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Branching allows neurons to make synaptic contacts with large numbers of other neurons, facilitating the high connectivity of nervous systems. Neuronal arbors have geometric properties such as branch lengths and diameters that are optimal in that they maximize signaling speeds while minimizing construction costs. In this work, we asked whether neuronal arbors have topological properties that may also optimize their growth or function. We discovered that for a wide range of invertebrate and vertebrate neurons the distributions of their subtree sizes follow power laws, implying that they are scale invariant. The power-law exponent distinguishes different neuronal cell types. Postsynaptic spines and branchlets perturb scale invariance. Through simulations, we show that the subtree-size distribution depends on the symmetry of the branching rules governing arbor growth and that optimal morphologies are scale invariant. Thus, the subtree-size distribution is a topological property that recapitulates the functional morphology of dendrites.
In the framework of the PNRA (Italian National Antarctic Research Program) project CARBONANT focusing on biogenic carbonates and held in January–February 2002, several Ross Sea banks were sampled to obtain samples of biogenic carbonates. In the Mawson Bank, species belonging to the isopod genus Chaetarcturus Brandt, 1990 were recorded, including a specimen that did not match any described species. In this paper we describe Chaetarcturus cervicornis sp. n., which is characterized by supraocular spines and two pairs of tubercle-like protrusions on the cephalothorax. The new species is very similar to C. bovinus (Brandt & Wägele, 1988) and C. adareanus (Hodgson, 1902), but has a clearly different spine pattern. The study of the species of the genus Chaetarcturus in the Ross Sea contributes to increase our knowledge on the diversity of the Antarcturidae in the Southern Ocean. Ross Sea banks seem to hold an interesting and not-well-known fauna, deserving attention in future research.