相关论文: Flocks of Cones: Star Flocks
Let $\cal R$ be an ordered vector space over an ordered division ring. We prove that every definable set $X$ is a finite union of relatively open definable subsets which are definably simply-connected, settling a conjecture from [5]. The…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
We discuss, from a statistical point of view, some leading issues that deal with the study of stellar populations in fully or partially unresolved aggregates, like globular clusters and distant galaxies. A confident assessment of the…
In this paper, we examine the combinatorial properties of conic arrangements in the complex projective plane that possess certain quasi-homogeneous singularities. First, we introduce a new tool that enables us to characterize the property…
We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid projection of the knot.
Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby discover, relate, and structure types: of behaviour,…
The realization that most stars form in clusters, raises the question of whether star/planet formation are influenced by the cluster environment. The stellar density in the most prevalent clusters is the key factor here. Whether dominant…
The triangulations of point configurations which decompose as a free sum are classified in terms of the triangulations of the summands. The methods employ two new kinds of partially ordered sets to be associated with any triangulation of a…
What is the nature of a star forming clump? Observations reveal these to be chaotic environments being modified and influenced by many physical processes. However, numerical simulations often define these initial star forming clumps to be…
We use quilted Floer theory to construct functor-valued invariants of tangles arising from moduli spaces of flat bundles on punctured surfaces. As an application, we show the non-triviality of certain elements in the symplectic mapping…
We study a one-dimensional lattice flocking model incorporating all three of the flocking criteria proposed by Reynolds [Computer Graphics vol.21 4 (1987)]: alignment, centring and separation. The model generalises that introduced by O. J.…
In this paper, we introduce the notion of the quadratic graph, that is a graph whose eigenvalues are integral or quadratic algebraic integral, and determine nine infinite families of quadratic starlike trees, which are just all the…
Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…
A Tangle is a smooth simple closed curve formed from arcs (or ``links'') of circles with fixed radius. Most previous study of Tangles has dealt with the case where these arcs are quarter-circles, but Tangles comprised of thirds and sixths…
A brief overview of the properties of massive star clusters in early-type galaxies is given. All ellipticals (with only one known exception) host massive star clusters in the form of globular clusters, suggesting that their formation is…
We show how to convert any clustering into a prediction set. This has the effect of converting the clustering into a (possibly overlapping) union of spheres or ellipsoids. The tuning parameters can be chosen to minimize the size of the…
We consider tessellations of the Euclidean $(d-1)$-sphere by $(d-2)$-dimensional great subspheres or, equivalently, tessellations of Euclidean $d$-space by hyperplanes through the origin; these we call conical tessellations. For random…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
Voronoi cells of a discrete set in Euclidean space are known as generalized polyhedra. We identify polyhedral cells of a discrete set through a direction cone. For an arbitrary set we distinguish polyhedral from non-polyhedral cells using…