Related papers: A Mathematical Theory of Stochastic Microlensing I…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
Obtaining accurate photometric redshift estimations is an important aspect of cosmology, remaining a prerequisite of many analyses. In creating novel methods to produce redshift estimations, there has been a shift towards using machine…
A small fraction of all quasars are strongly lensed and multiply imaged, with usually a galaxy acting as the main lens. Some, maybe all of these quasars are also affected by microlensing, the effects of stellar mass objects in the lensing…
High-resolution N-body simulations of dark matter halos indicate that the Milky Way contains numerous subhalos. When a dark matter subhalo passes in front of a star, the light from that star will be deflected by gravitational lensing,…
This paper presents a general formalism that allows the derivation of the cumulant generating function and one-point Probability Distribution Function (PDF) of the aperture mass ($\hat{M}_{ap}$), a common observable for cosmic shear…
The current methods available to estimate gravitational shear from astronomical images of galaxies introduce systematic errors which can affect the accuracy of weak lensing cosmological constraints. We study the impact of KSB shape…
We showcase machine learning (ML) inspired target selection algorithms to determine which of all potential targets should be selected first for spectroscopic follow up. Efficient target selection can improve the ML redshift uncertainties as…
The time delays between the multiple images of a strong lens system, together with a model of the lens mass distribution, allow a one-step measurement of a cosmological distance, namely, the "time-delay distance" of the lens (D_dt) that…
Mirror Descent is a popular algorithm, that extends Gradients Descent (GD) beyond the Euclidean geometry. One of its benefits is to enable strong convergence guarantees through smooth-like analyses, even for objectives with exploding or…
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small…
Simulated images are essential in algorithm development and instrument testing for optical telescopes. During real observations, images obtained by optical telescopes are affected by spatially variable point spread functions (PSFs), a…
We present a new algorithm for estimating the Point Spread Function (PSF) in wide-field astronomical images with extreme source crowding. Robust and accurate PSF estimation in crowded astronomical images dramatically improves the fidelity…
The Diffusion Map is a nonlinear dimensionality reduction technique used to analyze high-dimensional data, with recent applications extending to datasets from the social sciences. Previous research has given little attention to how the…
We derive the essentials of the skewed weak lensing likelihood via a simple Hierarchical Model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak…
The parallax effect in ground-based microlensing (ML) observations consists of a distortion to the standard ML light curve arising from the Earth's orbital motion. In most cases, the resolution in current ML surveys is not accurate enough…
Quantifying image distortions caused by strong gravitational lensing and estimating the corresponding matter distribution in lensing galaxies has been primarily performed by maximum likelihood modeling of observations. This is typically a…
The aim of this paper is to study the astrometric trajectory of microlensing events with an extended lens and/or source. We consider not only a dark lens but also a luminous lens as well. We find that the discontinuous finite-lens…
We consider the statistics of time delay in a chaotic cavity having $M$ open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay…
We present a quantitative analysis of the effect of microlensing caused by random motion of individual stars in the galaxy which is lensing a background quasar. We calculate a large number of magnification patterns for positions of the…
We investigate strong lensing by a spherically symmetric mass distribution in the framework of the Einstein-Straus solution with positive cosmological constant and concentrate on the case of a spatially closed Universe ($k=+1$). We develop…