Related papers: The self-consistent field iteration for p-spectral…
This paper concerns a class of monotone eigenvalue problems with eigenvector nonlinearities (mNEPv). The mNEPv is encountered in applications such as the computation of joint numerical radius of matrices, best rank-one approximation of…
Our general interest is in self-consistent-field (scf) theories of disordered fermions. They generate physically relevant sub-ensembles ("scf-ensembles") within a given Altland-Zirnbauer class. We are motivated to investigate such ensembles…
Complex time-varying networks are prominent models for a wide variety of spatiotemporal phenomena. The functioning of networks depends crucially on their connectivity, yet reliable techniques for learning communities in time-evolving…
The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. In this paper, using the shape difference quotient of eigenvalues, we propose a stable computation…
The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem, is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been…
We present a principled spectral approach to the well-studied constrained clustering problem. It reduces clustering to a generalized eigenvalue problem on Laplacians. The method works in nearly-linear time and provides concrete guarantees…
The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is a widely used method for graph partitioning. It can be seen as a natural relaxation to the NP-hard minimum ratio cut problem. In this…
Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering…
Supervised Learning has been successfully used to produce phase diagrams and identify phase boundaries when local order parameters are unavailable. Here, we apply unsupervised learning to this task. By using readily available clustering…
The reaction-diffusion model can generate a wide variety of spatial patterns, which has been widely applied in chemistry, biology, and physics, even used to explain self-regulated pattern formation in the developing animal embryo. In this…
Real-world visual search systems involve deployments on multiple platforms with different computing and storage resources. Deploying a unified model that suits the minimal-constrain platforms leads to limited accuracy. It is expected to…
The Schr\"odinger equation is at the heart of modern quantum mechanics. Since exact solutions of the ground state are typically intractable, standard approaches approximate Schr\"odinger equation as forms of nonlinear generalized eigenvalue…
The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavior and structural properties of many-body systems. In particular, polymeric SCFT has been successfully applied to inhomogeneous polymeric…
Spectral clustering has become one of the most popular algorithms in data clustering and community detection. We study the performance of classical two-step spectral clustering via the graph Laplacian to learn the stochastic block model.…
We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm…
Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space.…
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…
Self-consistent field theory (SCFT) is one of the useful methods to simulate phase separated structures of multi-component polymer systems. In this article, we propose an SCFT for semiflexible polymer melts, where the basic equations for…
Sparse coding (SC) is attracting more and more attention due to its comprehensive theoretical studies and its excellent performance in many signal processing applications. However, most existing sparse coding algorithms are nonconvex and…
Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…