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Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…
Anomaly detection aims to identify data instances that deviate significantly from majority of data, which has been widely used in fraud detection, network security, and industrial quality control. Existing methods struggle with datasets…
High energy experimental data can be viewed as a sampling of the relevant phase space. We point out that one can apply Voronoi tessellations in order to understand the underlying probability distributions in this phase space. Interesting…
An important open question in the modeling of biological tissues is how to identify the right scale for coarse-graining, or equivalently, the right number of degrees of freedom. For confluent biological tissues, both vertex and Voronoi…
Community detection is a ubiquitous problem in applied network analysis, yet efficient techniques do not yet exist for all types of network data. Most techniques have been developed for undirected graphs, and very few exist that handle…
Probability density estimation from observed data constitutes a central task in statistics. In this brief, we focus on the problem of estimating the copula density associated to any observed data, as it fully describes the dependence…
We introduce a new class of spatial-temporal point processes based on Voronoi tessellations. At each step of such a process, a point is chosen at random according to a distribution determined by the associated Voronoi cells. The point is…
Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
Breast density estimation is one of the key tasks in recognizing individuals predisposed to breast cancer. It is often challenging because of low contrast and fluctuations in mammograms' fatty tissue background. Most of the time, the breast…
The Voronoi tessellation is a natural way of space segmentation, which has many applications in various fields of science and technology, as well as in social sciences and visual art. The varieties of the Voronoi tessellation methods are…
Communication-enabled devices routinely carried by individuals have become pervasive, opening unprecedented opportunities for collecting digital metadata about the mobility of large populations. In this paper, we propose a novel methodology…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
The standard definition of pedestrian density produces scattered values, hence, many approaches have been developed to improve the features of the estimated density. This paper provides a review of generally applied methods and presents a…
This study addresses the challenge of classifying cell shapes from noisy contours, such as those obtained through cell instance segmentation of histological images. We assess the performance of various features for shape classification,…
Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space,…
Several systems involve spatial arrangements of elements such as molecules or cells, the characterization of which bears important implications to biological and physical investigations. Traditional approaches to quantify spatial order and…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
We describe two new -- stochastic-geometrical -- methods to obtain reliable velocity field statistics from N-body simulations and from any general density and velocity fluctuation field sampled at a discrete set of locations. These methods,…
The size distributions of 2D and 3D Voronoi cells and of cells of $V_p(2,3)$,--2D cut of 3D Voronoi diagram--are explored, with the single-parameter (re-scaled) gamma distribution playing a central role in the analytical fitting.…