A Bimodality Test in High Dimensions

We present a test for identifying clusters in high dimensional data based on the k-means algorithm when the null hypothesis is spherical normal. We show that projection techniques used for evaluating validity of clusters may be misleading for such data. In particular, we demonstrate that increasingly well-separated clusters are identified as the dimensionality increases, when no such clusters exist. Furthermore, in a case of true bimodality, increasing the dimensionality makes identifying the correct clusters more difficult. In addition to the original conservative test, we propose a practical test with the same asymptotic behavior that performs well for a moderate number of points and moderate dimensionality. ACM Computing Classification System (1998): I.5.3.

The Technology of Programming for a Cluster Computer by the Remote Terminal with OS Windows

The problem of preparation of a program to perform it on multiprocessor system of a cluster type is considered. When developing programs for a cluster computer the technology based on use of the remote terminal is applied. The situation when such remote terminal is the computer with operational system Windows is considered. The set of the tool means, allowing carrying out of editing program texts, compiling and starting programs on a cluster computer, is suggested. Advantage of an offered way of preparation of programs to execution is that it allows as much as possible to use practical experience of programmers used to working in OS Windows environment.

Cluster Management Processes Organization and Handling

The paper describes cluster management software and hardware of SCIT supercomputer clusters built in Glushkov Institute of Cybernetics NAS of Ukraine. The paper shows the performance results received on systems that were built and the specific means used to fulfil the goal of performance increase. It should be useful for those scientists and engineers that are practically engaged in a cluster supercomputer systems design, integration and services.

An Adaptation of the Hoshen-Kopelman Cluster Counting Algorithm for Honeycomb Networks

We develop a simplified implementation of the Hoshen-Kopelman cluster counting algorithm adapted for honeycomb networks. In our implementation of the algorithm we assume that all nodes in the network are occupied and links between nodes can be intact or broken. The algorithm counts how many clusters there are in the network and determines which nodes belong to each cluster. The network information is stored into two sets of data. The first one is related to the connectivity of the nodes and the second one to the state of links. The algorithm finds all clusters in only one scan across the network and thereafter cluster relabeling operates on a vector whose size is much smaller than the size of the network. Counting the number of clusters of each size, the algorithm determines the cluster size probability distribution from which the mean cluster size parameter can be estimated. Although our implementation of the Hoshen-Kopelman algorithm works only for networks with a honeycomb (hexagonal) structure, it can be easily changed to be applied for networks with arbitrary connectivity between the nodes (triangular, square, etc.). The proposed adaptation of the Hoshen-Kopelman cluster counting algorithm is applied to studying the thermal degradation of a graphene-like honeycomb membrane by means of Molecular Dynamics simulation with a Langevin thermostat. ACM Computing Classification System (1998): F.2.2, I.5.3.

A Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals

2000 Mathematics Subject Classification: 41A25, 41A36.

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.

Equivalence Between K-functionals Based on Continuous Linear Transforms

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.