Related papers: Nonstandard Methods in Ramsey Theory and Combinato…
A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number…
This paper analyzes the working or default assumptions researchers in the formal, statistical, and case study traditions typically hold regarding the sources of unexplained variance, the meaning of outliers, parameter values, human…
This note has two principal aims: to portray an essence of Non-Standard Analysis as a particular structure (which we call lim-rim), noting its interplay with the notion of ultrapower, and to present a construction of Non-Standard Analysis,…
This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification. We emphasize tools we deem particularly useful for a range of problems in this domain, such as…
We extend for the second time the Nonstandard Analysis by adding the left monad closed to the right, and right monad closed to the left, while besides the pierced binad (we introduced in 1998) we add now the unpierced binad - all these in…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
Ramsey Theorem [6] for pairs is intuitionistically but not classically provable: it is equivalent to a subclassical principle [2]. In this note we show that Ramsey may be restated in an intuitionistically provable form, which is informative…
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey…
In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a…
Ramsey theory looks for regularities in large objects. Model theory studies algebraic structures as models of theories. The structural Ramsey theory combines these two fields and is concerned with Ramsey-type questions about certain…
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…
Randomization is a common technique used in clinical trials to eliminate potential bias and confounders in a patient population. Equal allocation to treatment groups is the standard due to its optimal efficiency in many cases. However, in…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
We review the history of non-renormalisation theorems in global supersymmetry, as well as their importance in all attempts to apply supersymmetry to the real world.
This list presents problems in the Reverse Mathematics of infinitary Ramsey theory which I find interesting but do not personally have the techniques to solve. The intent is to enlist the help of those working in Reverse Mathematics to take…
We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in terms of certain ultrafilters related to tensor products…
We establish a practical and easy-to-implement sequential stopping rule for the martingale central limit theorem, focusing on Monte Carlo methods for estimating the mean of a non-iid sequence of martingale difference type. Starting with an…
Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
We introduce a simple yet powerful calculational tool useful in calculating averages of ratios and products of characteristic polynomials. The method is based on Dyson Brownian motion and Grassmann integration formula for determinants. It…