Related papers: A Conversation with Ulf Grenander
This is the paper "Niels Henrik Abel and the birth of fractional calculus", Podlubny, I., Magin, R. L., Trymorush I., Fractional Calculus and Applied Analysis, vol.20, no.5, pp.1068-1075, 2017 (https://doi.org/10.1515/fca-2017-0057) with…
During the period 1962--1964, I had a tenure track Assistant Professorship in Mathematics at Cornell University in Ithaca, New York, where I did research in probability theory, especially on linear diffusion processes. Being somewhat lonely…
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…
A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…
Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov…
Pranab K. Sen has contributed extensively to many areas of Statistics including order statistics, nonparametrics, robust inference, sequential methods, asymptotics, biostatistics, clinical trials, bioenvironmental studies and…
This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda…
Any empirical data can be approximated to one of Pearson distributions using the first four moments of the data (Elderton and Johnson, 1969; Pearson, 1895; Solomon and Stephens, 1978). Thus, Pearson distributions made statistical analysis…
Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs).…
We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process…
The results of Iv. Prodanov on abstract spectra and separative algebras were announced in the journal "Trudy Mat. Inst. Steklova", 154, 1983, 200--208, but their proofs were never written by him in the form of a manuscript, preprint or…
Michel Talagrand (Centre National de la Recherche Scientifique, France) has been awarded the prestigious Abel Prize for 2024 for his work in probability theory, functional analysis, and statistical physics. In this note, we introduce the…
It's hard to imagine human life in the digital and AI age without polynomials because they are everywhere but mostly invisible to ordinary people: in data trends, on computer screens, in the shapes around us, and in the very fabric of…
This is a historical review of "Prandtl and the G\"ottingen School" from his first work in 1898 to after WWII. We report the development of the boundary layer theory and the investigations that lead Ludwig Prandtl in the spring of 1945 to…
Stephen Fienberg's affinity for contingency table problems and reinterpreting models with a fresh look gave rise to a new approach for hypothesis testing of network models that are linear exponential families. We outline his vision and…
These notes have been adapted from an undergraduate course given by Professor Alan James at the University of Adelaide from around 1965 and onwards. This adaption has put a focus on the definition of projection matrices and the sweep…
The following conversation is based in part on a transcript of a 2009 interview funded by Pfizer Global Research-Connecticut, the American Statistical Association and the Department of Statistics at the University of Connecticut-Storrs as…
Born in New Zealand, Shayle Robert Searle earned a bachelor's degree (1949) and a master's degree (1950) from Victoria University, Wellington, New Zealand. After working for an actuary, Searle went to Cambridge University where he earned a…