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The article discusses the problem of the influence of the research goals on the structure of the multivariate model of regression analysis (in particular, on the implementation of the procedure for reducing the dimension of the model). It is shown how bringing the specification of the multiple regression model in line with the research objectives affects the choice of modeling methods. Two schemes for constructing a model are compared: the first does not allow taking into account the typology of primary predictors and the nature of their influence on the performance characteristics, the second scheme implies a stage of preliminary division of the initial predictors into groups, in accordance with the objectives of the study. Using the example of solving the problem of analyzing the causes of burnout of creative workers, the importance of the stage of qualitative analysis and systematization of a priori selected factors is shown, which is implemented not by computing means, but by attracting the knowledge and experience of specialists in the studied subject area. The presented example of the implementation of the approach to determining the specification of the regression model combines formalized mathematical and statistical procedures and the preceding stage of the classification of primary factors. The presence of this stage makes it possible to explain the scheme of managing (corrective) actions (softening the leadership style and increasing approval lead to a decrease in the manifestations of anxiety and stress, which, in turn, reduces the severity of the emotional exhaustion of the team members). Preclassification also allows avoiding the combination in one main component of controlled and uncontrolled, regulatory and controlled feature factors, which could worsen the interpretability of the synthesized predictors. On the example of a specific problem, it is shown that the selection of factors-regressors is a process that requires an individual solution. In the case under consideration, the following were consistently used: systematization of features, correlation analysis, principal component analysis, regression analysis. The first three methods made it possible to significantly reduce the dimension of the problem, which did not affect the achievement of the goal for which this task was posed: significant measures of controlling influence on the team were shown. allowing to reduce the degree of emotional burnout of its participants.

Variational inequalities constitute a broad class of problems with applications in a number of fields, including game theory, economics, and machine learning. Today’s practical applications of VIs are becoming increasingly computationally demanding. It is therefore necessary to employ distributed computations to solve such problems in a reasonable time. In this context, workers have to exchange data with each other, which creates a communication bottleneck. There are three main techniques to reduce the cost and the number of communications: the similarity of local operators, the compression of messages and the use of local steps on devices. There is an algorithm that uses all of these techniques to solve the VI problem and outperforms all previous methods in terms of communication complexity. However, this algorithm is limited to unbiased compression. Meanwhile, biased (contractive) compression leads to better results in practice, but it requires additional modifications within an algorithm and more effort to prove the convergence. In this work, we develop a new algorithm that solves distributed VI problems using data similarity, contractive compression and local steps on devices, derive the theoretical convergence of such an algorithm, and perform some experiments to show the applicability of the method.

The problem of centralized planning for data transmission routes in delay tolerant networks is considered. The original problem is extended with additional requirements to nodes storage and communication process. First, it is assumed that the connection between the nodes of the graph is established using antennas. Second, it is assumed that each node has a storage of finite capacity. The existing works do not consider these requirements. It is assumed that we have in advance information about messages to be processed, information about the network configuration at specified time points taken with a certain time periods, information on time delays for the orientation of the antennas for data transmission and restrictions on the amount of data storage on each satellite of the grouping. Two wellknown algorithms — CGR and Earliest Delivery with All Queues are improved to satisfy the extended requirements. The obtained algorithms solve the optimal message routing problem separately for each message. The problem of validation of the algorithms under conditions of lack of test data is considered as well. Possible approaches to the validation based on qualitative conjectures are proposed and tested, and experiment results are described. A performance comparison of the two implementations of the problem solving algorithms is made. Two algorithms named RDTNAS-CG and RDTNAS-AQ have been developed based on the CGR and Earliest Delivery with All Queues algorithms, respectively. The original algorithms have been significantly expanded and an augmented implementation has been developed. Validation experiments were carried to check the minimum «quality» requirements for the correctness of the algorithms. Comparative analysis of the performance of the two algorithms showed that the RDTNAS-AQ algorithm is several orders of magnitude faster than RDTNAS-CG.

