Binets: fundamental building blocks for phylogenetic networks

Phylogenetic networks are a generalization of evolutionary trees that are used by biologists to represent the evolution of organisms which have undergone reticulate evolution. Essentially, a phylogenetic network is a directed acyclic graph having a unique root in which the leaves are labelled by a given set of species. Recently, some approaches have been developed to construct phylogenetic networks from collections of networks on 2- and 3-leaved networks, which are known as binets and trinets, respectively. Here we study in more depth properties of collections of binets, one of the simplest possible types of networks into which a phylogenetic network can be decomposed. More speci_cally, we show that if a collection of level-1 binets is compatible with some binary network, then it is also compatible with a binary level-1 network. Our proofs are based on useful structural results concerning lowest stable ancestors in networks. In addition, we show that, although the binets do not determine the topology of the network, they do determine the number of reticulations in the network, which is one of its most important parameters. We also consider algorithmic questions concerning binets. We show that deciding whether an arbitrary set of binets is compatible with some network is at least as hard as the well-known Graph Isomorphism problem. However, if we restrict to level-1 binets, it is possible to decide in polynomial time whether there exists a binary network that displays all the binets. We also show that to _nd a network that displays a maximum number of the binets is NP-hard, but that there exists a simple polynomial-time 1/3-approximation algorithm for this problem. It is hoped that these results will eventually assist in the development of new methods for constructing phylogenetic networks from collections of smaller networks

Optimisation of battery usage in Smart Grids: Comparing mathematical optimisation methods for making charging decisions for a private battery in a smart grid

It is predicted that in about 100 years most of the earth's fossil fuels will have been depleted. Currently, fossil fuels still make up 80% of the Dutch energy production. Thus, to handle this depletion, the research on renewable energy production and its usage is being stimulated by governments. With the use of fossil fuel energy production, it is easy to increase production to meet the unexpected peaks in energy demand by burning more fuels. However, with renewable sources this is not possible. Thus, the way that the produced energy is being used needs to be altered. Furthermore, the amount of renewable energy that is privately generated has increased over the last couple of years. The energy that has been generated for private use and is not needed at that time, can either be sent back into the grid for other users or charged to a battery for later personal use. The electricity network that will regulate the buying and selling of energy is called a smart grid. When using a battery to store privately generated energy, the decisions that are made for the (dis)charging of the battery are of great influence on the total energy cost at the end of the month. When implementing a battery in a household or company that privately generates energy, these decisions need to be made within a fixed time limit of 15 minutes. In this thesis, four mathematical optimisation methods are compared to each other on result and run time. These methods are dynamic programming, local search, tabu search, and simulated annealing. Dynamic programming gives the solution with the lowest possible cost, but does not always have the lowest average run time. The total cost of the solution resulting from local search does not come close enough to the lowest possible cost generated by dynamic programming to be a viable alternative to dynamic programming. Tabu search is an extension of local search, it could result in a solution with a total cost close enough to the lowest possible cost if it runs more iterations than local search. However, due to this the average run time will exceed the run time of dynamic programming. Therefore, it is also not a viable alternative for dynamic programming. Simulated annealing has a shorter run time than dynamic programming when using a forecast time of 1 day or less. The total cost of the solutions come very close to those of dynamic programming. Therefore, while the run time of dynamic programming still fits within the available time limit, it is advisable to use this method to determine the charging decisions for a private battery in a smart grid. However, the simulations that were run in for this thesis do not encompass the entire real-life case. If after the expansion of the problem to be implemented in real-life the run time of dynamic programming were to exceed the available time period, then simulated annealing would be a good alternative for implementation.Applied Mathematic

The Dutch list of essential drugs for undergraduate medical education: A modified Delphi study

Aims: Prescribing errors among junior doctors are common in clinical practice because many lack prescribing competence after graduation. This is in part due to inadequate education in clinical pharmacology and therapeutics (CP&T) in the undergraduate medical curriculum. To support CP&T education, it is important to determine which drugs medical undergraduates should be able to prescribe safely and effectively without direct supervision by the time they graduate. Currently, there is no such list with broad-based consensus. Therefore, the aim was to reach consensus on a list of essential drugs for undergraduate medical education in the Netherlands. Methods: A two-round modified Delphi study was conducted among pharmacists, medical specialists, junior doctors and pharmacotherapy teachers from all eight Dutch academic hospitals. Participants were asked to indicate whether it was essential that medical graduates could prescribe specific drugs included on a preliminary list. Drugs for which ≥80% of all respondents agreed or strongly agreed were included in the final list. Results: In all, 42 (65%) participants completed the two Delphi rounds. A total of 132 drugs (39%) from the preliminary list and two (3%) newly proposed drugs were included. Conclusions: This is the first Delphi consensus study to identify the drugs that Dutch junior doctors should be able to prescribe safely and effectively without direct supervision. This list can be used to harmonize and support the teaching and assessment of CP&T. Moreover, this study shows that a Delphi method is suitable to reach consensus on such a list, and could be used for a European list