Related papers: Filaments and voids in planar central configuratio…
High resolution 21 cm observations of the Ursa Major cirrus revealed highly filamentary structures down to the 0.03 pc resolution. These filaments, still present in the line centroid map, show multi-Gaussian components and seem to be…
With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most…
High resolution surveys reveal that the interstellar medium in the Milky Way and nearby galaxies consists of interlinked hierarchies of filamentary structure and superbubbles extending from galactic to subpc scales. The characterization of…
Voids are dominant features of the cosmic web. We revisit the cosmological information content of voids and connect void properties with the parameters of the background universe. We combine analytical results with a suite of large n-body…
The classical picture of a star-forming filament is a near-equilibrium structure, with collapse dependent on its gravitational criticality. Recent observations have complicated this picture, revealing filaments as a mess of apparently…
The relative equilibria of planar Newtonian $N$-body problem become coorbital around a central mass in the limit when all but one of the masses becomes zero. We prove a variety of results about the coorbital relative equilibria, with an…
The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure…
This letter deals with the problem of clutter edge detection and localization in training data. To this end, the problem is formulated as a binary hypothesis test assuming that the ranks of the clutter covariance matrix are known, and…
We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over $\mathbb{F}_q$, conditioned on ensuring that…
We studied superclusters of galaxies in a volume-limited sample extracted from the Sloan Digital Sky Survey Data Release 7 (SDSS/DR7) and from mock catalogues based on a semi-analytical model of galaxy evolution in the Millenium Simulation.…
The characterization of our Galaxy's longest filamentary gas features has been the subject of several studies in recent years, producing not only a sizeable sample of large-scale filaments, but also confusion as to whether all these…
Galaxy bias, the unknown relationship between the clustering of galaxies and the underlying dark matter density field is a major hurdle for cosmological inference from large-scale structure. While traditional analyses focus on the absolute…
We outline our methods for obtaining high precision mass profiles, combining independent weak-lensing distortion, magnification, and strong-lensing measurements. For massive clusters the strong and weak lensing regimes contribute equal…
Evidence of excess filamentarity is considered for two spatial point process applications: local minima in whole earth precipitation modelling and locations of cold clumps in the Milky Way. A diagnostic test using the number of aligned…
In this paper, we study the necessary conditions and sufficient conditions for the central configurations formed by two twisted regular polygons (one N-regular polygon and one L-regular polygon). We wish to extend the results of the…
The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we…
In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined,…
We introduce a method for constructing collections of subsets of $\mathbb{R}^{n}$, using an iterated function system, a set $T,$ and a cost function. We refer to these collections as tilings. The special case where $T$ is the central open…
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…
We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our…