Related papers: Decorrelating the errors of the galaxy correlation…
We propose an anisotropic generalisation of the line correlation function (ALCF) to separate and quantify phase information in the large-scale structure of galaxies. The line correlation function probes the strictly non-linear regime of…
We present an algorithm enabling computation of the anisotropic redshift-space galaxy 3-point correlation function (3PCF) scaling as $N^2$, with $N$ the number of galaxies. Our previous work showed how to compute the isotropic 3PCF with…
Employing the operator algebra of the conformal group and the conformal Ward identities, we derive the constraints for the anomalies of dilatation and special conformal transformations of the local twist-2 operators in Quantum…
This paper focuses on exploring the sparsity of the inverse covariance matrix $\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky…
We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky…
Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors…
Weak gravitational lensing is one of the few direct methods to map the dark-matter distribution on large scales in the Universe, and to estimate cosmological parameters. We study a Bayesian inference problem where the data covariance…
Cosmological covariance matrices are fundamental for parameter inference, since they are responsible for propagating uncertainties from the data down to the model parameters. However, when data vectors are large, in order to estimate…
Measurements of the redshift-space galaxy clustering have been a prolific source of cosmological information in recent years. Accurate covariance estimates are an essential step for the validation of galaxy clustering models of the…
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…
Cholesky factorization provides photonic lattices that are the isospectral partners or the square root of other arrays of coupled waveguides. The procedure is similar to that used in supersymmetric quantum mechanics. However, Cholesky…
A rigorous analysis is carried out concerning the use of Cholesky decomposition (CD) of two-electron integrals in the case of quantum-chemical calculations with finite or perturbative magnetic fields and gauge-including atomic orbitals. We…
We measure the galaxy 2- and 3-point correlation functions at $z=[0.5,0.7]$ and $z=[0.7, 0.9]$, from the final data release of the VIPERS survey (PDR2). We model the two statistics including a nonlinear 1-loop model for the 2-point function…
We study the quantum corrections to the polarizability of isolated metallic mesoscopic systems using the loop-expansion in diffusive propagators. We show that the difference between connected (grand-canonical ensemble) and isolated…
This paper continues the research devoted to the design of numerically stable square-root implementations for the maximum correntropy criterion Kalman filtering (MCC-KF). In contrast to the previously obtained results, here we reveal the…
Compressed sensing magnetic resonance imaging (CS-MRI) heavily relies on the low mutual coherence between the measurement matrix and the sparsity basis. However, under highly accelerated Cartesian undersampling, the severe structural…
The next generation of galaxy surveys will provide highly accurate measurements of the large-scale structure of the Universe, allowing for more stringent tests of gravity on cosmological scales. Higher order statistics are a valuable tool…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
Disorder has long been a difficult subject in condensed matter systems and the The replica method is a well-known tool in this field. Implementing the replica method the AdS/CFT correspondence has been proposed and discussed in literatures.…
The Cholesky decomposition is a fundamental tool for solving linear systems with symmetric and positive definite matrices which are ubiquitous in linear algebra, optimization, and machine learning. Its numerical stability can be improved by…