Related papers: Comparing the morphology of molecular clouds witho…

Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…

Point clouds provide a compact and efficient representation of 3D shapes. While deep neural networks have achieved impressive results on point cloud learning tasks, they require massive amounts of manually labeled data, which can be costly…

The probability distribution function of column density (PDF) has become the tool of choice for cloud structure analysis and star formation studies. Its simplicity is attractive, and the PDF could offer access to cloud physical parameters…

We present synthetic Hi and CO observations of a simulation of decaying turbulence in the thermally bistable neutral medium. We first present the simulation, with clouds initially consisting of clustered clumps. Self-gravity causes these…

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…

We report on an experimental observation of classical diffusion distinguishing between structural universality classes of disordered systems in one dimension. Samples of hyperuniform and short-range disorder were designed, characterized by…

Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…

Encoded within the morphological structure of galaxies are clues related to their formation and evolutionary history. Recent advances pertaining to the statistics of galaxy morphology include sophisticated measures of concentration (C),…

Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…

Dataset summarisation is a fruitful approach to dataset inspection. However, when applied to a single dataset the discovery of visual concepts is restricted to those most prominent. We argue that a comparative approach can expand upon this…

We study the geometry and topology of the large-scale structure traced by galaxy clusters in numerical simulations of a box of side 320 $h^{-1}$ Mpc, and compare them with available data on real clusters. The simulations we use are…

Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…

Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these…

This article proposes a powerful scheme to monitor a large number of categorical data streams with heterogeneous parameters or nature. The data streams considered may be either nominal with a number of attribute levels or ordinal with some…

The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare…

New-generation spectroscopic surveys of the Milky Way plane have been revealing the structure of the interstellar medium, allowing the simultaneous study of dense structures from single star-forming objects or systems to entire spiral arms.…

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…

Physical properties of the tiny scale structures in the cold neutral medium (CNM) of galaxies is a long-standing puzzle. Only a few lines of sights in our Galaxy have been studies with mixed results on the scale-invariant properties of such…

In inference problems, we often have domain knowledge which allows us to define summary statistics that capture most of the information content in a dataset. In this paper, we present a hybrid approach, where such physics-based summaries…