Quantum nonlocality, cryptography and complexity

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Quantum pre-geometry models for Quantum Gravity

In this thesis we review the status of an approach to Quantum Gravity through lattice toy models, Quantum Graphity. In particular, we describe the two toy models introduced in the literature and describe with a certain level of details the results obtained so far. We emphasize the connection between Quantum Graphity and emergent gravity, and the relation with Variable Speed of Light theories

Intuition: The Experience of Formal Research

A new concept of Intuition, the Deep Unconscious is considered on the basis of the Paradigm of limiting generalizations. The book describes a high-level sketch. The results of the study can be used in education, economics, medicine, artificial intelligence, and the management of complex systems of various natures

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Mediated digraphs and quantum nonlocality

A digraph D=(V,A) is mediated if for each pair x,y of distinct vertices of D, either xyA or yxA or there is a vertex z such that both xz,yzA. For a digraph D, Δ-(D) is the maximum in-degree of a vertex in D. The nth mediation number μ(n) is the minimum of Δ-(D) over all mediated digraphs on n vertices. Mediated digraphs and μ(n) are of interest in the study of quantum nonlocality. We obtain a lower bound f(n) for μ(n) and determine infinite sequences of values of n for which μ(n)=f(n) and μ(n)>f(n), respectively. We derive upper bounds for μ(n) and prove that μ(n)=f(n)(1+o(1)). We conjecture that there is a constant c such that μ(n)f(n)+c. Methods and results of design theory and number theory are used

Mediated Digraphs and Quantum Nonlocality ∗

A digraph D = (V, A) is mediated if for each pair x, y of distinct vertices of D, either xy ∈ A or yx ∈ A or there is a vertex z such that both xz, yz ∈ A. For a digraph D, ∆ − (D) is the maximum in-degree of a vertex in D. The nth mediation number µ(n) is the minimum of ∆ − (D) over all mediated digraphs on n vertices. Mediated digraphs and µ(n) are of interest in the study of quantum nonlocality. We obtain a lower bound f(n) for µ(n) and determine infinite sequences of values of n for which µ(n) = f(n) and µ(n)> f(n), respectively. We derive upper bounds for µ(n) and prove that µ(n) = f(n)(1 + o(1)). We conjecture that there is a constant c such that µ(n) ≤ f(n) + c. Methods and results of design theory and number theory are used