Related papers: Sharp parameter bounds for certain maximal point l…
Keeping the exact general relativistic treatment of light bending as a reference, we compare the accuracy of commonly used approximate lens equations. We conclude that the best approximate lens equation is the Ohanian lens equation, for…
In the coming years, strong gravitational lens discoveries are expected to increase in frequency by two orders of magnitude. Lens-modelling techniques are being developed to prepare for the coming massive influx of new lens data, and blind…
Recent observational data from the Event Horizon Telescope (EHT) collaboration provide convincing realistic evidence for the existence of black hole rotation. From a phenomenological perspective, a recently proposed stable rotating regular…
We study the critical window of the symmetric binary perceptron, or equivalently, combinatorial discrepancy. Consider the problem of finding a binary vector $\sigma$ satisfying $\|A\sigma\|_\infty \le K$, where $A$ is an $\alpha n \times n$…
For $t \in [-1, 1)$, a set of points on the $(n-1)$-dimensional unit sphere is called $t$-almost equiangular if among any three distinct points there is a pair with inner product $t$. We propose a semidefinite programming upper bound for…
Sup-norm curve estimation is a fundamental statistical problem and, in principle, a premise for the construction of confidence bands for infinite-dimensional parameters. In a Bayesian framework, the issue of whether the…
$f(R)$ gravity, capable of driving the late-time acceleration of the universe, is emerging as a promising alternative to dark energy. Various $f(R)$ gravity models have been intensively tested against probes of the expansion history,…
The information about lensed gravitational waves is encapsulated by an amplification factor, which is calculated by an integration of an oscillatory function. The Born approximation, which has been studied in terms of wave optics in…
Strong gravitational lensing has been a powerful probe of cosmological models and gravity. To date, constraints in either domain have been obtained separately. We propose a new methodology through which the cosmological model, specifically…
Strong gravitational lensing from black holes results in the formation of relativistic images, in particular, relativistic Einstein rings. For objects with event horizons, the radius of the unstable light ring (photon sphere) is the lowest…
In the context of strong gravitational lensing, the magnification of image is of crucial importance to constrain various lens models. For several commonly used quadruple lens models, the magnification invariants, defined as the sum of the…
We investigate the mass structure of a strong gravitational lens galaxy at $z=0.350$, taking advantage of the milli-arcsecond (mas) angular resolution of very long baseline interferometric (VLBI) observations. In the first analysis of its…
The convolutional neural network (ConvNet or CNN) has proven to be very successful in many tasks such as those in computer vision. In this conceptual paper, we study the generative perspective of the discriminative CNN. In particular, we…
Strong gravitational lenses allow us to peer into the farthest reaches of space by bending the light from a background object around a massive object in the foreground. Unfortunately, these lenses are extremely rare, and manually finding…
The possibility of using lensed relativistic jets on very small angular scales to construct proper models of spiral lens galaxies and to independently determine the Hubble constant is considered. The system B0218+357 is used as an example…
Like light, gravitational waves can be gravitationally lensed by massive astrophysical objects. Strong gravitational lensing by galaxies and galaxy clusters is anticipated to become observable in the coming years. This phenomenon will…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
Inspired by a new compilation of strong lensing systems, which consist of 204 points in the redshift range $0.0625< z_{l} < 0.958$ for the lens and $0.196< z_{s} < 3.595$ for the source, we constrain three models that generate a late cosmic…
General Relativity gives that finitely many point masses between an observer and a light source create many images of the light source. Positions of these images are solutions of $r(z)=\bar{z},$ where $r(z)$ is a rational function. We study…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…