Related papers: Recent progress in PDF theory
The recent global analyses of the nuclear parton distribution functions (nPDFs) lend support to the validity of the factorization theorem of QCD in high-energy processes involving bound nucleons. With a special attention on our latest…
The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy…
Parton distributions are an essential ingredient of the LHC program. PDFs are relevant for precision Standard Model measurements, for Higgs boson characterization as well as for New Physics searches. In this contribution I review recent…
We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…
We present recent results of the NNPDF collaboration on a full DIS analysis of Parton Distribution Functions (PDFs). Our method is based on the idea of combining a Monte Carlo sampling of the probability measure in the space of PDFs with…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve state-of-the-art performance within…
We survey recent developments on the Restriction conjecture.
A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When…
We address the extraction of mathematical statements and their proofs from scholarly PDF articles as a multimodal classification problem, utilizing text, font features, and bitmap image renderings of PDFs as distinct modalities. We propose…
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems. This has resulted in an algorithmic toolbox that is by now…
We show how to account for correlations between theoretical uncertainties incorporated in parton distribution function (PDF) fits, and the theoretical uncertainties in the predictions made using these PDFs. We demonstrate by explicit…
The goodness of fit methods for classification problems relies traditionally on confusion matrices. This paper aims to enrich these methods with a risk evaluation and stability analysis tools. For this purpose, we present a parametric PDF…
A robust uncertainty estimate in global analyses of Parton Distribution Functions (PDFs) is essential at the Large Hadron Collider (LHC), especially in view of the high-precision data anticipated by experimentalists in the High-Luminosity…
The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [Colombo, Crippa, and Spirito, Calc. Var. Partial Differential Equations 2015] concerning existence and…
Accurate Standard Model predictions of proton-proton collisions are essential for interpreting the current and forthcoming experimental measurements from high-energy colliders. The quest for physics beyond the Standard Model is in fact…
This contribution to the Italian "Workshop sui Monte Carlo, la Fisica e le Simulazioni a LHC", held at LNF, Frascati, in February, May and October 2006, summarises the status of parton density functions (PDF's) and the impact of their…
We survey recent advances in the theory of graph and hypergraph decompositions, with a focus on extremal results involving minimum degree conditions. We also collect a number of intriguing open problems, and formulate new ones.
This paper presents an experience report on the development of Retrieval Augmented Generation (RAG) systems using PDF documents as the primary data source. The RAG architecture combines generative capabilities of Large Language Models…
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.