Let FN be a free group of finite rank N ≥ 2, and let T be an R-tree with a very small, minimal action of FN with dense orbits. For any basis A of FN there exists a heart KA ⊂ T (= the metric completion of T ) which is a compact subtree that has the property that the dynamical system of partial isometries ai : KA∩aiKA → a −1 i KA∩KA, for each ai ∈ A, defines a tree T(KA,A) which contains an isom...

AbstractUnderstanding operator bias in evolutionary computation is important because it is possible for the operator’s biases to work against the intended biases induced by the fitness function. In recent work we showed how developments in GP schema theory can be used to better understand the biases induced by the standard subtree crossover when genetic programming is applied to variable length...

Regions in an image graph can be described by their spanning tree. A graph pyramid is a stack of image graphs at different granularities. Integral features capture important properties of these regions and the associated trees. We compute the depth of a rooted tree, its diameter and the center which becomes the root in the top-down decomposition of a region. The integral tree is an intermediate...

Given a permutation σ $$ \sigma , its corresponding binary search tree is obtained by recursively inserting the values ( 1 ) … n (1),\dots, (n) into so that label of each node larger than labels left subtree and smaller right subtree. In this article, we study height trees drawn from record-biased model permutations whose probability measure on set proportional to θ record {\theta}^{\mathrm{rec...