Related papers: The Localization Method for High-Dimensional Inequ…

The Lovasz Local Lemma due to Erdos and Lovasz is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events,…

This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Through this method, old and new bounds are derived and numerical examples are provided, showing how former results…

We present LoD-Loc v3, a novel method for generalized aerial visual localization in dense urban environments. While prior work LoD-Loc v2 achieves localization through semantic building silhouette alignment with low-detail city models, it…

Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and…

In this work, we propose a high-order regularization method to solve the ill-conditioned problems in robot localization. Numerical solutions to robot localization problems are often unstable when the problems are ill-conditioned. A typical…

Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…

We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to simultaneously upscale the stochastic solutions in the physical…

Place Recognition enables the estimation of a globally consistent map and trajectory by providing non-local constraints in Simultaneous Localisation and Mapping (SLAM). This paper presents Locus, a novel place recognition method using 3D…

Weakly supervised localization aims at finding target object regions using only image-level supervision. However, localization maps extracted from classification networks are often not accurate due to the lack of fine pixel-level…

A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a…

These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our…

For systems of an arbitrary dimension, a theory of geometric chained Bell inequalities is presented. The approach is based on chained inequalities derived by Pykacz and Santos. For maximally entangled states the inequalities lead to a…

Wombling methods, first introduced in 1951, have been widely applied to detect boundaries and variations across spatial domains, particularly in biological, public health and meteorological studies. Traditional applications focus on…

In his 1996 paper, Talagrand highlighted that the Law of Large Numbers (LLN) for independent random variables can be viewed as a geometric property of multidimensional product spaces. This phenomenon is known as the concentration of…

The equation for the wave-function localization length in terms of the two-point correlation function of a weak random potential in 1D (F. M. Izrailev and A. A. Krokhin, Phys. Rev. Lett. vol. 82, 4062 (1999)) is rederived using the standard…

We introduce LDL, a fast and robust algorithm that localizes a panorama to a 3D map using line segments. LDL focuses on the sparse structural information of lines in the scene, which is robust to illumination changes and can potentially…

This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the…

Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…