Related papers: Research Problems in Function Theory (New Edition)
This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of…
Machine learning has now become an integral part of research and innovation. The field of machine learning density functional theory has continuously expanded over the years while making several noticeable advances. We briefly discuss the…
As a continuation of our previous work \cite{KV2} the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces…
User studies are paramount for advancing science. However, researchers face several barriers when performing them despite the existence of supporting tools. In this work, we study how existing tools and their features cope with previously…
As many of us in the information retrieval (IR) research community know and appreciate, search is far from being a solved problem. Millions of people struggle with tasks on search engines every day. Often, their struggles relate to the…
Large language models (LLMs) acquire vast knowledge from large text corpora, but this information can become outdated or inaccurate. Since retraining is computationally expensive, knowledge editing offers an efficient alternative --…
In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions…
A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great…
The rapid growth of scholarly literature makes it increasingly difficult for researchers to keep up with new knowledge. Automated tools are now more essential than ever to help navigate and interpret this vast body of information.…
Problems in program analysis can be solved by developing novel program semantics and deriving abstractions conventionally. For over thirty years, higher-order program analysis has been sold as a hard problem. Its solutions have required…
The integration of tools has extended the capabilities of language models (LMs) beyond vanilla text generation to versatile scenarios. However, tool-augmented language models (TaLMs) often assume 'perfect' information access and tool…
Deep research agents extend the role of search engines from retrieving keyword-matched pages to synthesizing knowledge, fundamentally changing how humans interact with information. However, frontier systems remain proprietary, while…
Background: Academic search engines (i.e., digital libraries and indexers) play an increasingly important role in systematic reviews however these engines do not seem to effectively support such reviews, e.g., researchers confront usability…
Lecture note topics: 1. Some tools from real and complex analysis, 2. Hilbert spaces, 3. Banach spaces, 4. Compact operators and their spectra, 5. Intermezzo: reproducing kernel Hilbert spaces, 6. Banach algebras ,7. Spectral theory of…
The number of Language Models (LMs) dedicated to processing scientific text is on the rise. Keeping pace with the rapid growth of scientific LMs (SciLMs) has become a daunting task for researchers. To date, no comprehensive surveys on…
This review article was first published in 2008 as chapter 11 in the book "Fast Fourier Transforms," edited by C. S. Burrus, for the Connexions project at Rice University, which is sadly no longer online. It gives a high-level overview of…
An introduction to the universal algebra approach to Higman-Thompson groups (including Thompson's group $V$) is given, following a series of lectures by Graham Higman in 1973. In these talks, Higman outlined an algorithm for the conjugacy…
In this new version, we correct some typos. For the readers' convenience, we also added some footnotes and more details for certain lemmas and theorems.
In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…
Multi-agent collaboration among models has shown promise in reasoning tasks but is underexplored in long-form generation tasks like summarization and question-answering. We extend multi-agent multi-model reasoning to generation,…