Probabilistic Clustering of Time-Evolving Distance Data

We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the underlying cluster structure and obtain a smooth cluster evolution. This approach allows the number of objects and clusters to differ at every time point, and no identification on the identities of the objects is needed. Further, the model does not require the number of clusters being specified in advance -- they are instead determined automatically using a Dirichlet process prior. We validate our model on synthetic data showing that the proposed method is more accurate than state-of-the-art clustering methods. Finally, we use our dynamic clustering model to analyze and illustrate the evolution of brain cancer patients over time

StarHorse: A Bayesian tool for determining stellar masses, ages, distances, and extinctions for field stars

Understanding the formation and evolution of our Galaxy requires accurate distances, ages and chemistry for large populations of field stars. Here we present several updates to our spectro-photometric distance code, that can now also be used to estimate ages, masses, and extinctions for individual stars. Given a set of measured spectro-photometric parameters, we calculate the posterior probability distribution over a given grid of stellar evolutionary models, using flexible Galactic stellar-population priors. The code (called {\tt StarHorse}) can acommodate different observational datasets, prior options, partially missing data, and the inclusion of parallax information into the estimated probabilities. We validate the code using a variety of simulated stars as well as real stars with parameters determined from asteroseismology, eclipsing binaries, and isochrone fits to star clusters. Our main goal in this validation process is to test the applicability of the code to field stars with known {\it Gaia}-like parallaxes. The typical internal precision (obtained from realistic simulations of an APOGEE+Gaia-like sample) are $\simeq 8\%$ in distance, $\simeq 20\%$ in age,$\simeq 6\$ in mass, and $\simeq 0.04$ mag in $A_V$. The median external precision (derived from comparisons with earlier work for real stars) varies with the sample used, but lies in the range of $\simeq [0,2]\%$ for distances, $\simeq [12,31]\%$ for ages, $\simeq [4,12]\%$ for masses, and $\simeq 0.07$ mag for $A_V$. We provide StarHorse distances and extinctions for the APOGEE DR14, RAVE DR5, GES DR3 and GALAH DR1 catalogues.Comment: 21 pages, 12 figures, accepte

The Stellar Metallicity Distribution Function of the Galactic Halo from SDSS Photometry

We explore the stellar metallicity distribution function of the Galactic halo based on SDSS ugriz photometry. A set of stellar isochrones is calibrated using observations of several star clusters and validated by comparisons with medium-resolution spectroscopic values over a wide range of metal abundance. We estimate distances and metallicities for individual main-sequence stars in the multiply scanned SDSS Stripe 82, at heliocentric distances in the range 5 - 8 kpc and |b| > 35 deg, and find that the in situ photometric metallicity distribution has a shape that matches that of the kinematically-selected local halo stars from Ryan & Norris. We also examine independent kinematic information from proper-motion measurements for high Galactic latitude stars in our sample. We find that stars with retrograde rotation in the rest frame of the Galaxy are generally more metal poor than those exhibiting prograde rotation, which is consistent with earlier arguments by Carollo et al. that the halo system comprises at least two spatially overlapping components with differing metallicity, kinematics, and spatial distributions. The observed photometric metallicity distribution and that of Ryan & Norris can be described by a simple chemical evolution model by Hartwick (or by a single Gaussian distribution); however, the suggestive metallicity-kinematic correlation contradicts the basic assumption in this model that the Milky Way halo consists primarily of a single stellar population. When the observed metallicity distribution is deconvolved using two Gaussian components with peaks at [Fe/H] ~ -1.7 and -2.3, the metal-poor component accounts for ~20% - 35% of the entire halo population in this distance range.Comment: Accepted for publication in Ap

Curvature-based Pooling within Graph Neural Networks

Over-squashing and over-smoothing are two critical issues, that limit the capabilities of graph neural networks (GNNs). While over-smoothing eliminates the differences between nodes making them indistinguishable, over-squashing refers to the inability of GNNs to propagate information over long distances, as exponentially many node states are squashed into fixed-size representations. Both phenomena share similar causes, as both are largely induced by the graph topology. To mitigate these problems in graph classification tasks, we propose CurvPool, a novel pooling method. CurvPool exploits the notion of curvature of a graph to adaptively identify structures responsible for both over-smoothing and over-squashing. By clustering nodes based on the Balanced Forman curvature, CurvPool constructs a graph with a more suitable structure, allowing deeper models and the combination of distant information. We compare it to other state-of-the-art pooling approaches and establish its competitiveness in terms of classification accuracy, computational complexity, and flexibility. CurvPool outperforms several comparable methods across all considered tasks. The most consistent results are achieved by pooling densely connected clusters using the sum aggregation, as this allows additional information about the size of each pool.Comment: ECMLPKDD 2023 - Workshop on Mining and Learning with Graph

