Simultaneous Estimation of Time Delays and Quasar Structure

We expand our Bayesian Monte Carlo method for analyzing the light curves of gravitationally lensed quasars to simultaneously estimate time delays and quasar structure including their mutual uncertainties. We apply the method to HE1104-1805 and QJ0158-4325, two doubly-imaged quasars with microlensing and intrinsic variability on comparable time scales. For HE1104-1805 the resulting time delay of (Delta t_AB) = t_A - t_B = 162.2 -5.9/+6.3 days and accretion disk size estimate of log(r_s/cm) = 15.7 -0.5/+0.4 at 0.2 micron in the rest frame are consistent with earlier estimates but suggest that existing methods for estimating time delays in the presence of microlensing underestimate the uncertainties. We are unable to measure a time delay for QJ0158-4325, but the accretion disk size is log(r_s/cm) = 14.9 +/- 0.3 at 0.3 micron in the rest frame.Comment: 21 pages, 6 figures, submitted to Ap

The Transverse Peculiar Velocity of the Q2237+0305 Lens Galaxy and the Mean Mass of Its Stars

Using 11-years of OGLE V-band photometry of Q2237+0305, we measure the transverse velocity of the lens galaxy and the mean mass of its stars. We can do so because, for the first time, we fully include the random motions of the stars in the lens galaxy in the analysis of the light curves. In doing so, we are also able to correctly account for the Earth's parallax motion and the rotation of the lens galaxy, further reducing systematic errors. We measure a lower limit on the transverse speed of the lens galaxy, v_t > 338 km/s (68% confidence) and find a preferred direction to the East. The mean stellar mass estimate including a well-defined velocity prior is 0.12 <= 1.94 at 68% confidence, with a median of 0.52 Msun. We also show for the first time that analyzing subsets of a microlensing light curve, in this case the first and second halves of the OGLE V-band light curve, give mutually consistent physical results.Comment: 11 pages, 9 figures, 1 table; animated magnification pattern video can be found at http://www.astronomy.ohio-state.edu/~sdp/animation.avi; accepted for publication in Ap

Generic form of Bayesian Monte Carlo for models with partial monotonicity

This paper presents a generic method for the safety assessments of models with partial monotonicity. For this purpose, a Bayesian interpolation method is developed and implemented in the Monte Carlo process. integrated approach is the generalization of the recently developed techniques used in safety assessment of monotonic models and it substantially increases the efficiency of Monte Carlo method. The formulation of this development is provided in this paper with an example showing its ability to dramatically improve efficiency of simulation. This is achieved by employing prior information obtained from monotonic models and outcomes of the preceding simulations. The theory and numerical algorithms of this method for multi-dimensional problems and their integration with the probabilistic finite element model of a real-world example are presente

Prognostics of Ball Bearings in Cooling Fans

Ball bearings have been used to support rotating shafts in machines such as wind turbines, aircraft engines, and desktop computer fans. There has been extensive research in the areas of condition monitoring, diagnostics, and prognostics of ball bearings. As the identification of ball bearing defects by inspection interrupts the operation of rotating machines and can be costly, the assessment of the health of ball bearings relies on the use of condition monitoring techniques. Fault detection and life prediction methods have been developed to improve condition-based maintenance and product qualification. However, intermittent and catastrophic system failures due to bearing problems still occur resulting in loss of life and increase of maintenance and warranty costs. Inaccurate life prediction of ball bearings is of concern to industry. This research focuses on prognostics of ball bearings based on vibration and acoustic emission analysis to provide early warning of failure and predict life in advance. The failure mechanisms of ball bearings in cooling fans are identified and failure precursors associated with the defects are determined. A prognostic method based on Bayesian Monte Carlo method and sequential probability ratio test is developed to predict time-to-failure of ball bearings in advance. A benchmark study is presented to demonstrate the application of the developed prognostic method to desktop computer fans. The prognostic method developed in this research can be extended as a general method to predict life of a component or system

Predicting battery aging trajectory via a migrated aging model and Bayesian Monte Carlo method

Thanks to the fast development in battery technologies, the lifespan of the lithium-ion batteries increases to more than 3000 cycles. This brings new challenges to reliability related researches because the experimental time becomes overly long. In response, a migrated battery aging model is proposed to predict the battery aging trajectory. The normal-speed aging model is established based on the accelerate aging model through a migration process, whose migration factors are determined through the Bayesian Monte Carlo method and the stratified resampling technique. Experimental results show that the root-mean-square-error of the predicted aging trajectory is limited within 1% when using only 25% of the cyclic aging data for training. The proposed method is suitable for both offline prediction of battery lifespan and online prediction of the remaining useful life

The Optical, Ultraviolet, and X-ray Structure of the Quasar HE 0435-1223

Microlensing has proven an effective probe of the structure of the innermost regions of quasars, and an important test of accretion disk models. We present light curves of the lensed quasar HE 0435-1223 in the R band and in the ultraviolet, and consider them together with X-ray light curves in two energy bands that are presented in a companion paper. Using a Bayesian Monte Carlo method, we constrain the size of the accretion disk in the rest-frame near- and far-UV, and constrain for the first time the size of the X-ray emission regions in two X-ray energy bands. The R-band scale size of the accretion disk is about 10^15.23 cm (~23 r_g), slightly smaller than previous estimates, but larger than would be predicted from the quasar flux. In the UV, the source size is weakly constrained, with a strong prior dependence. The UV to R-band size ratio is consistent with the thin disk model prediction, with large error bars. In soft and hard X-rays, the source size is smaller than ~10^14.8 cm (~10 r_g) at 95% confidence. We do not find evidence of structure in the X-ray emission region, as the most likely value for the ratio of the hard X-ray size to the soft X-ray size is unity. Finally, we find that the most likely value for the mean mass of stars in the lens galaxy is ~0.3 M_sun, consistent with other studies.Comment: 13 pages, 7 figures. Replaced with version accepted to Ap

Model-Based Reinforcement Learning with Continuous States and Actions

Finding an optimal policy in a reinforcement learning (RL) framework with continuous state and action spaces is challenging. Approximate solutions are often inevitable. GPDP is an approximate dynamic programming algorithm based on Gaussian process (GP) models for the value functions. In this paper, we extend GPDP to the case of unknown transition dynamics. After building a GP model for the transition dynamics, we apply GPDP to this model and determine a continuous-valued policy in the entire state space. We apply the resulting controller to the underpowered pendulum swing up. Moreover, we compare our results on this RL task to a nearly optimal discrete DP solution in a fully known environment

The Quasar Accretion Disk Size - Black Hole Mass Relation

We use the microlensing variability observed for nine gravitationally lensed quasars to show that the accretion disk size at 2500 Angstroms is related to the black hole mass by log(R_2500/cm) = (15.6+-0.2) + (0.54+-0.28)log(M_BH/10^9M_sun). This scaling is consistent with the expectation from thin disk theory (R ~ M_BH^(2/3)), but it implies that black holes radiate with relatively low efficiency, log(eta) = -1.29+-0.44 + log(L/L_E) where eta=L/(Mdot c^2). These sizes are also larger, by a factor of ~3, than the size needed to produce the observed 0.8 micron quasar flux by thermal radiation from a thin disk with the same T ~ R^(-3/4) temperature profile. More sophisticated disk models are clearly required, particularly as our continuing observations improve the precision of the measurements and yield estimates of the scaling with wavelength and accretion rate.Comment: 5 pages, 3 figures, submitted to ApJ