Near-infrared study of new embedded clusters in the Carina complex

We analyse the nature of a sample of stellar overdensities that we found projected on the Carina complex. This study is based on 2MASS photometry and involves the photometry decontamination of field stars, elaboration of intrinsic colour-magnitude diagrams J$\times$(J-Ks), colour-colour diagrams (J-H)$\times$(H-Ks) and radial density profiles, in order to determine the structure and the main astrophysical parameters of the best candidates. The verification of an overdensity as an embedded cluster requires a CMD consistent with a PMS content and MS stars, if any. From these results, we are able to verify if they are, in fact, embedded clusters. The results were, in general, rewarding: in a sample of 101 overdensities, the analysis provided 15 candidates, of which three were previously catalogued as clusters (CCCP-Cl$\,$16, Treasure Chest and FSR$\,$1555), and the 12 remaining are discoveries that provided significant results, with ages not above 4.5$\,$Myr and distances compatible with the studied complex. The resulting values for the differential reddening of most candidates were relatively high, confirming that these clusters are still (partially or fully) embedded in the surrounding gas and dust, as a rule within a shell. Histograms with the distribution of the masses, ages and distances were also produced, to give an overview of the results. We conclude that all the 12 newly found embedded clusters are related to the Carina complex.Comment: 10 pages, 14 figures, accepted for publication in MNRA

Corrections to Finite Size Scaling in Percolation

A 1/L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at pc for an annulus with aspect ratio r=1/2 is estimated as C = 0.876657(45)

Efficient algorithms for tensor scaling, quantum marginals and moment polytopes

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our algorithm provides an efficient weak membership oracle for the associated moment polytopes, an important family of implicitly-defined convex polytopes with exponentially many facets and a wide range of applications. These include the entanglement polytopes from quantum information theory (in particular, we obtain an efficient solution to the notorious one-body quantum marginal problem) and the Kronecker polytopes from representation theory (which capture the asymptotic support of Kronecker coefficients). Our algorithm can be applied to succinct descriptions of the input tensor whenever the marginals can be efficiently computed, as in the important case of matrix product states or tensor-train decompositions, widely used in computational physics and numerical mathematics. We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries