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Capacitated spatial clustering, a type of unsupervised machine learning method, is often used to tackle problems in compressing, classifying, logistic optimization and infrastructure optimization. Depending on the application at hand, a…
Factor analysis and principal component analysis (PCA) are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of…
Healthcare data often come from multiple sites in which the correlations between confounding variables can vary widely. If deep learning models exploit these unstable correlations, they might fail catastrophically in unseen sites. Although…
We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete…
We analyze the Accelerated Noisy Power Method, an algorithm for Principal Component Analysis in the setting where only inexact matrix-vector products are available, which can arise for instance in decentralized PCA. While previous works…
Coupled cluster theory provides hierarchical many-particle models and is presently considered as the ultimate benchmark in quantum chemistry. Despite is practical significance, a rigorous mathematical analysis of its properties is still in…
This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical…
The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms, which would…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
We report a new version of fermion coupled coherent states method (FCCS-II) to simulate two-electron systems based on a self-symmetrized six-dimensional (6D) coherent states grid. Unlike the older fermion coupled coherent states method…
Exceptional points (EPs) in non-Hermitian systems offer a remarkably strong response to weak perturbations, but the nonorthogonal nature of the corresponding eigenvectors causes noise to diverge, hindering EPs practical application. Here,…
This paper studies computationally efficient methods and their minimax optimality for high-dimensional clustering and signal recovery under block signal structures. We propose two sets of methods, cross-block feature aggregation PCA…
We examine a central approximation of the recently introduced Dynamical Cluster Approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study non-compact and compact contributions to the thermodynamic…
We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a…
By combining the tetrahedron method with the cluster perturbation theory (CPT), we present an accurate method to numerically calculate the density of states of interacting fermions without introducing the Lorentzian broadening parameter…
Existing coordinated cyber-attack detection methods have low detection accuracy and efficiency and poor generalization ability due to difficulties dealing with unbalanced attack data samples, high data dimensionality, and noisy data sets.…
Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…
We propose a novel approach to electron correlation for multireference systems. It is based on particle-hole (ph) and particle-particle (pp) theories in the second-order, developed in the random phase approximation (RPA) framework for…
Compressive focal plane arrays (FPA) enable cost-effective high-resolution (HR) imaging by acquisition of several multiplexed measurements on a low-resolution (LR) sensor. Multiplexed encoding of the visual scene is typically performed via…