Related papers: On Reconstructing Conservative and Primitive Varia…
Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as a major theme in theoretical and applied optics. Here we demonstrate, both analytically and…
Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…
We present a novel weighted $\ell_2$ projection method for estimating autocovariance sequences and spectral density functions from reversible Markov chains. Berg and Song (2023) introduced a least-squares shape-constrained estimation…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
Statistical inference and information processing of high-dimensional data often require efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition…
We establish annealed and quenched invariance principles for random walks in random conductances lifted to the p-variation rough path topology, allowing for degenerate environments and long-range jumps. Our proof is based on a unified…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
In this paper, we introduce and discuss an exactly energy-conserving Particle-in-Cell method for arbitrary curvilinear coordinates. The flexibility provided by curvilinear coordinates enables the study of plasmas in complex-shaped domains…
In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum…
This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by…
We formulate confinement in QCD as an entropic surface phenomenon. Quark and gluon quantum information is localized on a transverse entangling two-sphere of radius $R_{EE}$; at this radius the QCD vacuum -- partitioned by a hadron into…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
In statistics and machine learning, people are often interested in the eigenvectors (or singular vectors) of certain matrices (e.g. covariance matrices, data matrices, etc). However, those matrices are usually perturbed by noises or…
Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one-electron reduced density matrix (1-RDM) satisfying N-representability conditions can be reconstructed using jointly…
We give rigidity results for the discrete Bonnet-Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use well-known semigroup methods as…
The Q-curvature has been playing a central role in conformal geometry since its discovery by T. Branson. It has natural analogy in CR geometry, however, the CR Q-curvature vanishes on the boundary of a strictly pseudoconvex domain in…
We focus on the study of dynamics of two kinds of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley trees and ladder graphs. The stationary probability distribution for MERW is given…
In this reproduction study, we revisit recent claims that self-attention implements kernel principal component analysis (KPCA) (Teo et al., 2024), positing that (i) value vectors $V$ capture the eigenvectors of the Gram matrix of the keys,…
A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…
This paper presents a family of algorithms for decentralized convex composite problems. We consider the setting of a network of agents that cooperatively minimize a global objective function composed of a sum of local functions plus a…