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The three gap theorem, also known as the Steinhaus conjecture or three distance theorem, states that the gaps in the fractional parts of $\alpha,2\alpha,\ldots, N\alpha$ take at most three distinct values. Motivated by a question of…
In this work we study the method of Bregman projections for deterministic and stochastic convex feasibility problems with three types of control sequences for the selection of sets during the algorithmic procedure: greedy, random, and…
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…
In the typical analysis of a data set, a single method is selected for statistical reporting even when equally applicable methods yield very different results. Examples of equally applicable methods can correspond to those of different…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of given dimension and bounded degree. We call this "testing the…
A simple graph more often than not contains adjacent vertices with equal degrees. This in particular holds for all pairs of neighbours in regular graphs, while a lot such pairs can be expected e.g. in many random models. Is there a…
Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, prescribed experiments are then performed and the resulting…
In this work, we consider a binary hypothesis testing problem involving a group of human decision-makers. Due to the nature of human behavior, each human decision-maker observes the phenomenon of interest sequentially up to a random length…
Common models for random graphs, such as Erd\H{o}s-R\'{e}nyi and Kronecker graphs, correspond to generating random adjacency matrices where each entry is non-zero based on a large matrix of probabilities. Generating an instance of a random…
Tests of equality of copulas between two samples are introduced and studied using the empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a subsampling Bernstein…
A new nonparametric approach, based on a decision tree algorithm, is proposed to calculate the overlap between two probability distributions. The devised framework is described analytically and numerically. The convergence of the estimated…
Can you decide if there is a coincidence in the numbers counting two different combinatorial objects? For example, can you decide if two regions in $\mathbb{R}^3$ have the same number of domino tilings? There are two versions of the…
For computing efficient approximate designs of multifactor experiments, we propose a simple algorithm based on adaptive exploration of the grid of all combinations of factor levels. We demonstrate that the algorithm significantly…
A general challenge in statistics is prediction in the presence of multiple candidate models or learning algorithms. Model aggregation tries to combine all predictive distributions from individual models, which is more stable and flexible…
This paper considers the two-dataset problem, where data are collected from two potentially different populations sharing common aspects. This problem arises when data are collected by two different types of researchers or from two…
We consider the hypothesis that Evolution promotes population-wide genome patterns that, under randomization, ensures the External Validity of adaptations across population members. An adaptation is Externally Valid (EV) if its effect holds…
In this paper, we provide new insights and analysis for the two elementary tree-based data structures - the AVL tree and binary heap. We presented two simple properties that gives a more direct way of relating the size of an AVL tree and…
A classic three-jug puzzle asks, given three jugs $A$, $B$, and $C$ with fixed maximum capacities, with jug $A$ filled with wine to its maximum capacity, whether is it possible to divide the wine into two halves by pouring it from one jug…
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…