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• A METHOD FOR PLANNING ROBOTIC MOVEMENTS IN COMPLEX CONFLICT ENVIRONMENTS WITH POLYGONAL OBSTACLES

  V.А. Kostyukov

  2026-04-29

  Abstract ▼

  When developing algorithms for real-time robot path planning, the problem of performance limitations of the corresponding classical algorithms arises. This paper considers a method for planning robot movements in a two-dimensional complex conflict environment. For planning in complex environments, a hybrid planning algorithm is proposed, based on a combination and synthesis of the classical cellular decomposition algorithm and a recently proposed algorithm based on the characteristic visibility graph. This algorithm involves a preliminary analysis of the complexity of the obstacle scene, based on the results of which one of the two specified particular algorithms is selected. It is shown that this approach can significantly overcome the limitations of both of these algorithms. A disturbance avoidance method based on the apparatus of characteristic probability functions is described in a compact form, and its relationship with planning methods in complex environments is demonstrated when solving corresponding problems of global optimization of the probability of successful completion of a target trajectory. The developed approach examines the relationship between the probability of successful path completion in a source field and the corresponding risk function. To solve global robot motion planning problems in complex conflict environments, the proposed hybrid algorithm is first proposed for constructing a family of initial curves within the appropriate feasible motion corridors, ignoring sources. A family of local optimization problems is then solved within the feasible motion corridors, taking sources into account. Next, the trajectory with the maximum probability of successful completion or the normalized safe motion function is selected

• STUDY OF POSSIBILITIES OF USING PHOTONIC AND QUANTUM COMPUTING TECHNOLOGIES TO CALCULATE EXACT PROBABILITY DISTRIBUTIONS OF STATISTIC VALUES FROM FINITE DISCRETE SEQUENCES

  А.К. Melnikov

  121-136

  2025-12-30

  Abstract ▼

  This article explores the feasibility of using photonic and quantum computing technologies to calculate exact probability distributions of discrete sequence statistics, assuming the existence of working hardware prototypes of computing systems and the development of the required quantum algorithms. The performance evaluation of computing systems based on photonic computing technologies is based on materials from the Sarov Scientific Center for Physics and Microphysics of the Russian Academy of Sciences. The performance of a quantum computing system is assessed by comparing the time it takes to solve a boson sampling problem from a given distribution on a computing system with known performance and the time it takes to solve it on a quantum computing system. To assess the feasibility of using photonic and quantum computing technologies to calculate exact distributions, modern methods for calculating them are considered. These methods are based on solving the type multiplicity equation and a system of linear equations in non-negative integers. Analytical expressions determining the computational complexity of these methods are presented. The values of the boundaries of the parameters of exact distributions accessible for calculation using photonic and quantum computing technologies are determined. A comparison of the obtained results with the results of using multiprocessor computing technologies to calculate exact distributions using various methods is presented. An analysis of the feasibility of using photonic and quantum computing technologies to calculate exact distributions is conducted by comparing the number of parameter pairs that can be calculated for exact distributions with the total number of distribution parameters within the Fisher region, which determines a fivefold increase in sample size over the alphabet size. An analysis of the data on the number of sample parameters shows that with increasing performance of the computing technologies used, the ability to calculate exact distributions increases. However, even with the most powerful quantum technologies, this number does not exceed one-tenth of the total number of exact distributions required for statistical analysis of discrete sequences in alphabets up to 256 characters long

• VERIFICATION OF DYNAMIC BIOMETRIC PARAMETERS OF A PERSONALITY BASED ON A PROBABLE NEURAL NETWORK

  Y.A. Bryuhomitsky

  2021-01-19

  Abstract ▼

  Biometric identity verification is used primarily for access to computer and mobile systems, as
  well as for remote (voice) verification. In fact, the most widespread systems are biometric verification
  systems based on a fixed passphrase, which are quite simple to implement, but very vulnerable to
  attacks of reproduction of a compromised short text. To eliminate this drawback, it is proposed to
  carry out identity verification using a text that is arbitrary in terms of volume, content and language
  (text-independent biometric verification). This paper proposes a generalized approach to solve the
  problem of identity verification by dynamic biometric parameters of different modality (keyboard
  writing, handwriting, voice). The presentation of dynamic biometrics signals is carried out by converting
  them into a sequences of information units, each of which contains the same number of counts
  of biometric signal of corresponding modality. The solution to this problem is carried out by monitoring
  the degree of concentration of closely located information units (clusters) at certain points of the
  multidimensional feature space. Such control is implemented on a probabilistic neural network thatstatistically evaluates the probability density of the distribution of information units in the corresponding
  clusters with the subsequent determination of the total probability density for the entire
  class of objects. The advantages of the proposed approach are: generalization of substantially different
  methods of text-independent identity verification by dynamic biometric parameters of different
  modality; the ability to make a verification decision for a fixed time of receipt of biometric data, determined
  by the size of the model used; the ability to set the verification accuracy by changing the
  dimension of the layer of probabilistic network samples. The disadvantage of the proposed approach
  is the need for software implementation of a large-scale neural network. However, this drawback is
  quickly leveled with an increase in the productivity of computer technology.

