Universality of Signatures in Rough Path Spaces: A Kernel-Theoretic Approach to Local and Global Approximations

This thesis examines the approximation capabilities of path signatures within rough path spaces, focusing on both local and global universality. To this end, we provide a self-contained introduction to Rough Path theory, highlighting the interplay between additive and multiplicative functionals. This leads to the renowned Lyons' Extension...

Ik zie, ik zie, wat jij niet ziet: On how quantum mechanics uses indistinguishable states to express

In the current thesis we argue that quantum mechanics is best understood as a classical theory in which each measurement hides a set of its states. Our aim will however not be to replace quantum mechanical theory by a classical theory of hidden states or to avoid any of its possibly unfavourable metaphysical implications by replacing the current...

Classical simulations of quantum prepare and measure communication processes

Quantum communication has been shown to be vastly superior to classical communication in many problems. However no general statements exist which tells us how much better quantum communication is to its classical counterpart. In this thesis it was studied the minimum amount of classical bits required to exactly simulate a quantum communication...

CLT for Nonlinear Shrinkage Estimators of Large Covariance Matrices

This thesis is concerned with finding the asymptotic distributions of linear spectral statistics of the nonlinear shrinkage estimator for large covariance matrices derived by Ledoit and Wolf (2012). It provides some new inferential procedures for large-dimensional data and shed some light on the power of the new statistical tests on the...

The Krein-Milman theorem and its applications

Gradient flow and quantum Markov semigroups with detailed balance

In this thesis we present a study of quantum Markov semigroups. In particular, we mainly consider quantum Markov semigroups with detailed balance that are defined on finite-dimensional C*-algebras. They have an invariant density matrix ρ. Carlen and Maas showed that the evolution on the set of invertible density matrices that is given by such a...

Constructing gradient-S_p quantum Markov semi-groups to obtain strong solidity results for von Neumann algebras

In this thesis we will for a quantum Markov semi-group (Φt)t≥0 on a finite von Neumann algebra N with a trace τ , investigate the property of the semi-group being gradient-Sp for some p ∈ [1, ∞]. This property was introduced in [12] (see also [9]) and has been studied in [9, 10, 12] for quantum Markov semi-groups on compact...

Random Graphs with Time-Varying Fitness

The random graph is a mathematical model simulating common daily cases, such as ranking and social networks. Generally, the connection between different users in the network is established through preference, and this phenomenon leads to a power-law behaviour of the degree sequence of the random graph. Other than studying this feature, the...

A simulation based approach to synchromodal container transport

Logistics service providers (LSPs) offering container transport to the hinterland of the Netherlands face the challenge of efficiently using the capacity of the barge in order to minimize cost, while part of the relevant information is still lacking at the moment decisions have to be made. The existing infrastructure and the transportation...