Related papers: Error Resilient Space Partitioning

In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…

This work is motivated by the problem of error correction in bit-shift channels with the so-called $ (d,k) $ input constraints (where successive $ 1 $'s are required to be separated by at least $ d $ and at most $ k $ zeros, $ 0 \leq d < k…

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…

Let $P_r(n)$ be the set of partitions of n with non negative rth differences. Let $\lambda$ be a partition chosen uniformly at random among the set $P_r(n)$. Let $d(\lambda)$ be a positive rth difference chosen uniformly at random in…

We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…

We study the colorful sum of radii problem, where the input is a point set $P$ partitioned into classes $P_1, P_2, \dots, P_\omega$, along with per-class outlier bounds $m_1, m_2, \dots, m_\omega$, summing to $m$. The goal is to select a…

We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on the space of partially labeled points on…

This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the…

We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset $X$ of $\mathbb{R}^d$ from a set $Y$ that is close in the Hausdorff distance. This estimator enjoys a linear rate of convergence as…

We develop an algorithmic framework for graph colouring that reduces the problem to verifying a local probabilistic property of the independent sets. With this we give, for any fixed $k\ge 3$ and $\varepsilon>0$, a randomised…

We consider the problem of constructing small coresets for $k$-Median in Euclidean spaces. Given a large set of data points $P\subset \mathbb{R}^d$, a coreset is a much smaller set $S\subset \mathbb{R}^d$, so that the $k$-Median costs of…

We revisit the problem of empirical risk minimziation (ERM) with differential privacy. We show that noisy AdaGrad, given appropriate knowledge and conditions on the subspace from which gradients can be drawn, achieves a regret comparable to…

The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered. We first use the quadrature-based finite difference schemes…

In the Priority $k$-Supplier problem the input consists of a metric space $(F \cup C, d)$ over set of facilities $F$ and a set of clients $C$, an integer $k > 0$, and a non-negative radius $r_v$ for each client $v \in C$. The goal is to…

In this work we introduce a new type of urn model with infinite but countable many colors indexed by an appropriate infinite set. We mainly consider the indexing set of colors to be the $d$-dimensional integer lattice and consider balanced…

The 1D Schr\"odinger equation closed with the transparent boundary conditions(TBCs) is known as a successful model for describing quantum effects, and is usually considered with a self-consistent Poisson equation in simulating quantum…

In this article we describe applications of the numerical method of discrete differential forms in computational GR. In particular we consider the initial value problem for vacuum space-times that admit plane gravitational waves. As…

We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…

In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…

In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…