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.

Many-core processor architecture is a promising paradigm for the development of modern supercomputers. In this paper, we consider the parallel implementation of the generic molecular dynamics algorithm for the many-core Epiphany architecture. This architecture implements a new type of many-core processor composed of 16 simple cores connected by a network on chip with mesh topology. New approaches to parallel programming are required to deploy this processor. We use LAMMPS running on one 64-bit ARMv8 Cortex-A53 CPU core for comparing the accuracy of the results of the presented variant of the molecular dynamics algorithm for Epiphany and its computational efficiency.

We study the signal extraction problemwhere a smooth signal is to be estimated against a long-range dependent noise. We consider an approach employing local estimates and derive a theoretically optimal (maximum likelihood) filter for a polynomial signal. On its basis, we propose a practical signal extraction algorithm and adapt it to the extraction of quasi-seasonal signals. We further study the performance of the proposed signal extraction scheme in comparison with conventional methods using the numerical analysis and real-world datasets.

The paper is devoted to modeling multi depot vehicle routing problem (VRP) with capacity constraints for petroleum products delivery. Applying efficient metaheuristics algorithms combined with local search procedures, we present how to get suboptimal solutions for this NP-hard problem in an acceptable time. Some parallel computing techniques are also used to reduce the execution time. Experimental results are performed by the case of VRP for petroleum products.

In this article we apply methods of representation theory and combinatorial algebra to the different problems related to quantum tomography. For this purpose, we introduce the algebra generated by projectors satisfying some commutator relation. In this paper we study this commutator relation by combinatorialmethods and develop the representation theory of this algebra. Also, we apply our results to the case of mutually unbiased bases in dimension 7.

We consider a mathematical model of a spherical inverted pendulum on a movable cart. The cart moves on a horizontal plane under the influence of a planar bounded force. We study an optimal control problem related to this model. The control objective is to stabilize the inverted pendulum in the upright equilibrium position. For the linearized model it is shown that the optimal trajectories contains arcs with more and more frequent control switchings.

An algorithm of MPI processes mapping optimization is adapted for supercomputers with interconnect Angara. The mapping algorithm is based on partitioning of parallel program communication pattern. It is performed in such a way that the processes between which the most intensive exchanges take place are tied to the nodes/processors with the highest bandwidth. The algorithm finds a near-optimal distribution of its processes for processor cores to minimize the total execution time of exchanges between MPI processes. The analysis of results of optimized placement of processes using proposed method on small supercomputers is shown. The analysis of the dependence of the MPI program execution time on supercomputer parameters and task parameters is performed. A theoretical model is proposed for estimation of effect of mapping optimization on the execution time for several types of supercomputer topologies. The prospect of using implemented optimization library for large-scale supercomputers with the interconnect Angara is discussed.

We introduce a class of stochastic networks in which synchronization between nodes is modelled by a message passing mechanism with heterogeneous Markovian routing. We present a series of results about probability distribution related to steady states of such models.

The density functional theory (DFT) is a research tool of the highest importance for electronic structure calculations. It is often the only affordable method for ab initio calculations of complex materials. The pseudopotential approach allows reducing the total number of electrons in the model that speeds up calculations. However, there is a lack of pseudopotentials for heavy elements suitable for condensed matter DFT models. In this work, we present a pseudopotential for uranium developed in the Goedecker–Teter–Hutter form. Its accuracy is illustrated using several molecular and solid-state calculations.

We prove that a foliation (M;F) of codimension q on a ndimensional pseudo-Riemannian manifold is pseudo-Riemannian if and only if any geodesic that is orthogonal at one point to a leaf is orthogonal to every leaf it intersects.

We show that on the graph G = G(F) of a pseudo-Riemannian foliation there exists a unique pseudo-Riemannian metric such that canonical projections are pseudo-Riemannian submersions and the fibers of different projections are orthogonal at common points. Relatively this metric the induced foliation (G;F) on the graph is pseudo-Riemannian and the structure of the leaves of (G;F) is described. Special attention is given to the structure of graphs of transversally (geodesically) complete pseudo-Riemannian foliations which are totally geodesic pseudo-Riemannian ones.

In this paper we investigate multi-server queueing systems with regenerative input flow and independent service times with finite mean. Various service disciplines are considered: systems with a common queue and systems with parallel queues when an arrived customer chooses server in accordance with a certain rule and stays in a chosen queue until the moment of service start. We define some classes of disciplines and establish the necessary and suffcient condition of stability.

We simulate model for evolution of local virtual time profile in conservative parallel discrete event the simulation (PDES) algorithm with long-range communication links. The main findings of simulation are that i) growth exponent depends logarithmically on the concentration *p* of long-range links; ii) utilisation of processing elements time decreases slowly with *p*. Thismeans that the conservative PDES with long-range communication links is fully scalable.

The paper is presented some classes of MDS matrices of size 4 × 4 with the maximum number of units and minimal number of non unit elements. This class of matrices is widely used as diffusemaps when building block type algorithms and hash functions that provide protection against certain methods of analysis.

We propose a new mathematical model of virus spreading over local area networks. We define a cost functional and consider a maximization problem for the average income given by the computer network per unit time.

For a complete Cartan foliation (M; F) we introduce two algebraic invariants g0(M; F) and g1(M; F) which we call structure Lie algebras. If the transverse Cartan geometry of (M; F) is eective then g0(M; F) = g1(M; F). We prove that if g0(M; F) is zero then in the category of Cartan foliations the group of all basic automorphisms of the foliation (M; F) admits a unique structure of nite-dimensional Lie group. In particular, we obtain sucient conditions for this group to be discrete. We give some exact (i.e. best possible) estimates of the dimension of this group depending on the transverse geometry and topology of leaves. We construct several examples of groups of all basic automorphisms of complete Cartan foliations.

The graph anomaly detection problem occurs in many application areas and can be solved by spotting outliers in unstructured collections of multi-dimensional data points, which can be obtained by graph analysis algorithms. We implement the algorithm for the small community analysis and the approximate LOF algorithm based on Locality-Sensitive Hashing, apply the algorithms to a real world graph and evaluate scalability of the algorithms. We use Apache Spark as one of the most popular Big Data frameworks.