Related papers: A Mathematical Theory of Stochastic Microlensing I…
The modern time-delay cosmography aims to infer the cosmological parameters with a competitive precision from observing a multiply imaged quasar. The success of this technique relies upon a robust modeling of the lens mass distribution.…
Starting from a recently proposed framework for the evaluation of the cosmological averages, we evaluate the higher-order moments for the distribution of a given observable. Then, we explicitly discuss the case of the Hubble-Lema\^itre…
Owing to the advent of large area photometric surveys, the possibility to use broad band photometric data, instead of spectra, to measure the size of the broad line region of active galactic nuclei, has raised a large interest. We describe…
Machine learning has been widely applied to clearly defined problems of astronomy and astrophysics. However, deep learning and its conceptual differences to classical machine learning have been largely overlooked in these fields. The broad…
Aims:Calibrating the point spread function (PSF) is a fundamental part of weak gravitational lensing analyses. Even with corrected galaxy images, imperfect calibrations can introduce biases. We propose an analytical framework for…
The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of $H_0$. A Bayesian hierarchical…
We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often…
Double-plane gravitational lensing is a rare but increasingly observed phenomenon in which the light from a distant source is lensed by two foreground objects at different redshifts. Such systems can be used to provide simultaneous…
Residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of…
A novel application of machine-learning (ML) based image processing algorithms is proposed to analyze an all-sky map (ASM) obtained using the Fermi Gamma-ray Space Telescope. An attempt was made to simulate a one-year ASM from a…
A standard method to study the mass distribution in galaxy clusters is through strong lensing of background galaxies in which the positions of multiple images of the same source constrain the surface mass distribution of the cluster.…
Strongly lensed quasars with time-delay measurements are well known to provide the "time-delay distances" $D_{\Delta t}=(1+z_L)D_LD_S/D_{LS}$ and the angular diameter distances to lens galaxies $D_L$. These two kinds of distances give…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
Cosmological gravitational microlensing is a useful technique for understanding the structure of the inner parts of a quasar, especially the accretion disk and the central supermassive black hole. So far, most of the cosmological…
We present a comprehensive treatment of the pixel-lensing theory and apply it to lensing experiments and their results toward M31. Using distribution functions for the distances, velocities, masses, and luminosities of stars, we derive…
The microlensing effect has developed into a powerful technique for a diverse range of applications including exoplanet discoveries, structure of the Milky Way, constraints on MAssive Compact Halo Objects, and measurements of the size and…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
Time-delay cosmography in strongly lensed quasars offer an independent way of measuring the Hubble constant, $H_0$. However, it has been proposed that the combination of microlensing and source-size effects, also known as microlensing time…