General fragmentation trees

General Fragmentation Trees

We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured R-tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes.

Fragmentation trees reloaded

BACKGROUND Untargeted metabolomics commonly uses liquid chromatography mass spectrometry to measure abundances of metabolites; subsequent tandem mass spectrometry is used to derive information about individual compounds. One of the bottlenecks in this experimental setup is the interpretation of fragmentation spectra to accurately and efficiently identify compounds. Fragmentation trees have beco...

Fragmentation of Random Trees

We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected existing node. As nodes are removed from the tree, one at a time, the tree dissolves into an ensemble of separate trees, namely, a forest. We study statistical pr...

Gibbs fragmentation trees

We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs type fragmentation tree with Aldous’s beta-splitting model, which has an extended parameter range β > −2 with respect to the beta(β + 1, β + 1) probability distributions on which it is based. In the multifurcating case, we show that Gibbs fragmentation trees are associated with the two-parameter P...

Rainforest fragmentation kills big trees.