Quantifying topological invariants of neuronal morphologies
  Nervous systems are characterized by neurons displaying a diversity of morphological shapes. Traditionally, different shapes have been qualitatively described based on visual inspection and quantitatively described based on morphometric parameters. Neither process provides a solid foundation for categorizing the various morphologies, a problem that is important in many fields. We propose a stable topological measure as a standardized descriptor for any tree-like morphology, which encodes its skeletal branching anatomy. More specifically it is a barcode of the branching tree as determined by a spherical filtration centered at the root or neuronal soma. This Topological Morphology Descriptor (TMD) allows for the discrimination of groups of random and neuronal trees at linear computational cost. 
Lida Kanari, Pawe{\l} D{\l}otko, Martina Scolamiero, Ran Levi, Julian   Shillcock, Kathryn Hess, Henry Markram
q-bio.NC cs.DS math.AT