Related papers: A New Version of Algorithmic Information Theory
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects,…
Unabridged version of the Thesis presented to the University of L' Aquila, in partial fulfillment of the requirements for the ``Laurea'' degree in Physics, October 1998. Work carried out at the University of L'Aquila and at the University…
This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between…
This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations.
These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…
This in an introduction to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. The material is mainly based on the two books of the lecturer, one…
Public lecture given at The Fields Institute, June 2, 2005.
This note is an extended version of my presentation at the "Focused Research Workshop on Exterior Di{\S}erential Systems and Lie Theory" held at the Fields Institute in Toronto, December 9-13, 2013. Some ideas and constructions of this note…
This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one…
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
This thesis details a class of partial orders on the space of probability distributions and the space of density operators which capture the idea of information content. Some links to domain theory and computational linguistics are also…
This is an updated version of my PhD thesis, defended at the University of Waterloo on the 2nd of April 2025, uploaded to the ArXiv with the goal of reaching a wider audience. The thesis is divided into 5 chapters, respectively containing…
The first edition of the workshop on Large Language Model for Evaluation in Information Retrieval (LLM4Eval 2024) took place in July 2024, co-located with the ACM SIGIR Conference 2024 in the USA (SIGIR 2024). The aim was to bring…
The legendary 1951 Dyson Lectures on Advanced Quantum Mechanics are finally LaTeXed, with thorough annotations and an index as an added bonus. See the Typist's Afterward preceding the backmatter for an explanation of this new version, and…
This is a write-up of the lectures given by the author during the Master Class "Categorification" at {\AA}rhus University, Denmark in October 2010.
In recent years, Artificial Intelligence techniques have emerged as useful tools for solving various engineering problems that were not possible or convenient to handle by traditional methods. AI has directly influenced many areas of…
These informal notes are based on the author's lecture at the National Academies of Science, Engineering, and Mathematics workshop on "AI to Assist Mathematical Reasoning" in June 2023. The goal is to think through a path by which we might…
This is the Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence, which was held in Banff, Canada, July 7 - 11 2004.
A slightly revised version of notes distributed during a short course on GPTs, given at the Perimeter Institute for Theoretical Physics in March and April of 2024.
Knowledge about programming is part of the knowledge matrix that will be required of the professionals of the future. Based on this, this work aims to report the development of a teaching tool developed during the monitoring program of the…