相关论文: From Combinatorics to Partial Differential Equatio…

We present a new method for real-time non-rigid dense correspondence between point clouds based on structured shape construction. Our method, termed Deep Point Correspondence (DPC), requires a fraction of the training data compared to…

Although 3D point cloud data has received widespread attentions as a general form of 3D signal expression, applying point clouds to the task of dense correspondence estimation between 3D shapes has not been investigated widely. Furthermore,…

We introduce new probabilistic arguments to derive optimal-order central moment bounds in planar directed last-passage percolation. Our technique is based on couplings with the increment-stationary variants of the model, and is presented in…

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

In robot learning, the observation space is crucial due to the distinct characteristics of different modalities, which can potentially become a bottleneck alongside policy design. In this study, we explore the influence of various…

Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing…

We study some properties of a class of random connected planar fractal sets induced by a Poissonian scale-invariant and translation-invariant point process. Using the second-moment method, we show that their Hausdorff dimensions are…

In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…

Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and…

Autonomous perception requires high-quality environment sensing in the form of 3D bounding boxes of dynamic objects. The primary sensors used in automotive systems are light-based cameras and LiDARs. However, they are known to fail in…

We study iterative methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. We propose a machine-learning-based heuristic to determine starting scenarios that provide strong lower bounds. To this end, we…

In this paper, we propose a new distortion quantification method for point clouds, the multiscale potential energy discrepancy (MPED). Currently, there is a lack of effective distortion quantification for a variety of point cloud perception…

Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even…

A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…

For the registration of partially overlapping point clouds, this paper proposes an effective approach based on both the hard and soft assignments. Given two initially posed clouds, it firstly establishes the forward correspondence for each…

Determinantal consensus clustering is a promising and attractive alternative to partitioning about medoids and k-means for ensemble clustering. Based on a determinantal point process or DPP sampling, it ensures that subsets of similar…

Let $G$ be a group, $\mathcal{P}_G$ be the family of all subsets of $G$. For a subset $A\subseteq G$, we put $\Delta(A)=\{g\in G:|gA\cap A|=\infty\}$. The mapping $\Delta:\mathcal{P}_G\rightarrow\mathcal{P}_G$, $A\mapsto\Delta(A)$, is…

The random convex hull of a Poisson point process in $\mathbb{R}^d$ whose intensity measure is a multiple of the standard Gaussian measure on $\mathbb{R}^d$ is investigated. The purpose of this paper is to invent a new viewpoint on these…

In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…

We investigate random interlacements on Z^d, d bigger or equal to 3. This model recently introduced in arXiv:0704.2560 corresponds to a Poisson cloud on the space of doubly infinite trajectories modulo time-shift tending to infinity at…