Related papers: The L\"uroth problem
A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181,…
In the 1980s, category theorists introduced the Lawvere-Tierney $(\leq_{\mathrm{LT}})$ order in the Effective Topos, known to effectively embed the Turing degrees. Understanding its structure is a longstanding open problem in the area. In…
Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
Many reasoning techniques for large multimodal models adapt language model approaches, such as Chain-of-Thought (CoT) prompting, which express reasoning as word sequences. While effective for text, these methods are suboptimal for…
Although large language models (LLMs) have demonstrated remarkable proficiency in modeling text and generating human-like text, they may exhibit biases acquired from training data in doing so. Specifically, LLMs may be susceptible to a…
This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda…
What is reasoning? This question has driven centuries of philosophical inquiry, from Aristotle's syllogisms to modern computational complexity theory. In the age of large language models achieving superhuman performance on benchmarks like…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
Large Language Models (LLMs) are increasingly ubiquitous, yet their ability to retain and reason about temporal information remains limited, hindering their application in real-world scenarios where understanding the sequential nature of…
Quantification of historical sociological processes have recently gained attention among theoreticians in the effort of providing a solid theoretical understanding of the behaviors and regularities present in sociopolitical dynamics. Here…
Doctoral Thesis, year 2002, about Lie systems and applications in Physics and Control Theory. The text is in English. Advisor: Jos\'e F. Cari\~nena
Large language models (LLMs) often solve problems using step-by-step Chain-of-Thought (CoT) reasoning, yet these intermediate steps are frequently unfaithful or hard to interpret. Inspired by the Uniform Information Density (UID) hypothesis…
This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…
The SemEval task on Argument Reasoning in Civil Procedure is challenging in that it requires understanding legal concepts and inferring complex arguments. Currently, most Large Language Models (LLM) excelling in the legal realm are…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
In 1763, Euler published "Dilucidationes de resistentia fluidorum" (Explanations on the resistance of fluids), a memoir that challenges the fluid resistance theories proposed by Isaac Newton and d'Alembert. Euler's work explores the…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
In this invited talk, I will review five basic concepts of Axiomatic Rewriting Theory, an axiomatic and diagrammatic theory of rewriting started 25 years ago in a LICS paper with Georges Gonthier and Jean-Jacques L\'evy, and developed along…