Comparison of Various Improved-Partition Fuzzy c-Means Clustering Algorithms in Fast Color Reduction

This paper provides a comparative study of sev- eral enhanced versions of the fuzzy c -means clustering al- gorithm in an application of histogram-based image color reduction. A common preprocessing is performed before clus- tering, consisting of a preliminary color quantization, histogram extraction and selection of frequently occurring colors of the image. These selected colors will be clustered by tested c -means algorithms. Clustering is followed by another common step, which creates the output image. Besides conventional hard (HCM) and fuzzy c -means (FCM) clustering, the so-called generalized improved partition FCM algorithm, and several versions of the suppressed FCM (s-FCM) in its conventional and generalized form, are included in this study. Accuracy is measured as the average color difference between pixels of the input and output image, while efficiency is mostly characterized by the total runtime of the performed color reduction. Nu- merical evaluation found all enhanced FCM algorithms more accurate, and four out of seven enhanced algorithms faster than FCM. All tested algorithms can create reduced color images of acceptable quality

Well-Posed Initial-Boundary Evolution in General Relativity

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code which satisfies convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.Comment: 5 pages, 6 figures; added another convergence plot to Fig. 2 + minor change

Numerical stability for finite difference approximations of Einstein's equations

We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol of the second order system, we obtain necessary and sufficient conditions for stability in a discrete norm containing one-sided difference operators. We prove stability for certain toy models and the linearized Nagy-Ortiz-Reula formulation of Einstein's equations. We also find that, unlike in the fully first order case, standard discretizations of some well-posed problems lead to unstable schemes and that the Courant limits are not always simply related to the characteristic speeds of the continuum problem. Finally, we propose methods for testing stability for second order in space hyperbolic systems.Comment: 18 pages, 9 figure

Algebraic stability analysis of constraint propagation

The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint equations inadvertently leads to 'constraint violating modes' propagating into the computational domain from the boundary. The other source for constraint violation is intrinsic. It is already present in the initial value problem, i.e. even when no boundary conditions have to be specified. Its origin is due to the instability of the constraint surface in the phase space of initial conditions for the time evolution equations. In this paper, we present a technique to study in detail how this instability depends on gauge parameters. We demonstrate this for the influence of the choice of the time foliation in context of the Weyl system. This system is the essential hyperbolic part in various formulations of the Einstein equations.Comment: 25 pages, 5 figures; v2: small additions, new reference, publication number, classification and keywords added, address fixed; v3: update to match journal versio

A geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad

We investigate the suitability and properties of a quasi-Kinnersley tetrad and a geometrically motivated coordinate system as tools for quantifying both strong-field and wave-zone effects in numerical relativity (NR) simulations. We fix the radial and latitudinal coordinate degrees of freedom of the metric, using the Coulomb potential associated with the quasi-Kinnersley transverse frame. These coordinates are invariants of the spacetime and can be used to unambiguously fix the outstanding spin-boost freedom associated with the quasi-Kinnersley frame (resulting in a preferred quasi-Kinnersley tetrad (QKT)). In the limit of small perturbations about a Kerr spacetime, these coordinates and QKT reduce to Boyer-Lindquist coordinates and the Kinnersley tetrad, irrespective of the simulation gauge choice. We explore the properties of this construction both analytically and numerically, and we gain insights regarding the propagation of radiation described by a super-Poynting vector. We also quantify in detail the peeling properties of the chosen tetrad and gauge. We argue that these choices are particularly well suited for a rapidly converging wave-extraction algorithm as the extraction location approaches infinity, and we explore numerically the extent to which this property remains applicable on the interior of a computational domain. Using a number of additional tests, we verify that the prescription behaves as required in the appropriate limits regardless of simulation gauge. We explore the behavior of the geometrically motivated coordinate system in dynamical binary-black-hole NR mergers, and find them useful for visualizing features in NR simulations such as the spurious "junk" radiation. Finally, we carefully scrutinize the head-on collision of two black holes and, for example, the way in which the extracted waveform changes as it moves through the computational domain.Comment: 30 pages, 17 figures, 2 table

Tailoring Fe/Ag Superparamagnetic Composites by Multilayer Deposition

The magnetic properties of Fe/Ag granular multilayers were examined by SQUID magnetization and Mossbauer spectroscopy measurements. Very thin (0.2 nm) discontinuous Fe layers show superparamagnetic properties that can be tailored by the thickness of both the magnetic and the spacer layers. The role of magnetic interactions was studied in novel heterostructures of superparamagnetic and ferromagnetic layers and the specific contribution of the ferromagnetic layers to the low field magnetic susceptibility was identified.Comment: 5 pages and 3 figure