Monte Carlo algorithms for performing Bayesian inference on Piecewise Deterministic Processes

Since their introduction in 1993, particle filters are amongst the most popular algorithms for performing Bayesian inference on state space models that do not admit an analytical solution. In this thesis, we will present several particle filtering algorithms adapted to a class of models known as Piecewise Deterministic Markov Processes (PDMP), i...

Breaking the knapsack cryptosystem

We live in an online world: we date online, we do business online and we communicate online. To make sure this happens securely, almost all transferred data is encrypted by cryptosystems. This paper focuses on one of these: the knapsack cryptosystem of Merkle and Hellman, which relies on the hardness of solving the knapsack problem (1978). In...

Maximum Coverage Problems: Theory and Application in Optimal Sensor Selection

In this thesis we analyse the class of <i>maximum coverage</i> problems. For all discussed problems, linear programs are formulated. Using the notion of <i>submodularity</i>, we prove that for the weighted version of the basic <i>Maximum Coverage</i> problem, where the weights differ per set, a polynomial-time greedy algorithm guarantees a (1 -...

Comparison on estimations for the extremal index: Vergelijken van schatters van de extreme index

The clustering of events can have a large impact on society. The extremal index $\theta$ tells how much extreme events cluster. We will compare different types of estimators in this project. First, we review the extremes of different sequences which have different values of $\theta$. We have found significant differences between the extremes....