Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation non-treelike evolutionary events such as hybridization. Typically, have been analyzed based on their ‘level’, i.e. complexity 2-edge-connected components. However, recently question how ‘treelike’ network is has become center attention in various studies. This led to introduction tree-based networks...

A partial order is called semilinear iff the upper bounds of each element are linearly ordered and any two elements have a common upper bound. There exists, up to isomorphism, a unique countable semilinear order which is dense, unbounded, binary branching, and without joins, which we denote by (S2;≤). We study the reducts of (S2;≤), that is, the relational structures with domain S2, all of whos...

We give a new proof showing that it is not possible to define in monadic second-order logic (MSO) a choice function on the infinite binary tree. This result was first obtained by Gurevich and Shelah using set theoretical arguments. Our proof is much simpler and only uses basic tools from automata theory. We discuss some applications of the result concerning unambiguous tree automata and definab...

Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs computationally efficient as they inference along one route (root-to-leaf) that is dependent on the input data. In this paper, we present DecisioNet (DN), a binary-tree structured network. We propose systematic way convert a...