相关论文: Effective Subdivision Algorithm for Isolating Zero…

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…

Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…

Given a matrix-valued function $\mathcal{F}(\lambda)=\sum_{i=1}^d f_i(\lambda) A_i$, with complex matrices $A_i$ and $f_i(\lambda)$ entire functions for $i=1,\ldots,d$, we discuss a method for the numerical approximation of the distance to…

Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the…

With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation.…

Considering the issue of estimating small probabilities p, ie. measuring a rare domain F = {x | g(x) > q} with respect to the distribution of a random vector X, Multilevel Splitting strategies (also called Subset Simulation) aim at writing…

In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…

Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…

In the measurement-constrained problems, despite the availability of large datasets, we may be only affordable to observe the labels on a small portion of the large dataset. This poses a critical question that which data points are most…

In this work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a…

The validation of biclustering algorithms remains a challenging task, even though a number of measures have been proposed for evaluating the quality of these algorithms. Although no criterion is universally accepted as the overall best, a…

This paper proposes a random subspace trust-region algorithm for general convex-constrained derivative-free optimization (DFO) problems. Similar to previous random subspace DFO methods, the convergence of our algorithm requires a certain…

The main focus of this paper is the study of efficient multigrid methods for large linear systems with a particular saddle-point structure. Indeed, when the system matrix is symmetric, but indefinite, the variational convergence theory that…

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…

Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate the construction…

The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…

We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…

In this paper we continue the development of a new technique for computing elimination ideals by substitution which has been called $Z$-separating re-embeddings. Given an ideal $I$ in the polynomial ring $K[x_1,\dots,x_n]$ over a field $K$,…

We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…

We present a general framework for analyzing the complexity of subdivision-based algorithms whose tests are based on the sizes of regions and their distance to certain sets (often varieties) intrinsic to the problem under study. We call…