Related papers: Use of Singular-Value Decomposition in Gravitation…
Inspiraling compact binaries are promising sources of gravitational waves for ground and space-based laser interferometric detectors. The time-dependent signature of these sources in the detectors is a well-characterized function of a…
Searching for a signal depending on unknown parameters in a noisy background with matched filtering techniques always requires an analysis of the data with several templates in parallel in order to ensure a proper match between the filter…
This paper provides an advanced mathematical theory of the Generalized Singular Value Decomposition (GSVD) and its applications. We explore the geometry of the GSVD which provides a long sought for ellipse picture which includes a…
This paper aims at a better understanding of matrix factorization (MF), factorization machines (FM), and their combination with deep algorithms' application in recommendation systems. Specifically, this paper will focus on Singular Value…
We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for non-spinning compact binary coalescences, and we find that for accuracies of 99%…
We have studied the effects of imperfections in spherical gravitational wave antenna on our ability to properly interpret the data it will produce. The results of a numerical simulation are reported that quantitatively describe the…
The wavelet transform and related techniques are used to analyze singular and fractal signals. The normalized wavelet scalogram is introduced to detect singularities including jumps, cusps and other sharply changing points. The wavelet…
Gravitational wave denoising is an ongoing task for revealing the events of compact binary objects in the universe. Recently, with the aid of deep learning, gravitational waves have been efficiently and delicately extracted from the noisy…
Gravitational coupling of the propagation four-vectors of matter wave functions is formulated in flat space-time. Coupling at the momentum level rather than at the "force-law" level greatly simplifies many calculations. This locally…
Despite growing interest, there is a scarcity of known predictions in the regime where both quantum and general relativistic effects become observable. Here, we investigate a combined atom-field system in a curved spacetime, with a specific…
Gravitational Wave Inspiral search with a global network of interferometers when carried in a phase coherent fashion would mimic an effective multi-detector network with synthetic streams constructed by the linear combination of the data…
I define here a novel function on a modeled space of gravitational-wave signals, before studying its properties as a statistic for detection, as an objective function for identification, and as an effective likelihood function for…
We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…
In spherical surface wave tomography, one measures the integrals of a function defined on the sphere along great circle arcs. This forms a generalization of the Funk--Radon transform, which assigns to a function its integrals along full…
We propose a Conditional Singular Value Decomposition in the form of A_{mn} =H_{mk} B_{kl} M_{ln}^* for given general matrices A_{mn} and B_{kl} .
We investigate the gravitational waves phenomena in the geometric scalar theory of gravity (GSG) that belongs to a class of theories such that gravity is described by a single scalar field. The associated physical metric describing the…
A parallel, blocked, one-sided Hari--Zimmermann algorithm for the generalized singular value decomposition (GSVD) of a real or a complex matrix pair $(F,G)$ is here proposed, where $F$ and $G$ have the same number of columns, and are both…
Models of gravitational waveforms play a critical role in detecting and characterizing the gravitational waves (GWs) from compact binary coalescences. Waveforms from numerical relativity (NR), while highly accurate, are too computationally…
Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…
This paper defines an angular velocity for time-dependent functions on the sphere, and applies it to gravitational waveforms from compact binaries. Because it is geometrically meaningful and has a clear physical motivation, the angular…