相关论文: A Triangle Algorithm for Semidefinite Version of C…

We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the…

Let $G$ be a finite group given as input by its multiplication table. For a subset $S$ of $G$ and an element $g\in G$ the Cayley Group Membership Problem (denoted CGM) is to check if $g$ belongs to the subgroup generated by $S$. While this…

Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…

The multiplicative multiple Horn problem is asking to determine possible singular values of the combinations $AB, BC$ and $ABC$ for a triple of invertible matrices $A,B,C$ with given singular values. There are similar problems for…

A symmetric doubly stochastic matrix A is said to be determined by its spectra if the only symmetric doubly stochastic matrices that are similar to A are of the form $P^TAP$ for some permutation matrix P. The problem of characterizing such…

The Separating Hyperplane theorem is a fundamental result in Convex Geometry with myriad applications. Our first result, Random Separating Hyperplane Theorem (RSH), is a strengthening of this for polytopes. $\rsh$ asserts that if the…

We study the following range searching problem: Preprocess a set $P$ of $n$ points in the plane with respect to a set $\mathcal{O}$ of $k$ orientations % , for a constant, in the plane so that given an $\mathcal{O}$-oriented convex polygon…

Given a set $\Sigma$ of spheres in $\mathbb{E}^d$, with $d\ge{}3$ and $d$ odd, having a fixed number of $m$ distinct radii $\rho_1,\rho_2,...,\rho_m$, we show that the worst-case combinatorial complexity of the convex hull $CH_d(\Sigma)$ of…

A set $S \subset \mathbb{Z}^d$ is digital convex if $conv(S) \cap \mathbb{Z}^d = S$, where $conv(S)$ denotes the convex hull of $S$. In this paper, we consider the algorithmic problem of testing whether a given set $S$ of $n$ lattice points…

Let $P$ be a planar set of $n$ points in general position. We consider the problem of computing an orientation of the plane for which the Rectilinear Convex Hull of $P$ has minimum area. Bae et al. (Computational Geometry: Theory and…

Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…

For a given complex finite dimensional subspace $S$ of $\mathbb{C}^n$ and a fixed basis, we study the compact and convex subset of $\left(\mathbb{R}_{\geq 0}\right)^n$ that we call the moment of $S$ $m_S=$ convex hull…

The mixed membership stochastic blockmodel is a statistical model for a graph, which extends the stochastic blockmodel by allowing every node to randomly choose a different community each time a decision of whether to form an edge is made.…

We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construction of provably stable discretizations of arbitrary order…

The System of Linear Equations Problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\kappa$ of $A$, a vector $b$, a Hermitian matrix $M$ and an accuracy $\epsilon$, and the task is to estimate $x^\dagger…

In two previous papers (Price & Monaghan 2004a,b) (papers I,II) we have described an algorithm for solving the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses dissipative…

We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact}…

Higher-order multiway data is ubiquitous in machine learning and statistics and often exhibits community-like structures, where each component (node) along each different mode has a community membership associated with it. In this paper we…

Spectral algorithms are an important building block in machine learning and graph algorithms. We are interested in studying when such algorithms can be applied directly to provide optimal solutions to inference tasks. Previous works by…

Given symmetric matrices $A_0, A_1, \ldots, A_n$ of size $m$ with rational entries, the set of real vectors $x = (x_1, \ldots, x_n)$ such that the matrix $A_0 + x_1 A_1 + \cdots + x_n A_n$ has non-negative eigenvalues is called a…