuming blackbody grains (~ 22 AU). The light scattered by the ring appears bilaterally symmetric, exhibits directionally preferential scattering well represented by a Henyey-Greenstein scattering phase function with g = 0.30 +/- 0.03, and has an azimuthally medianed SB at the 86.3 AU radius of peak SB of 1.00 +/- 0.07 mJy arcsec^-2. No photocentric offset is seen in the ring relative to the position of the central star. A low surface brightness diffuse halo is seen in the NICMOS image to a distance of ~ 4" Deeper 0.6 micron HST/ACS PSF-subtracted coronagraphic observations reveal a faint outer nebulosity, asymmetrically brighter to the North of the star. We discuss models of the disk and properties of its grains, from which we infer a maximum vertical scale height of 4 - 8 AU at the 87.6 AU radius of maximum surface density, and a total maximum dust mass of collisionally replenished grains with minimum grain sizes of ~ 1 micron of ~ 4 M(moon).Comment: 45 pages, 15 figures, accepted for publication in Ap

Discovery of a Fifth Image of the Large Separation Gravitationally Lensed Quasar SDSS J1004+4112

We report the discovery of a fifth image in the large separation lensed quasar system SDSS J1004+4112. A faint point source located 0.2'' from the center of the brightest galaxy in the lensing cluster is detected in images taken with the Advanced Camera for Surveys (ACS) and the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) on the Hubble Space Telescope. The flux ratio between the point source and the brightest lensed component in the ACS image is similar to that in the NICMOS image. The location and brightness of the point source are consistent with lens model predictions for a lensed image. We therefore conclude that the point source is likely to be a fifth image of the source quasar. In addition, the NICMOS image reveals the lensed host galaxy of the source quasar, which can strongly constrain the structure of the lensing critical curves and thereby the mass distribution of the lensing cluster.Comment: 5 pages, 5 figures, accepted for publication in PAS

Identifying wildlife reservoirs of neglected taeniid tapeworms : non-invasive diagnosis of endemic Taenia serialis infection in a wild primate population

Despite the global distribution and public health consequences of Taenia tapeworms, the life cycles of taeniids infecting wildlife hosts remain largely undescribed. The larval stage of Taenia serialis commonly parasitizes rodents and lagomorphs, but has been reported in a wide range of hosts that includes geladas (Theropithecus gelada), primates endemic to Ethiopia. Geladas exhibit protuberant larval cysts indicative of advanced T. serialis infection that are associated with high mortality. However, non-protuberant larvae can develop in deep tissue or the abdominal cavity, leading to underestimates of prevalence based solely on observable cysts. We adapted a non-invasive monoclonal antibody-based enzyme-linked immunosorbent assay (ELISA) to detect circulating Taenia spp. antigen in dried gelada urine. Analysis revealed that this assay was highly accurate in detecting Taenia antigen, with 98.4% specificity, 98.5% sensitivity, and an area under the curve of 0.99. We used this assay to investigate the prevalence of T. serialis infection in a wild gelada population, finding that infection is substantially more widespread than the occurrence of visible T. serialis cysts (16.4% tested positive at least once, while only 6% of the same population exhibited cysts). We examined whether age or sex predicted T. serialis infection as indicated by external cysts and antigen presence. Contrary to the female-bias observed in many Taenia-host systems, we found no significant sex bias in either cyst presence or antigen presence. Age, on the other hand, predicted cyst presence (older individuals were more likely to show cysts) but not antigen presence. We interpret this finding to indicate that T. serialis may infect individuals early in life but only result in visible disease later in life. This is the first application of an antigen ELISA to the study of larval Taenia infection in wildlife, opening the doors to the identification and description of infection dynamics in reservoir populations