Related papers: Lecture notes on complexity of quantifier eliminat…
This is a set of lecture notes for a graduate-level course on quantum algorithms, with an emphasis on quantum optimization algorithms. It is developed for applied mathematicians and engineers, and requires no previous background in quantum…
These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…
We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably, Schnorr,…
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
These lecture notes provide a unified overview of most known canonical desingularization methods in characteristic zero. It starts with discussing the classical method, and then proceeds with the recently discovered ones: logarithmic…
An edited version is given of the text of G\"odel's unpublished manuscript of the notes for a course in basic logic he delivered at the University of Notre Dame in 1939. G\"odel's notes deal with what is today considered as important…
These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…
This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition). It aims to provide students…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
These are the lecture notes of the master's course "Quantum Computing", taught at Chalmers University of Technology every fall since 2020, with participation of students from RWTH Aachen and Delft University of Technology. The aim of this…
I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
This habilitation thesis is intended to be a good introduction to enumeration, the problem of listing solutions. It focuses on the different ways of measuring complexity in enumeration, with a particular emphasis on my contributions to the…
These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix…
The Existential Theory of the Reals (ETR) consists of existentially quantified Boolean formulas over equalities and inequalities of polynomial functions of variables in $\mathbb{R}$. In this paper we propose and study the approximate…
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…