18,490 research outputs found
Connecting a Set of Circles with Minimum Sum of Radii
Abstract. We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of circles is connected, and the sum of radii is minimized. We show that the problem is polynomially solvable if a connectivity tree is given. If the connectivity tree is unknown, the problem is NP-hard if there are upper bounds on the radii and open otherwise. We give approximation guarantees for a variety of polynomialtime algorithms, describe upper and lower bounds (which are matching in some of the cases), provide polynomial-time approximation schemes, and conclude with experimental results and open problems
Automated detection of filaments in the large scale structure of the universe
We present a new method to identify large scale filaments and apply it to a
cosmological simulation. Using positions of haloes above a given mass as node
tracers, we look for filaments between them using the positions and masses of
all the remaining dark-matter haloes. In order to detect a filament, the first
step consists in the construction of a backbone linking two nodes, which is
given by a skeleton-like path connecting the highest local dark matter (DM)
density traced by non-node haloes. The filament quality is defined by a density
and gap parameters characterising its skeleton, and filament members are
selected by their binding energy in the plane perpendicular to the filament.
This membership condition is associated to characteristic orbital times;
however if one assumes a fixed orbital timescale for all the filaments, the
resulting filament properties show only marginal changes, indicating that the
use of dynamical information is not critical for the method. We test the method
in the simulation using massive haloes(h) as
filament nodes. The main properties of the resulting high-quality filaments
(which corresponds to of the detected filaments) are, i) their
lengths cover a wide range of values of up to hMpc, but are mostly
concentrated below 50hMpc; ii) their distribution of thickness peaks at
hMpc and increases slightly with the filament length; iii) their
nodes are connected on average to filaments for nodes; this number increases with the node mass to filaments for nodes.Comment: 17 pages, 13 figures, MNRAS Accepte
Power adjustment and scheduling in OFDMA femtocell networks
Densely-deployed femtocell networks are used to enhance wireless coverage in public spaces like office buildings, subways, and academic buildings. These networks can increase throughput for users, but edge users can suffer from co-channel interference, leading to service outages. This paper introduces a distributed algorithm for network configuration, called Radius Reduction and Scheduling (RRS), to improve the performance and fairness of the network. RRS determines cell sizes using a Voronoi-Laguerre framework, then schedules users using a scheduling algorithm that includes vacancy requests to increase fairness in dense femtocell networks. We prove that our algorithm always terminate in a finite time, producing a configuration that guarantees user or area coverage. Simulation results show a decrease in outage probability of up to 50%, as well as an increase in Jain's fairness index of almost 200%
On compact packings of the plane with circles of three radii
A compact circle-packing of the Euclidean plane is a set of circles which
bound mutually disjoint open discs with the property that, for every circle
, there exists a maximal indexed set so that, for every , the circle is tangent to
both circles and
We show that there exist at most pairs with for
which there exist a compact circle-packing of the plane consisting of circles
with radii , and .
We discuss computing the exact values of such as roots of
polynomials and exhibit a selection of compact circle-packings consisting of
circles of three radii. We also discuss the apparent infeasibility of computing
\emph{all} these values on contemporary consumer hardware with the methods
employed in this paper.Comment: Dataset referred to in the text can be obtained at
http://dx.doi.org/10.17632/t66sfkn5tn.
Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
The Faddeev-Volkov solution of the star-triangle relation is connected with
the modular double of the quantum group U_q(sl_2). It defines an Ising-type
lattice model with positive Boltzmann weights where the spin variables take
continuous values on the real line. The free energy of the model is exactly
calculated in the thermodynamic limit. The model describes quantum fluctuations
of circle patterns and the associated discrete conformal transformations
connected with the Thurston's discrete analogue of the Riemann mappings
theorem. In particular, in the quasi-classical limit the model precisely
describe the geometry of integrable circle patterns with prescribed
intersection angles.Comment: 26 pages, 18 color figures, minor correction
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