The young star cluster population of M51 with LEGUS – I. A comprehensive study of cluster formation and evolution

Recently acquired WFC3 UV (F275W and F336W) imaging mosaics under the Legacy Extragalactic UV Survey (LEGUS), combined with archival ACS data of M51, are used to study the young star cluster (YSC) population of this interacting system. Our newly extracted source catalogue contains 2834 cluster candidates, morphologically classified to be compact and uniform in colour, for which ages, masses and extinction are derived. In this first work we study the main properties of the YSC population of the whole galaxy, considering a mass-limited sample. Both luminosity and mass functions follow a power-law shape with slope −2, but at high luminosities and masses a dearth of sources is observed. The analysis of the mass function suggests that it is best fitted by a Schechter function with slope −2 and a truncation mass at 1.00 ± 0.12 × 10^5 M⊙. Through Monte Carlo simulations, we confirm this result and link the shape of the luminosity function to the presence of a truncation in the mass function. A mass limited age function analysis, between 10 and 200 Myr, suggests that the cluster population is undergoing only moderate disruption. We observe little variation in the shape of the mass function at masses above 1 × 10^4 M⊙ over this age range. The fraction of star formation happening in the form of bound clusters in M51 is ∼ 20 per cent in the age range 10–100 Myr and little variation is observed over the whole range from 1 to 200 Myr

Extinction Maps and Dust-to-gas Ratios in Nearby Galaxies with LEGUS

We present a study of the dust-to-gas ratios in five nearby galaxies: NGC 628 (M74), NGC 6503, NGC 7793, UGC 5139 (Holmberg I), and UGC 4305 (Holmberg II). Using Hubble Space Telescopebroadband WFC3/UVIS UV and optical images from the Treasury program Legacy ExtraGalactic UV Survey (LEGUS) combined with archival HST/Advanced Camera for Surveys data, we correct thousands of individual stars for extinction across these five galaxies using an isochrone-matching (reddening-free Q) method. We generate extinction maps for each galaxy from the individual stellar extinctions using both adaptive and fixed resolution techniques and correlate these maps with neutral H I and CO gas maps from the literature, including the H I Nearby Galaxy Survey and the HERA CO-Line Extragalactic Survey. We calculate dust-to-gas ratios and investigate variations in the dust-to-gas ratio with galaxy metallicity. We find a power-law relationship between dust-to-gas ratio and metallicity, consistent with other studies of dust-to-gas ratio compared to metallicity. We find a change in the relation when H2 is not included. This implies that underestimation of N_(H2) in low-metallicity dwarfs from a too-low CO-to-H_2 conversion factor X_(CO) could have produced too low a slope in the derived relationship between dust-to-gas ratio and metallicity. We also compare our extinctions to those derived from fitting the spectral energy distribution (SED) using the Bayesian Extinction and Stellar Tool for NGC 7793 and find systematically lower extinctions from SED fitting as compared to isochrone matching

Stratified decision forests for accurate anatomical landmark localization in cardiac images

Accurate localization of anatomical landmarks is an important step in medical imaging, as it provides useful prior information for subsequent image analysis and acquisition methods. It is particularly useful for initialization of automatic image analysis tools (e.g. segmentation and registration) and detection of scan planes for automated image acquisition. Landmark localization has been commonly performed using learning based approaches, such as classifier and/or regressor models. However, trained models may not generalize well in heterogeneous datasets when the images contain large differences due to size, pose and shape variations of organs. To learn more data-adaptive and patient specific models, we propose a novel stratification based training model, and demonstrate its use in a decision forest. The proposed approach does not require any additional training information compared to the standard model training procedure and can be easily integrated into any decision tree framework. The proposed method is evaluated on 1080 3D highresolution and 90 multi-stack 2D cardiac cine MR images. The experiments show that the proposed method achieves state-of-theart landmark localization accuracy and outperforms standard regression and classification based approaches. Additionally, the proposed method is used in a multi-atlas segmentation to create a fully automatic segmentation pipeline, and the results show that it achieves state-of-the-art segmentation accuracy

