Roy R Lederman,Stefan Steinerberger
Roy R Lederman
Let G be a tree on n vertices and let L = D - A denote the Laplacian matrix on G . The second-smallest eigenvalue λ 2 ( G ) > 0 , also known as the algebraic connectivity, as well as the associated eigenvector have been of substanti...
Luke Duttweiler,Anthony Almudevar
Luke Duttweiler
Recent developments in the spectral theory of Bayesian Networks has led to a need for a developed theory of estimation and inference on the eigenvalues of the normalized precision matrix, Ω . In this paper, working under conditions whe...
Luke Duttweiler,Sally W Thurston,Anthony Almudevar
Luke Duttweiler
A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often lea...
Anna Seigal
Anna Seigal
A binary tensor consists of 2 n entries arranged into hypercube format 2 × 2 × ⋯ × 2. There are n ways to flatten such a tensor into a matrix of size 2 × 2 n-1. For each flattening, M, we take the determinant of its Gram matrix, det(MM...
Teng Zhang,Amit Singer
Teng Zhang
Motivated by a certain molecular reconstruction methodology in cryo-electron microscopy, we consider the problem of solving a linear system with two unknown orthogonal matrices, which is a generalization of the well-known orthogonal Procrus...
Johannes Bausch,Toby Cubitt
Johannes Bausch
We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We...
OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE [0.03%]
划分格上张量展平间的算子范数不等式
Miaoyan Wang,Khanh Dao Duc,Jonathan Fischer et al.
Miaoyan Wang et al.
Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-r...
Marta Abril Bucero,Chandrajit Bajaj,Bernard Mourrain
Marta Abril Bucero
We describe a new method to compute general cubature formulae. The problem is initially transformed into the computation of truncated Hankel operators with flat extensions. We then analyze the algebraic properties associated to flat extensi...
Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data [0.03%]
基于高角度分辨率扩散取向的积分曲线估计算法研究
Owen Carmichael,Lyudmila Sakhanenko
Owen Carmichael
We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the m...
Matthew M Lin,Moody T Chu
Matthew M Lin
The Euclidean distance matrix for n distinct points in ℝ r is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n. ...