Synthetic Test Data Generation for Hierarchical Graph Clustering Methods

Recent achievements in graph-based clustering algorithms revealed the need for large-scale test data sets. This paper introduces a procedure that can provide synthetic but realistic test data to the hi- erarchical Markov clustering algorithm. Being created according to the structure and properties of the SCOP95 protein sequence data set, the synthetic data act as a collection of proteins organized in a four-level hierarchy and a similarity matrix containing pairwise similarity values of the proteins. An ultimate high-speed TRIBE-MCL algorithm was em- ployed to validate the synthetic data. Generated data sets have a healthy amount of variability due to the randomness in the processing, and are suitable for testing graph-based clustering algorithms on large-scale data

The Merger of Small and Large Black Holes

We present simulations of binary black holes mergers in which, after the common outer horizon has formed, the marginally outer trapped surfaces (MOTSs) corresponding to the individual black holes continue to approach and eventually penetrate each other. This has very interesting consequences according to recent results in the theory of MOTSs. Uniqueness and stability theorems imply that two MOTSs which touch with a common outer normal must be identical. This suggests a possible dramatic consequence of the collision between a small and large black hole. If the penetration were to continue to completion then the two MOTSs would have to coalesce, by some combination of the small one growing and the big one shrinking. Here we explore the relationship between theory and numerical simulations, in which a small black hole has halfway penetrated a large one.Comment: 17 pages, 11 figure

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

Sensor Drift Compensation Using Fuzzy Interference System and Sparse-Grid Quadrature Filter in Blood Glucose Control

Diabetes mellitus is a serious chronic condition of the human metabolism. The development of an automated treatment has reached clinical phase in the last few years. The goal is to keep the blood glucose concentration within a certain region with minimal interaction required by the patient or medical personnel. However, there are still several prac- tical problems to solve. One of these would be that the available sensors have significant noise and drift. The latter is rather difficult to manage, because the deviating signal can cause the controller to drive the glu- cose concentration out of the safe region even in the case of frequent calibration. In this study a linear-quadratic-Gaussian (LQG) controller is employed on a widely used diabetes model and enhanced with an ad- vanced Sparse-grid quadratic filter and a fuzzy interference system-based calibration supervisor

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

An explicit harmonic code for black-hole evolution using excision

We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the well-posedness and numerical stability of the initial-boundary problem for the quasilinear wave equation. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code. Such tests range from the evolution of isolated black holes to the head-on collision of two black holes and then to a binary black hole inspiral and merger. Besides assessing the accuracy of the code, the inspiral and merger test has revealed that individual apparent horizons can touch and even intersect. This novel feature in the dynamics of the marginally trapped surfaces is unexpected but consistent with theorems on the properties of apparent horizons

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