We propose a family of Gauss –Newton methods for solving optimization problems and systems of nonlinear equations based on the ideas of using the upper estimate of the norm of the residual of the system of nonlinear equations and quadratic regularization. The paper presents a development of the «Three Squares Method» scheme with the addition of a momentum term to the update rule of the sought parameters in the problem to be solved. The resulting scheme has several remarkable properties. First, the paper algorithmically describes a whole parametric family of methods that minimize functionals of a special kind: compositions of the residual of a nonlinear equation and an unimodal functional. Such a functional, entirely consistent with the «gray box» paradigm in the problem description, combines a large number of solvable problems related to applications in machine learning, with the regression problems. Secondly, the obtained family of methods is described as a generalization of several forms of the Levenberg –Marquardt algorithm, allowing implementation in non-Euclidean spaces as well. The algorithm describing the parametric family of Gauss –Newton methods uses an iterative procedure that performs an inexact parametrized proximal mapping and shift using a momentum term. The paper contains a detailed analysis of the efficiency of the proposed family of Gauss – Newton methods; the derived estimates take into account the number of external iterations of the algorithm for solving the main problem, the accuracy and computational complexity of the local model representation and oracle computation. Sublinear and linear convergence conditions based on the Polak – Lojasiewicz inequality are derived for the family of methods. In both observed convergence regimes, the Lipschitz property of the residual of the nonlinear system of equations is locally assumed. In addition to the theoretical analysis of the scheme, the paper studies the issues of its practical implementation. In particular, in the experiments conducted for the suboptimal step, the schemes of effective calculation of the approximation of the best step are given, which makes it possible to improve the convergence of the method in practice in comparison with the original «Three Square Method». The proposed scheme combines several existing and frequently used in practice modifications of the Gauss –Newton method, in addition, the paper proposes a monotone momentum modification of the family of developed methods, which does not slow down the search for a solution in the worst case and demonstrates in practice an improvement in the convergence of the method.

This work is devoted to molecular dynamic modeling of the thermal impact processes on the metal sample consisting of nickel atoms. For the solution of this problem, a continuous mathematical model on the basis of the classical Newton mechanics equations has been used; a numerical method based on the Verlet scheme has been chosen; a parallel algorithm has been offered, and its realization within the MPI and OpenMP technologies has been executed. By means of the developed parallel program, the investigation of thermodynamic equilibrium of nickel atoms’ system under the conditions of heating a sample to desired temperature has been executed. In numerical experiments both optimum parameters of calculation procedure and physical parameters of analyzed process have been defined. The obtained numerical results are well corresponding to known theoretical and experimental data.

Parameter sweep applications are a very important class of applications, which are typically defined as a set of computational experiments over a set of input parameters, each of which is executed with its own parameter combination. These computations arise in many scientific contexts. This article introduces the Parameter Sweep web service that runs such applications in distributed computing environment. Also discussed is the Everest cloud platform, on which this service is built.

This work describes the idea of the system of informational support for the scientific projects and the development of computational task tracking complex. Due to large requirements for computational experiments the problem of presentation of the information about HPC tasks becomes one of the most important. Nonstandard usage of the service desk system as a basis of the computational task tracking and support system can be the solution of this problem. Particular attention is paid to the analysis and the satisfaction of the conflicting requirements to the task tracking complex from the different user groups. Besides the web service kit used for the integration of the task tracking complex and the datacenter environment is considered. This service kit became the main interconnect between the parts of the scientific project support system and also this kit allows to reconfigure the whole system quickly and safely.

The review of the distributed computing infrastructure of the Tier-1 sites for the Alice, ATLAS, LHCb experiments at the LHC is given. The special emphasis is placed on the main tasks and services of the Tier-1 site, which operates in the Kurchatov Institute in Moscow.

The paper presents the results of application of machine learning methods: principle component analysis and support vector machine for classification of diffraction images produced in experiments at free-electron lasers. High efficiency of this approach presented by application to simulated data of adenovirus capsid and bluetongue virus core. This dataset were simulated with taking into account the real conditions of the experiment on lasers free electrons such as noise and features of used detectors.

Efficiency and completeness of the numerical simulation in oceanography and hydrometeorology are entirely determined by algorithmic features of the construction of an interactive computer simulations in the scale of the oceans with adaptive coated closed seas and coastal waters refined mathematical models, with the possibility of specifying software parallelization calculations near the concrete — the protected areas of the sea coast. An important component of the research is continuous graphical visualization techniques in the course of calculations, including those undertaken in parallel processes with shared RAM or test points on the external media. The results of computational experiments are used in the description of hydrodynamic processes near the coast, which is important in keeping the organization of sea control services and forecasting marine hazards.