Related papers: Gap Distributions in Circle Packings
The paper starts with discussion of applications of cycle spaces to transportation cost. After a short survey of the known results on cycle spaces, we turn to the study of minimal projections onto cycle spaces in the corresponding…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
We state and prove some counting formulas relating to cliques in the distant graphs of projective lines over finite rings. As a preliminary to this, we prove a decomposition theorem for the graphs in terms of the direct-product…
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
In two-dimensional rotating drum experiments, we find two separate influences of the packing fraction of a granular heap on its stability. For a fixed grain shape, the stability increases with packing fraction. However, in determining the…
Dark gaps are commonly seen in early-to-intermediate type barred galaxies having inner and outer rings or related features. In this paper, the morphologies of 54 barred and oval ringed galaxies have been examined with the goal of…
A basic property of objects, like galaxies and halos that form in cosmological structure formation simulations, is their shape. Here, we critically investigate shape determination methods that are commonly used in the literature. It is…
We study the autocorrelations of observables constructed from the topological charge density, such as the topological charge on a time slice or in a subvolume, using a series of hybrid Monte Carlo simulations of pure SU(3) gauge theory with…
\textit{Parastichies} are spiral patterns observed in plants and numerical patterns generated using golden angle method. We generalize this method by using Markoff theory and the theory of product of linear forms, to obtain a theory for…
We determine the maximal number of steps required to sort $n$ labeled points on a circle by adjacent swaps. Lower bounds for sorting by all swaps, not necessarily adjacent, are given as well.
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…
Generalizing the well-known relations on characteristic functions on a plane to the case of a one-dimensional regular surface (curve) with compact support, we establish implicit equations for these functions. Introducing an approximation,…
We formulate self-consistency equations for the distribution of links in spin models and of plaquettes in gauge theories. This improves upon known mean-field, mean-link, and mean-plaquette approximations in such that we self-consistently…
Experiment, theory, and simulation are employed to understand the dispersion of colloidal particles in a periodic array of oscillating harmonic traps generated by optical tweezers. In the presence of trap oscillation, a non-monotonic and…
Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. It observed…
We investigate the class field theory for products of open curves over a local field. In particular, we determine the kernel of the reciprocity homomorphism.
We study the size-topology relations in random packings of dry adhesive polydisperse microspheres with Gaussian and lognormal size distributions through a geometric tessellation. We find that the dependence of the neighbour number on the…