Related papers: Partial Coherence Estimation via Spectral Matrix S…
Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect…
Quantifying coherence is a key task in both quantum mechanical theory and practical applications. Here, a reliable quantum coherence measure is presented by utilizing the quantum skew information of the state of interest subject to a…
We present a new mathematical framework for incorporating partial coherence effects into wave optics simulations through a comprehensive surface-to-detector approach. Unlike traditional ensemble averaging methods, our dual-component…
Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as…
In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were…
Error estimates are rigorously derived for a semi-discrete version of a conservative spectral method for approximating the space-homogeneous Fokker-Planck-Landau (FPL) equation associated to hard potentials. The analysis included shows that…
The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…
Equilibrium measures are special invariant measures of chaotic dynamical systems and iterated function systems, commonly studied as salient examples of fractal measures. While useful analytic expressions are rare, computational exploration…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
In a coherent reliability system composed of multiple components configured according to a specific structure function, the distribution of system time to failure, or system lifetime, is often of primary interest. Accurate estimation of…
The complete characterization of spatial coherence is difficult because the mutual coherence function is a complex-valued function of four independent variables. This difficulty limits the ability of controlling and optimizing spatial…
In absence of a lens to form an image, incoherent or partially coherent light scattering off an obstructive or reflective object forms a broad intensity distribution in the far field with only feeble spatial features. We show here that…
This chapter reviews methods for linear shrinkage of the sample covariance matrix (SCM) and matrices (SCM-s) under elliptical distributions in single and multiple populations settings, respectively. In the single sample setting a popular…
Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which…
Much research has been carried out on shrinkage methods for real-valued covariance matrices. In spectral analysis of $p$-vector-valued time series there is often a need for good shrinkage methods too, most notably when the complex-valued…
The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…
A transfer-matrix algorithm is presented herein as a beginning to study the transmission characteristics of coherent light through three-dimensional periodic microstructures, in which the structures are treated as two-dimensional-layer…
The concept of coherence is one of cornerstones in physics. The development of quantum information science has lead to renewed interest in properly approaching the coherence at the quantum level. Various measures could be proposed to…