Related papers: SPARC: Accurate and efficient finite-difference fo…

A system of electrons in a local or nonlocal external potential can be studied with 1-matrix functional theory (1MFT), which is similar to density functional theory (DFT) but takes the one-particle reduced density matrix (1-matrix) instead…

One of the most promising techniques used for studying the electronic properties of materials is based on Density Functional Theory (DFT) approach and its extensions. DFT has been widely applied in traditional solid state physics problems…

We present a versatile density functional approach (DFT) for calculating the depletion potential in general fluid mixtures. In contrast to brute force DFT, our approach requires only the equilibrium density profile of the small particles…

The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block…

In inverting large sparse matrices, the key difficulty lies in effectively exploiting sparsity during the inversion process. One well-established strategy is the nested dissection, which seeks the so-called sparse Cholesky factorization. We…

Clustering multidimensional points is a fundamental data mining task, with applications in many fields, such as astronomy, neuroscience, bioinformatics, and computer vision. The goal of clustering algorithms is to group similar objects…

Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data…

The extension of the density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the…

Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the…

Accurate land cover segmentation of spectral images is challenging and has drawn widespread attention in remote sensing due to its inherent complexity. Although significant efforts have been made for developing a variety of methods, most of…

We introduce an analytical framework to calculate the values of key observables in a strongly disordered discrete time crystal (DTC) without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement…

This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel function. Given points in a domain, a tree structure is first…

Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…

Linear scaling density functional theory approaches to electronic structure are often based on the tendency of electrons to localize even in large atomic and molecular systems. However, in many cases of actual interest, for example in…

A formulation for the efficient calculation of the electromagnetic retarded potential generated by time-dependent electron density in the context of real-time time dependent density functional theory (RT-TDDFT) is presented. The electron…

Million-atom quantum simulations are in principle feasible with Orbital-Free Density Functional Theory (OF-DFT) because the algorithms only require simple functional minimizations with respect to the electron density function. In this…

Dimensionality reduction, cluster analysis, and sparse representation are basic components in machine learning. However, their relationships have not yet been fully investigated. In this paper, we find that the spectral graph theory…

Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix…

Linear-scaling techniques for Kohn-Sham density functional theory (KS-DFT) are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the locality of the density matrix or on accurate…

The low-T part of the phase diagram in self-assembling systems is correctly predicted by the known versions of the density functional theory (DFT). The high-T part obtained in DFT, however, does not agree with simulations even on the…