Related papers: Valeriepieris Circles for Spatial Data Analysis
We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our…
A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices $n$. Many instances are already solved in the literature, namely for all odd $n$, and for…
As a result of the slow action of two-body encounters, globular clusters develop mass segregation and attain a condition of only partial energy equipartition even in their central, most relaxed regions. Realistic numerical simulations show…
Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian…
We present cosmological simulations which closely mimic the real Universe within 100Mpc of the Local Group. The simulations, called Constrained Simulations, reproduce the large-scale density field with major nearby structures, including the…
Many scientific and engineering problems are modelled by simulating scalar fields defined either on space-filling meshes (Eulerian) or as particles (Lagrangian). For analysis and visualization, topological primitives such as contour trees…
Evacuation plans have been historically used as a safety measure for the construction of buildings. The existing crowd simulators require fully-modeled 3D environments and enough time to prepare and simulate scenarios, where the…
Choropleth maps have been studied and extended in many ways to counteract the many biases that can occur when using them. Two recent techniques, Surprise metrics and Value Suppressing Uncertainty Palettes (VSUPs), offer promising solutions…
Solving population balance equations, we derive analytical steady-state cell size distributions for single-lineage experiments, such as the mother machine. These experiments are fundamentally different from batch cultures where populations…
Let P be a set of points in R^d, and let M be a function that maps any subset of P to a positive real number. We examine the problem of computing the exact mean and variance of M when a subset of points in P is selected according to a…
In a typical online learning scenario, a learner is required to process a large data stream using a small memory buffer. Such a requirement is usually in conflict with a learner's primary pursuit of prediction accuracy. To address this…
We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function in combining information from multiple sources to improve traditional survey estimates of finite population…
Betweenness centrality is a popular centrality measure with applications in several domains, and whose exact computation is impractical for modern-sized networks. We present SILVAN, a novel, efficient algorithm to compute, with high…
Clusters of galaxies, the most massive virialized systems known, provide a powerful tool for studying the structure, the mass density, and the cosmology of our universe. Clusters furnish one of the best estimates of the dynamical mass…
High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an…
We introduce a novel family of projected distributions on the circle and the sphere, namely the circular and spherical projected Cauchy distributions, as promising alternatives for modelling circular and spherical data. The circular…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in…
A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this note establishes that Riemannian spheres with all geodesics closed and…
Spatial statistical analysis of multivariate volumetric data can be challenging due to scale, complexity, and occlusion. Advances in topological segmentation, feature extraction, and statistical summarization have helped overcome the…