Related papers: On the Reparameterization Between Cartesian Positi…
In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set…
Microlensing events are being discovered and alerted by the two survey teams OGLE and MOA at an increasing rate. Around ten percent of these events involve binary lenses. Such events potentially contain much information on the physical…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
The Kepler DR25 planet candidate catalog was produced using an automated method of planet candidate identification based on various tests. These tests were tuned to obtain a reasonable but arbitrary balance between catalog completeness and…
We compute the next-to-leading-order radiation-reaction modification to the harmonic coordinate quasi-Keplerian parametrization of the binary dynamics, the two bodies undergoing a scattering process. The solution for the radiation-reaction…
Many imaging problems can be formulated as inverse problems expressed as finite-dimensional optimization problems. These optimization problems generally consist of minimizing the sum of a data fidelity and regularization terms. In [23,26],…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
We propose a new approach to inference in tightly identified and large-scale structural vector autoregressions based on a reparameterization that enables imposing identifying inequality restrictions through continuously differentiable…
In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such a degeneracy is removed when a post-Keplerian perturbing acceleration enters…
We compute the dimensionless relativistic periastron advance parameter $k$, which is measurable from the timing of relativistic binary pulsars. We employ for the computation the recently derived Keplerian-type parametric solution to the…
We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit is not a minimizer of the fixed-time action, for any…
Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…
Cosmological weak lensing has been a highly successful and rapidly developing research field since the first detection of cosmic shear in 2000. However, it has recently been pointed out in Yoo et al. that the standard weak lensing formalism…
The geometric calibration of the Planck satellite using the planetary transits is investigated, together with the reconstruction of any offsets from the nominal layout of the focal plane. The methods presented here may be applied to a…
Most of today's state-of-the-art methods for perspective shape from shading are modelled in terms of partial differential equations (PDEs) of Hamilton-Jacobi type. To improve the robustness of such methods w.r.t. noise and missing data,…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits,…
Error estimates are proved for finite element approximations to the solution of second-order hyperbolic partial differential equations with coefficients varying in both space and time. Optimal rates of convergence in the energy norm are…
This study aims to investigate the utilization of Bayesian techniques for the calibration of micro-electro-mechanical systems (MEMS) accelerometers. These devices have garnered substantial interest in various practical applications and…