The Hi-GAL compact source catalogue - II. The 360\ub0 catalogue of clump physical properties

We present the 360\ub0 catalogue of physical properties of Hi-GAL compact sources, detected between 70 and 500 $\mu$m. This release not only completes the analogous catalogue previously produced by the Hi-GAL collaboration for -71\ub0 2 \ue1 2 67\ub0, but also meaningfully improves it because of a new set of heliocentric distances, 120 808 in total. About a third of the 150 223 entries are located in the newly added portion of the Galactic plane. A first classification based on detection at 70 $\mu$m as a signature of ongoing star-forming activity distinguishes between protostellar sources (23 per cent of the total) and starless sources, with the latter further classified as gravitationally bound (pre-stellar) or unbound. The integral of the spectral energy distribution, including ancillary photometry from λ = 21 to 1100 $\mu$m, gives the source luminosity and other bolometric quantities, while a modified blackbody fitted to data for $\lambda \ge 160∼\mu$m yields mass and temperature. All tabulated clump properties are then derived using photometry and heliocentric distance, where possible. Statistics of these quantities are discussed with respect to both source Galactic location and evolutionary stage. No strong differences in the distributions of evolutionary indicators are found between the inner and outer Galaxy. However, masses and densities in the inner Galaxy are on average significantly larger, resulting in a higher number of clumps that are candidates to host massive star formation. Median behaviour of distance-independent parameters tracing source evolutionary status is examined as a function of the Galactocentric radius, showing no clear evidence of correlation with spiral arm positions

Quadratic kernelization for convex recoloring of trees

The Convex Recoloring (CR) problem measures how far a tree of characters differs from exhibiting a so-called "perfect phylogeny". For an input consisting of a vertex-colored tree T, the problem is to determine whether recoloring at most k vertices can achieve a convex coloring, meaning by this a coloring where each color class induces a subtree. The problem was introduced by Moran and Snir (J. Comput. Syst. Sci. 73:1078-1089, 2007; J. Comput. Syst. Sci. 74:850-869, 2008) who showed that CR is NP-hard, and described a search-tree based FPT algorithm with a running time of O(k(k/log k) (k) n (4)). The Moran and Snir result did not provide any nontrivial kernelization. In this paper, we show that CR has a kernel of size O(k (2))