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 Âûïóñê 43
- Gubanov D., Makarenko A., Novikov D. Methods to analyse terminological structure of subject area
We propose an automated expert approach to analysis and synthesis of a terminological structure of a subject area. The key novelty is that the method employs formal analytical operation to obtain numerical characteristics of terminological structure of the studied subject area. Basic features of the developed approach are illustrated by the subject area of general methodology
- Zhilyakova L. Ergodic cyclic resource networks. I. Oscillations and equilibrium at low resource
We study operation of ergodic nonregular resource networks when total amount of resource is small. We show that for an arbitrary initial state undamped oscillations occur between several limit vectors. The number of different limit vectors is equal to the number of cyclic classes of a network. The global equilibrium can be achieved when all limit vectors coincide. We derive conditions on initial states leading to the global equilibrium, and obtain formulae for the limit powers of stochastic matrices and for limit vectors.
- Chebotarev P., Agaev R. On the asymptotics of consensus protocols
It is shown that the limiting state vector of the differential consensus seeking model with an arbitrary communication digraph is obtained by multiplying the eigenprojection of the Laplacian matrix of the model by the vector of the initial state. Furthermore, the eigenprojection coincides with the matrix of maximum out-forests of the weighted communication digraph. These statements make the forest consensus theorem. A similar result for DeGroot’s iterative pooling model involves the Ces`aro limit in the general case. The forest consensus theorem is useful for the analysis of distributed control models.
- Panyukov A., Golodov V. Software implementation of algorithm for solving a set of linear equations under interval uncertainty
We consider a set of linear equations Ax=b with
interval matrices A, b. Solutions are items of tol(A,b)={x: A?x2
? b}. Let
tol(A,b(z))={x: Ax=(1+z)b)}, z
=
inf{z:
tol(A,b(z))6=
;
}
be.
Items of the set tol(A,b(z )) are referred to as pseudosolutions.
We prove existence of a pseudosolution for all sets of interval
algebraic linear equations, suggest a technique to search for the
pseudosolution via solving the corresponding linear programming
problem. The obtained problem is singular, thus computations demand
accuracy exceeding that of standard data types of programming
languages. Simplex method coupled with errorless rational-fractional
computations gives an efficient solution of the problem. Coarsegrained
parallelism for distributed computer systems with MPI gives
a software implementation tool. CUDA C software is suggested for
errorless rational-fractional calculations.
- Pozdyayev V. Atomic optimization, part 2: multidimensional problems and polynomial matrix inequalities
We investigate multidimensional optimization problems with polynomial objective function and polynomial matrix inequality constraints and suggest a transformation of the moment-theory-based solution technique. It allows reducing significantly the computational complexity while keeping the ability to solve the problems of the class under consideration.
- Zhuchkov R. Stabilizing networked control of linear discrete-time systems with sensors and actuators banks
We consider a stabilization problem for a networked plant with several banks of sensors and actuators. Banks of sensors and actuators are considered as a system with stochastic structure. We employ technique of linear matrix inequalities to build dynamic feedback control based on system outputs.
- Zaikin O., Semenov A., Posypkin M. Constructing decomposition sets for distributed solution of sat problems in volunteer computing project sat@home
We suggest an approach to construct decomposition sets for coarse-grained parallelization of SAT problems. Decomposition sets are used for distributed solving of hard SAT problems. The proposed algorithms are used in the volunteer computing project SAT@home.
- Tarkov M. On efficient construction of hamiltonian cycles in distributed computer systems by recurrent neural networks
Construction of Hamiltonian cycles in a graph of distributed computer system with vertices by a recurrent neural network is considered. The method of partial sums is proposed to reduce time of differential equations solution, which describe the neural network, from O(n3) to O(n2). It is shown that the neural network algorithm which uses partial sums is competitive with known permutation methods.
- Algazin G., Algazina D. Modelling network interactions on competitive markets
We suggest a game-theoretical model of a multi-agent network, whose purpose is promotion of a homogeneous product (or a service) on a competitive market. We study efficiency of networks employing Cournot and Stackelberg equilibria for the basic applied model of «franchisor-franchisee-market» and that of «producer-mediator-market» under linear costs and inverse demands (which is typical for models of oligopoly), and obtain close-form solutions. The novel feature of the model is the presence of a principal who is responsible for network interactions management and network efficiency improvement.
- Bazenkov N. Double best response dynamics in topology formation game for ad hoc networks
We consider a topology formation problem for wireless ad hoc networks. There are wireless nodes located on a plane. Every node can dynamically adjust its transmission power. The global objective is to assign optimal transmission power to every node such that the resulting topology is connected and minimizes total power cost. The topology formation problem is studied as a noncooperative game. We propose two algorithms of collective behavior based on the, so-called, "double best response" decision rule . This decision rule originates from a reflexive game framework and describes behavior of an agent with the first rank of reflection. Efficiency of proposed algorithms is evaluated by simulations and is compared with a conventional best response algorithm
- Sharov V. Application of bayesian approach to update events’ probabilities in automated system of aviation accidents forecasting and prevention
In the automated system of aviation accidents forecasting and prevention, which is being developed for Volga-Dnepr air carrier, the method of probabilistic analysis of safety with construction of "event trees” is used. Probabilities of initiating events at the lowest level of a tree are estimated using the data from various sources. In the course of company’s operation additional information arrives to the system in the form of audit reports, cases investigations reports, and other obligatory and voluntary messages. These reports testify occurrence of danger factors influencing events’ probabilities. We suggest the method of using this information for probabilities update on the basis of Bayes formula.
- Tuphanov I., Scherbatyuk À. On algorithms of high-precision measurement of underwater environment parameters, based on auv group usage
We consider a problem of measurement of underwater environment parameters by using a group of autonomous underwater vehicles /AUVs/. It is supposed that measurement is done for further mapping of a given area. We suggest a method of group work planning and consider re-planning for the case when one of AUVs completes its task. We also provide the results of simulation of algorithms suggested.
- Znamenskij S. Distributed memory architecture for changing computing environment
The new methodology (retrospective shared memory) is presented as a basis for highly available and infinitely adaptive computing services.
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