Related papers: Decomposition tables for experiments. II. Two--one…
Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued…
Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
In this paper we introduce and experimentally compare alternative algorithms to join uncertain relations. Different algorithms are based on specific principles, e.g., sorting, indexing, or building intermediate relational tables to apply…
In this review, we present econometric and statistical methods for analyzing randomized experiments. For basic experiments we stress randomization-based inference as opposed to sampling-based inference. In randomization-based inference,…
Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
We develop a new statistical procedure to test whether the dependence structure is identical between two groups. Rather than relying on a single index such as Pearson's correlation coefficient or Kendall's Tau, we consider the entire…
This paper introduces a version of decoupling and randomization to establish concentration inequalities for double-indexed permutation statistics. The results yield, among other applications, a new combinatorial Hanson-Wright inequality and…
The randomization of a complete first order theory $T$ is the complete continuous theory $T^R$ with two sorts, a sort for random elements of models of $T$, and a sort for events in an underlying probability space. We study various notions…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
We consider Gallai's graph Modular Decomposition theory for network analytics. On the one hand, by arguing that this is a choice tool for understanding structural and functional similarities among nodes in a network. On the other, by…
This is the second of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. This paper outlines how the framework can assist in the development of homotopy…
This is a sequel to our paper "Permute, Graph, Map, Derange", involving decomposable combinatorial labeled structures in the exp-log class of type a=1/2, 1, 3/2, 2. As before, our approach is to establish how well existing theory matches…
The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this…
This paper introduces a novel decomposition framework to explain heterogeneity in causal effects observed across different studies, considering both observational and randomized settings. We present a formal decomposition of between-study…
We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…