Related papers: Research Problems in Function Theory (New Edition)

These notes are a summary of the problem session discussions at various CANT (Combinatorial and Additive Number Theory Conferences). Currently they include all years from 2009 through 2019 (inclusive); the goal is to supplement this file…

This article is a rough, quirky overview of both the history and present state of the art of density functional theory. The field is so huge that no attempt to be comprehensive is made. We focus on the underlying exact theory, the origin of…

This is a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their groundbreaking papers titled "Some continuous functions related…

Deficiencies in Kauffman's proposal regarding a new way for building scientific theories are pointed out. A suggestion to overcome them, and in fact, independently construct mathematical theories which are beyond the reach of Goedel's…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

Inference on common parameters in panel data models with individual-specific fixed effects is a classic example of Neyman and Scott's (1948) incidental parameter problem (IPP). One solution to this IPP is functional differencing (Bonhomme…

This article discusses a number of incorrect statements appearing in textbooks on data analysis, machine learning, or computational methods; the common theme in all these cases is the relevance and application of statistics to the study of…

We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…

We consider regularity for solutions of a class of de Rham's functional equations. Under some smoothness conditions of functions consisting the equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our results are…

The field of ageing science has gone through remarkable progress in recent decades, yet many fundamental questions remain unanswered or unexplored. Here we present a curated list of 100 open problems in ageing and longevity science. These…

The evolution of Neural Machine Translation (NMT) has been significantly influenced by six core challenges (Koehn and Knowles, 2017), which have acted as benchmarks for progress in this field. This study revisits these challenges, offering…

Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, the authors present in a unified manner, a detailed account or rather a brief survey of the Mittag- Leffler…

This article surveys work done in the last six years on the unification of various functional interpretations including G\"odel's dialectica interpretation, its Diller-Nahm variant, Kreisel modified realizability, Stein's family of…

The importance of tasks in information retrieval (IR) has been long argued for, addressed in different ways, often ignored, and frequently revisited. For decades, scholars made a case for the role that a user's task plays in how and why…

This survey presents recent Helly-type geometric theorems published since the appearance of the last comprehensive survey, more than ten years ago. We discuss how such theorems continue to be influential in computational geometry and in…

The goal of TFPIE is to gather researchers, professors, teachers, and all professionals interested in functional programming in education. This includes the teaching of functional programming, but also the application of functional…

The interactive textbook is created for English-speaking students whose study on Mathematical Calculus is based on modern programs of Ukrainian higher educational institutions. It includes personal tasks and samples on ``Integral Calculus…

This paper presents a detailed case study of how artificial intelligence, especially large language models, can be integrated into historical research workflows. The workflow is divided into nine steps, covering the full research cycle from…

We give a new proof of an approximate functional equation, due to J. R. Wilton, for a trigonometric sum involving the divisor function. This allows us to improve on Wilton's error term and to give an explicit formula for an unspecified…

Despite growing interest in using large language models (LLMs) to automate annotation, their effectiveness in complex, nuanced, and multi-dimensional labelling tasks remains relatively underexplored. This study focuses on annotation for the…