This paper proposes a binary classification tree aiming at solving multi-class classification problems using binary classifiers. The tree design is achieved in a way that a class group is partitioned into two distinct subgroups at a node. The node adopts the class-modular scheme to improve the binary classification capability. The partitioning is formulated as an optimization problem and a gene...

A fundamental part of many computer algorithms involves traversing a binary tree. One notable example is traversing a space-partitioning acceleration structure when computing ray-traced images. Traditionally, the traversal requires a stack to be temporarily stored for each ray, which results in both additional storage and memorybandwidth usage. We present a novel algorithm for traversing a bina...

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...