Related papers: Generalizations of Fourier analysis, and how to ap…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
These are notes to accompany four lectures that I gave at the School on Additive Combinatorics, held in Montreal, Quebec between March 30th and April 5th 2006. My aim is to introduce ``quadratic fourier analysis'' in so far as we understand…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
We give an entirely new approach to the problem of mutually unbiased bases (MUBs), based on a Fourier analytic technique in additive combinatorics. The method provides a short and elegant generalization of the fact that there are at most…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem…
The field of compositional generalization is currently experiencing a renaissance in AI, as novel problem settings and algorithms motivated by various practical applications are being introduced, building on top of the classical…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
The Flavour Expansion Theorem, which has been recently proposed as a more general and elegant algebraic method, for the derivation of the commonly used Mass Insertion Approximation, is revisited. The theorem is reviewed, with respect to its…
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…
The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment…
There is a large literature on semiparametric estimation of average treatment effects under unconfounded treatment assignment in settings with a fixed number of covariates. More recently attention has focused on settings with a large number…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…