Random Projections For Large-Scale Regression

Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool in machine learning and statistics. We discuss the applications of random projections in linear regression problems, developed to decrease computational costs, and give an overview of the theoretical guarantees of the generalization error. It can be shown that the combination of random projections with least squares regression leads to similar recovery as ridge regression and principal component regression. We also discuss possible improvements when averaging over multiple random projections, an approach that lends itself easily to parallel implementation.Comment: 13 pages, 3 Figure

Power Spectra of a Constrained Totally Asymmetric Simple Exclusion Process

To synthesize proteins in a cell, an mRNA has to work with a finite pool of ribosomes. When this constraint is included in the modeling by a totally asymmetric simple exclusion process (TASEP), non-trivial consequences emerge. Here, we consider its effects on the power spectrum of the total occupancy, through Monte Carlo simulations and analytical methods. New features, such as dramatic suppressions at low frequencies, are discovered. We formulate a theory based on a linearized Langevin equation with discrete space and time. The good agreement between its predictions and simulation results provides some insight into the effects of finite resoures on a TASEP.Comment: 4 pages, 2 figures v2: formatting change

Negative-weight percolation

We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are spanning paths or loops of total negative weight. This kind of percolation problem is fundamentally different from conventional percolation problems, e.g. it does not exhibit transitivity, hence no simple definition of clusters, and several spanning paths/loops might coexist in the percolation regime at the same time. Furthermore, to study this percolation problem numerically, one has to perform a non-trivial transformation of the original graph and apply sophisticated matching algorithms. Using this approach, we study the corresponding percolation transitions on large square, hexagonal and cubic lattices for two types of disorder distributions and determine the critical exponents. The results show that negative-weight percolation is in a different universality class compared to conventional bond/site percolation. On the other hand, negative-weight percolation seems to be related to the ferromagnet/spin-glass transition of random-bond Ising systems, at least in two dimensions.Comment: v1: 4 pages, 4 figures; v2: 10 pages, 7 figures, added results, text and reference

Entropy landscape and non-Gibbs solutions in constraint satisfaction problems

We study the entropy landscape of solutions for the bicoloring problem in random graphs, a representative difficult constraint satisfaction problem. Our goal is to classify which type of clusters of solutions are addressed by different algorithms. In the first part of the study we use the cavity method to obtain the number of clusters with a given internal entropy and determine the phase diagram of the problem, e.g. dynamical, rigidity and SAT-UNSAT transitions. In the second part of the paper we analyze different algorithms and locate their behavior in the entropy landscape of the problem. For instance we show that a smoothed version of a decimation strategy based on Belief Propagation is able to find solutions belonging to sub-dominant clusters even beyond the so called rigidity transition where the thermodynamically relevant clusters become frozen. These non-equilibrium solutions belong to the most probable unfrozen clusters.Comment: 38 pages, 10 figure

Random billiards with wall temperature and associated Markov chains

By a random billiard we mean a billiard system in which the standard specular reflection rule is replaced with a Markov transition probabilities operator P that, at each collision of the billiard particle with the boundary of the billiard domain, gives the probability distribution of the post-collision velocity for a given pre-collision velocity. A random billiard with microstructure (RBM) is a random billiard for which P is derived from a choice of geometric/mechanical structure on the boundary of the billiard domain. RBMs provide simple and explicit mechanical models of particle-surface interaction that can incorporate thermal effects and permit a detailed study of thermostatic action from the perspective of the standard theory of Markov chains on general state spaces. We focus on the operator P itself and how it relates to the mechanical/geometric features of the microstructure, such as mass ratios, curvatures, and potentials. The main results are as follows: (1) we characterize the stationary probabilities (equilibrium states) of P and show how standard equilibrium distributions studied in classical statistical mechanics, such as the Maxwell-Boltzmann distribution and the Knudsen cosine law, arise naturally as generalized invariant billiard measures; (2) we obtain some basic functional theoretic properties of P. Under very general conditions, we show that P is a self-adjoint operator of norm 1 on an appropriate Hilbert space. In a simple but illustrative example, we show that P is a compact (Hilbert-Schmidt) operator. This leads to the issue of relating the spectrum of eigenvalues of P to the features of the microstructure;(3) we explore the latter issue both analytically and numerically in a few representative examples;(4) we present a general algorithm for simulating these Markov chains based on a geometric description of the invariant volumes of classical statistical mechanics