Related papers: Scalar actions in Lean's mathlib
Elegant 'microlocal' methods have long since been extensively developed for the analysis of conventional Schroedinger eigenvalue problems. For technical reasons though these methods have not heretofore been applicable to quantum field…
Interactive behaviors are ubiquitous in modern cryptography, but are also present in $\lambda$-calculi, in the form of higher-order constructions. Traditionally, however, typed $\lambda$-calculi simply do not fit well into cryptography,…
The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…
We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive…
We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In…
We study scaling properties and topological aspects of the 2--d O(3) non--linear $\sigma$--model on the lattice with the parametrized fixed point action recently proposed by P.~Hasenfratz and F.~Niedermayer. The behavior of the mass gap…
This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space $x$ and frequency $\xi$. The symbol smoothness conditions obeyed by many…
In this paper, we describe our experience incorporating gradual types in a statically typed functional language with Hindley-Milner style type inference. Where most gradually typed systems aim to improve static checking in a dynamically…
Large language models (LLMs) were invented for natural language tasks such as translation, but they have proved that they can perform highly complex functions across domains. Additionally, they have been thought to develop new skills…
Class-imbalanced learning (CIL) on tabular data is important in many real-world applications where the minority class holds the critical but rare outcomes. In this paper, we present CLIMB, a comprehensive benchmark for class-imbalanced…
Type classes are a popular tool for implementing generic algorithms and data structures without loss of efficiency, bridging the gap between parametric and ad-hoc polymorphism. Since their initial development in Haskell, they now feature…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge,…
In this paper we study analogues of the perfect splines for weighted Sobolev classes of functions defined on the half-line. Maximally oscillating splines play important role in the solution of certain extremal problems. In particular, using…
For research to go in the right direction, it is essential to be able to compare and quantify performance of different algorithms focused on the same problem. Choosing a suitable evaluation metric requires deep understanding of the pursued…
In recent years, Teichm\"uller theory, which is the study of moduli spaces of marked Riemann surfaces, has come to be considered more and more from the point of view of actions of surface groups inside certain semi-simple Lie groups. In…
Tables have gained significant attention in large language models (LLMs) and multimodal large language models (MLLMs) due to their complex and flexible structure. Unlike linear text inputs, tables are two-dimensional, encompassing formats…
Machine learning (ML) is increasingly being used in high-stakes applications impacting society. Therefore, it is of critical importance that ML models do not propagate discrimination. Collecting accurate labeled data in societal…
The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier (for example, see [27,…
We study isometric actions on Riemannian symmetric spaces of noncompact type which are induced by reductive algebraic subgroups of the isometry group. We show that for such an action there exists a corresponding isometric action on a dual…