Related papers: Particle Density Estimation with Grid-Projected Ad…
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…
Solute transport in fluid-particle systems is a fundamental process in numerous scientific and engineering disciplines. The simulation of it necessitates the consideration of solid particles with intricate shapes and sizes. To address this…
Predictive hotspot mapping plays a critical role in hotspot policing. Existing methods such as the popular kernel density estimation (KDE) do not consider the temporal dimension of crime. Building upon recent works in related fields, this…
The accuracy of Lagrangian point-particle models for simulation of particle-laden flows may degrade when the particle and fluid momentum equations are two-way coupled. In these cases the fluid velocity at the location of the particle, which…
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using…
We establish heat-kernel bounds and regularity estimates for the transition densities of the diffusion associated with the martingale problem corresponding to the generator of a formal multidimensional Brownian SDE with singular drift. As a…
Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for…
Particle probability hypothesis density filtering has become a promising means for multi-target tracking due to its capability of handling an unknown and time-varying number of targets in non-linear non-Gaussian system. However, its…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…
This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density…
In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we…