Comments to Chapter 1 35 Chapter 2. Boolean Functions 37 2.1. Basic concepts and definitions 37 2.2. Numerical and metric characteristics 44 2.3. Autocorrelation and crosscorrelation 56 2.4. Group algebra of Boolean functions 61 2.5. Cryptographic properties of Boolean functions and mappings 65 2.6. Covering sequences of Boolean functions 74 Comments to Chapter 2 76 Chapter 3. Classifications of Boolean Functions 77 3.1. Group equivalence of mappings. Polya's theorem 77 3.2. Classification of Boolean functions of five variables 83
In this paper we propose method for estimating and analysis measurements of delays in the computational cluster interconnection subsystem. Delays are combined into the set of pairs (source, destination). We have measurements of delays extracted by network_test2 utility from interconnections of following supercomputers: BlueGene/P, Lomonosov-1, Lomonosov-2 (Lomonosov MSU) and Jurope (Julich). We have clustered pairs of delays by DBscan and Divisive algorithms. Results of clusterisation revealed that DBScan is more accurate algorithm then divisive and allows to extract clusters, which correspond to the actual features in the supercomputer interconnections. Clusters gather near the same components of supercomputer network infrastructure. Gained clusters were visualized in 2-D by special tool, developed by authors.Introduction. Modern supercomputers are used to solve a wide range of problems, in particular: mathematical modeling and processing of large amounts of data. Supercomputers typically have an architecture of a computer cluster. Computations on supercomputers occur in parallel on many processing elements: cluster nodes equipped with multi-core processors, however, transfers between processors and cluster nodes can significantly slow down the parallel program. In order to minimize application performance losses, it is necessary to understand between which processors the delivery of messages occurs most quickly or vice versa slowly. It is necessary to optimally distribute the computations for the processors making up the supercomputer.
The paper analyzes the statistical and temporal seasonal and decadal variability of the atmospheric pressure field in the Arctic region of Russia. Schemes for the frequency analysis of probability transitions for characteristics of stochastic-diffusion processes were used as the main research method. On the basis of the given series of 60 years long from 1948 to 2008, such parameters of diffusion processes as the mean (drift process) and variance (diffusion process) were calculated and their maps and time curves were constructed. The seasonal and long-term variability of calculated fields was studied as well as their dependencies on a discretization of the frequency intervals. These characteristics were analyzed and their geophysical interpretation was carried out. In particular, the known cycles of solar activity in 11 and 22 years were revealed. Numerical calculations were performed on the Lomonosov-2 supercomputer of the Lomonosov Moscow State University.
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