The objective of this thesis is to perform schedulability analysis of probabilistic real-time systems. The task execution is described using a probabilistic Worst Case Execution Time (pWCET) which is a probability distribution. The pWCETs are assumed given. The tasks are scheduled to ensure that all tasks are allowed a processor time. In order to e...
We consider the classic problem of NETWORK RELIABILITY. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge of the network is operable with its associated probability and the problem is to determine the probability of having at least one source-to-target path that...
Polarization is a powerful technique in algebra which provides combinatorial tools to study algebraic invariants of monomial ideals. We study the reverse of this process, depolarization which leads to a family of ideals which share many common features with the original ideal. Given a squarefree monomial ideal, we describe a combinatorial method to...
We construct two examples of shareholder networks in which shareholders are connected if they have shares in the same company. We do this for the shareholders in Turkish companies and we compare this against the network formed from the shareholdings in Dutch companies. We analyse the properties of these two networks in terms of the different types ...
Let $\Omega_i$ and $\Omega_j$ be the sets of elements of respective types $i$ and $j$ of a polar space~$\Delta$ of rank at least $3$, viewed as a Tits-building. For any Weyl distance $\delta$ between $\Omega_i$ and $\Omega_j$, we show that $\delta$ is characterised by $i$ and $j$ and two additional numerical parameters $k$ and $\ell$. We consider p...
We present SUSPECT, an open source toolkit that symbolically analyzesmixed-integer nonlinear optimization problems formulated using the Python alge-braic modeling library Pyomo. We present the data structures and algorithms used toimplement SUSPECT. SUSPECT works on a directed acyclic graph representation ofthe optimization problem to perform: boun...
A graph is called maximally non-hamiltonian if it is non-hamiltonian, yet for any two non-adjacent vertices there exists a hamiltonian path between them. In this paper, we naturally extend the concept to directed graphs and bound their size from below and above. Our results on the lower bound constitute our main contribution, while the upper bound ...
