相关论文: Testing the disjunction hypothesis using Voronoi d…

Since the Voronoi diagram appears in many applications, the topic of improving its computational efficiency remains attractive. We propose a novel yet efficient method to compute Voronoi diagrams bounded by a given domain, i.e., the clipped…

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…

Next-generation sequencing technologies now constitute a method of choice to measure gene expression. Data to analyze are read counts, commonly modeled using Negative Binomial distributions. A relevant issue associated with this…

While multiple testing procedures have been the focus of much statistical research, an important facet of the problem is how to deal with possible confounding. Procedures have been developed by authors in genetics and statistics. In this…

Topological data analysis involves the statistical characterization of the shape of data. Persistent homology is a primary tool of topological data analysis, which can be used to analyze topological features and perform statistical…

Modeling microstructures is an interesting problem not just in Materials Science but also in Mathematics and Statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive…

In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to…

The pair correlation function (PCF) has proven an effective tool for analyzing many physical systems due to its simplicity and its applicability to simulated and experimental data. However, as an averaged quantity, the PCF can fail to…

Genetic investigations often involve the testing of vast numbers of related hypotheses simultaneously. To control the overall error rate, a substantial penalty is required, making it difficult to detect signals of moderate strength. To…

We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…

In many statistical problems the hypotheses are naturally divided into groups, and the investigators are interested to perform group-level inference, possibly along with inference on individual hypotheses. We consider the goal of…

Large-scale multiple testing tasks often exhibit dependence, and leveraging the dependence between individual tests is still one challenging and important problem in statistics. With recent advances in graphical models, it is feasible to…

Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…

The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi…

Motivated by gene set enrichment analysis, we investigate the problem of combined hypothesis testing on a graph. We introduce a general framework to effectively use the structural information of the underlying graph when testing…

Public data repositories have enabled researchers to compare results across multiple genomic studies in order to replicate findings. A common approach is to first rank genes according to an hypothesis of interest within each study. Then,…

Given two sets of training samples, general method is to estimate the density function and classify the test sample according to higher values of estimated densities. Natural way to estimate the density should be histogram tending to…

The standard methods for detecting differential gene expression are mostly designed for analyzing a single gene expression experiment. When data from multiple related gene expression studies are available, separately analyzing each study is…

We investigate the problem of detecting correlation between two Erd\H{o}s-R\'enyi graphs $G(n,p)$, formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent, while under the alternative…

The point inclusion tests for polygons, in other words the point-in-polygon (PIP) algorithms, are fundamental tools for many scientific fields related to computational geometry, and they have been studied for a long time. The PIP algorithms…