相关论文: Multi-parameter Tests of General Relativity Using …

Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

General relativity (GR) has been extensively tested in the solar system and in binary pulsars, but never in the strong-field, dynamical regime. Soon, gravitational-wave (GW) detectors like Advanced LIGO and eLISA will be able to probe this…

Model-independent analysis (MIA) methods are generally useful for analysing complex systems in which relationships between the observables are non-trivial and noise is present. Principle Component Analysis (PCA) is one of MIA methods…

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

The detection of gravitational waves from compact binary coalescence (CBC) has allowed us to probe the strong-field dynamics of General Relativity (GR). Among various tests performed by the LIGO-Virgo-KAGRA collaboration are parameterized…

We test General Relativity (GR) using current cosmological data: the cosmic microwave background (CMB) from WMAP5 (Komatsu et al. 2009), the integrated Sachs-Wolfe (ISW) effect from the cross-correlation of the CMB with six galaxy catalogs…

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…

The nature of gravity can be tested by how gravitational waves (GWs) are emitted, detected, and propagate through the universe. Propagation tests are powerful, as small deviations compound over cosmological distances. However, GW…

The Laser Interferometer Space Antenna (LISA) will observe gravitational-wave signals from a wide range of sources, including massive black hole binaries. Although numerous techniques have been developed to perform Bayesian inference for…

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

The dispersion in the speed of gravitational waves is a novel way to test the general theory of relativity and understand whether the origin of cosmic acceleration is due to any alternative theory of gravity. Several alternative theories of…

In this paper, we analyze the applicability of the principal component analysis (PCA) as a tool to extract the Sq variation of the geomagnetic field. We tested different geomagnetic field components and used data measured at different…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

This is a whitepaper submitted to the 2010 Astronomy Decadal Review process, addressing the potential tests of gravity theory that could be made by observations of gravitational waves in the milliHertz frequency band by the proposed…

We present a first-stage study of the effect of using knowledge from electromagnetic (EM) observations in the gravitational wave (GW) data analysis of Galactic binaries that are predicted to be observed by the new Laser Interferometer Space…

Gravitational waves (GW) from chirping binary black holes (BBHs) provide unique opportunities to test general relativity (GR) in the strong-field regime. However, testing GR can be challenging when incomplete physical modeling of the…

Second generation interferometric gravitational wave detectors, such as Advanced LIGO and Advanced Virgo, are expected to begin operation by 2015. Such instruments plan to reach sensitivities that will offer the unique possibility to test…

General relativity (GR) has proven to be a highly successful theory of gravity since its inception. The theory has thrivingly passed numerous experimental tests, predominantly in weak gravity, low relative speeds, and linear regimes, but…

Principal component analysis (PCA) represents a standard approach to identify collective variables $\{x_i\}\!=\!\boldsymbol{x}$, which can be used to construct the free energy landscape $\Delta G(\boldsymbol{x})$ of a molecular system.…