Related papers: Urgent problems at small x

We find that the continuous matter fields are ill-defined in Regge calculus in the physical 4D theory since the corresponding effective action has infinite terms unremovable by the UV renormalisation procedure. These terms are connected…

Retrieval-Augmented Generation (RAG) enhances language models by grounding responses in external information, yet explainability remains a critical challenge, particularly when retrieval relies on unstructured text. Knowledge graphs (KGs)…

The properties of the Bigeometric or proportional derivative are presented and discussed explicitly. Based on this derivative, the Bigeometric Taylor theorem is worked out. As an application of this calculus, the Bigeometric Runge-Kutta…

We study the high-energy limit of $2 \to 2$ one-loop string amplitudes at fixed momentum transfer. For the closed string, the high-energy behaviour of the amplitudes can be determined from Regge theory just like in field theory, as was…

Retrieval-Augmented Large Language Models (LLMs), which incorporate the non-parametric knowledge from external knowledge bases into LLMs, have emerged as a promising approach to enhancing response accuracy in several tasks, such as…

The main aim of this article is to study quantitative structure of small Ree Groups $^{2}G_{2}(q)$. Here, we prove that small Ree groups are uniquely determined by their orders and the set of the number of elements of the same order. As a…

The Retrieval Augmented Generation (RAG) framework utilizes a combination of parametric knowledge and external knowledge to demonstrate state-of-the-art performance on open-domain question answering tasks. However, the RAG framework suffers…

Retrieval-Augmented Generation (RAG) has become a powerful and widely used approach for improving large language models by grounding generation in retrieved evidence. However, RAG systems still produce incorrect answers in many cases. Why…

We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…

A (3+1)-evolutionary method in the framework of Regge Calculus, essentially a method of approximating manifolds with rigid simplices, makes an excellent tool to probe the evolution of manifolds with non-trivial topology or devoid of…

We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…

Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…

We determine extremal entire functions for the problem of majorizing, minorizing, and approximating the Gaussian function $e^{-\pi\lambda x^2}$ by entire functions of exponential type. This leads to the solution of analogous extremal…

Retrieval-Augmented Generation (RAG) has been proposed to mitigate hallucinations in large language models (LLMs), where generated outputs may be factually incorrect. However, existing RAG approaches predominantly rely on vector similarity…

We construct an anomalous dimension for small x evolution which goes beyond standard fixed order perturbative evolution by including resummed small x logarithms deduced from the leading order BFKL equation with running coupling.…

We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We…

A world-sheet sigma model approach is applied to string theories dual to four-dimensional gauge theories, and semi-classical soliton solutions representing highly excited string states are identified which correspond to gauge theory…

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a…

The small $x$ behaviour of the structure function $h_1(x,Q^2)$ is studied within the leading logarithmic approximation of perturbative QCD. There are two contributions relevant at small $x$. The leading one behaves like $(\frac{1}{x})^0$…

In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…