Vol 40, No 5 (2019)

One of the key methods for increasing efficiency of computational resources usage is the use of containerization technology. In the process of high-performance computations, containerization makes it possible to solve the user jobs binary portability problem with minimum overhead. The article describes the choice of methods and tools for preparing a supercomputer job in the form of a Docker container with arbitrary user-defined content. The article presents the methods and recommendations for preparing of the image of container for a job, the issues of arising information security. The authors reviewed the methods and tools for dynamic reconfiguration of the networks in a supercomputer before start of a job.

Practical applicability of many statistical algorithms is limited by large sizes of corresponding covariance matrices. These limitations can be significantly weakened due to effective use of the structure of covariance matrices, properties of the autocorrelation function, and advantages of the architecture of modern GPUs. This paper presents GPU implementations of the algorithms for inversion of a covariance matrix and solution of a system of linear equations whose coefficient matrix is a covariance matrix. Inversion of close to sparse covariance matrices is also considered in the work. For all the cases considered, significant accelerations were obtained in comparison with Octave mathematical software and ViennaCL computational library. For example, implemented algorithm of solution of a linear system was 6 times faster as compared with the implementation of Octave on the CPU and 3 times faster as compared with the ViennaCL implementation on the GPU for general matrices. The performance of inversion of a covariance matrix was 14 times faster than inversion algorithm of Octave on the CPU and 6 times faster than ViennaCL inversion algorithm on GPU.

The article discusses methods for constructing the transmission of multimodal data in conditions of limited communication channels. The method of transmitting multimodal data using caching repeaters is considered in detail.

This article considers the growth of the size of the global routing table. The authors attempt to estimate the scale of the growth and its impact for research networks and telecom operators using full-size global routing tables. The article also concerns the impact of the table growth on the stability of the access to the World Wide Web.

The paper considers the problem of controlling the final state of dynamic systems characterized by classical fuzzy relations. The solution of the problem is reduced to solving a functional equation of the Bellman equation type. On the basis of modern methods of the general theory of dynamical systems, the asymptotic properties of the solutions of the obtained functional equation are studied. The problem of the existence and construction of a suboptimal autonomous control law with feedback is studied.

In some non-homogeneous generalized allocation schemes we formulate conditions under which the number of given value cells from the first K cells converges to a Poisson random variable. The method of the proofs is founded on some analog of Kolchin formula. As corollary we obtain a Poisson limit theorems for the number of given value cells from the first K cells in non-homogeneous allocation scheme of distinguishing particles by different cells.

We find a necessary and sufficient condition on the natural number n in order that the conjugates of an entire algebraic number α = 2 cos(π/n) form a normal basis of the field ℚ(α); we show that this normal basis at the same time is fundamental.

We continue our previous results from the functions of one complex variable in the unit disk to the functions of several variables in the unit ball. Let M be a δ-subharmonic function with Riesz charge µ_M on the unit ball \(\mathbb{B}\) in ℂⁿ. Let f be a nonzero holomorphic function on \(\mathbb{B}\) such that f vanishes on Z ⊂ \(\mathbb{B}\), and satisfies the inequality ∣f∣ ≤ exp M on \(\mathbb{B}\). Then restrictions on the growth of µ_M near the boundary of B imply certain restrictions on the distribution of Z. We give a quantitative study of this phenomenon in terms of (2n − 2)-Hausdorff measure of zero subset Z, and special non-radial test subharmonic functions constructed using ρ-subspherical functions.

The note is concerned with inductive systems of Toeplitz algebras and their *-homomorphisms over arbitrary partially ordered sets. The Toeplitz algebra is the reduced semigroup C*-algebra for the additive semigroup of non-negative integers. It is known that every partially ordered set can be represented as the union of the family of its maximal upward directed subsets indexed by elements of some set. In our previous work we have studied a topology on this set of indexes. For every maximal upward directed subset we consider the inductive system of Toeplitz algebras that is defined by a given inductive system over an arbitrary partially ordered set and its inductive limit. Then for a base neighbourhood U_a of the topology on the set of indexes we construct the C*-algebra \(\mathfrak{B}\)_a which is the direct product of those inductive limits. In this note we continue studying the connection between the properties of the topology on the set of indexes and properties of inductive limits for systems consisting of C*-algebras \(\mathfrak{B}\)_a and their *-homorphisms. It is proved that there exists an embedding of the reduced semigroup C*-algebra for a semigroup in the additive group of all rational numbers into the inductive limit for the system of C*-algebras \(\mathfrak{B}\)_a.

We prove that the L₁-norms associated with a positive elements a^α is equivalent to the L₁-norm associated with a positive element a^β if and only if it is equivalent to the natural norm of a C*-algebra, which means the invertibility of a in the case of unital C*-algebra. The same propositions are proved for L_∞-norms associated with positive element a^α and a^β.

We solve some computational problems for triangulated closed three-dimensional manifolds using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms for computing intersection numbers of 1- and 2-dimensional cycles are developed. Using these algorithms it is possible to construct a basis of the cohomology group from a given basis of the homology group of complementary dimension.