Related papers: Recent progress in PDF theory

Recent advancements in the field of Natural Language Processing, particularly the development of large-scale language models that are pretrained on vast amounts of knowledge, are creating novel opportunities within the realm of Knowledge…

This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…

We develop the theory of logarithmic p-divisible groups and the theory of logarithmic finite locally free commutative group schemes.

We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion…

This paper summarizes the results in Integral Biomathics obtained to this moment and provides an outlook for future research in the field.

The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.

The explosive growth of scientific publications has created an urgent need for automated methods that facilitate knowledge synthesis and hypothesis generation. Literature-based discovery (LBD) addresses this challenge by uncovering…

The paper presents an enriched categorical account of homological perturbation theory, including the formulation, proof and functoriality properties of the homological perturbation lemma.

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…

This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.

Continuously comparing theory predictions to experimental data is a common task in analysis of particle physics such as fitting parton distribution functions (PDFs). However, typically, both the computation of scattering amplitudes and the…

This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described…

Document parsing (DP) transforms unstructured or semi-structured documents into structured, machine-readable representations, enabling downstream applications such as knowledge base construction and retrieval-augmented generation (RAG).…

We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.

We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found…

The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We prove the following results: to an arbitrary degree of accuracy, (a) location-scale…

In the paper, some lower bounds for polygamma functions are refined.

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…

The accurate determination of the Parton Distribution Functions (PDFs) of the proton is an essential ingredient of the Large Hadron Collider (LHC) program. PDF uncertainties impact a wide range of processes, from Higgs boson…