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The purpose of this paper is to present a systematic exposition of the main results obtained in the studies carried out in groupoid theory. Key words and phrases: groupoid, topological groupoid, Lie groupoid, group-groupoid, vector…
This is a survey of recent and classical results concerning various types of homogeneity, such as n-homogeneity, discrete homogeneity, and countable dense homogeneity. Some new results are also presented, and several problems are posed.
Most people participate in meetings almost every day, multiple times a day. The study of meetings is important, but also challenging, as it requires an understanding of social signals and complex interpersonal dynamics. Our aim this work is…
I discuss group averaging as a method for quantising constrained systems whose gauge group is a noncompact Lie group. Focussing on three case studies, I address the convergence of the averaging, possible indefiniteness of the prospective…
In this document, we make a round up of the theory of asymptotic normality of sums of associated random variables, in a coherent approach in view of further contributions for new researchers in the field. (Version 01)
In this note we give an overview of some of our recent work on Anosov representations of discrete groups into higher rank semisimple Lie groups.
A short survey about combinatorics on words and algorithmic methods in a ring. Special attention is given to Shirshov's results. Adopted for undegraduate students.
In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.
In this paper we provide an overview of important research works on response-adaptive randomization completed in the past decades.
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds,…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
Estimation of social influence in networks can be substantially biased in observational studies due to homophily and network correlation in exposure to exogenous events. Randomized experiments, in which the researcher intervenes in the…
Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…
The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of…
This paper focuses on rotational phenomena of rigid body kinematics. It discusses them in a group-theoretic approach as completely as possible, using methods and notations as intuitive as possible. With a review of current literature, this…
The only acceptable form of polling in the multi-billion dollar survey research field utilizes representative samples. We argue that with proper statistical adjustment, non-representative polling can provide accurate predictions, and often…
The problem of defining a statistical ensemble of random graphs with an arbitrary connectivity distribution is discussed. Introducing such an ensemble is a step towards uderstanding the geometry of wide classes of graphs independently of…
Simulation studies are computer experiments that involve creating data by pseudorandom sampling. The key strength of simulation studies is the ability to understand the behaviour of statistical methods because some 'truth' (usually some…
This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.
This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…