Related papers: Nonstandard Analysis: Its Creator and Place
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.
Non-canonical phenomena - defined here as observables which are either insufficiently characterized by existing theory, or otherwise represent inconsistencies with prior observations - are of burgeoning interest in the field of…
Was Einstein wrong? This paper provides a detailed technical review of Einstein's special and general relativity from an astrophysical perspective, including the historical development of the theories, experimental tests, modern…
Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high…
In the early twentieth century, L.E.J. Brouwer pioneered a new philosophy of mathematics, called intuitionism. Intuitionism was revolutionary in many respects but stands out -mathematically speaking- for its challenge of Hilbert's formalist…
April 25, 2003, marked the 100th anniversary of the birth of Andrei Nikolaevich Kolmogorov, the twentieth century's foremost contributor to the mathematical and philosophical foundations of probability. The year 2003 was also the 70th…
This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon…
Based at a talk given at the Kato Centennial Symposium in Sept. 2017, this article discusses the scientific life and some of the scientific work of T. Kato.
2023 year marks the hundredth birth anniversary of prominent Russian mathematician and thinker Igor Rostislavovich Shafarevich (1923-2017). The article presents a selection of quotations from various works of him, devoted to the future of…
Though the statistical analysis of ranking data has been a subject of interest over the past centuries, especially in economics, psychology or social choice theory, it has been revitalized in the past 15 years by recent applications such as…
This paper is a top down historical perspective on the several phases in the development of probability from its prehistoric origins to its modern day evolution, as one of the key methodologies in artificial intelligence, data science, and…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
In 1956, Charles Stein published an article that was to forever change the statistical approach to high-dimensional estimation. His stunning discovery that the usual estimator of the normal mean vector could be dominated in dimensions 3 and…
This article is dedicated to the centenary of the birth of Aleksandr D. Alexandrov (1912-1999). His functional-analytical approach to the solving of the Minkowski problem is examined and applied to the extremal problems of isoperimetric…
Selected stories about the life of A. L. Onishchik, and a review of his contribution to the classification of non-split supermanifolds, in particular, supercurves a.k.a. superstrings; his editorial and educational work. A brief overview of…
Approximate Bayesian computation (ABC) is one of the most popular "likelihood-free" methods. These methods have been applied in a wide range of fields by providing solutions to intractable likelihood problems in which exact Bayesian…
In this paper I shall try to sketch some typical aspects of Erich Lehmann's contributions to statistics through his research, his teaching, his service to the profession and his personality.
We construct the non-standard complex (and real) numbers using the ultrapower method in the spirit of Cauchy's construction of the real numbers. We show that the non-standard complex numbers are a non-archimedean, algebraically closed…
(Abbr.) We consider a direct representation of a periodic time-function by means of its zero-crossings. The use of the zero-crossings as the describing parameters is made possible by a singular model of a strongly nonlinear electrical…
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard…