Related papers: Numerical relativity with characteristic evolution…
In this paper we propose the use of image pixel position coordinate system to improve image classification accuracy in various applications. Specifically, we hypothesize that the use of pixel coordinates will lead to (a) Resolution…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…
The iterated Crank-Nicholson method has become a popular algorithm in numerical relativity. We show that one should carry out exactly two iterations and no more. While the limit of an infinite number of iterations is the standard…
Deep neural networks have been shown to be susceptible to adversarial examples -- small, imperceptible changes constructed to cause mis-classification in otherwise highly accurate image classifiers. As a practical alternative, recent work…
Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…
We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
The normalized eight-point algorithm has been widely viewed as the cornerstone in two-view geometry computation, where the seminal Hartley's normalization has greatly improved the performance of the direct linear transformation algorithm. A…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
The two-point angular correlation function is a traditional method used to search for deviations from expectations of isotropy. In this paper we develop and explore a statistically descriptive three-point method with the intended…
We consider coordinate descent (CD) methods with exact line search on convex quadratic problems. Our main focus is to study the performance of the CD method that use random permutations in each epoch and compare it to the performance of the…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
Throughout the Universe many powerful events are driven by strong gravitational effects that require general relativity to fully describe them. These include compact binary mergers, black hole accretion and stellar collapse, where…
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…
Accurately tracking particles and determining their coordinate along the optical axis is a major challenge in optical microscopy, especially when extremely high precision is needed. In this study, we introduce a deep learning approach using…
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
This paper proposes a geometric interpretation of the angles and scales which the orientation- and scale-covariant feature detectors, e.g. SIFT, provide. Two new general constraints are derived on the scales and rotations which can be used…
Upcoming large-scale structure surveys will be able to measure new features in the galaxy two point correlation function. Relativistic effects appear on large scales as subtle corrections to redshift-space distortions, showing up as a…