An Exploration Of Geographic Scope: The Cluster Of Grenoble

This article examines the high-tech cluster of Grenoble in the light of regional studies. In particular, we explore the geographic scope of organizations, knowledge flows and risk perceptions. Using a large quantitative dataset, we observe that trial-driven synthetic knowledge-flow dynamics are generally based on the engineering sciences and develop over large distances, posing a challenge to well-established clusters. Our results emphasize significant differences across organization types (firms, research centers, universities, and public bodies) and organization sizes (small, medium, and large). We find that large firms develop knowledge-flows dynamics over greater distances than small firms and that research centers, universities and medium-sized firms perceive greater knowledge anchoring than do small and large firms. In addition, we find that theory-driven analytical and branding-driven symbolic knowledge are more anchored than synthetic knowledge, which is the type of knowledge of greatest value in information and communication technologies (ICT). Finally, we argue that the increase of geographical distance between knowledge senders and receivers increases the perception of the risk of unintended knowledge spillovers

Nonparametric Feature Extraction from Dendrograms

We propose feature extraction from dendrograms in a nonparametric way. The Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level function and a distance function over that. Therefore, we extend this method to arbitrary dendrograms. We develop a generalized framework wherein different distance measures can be inferred from different types of dendrograms, level functions and distance functions. Via an appropriate embedding, we compute a vector-based representation of the inferred distances, in order to enable many numerical machine learning algorithms to employ such distances. Then, to address the model selection problem, we study the aggregation of different dendrogram-based distances respectively in solution space and in representation space in the spirit of deep representations. In the first approach, for example for the clustering problem, we build a graph with positive and negative edge weights according to the consistency of the clustering labels of different objects among different solutions, in the context of ensemble methods. Then, we use an efficient variant of correlation clustering to produce the final clusters. In the second approach, we investigate the sequential combination of different distances and features sequentially in the spirit of multi-layered architectures to obtain the final features. Finally, we demonstrate the effectiveness of our approach via several numerical studies

An updated maximum likelihood approach to open cluster distance determination

An improved method for estimating distances to open clusters is presented and applied to Hipparcos data for the Pleiades and the Hyades. The method is applied in the context of the historic Pleiades distance problem, with a discussion of previous criticisms of Hipparcos parallaxes. This is followed by an outlook for Gaia, where the improved method could be especially useful. Based on maximum likelihood estimation, the method combines parallax, position, apparent magnitude, colour, proper motion, and radial velocity information to estimate the parameters describing an open cluster precisely and without bias. We find the distance to the Pleiades to be $120.3 \pm 1.5$ pc, in accordance with previously published work using the same dataset. We find that error correlations cannot be responsible for the still present discrepancy between Hipparcos and photometric methods. Additionally, the three-dimensional space velocity and physical structure of Pleiades is parametrised, where we find strong evidence of mass segregation. The distance to the Hyades is found to be $46.35\pm 0.35$ pc, also in accordance with previous results. Through the use of simulations, we confirm that the method is unbiased, so will be useful for accurate open cluster parameter estimation with Gaia at distances up to several thousand parsec.Comment: 14 pages, 8 figures, 6 tables, 3 appendices. Accepted in A&

Cosmicflows-2: I-band Luminosity - HI Linewidth Calibration

In order to measure distances with minimal systematics using the correlation between galaxy luminosities and rotation rates it is necessary to adhere to a strict and tested recipe. We now derive a measure of rotation from a new characterization of the width of a neutral Hydrogen line profile. Additionally, new photometry and zero point calibration data are available. Particularly the introduction of a new linewidth parameter necessitates the reconstruction and absolute calibration of the luminosity-linewidth template. The slope of the new template is set by 267 galaxies in 13 clusters. The zero point is set by 36 galaxies with Cepheid or Tip of the Red Giant Branch distances. Tentatively, we determine H0 = 75 km s-1 Mpc-1. Distances determined using the luminosity-linewidth calibration will contribute to the distance compendium Cosmicflows-2.Comment: Accepted for publication in The Astrophysical Journal, 27 pages, 18 figure

Cosmicflows-2: SNIa Calibration and H0

The construction of the Cosmicflows-2 compendium of distances involves the merging of distance measures contributed by the following methods: (Cepheid) Period-Luminosity, Tip of the Red Giant Branch (TRGB), Surface Brightness Fluctuation (SBF), Luminosity-Linewidth (TF), Fundamental Plane (FP), and Type Ia supernova (SNIa). The method involving SNIa is at the top of an interconnected ladder, providing accurate distances to well beyond the expected range of distortions to Hubble flow from peculiar motions. In this paper, the SNIa scale is anchored by 36 TF spirals with Cepheid or TRGB distances, 56 SNIa hosts with TF distances, and 61 groups or clusters hosting SNIa with Cepheid, SBF, TF, or FP distances. With the SNIa scale zero point set, a value of the Hubble Constant is evaluated over a range of redshifts 0.03 < z < 0.5, assuming a cosmological model with Omega_m = 0.27 and Omega_Lambda = 0.73. The value determined for the Hubble Constant is H0 = 75.9 \pm 3.8 km s-1 Mpc-1.Comment: Accepted for publication in The Astrophysical Journal. 11 pages, 8Figures, 5 Table