Related papers: Numerical Relativity with Arbitrary Precision Arit…
The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as…
Einstein's field equation of General Relativity (GR) has been known for over 100 years, yet it remains challenging to solve analytically in strongly relativistic regimes, particularly where there is a lack of a priori symmetry. Numerical…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
We propose an accelerated version of stochastic variance reduced coordinate descent -- ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
We present the generalization of a recently introduced modified gravitational potential for self-gravitating fluids. The use of this potential allows for an accurate approximation of general relativistic effects in an otherwise Newtonian…
Nested sampling (NS) is the preferred stochastic sampling algorithm for gravitational-wave inference for compact binary coalenscences (CBCs). It can handle the complex nature of the gravitational-wave likelihood surface and provides an…
This paper studies gravitational collapse of a complex scalar field at the threshold for black hole formation, assuming that the collapse is spherically symmetric and continuously self-similar. A new solution of the coupled Einstein-scalar…
The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…
This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…
We present a novel direct integral pseudospectral (PS) method (a direct IPS method) for solving a class of continuous-time infinite-horizon optimal control problems (IHOCs). The method transforms the IHOCs into finite-horizon optimal…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
Although it is not a fundamental question, to determine exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting…
In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (NPSC) for the finite neuron method that approximates numerical solutions of partial differential equations (PDEs) using neural network…
Theory can provide important support at all the stages of spectroscopic experiments, from planning the measurements to the interpretation of the results. Such support is particularly valuable for the challenging experiments on heavy,…
We study a natural geometric variant of the classic Knapsack problem called 2D-Knapsack: we are given a set of axis-parallel rectangles and a rectangular bounding box, and the goal is to pack as many of these rectangles inside the box…
Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
In this paper, we use Proximal Cubic regularized Newton Methods (PCNM) to optimize the sum of a smooth convex function and a non-smooth convex function, where we use inexact gradient and Hessian, and an inexact subsolver for the cubic…
The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers respecting a given order of retrieval. While the problem is known…