• CALCULATION OF THE NUMBER OF SOLUTIONS TO THE EQUATION OF THE FIRST MULTIPLICITY OF TYPES UNDER RESTRICTIONS ON THE FREQUENCY OF OCCURRENCE OF ALPHABET CHARACTERS

  A.K. Melnikov

  2021-02-25

  Abstract ▼

  The article considers the number of solutions to the equation of the first multiplicity of types,
  composed of vectors of multiplicity of types, each element of which is the number of occurrences of
  elements of a certain type (any sign of the alphabet) in the sample under consideration. The equation
  of the first multiplicity of types relates the number of occurrences of elements of all types in
  the sample under consideration and the volume of this sample. The main attention is paid to the
  conclusion and proof of the correctness of the expression that determines the number of nonnegative
  integer solutions of the equation of the first multiplicity of types under conditions of restrictions
  on the frequency of occurrence of alphabet characters. The solution of the equation ofthe first multiplicity of types is the basis for calculating exact approximations of the probabilities
  of statistical values by the first multiplicity method, where the exact approximations are Δexact
  distributions that differ from the exact distributions by no more than a predetermined, arbitrarily
  small value Δ. The value that expresses the number of solutions to the equation of the first multiplicity
  of types is one of the values that determine the algorithmic complexity of the method of the
  first multiplicity, without knowing the value of which it is impossible to determine the parameters
  of samples for which, under restrictions on the computational resource, exact approximations of
  distributions can be calculated. Also, the value expressing the number of solutions to the equation
  of the first multiplicity of types is used in the method of the first multiplicity to limit the search area
  for solutions to the equation. The number of solutions to the equation of the first multiplicity is
  considered under conditions of restriction on the maximum value of the elements of the multiplicity
  vector, and the case is considered when one or more elements of the alphabet may be missing in
  the sample. First obtained the expression that defines the number of nonnegative integer solutions
  to equations of the first multiplicity of types in terms of restrictions on the values of the frequencies
  of occurrence of signs and the possibility of absence of one or more characters of the alphabet in
  the sample reviewed. Analytical expressions are obtained that allow calculating the number of
  integer nonnegative solutions of the equation of the first multiplicity of types for any values of the
  alphabet power, the sample size, and the limit on the maximum frequency of occurrence of alphabet
  characters. The form of the obtained expression allows you to use it when studying the algorithmic
  complexity of calculating exact approximations of probability distributions of statistical
  values with a pre-specified accuracy Δ.

• ALGORITHMIC COMPLEXITY OF CALCULATING EXACT APPROXIMATIONS OF PROBABILITY DISTRIBUTIONS OF STATISTICAL VALUES BY SOLVING THE EQUATION OF THE FIRST MULTIPLICITY OF TYPES

  A.K. Melnikov

  2021-02-25

  Abstract ▼

  We consider the algorithmic complexity of calculating the exact probability distributions of
  statistical values and their exact approximations by solving the first multiplicity equation. As exact
  approximations of probability distributions of statistical values, we consider their Δ−exact distributions
  that differ from the exact distributions by no more than a predetermined, arbitrarily small
  valueΔ. It is shown that the basis of the method for calculating the exact probability distributions
  of statistical values is the enumeration of elements of the search area for solutions to a linear
  equation of multiplicity of types, composed of vectors of multiplicity of types, each element of
  which is the number of occurrences of elements of a certain type (any sign of the alphabet) in the
  sample under consideration. At the same time, it is shown that the method of limiting the search
  area for solutions is used to calculate exact approximations of the probability distribution of statistical
  values. An expression is given that defines the algorithmic complexity of calculating exact
  distributions by solving the first multiplicity equation. The given expression is finite and allows for
  each value of the alphabet power to determine the maximum sample size for which, using a limited
  computational resource, exact distributions can be calculated by solving the first multiplicity
  equation. The range of parameters represented by the sample size and alphabet power for which
  exact distributions can be calculated with a limited computing resource is defined. To estimate the
  algorithmic complexity of calculating exact approximations of distributions, we present an expression
  for the first time obtained for the number of solutions to the equation of the first multiplicity
  with a restriction on the coordinate values of the solution vectors. An expression is given that defines
  the algorithmic complexity of calculating exact approximations by solving the first multiplicity
  equation with a restriction on the coordinate values of the solution vectors. As a parameter for
  limiting the coordinates of solution vectors, the maximum frequency statistic value is used, the
  probability of exceeding it is less than a pre-set, arbitrarily small valueΔ, which allows calculating
  exact approximations of distributions that differ from their exact distributions by no more than the
  selected value Δ. The given expression is finite and allows for each value of the alphabet to determine
  the maximum sample size for which, when using a limited computational resource, exact
  approximations can be calculated by solving the equation of the first multiplicity under the restrictions
  set using the valueΔ. The results of calculations of the maximum sample volumes for
  which exact approximations can be calculated are presented. It is shown that the algorithmiccomplexity of calculating exact distributions exceeds the complexity of calculating their exact approximations
  by many orders of magnitude. It is shown that the use of the first multiplicity method
  for calculating exact approximations allows for the same values of the alphabet power to increase
  the sample volume by two or more times compared to the calculation of exact distributions.

• ANALYSIS OF ADVANCED COMPUTER TECHNOLOGIES FOR CALCULATION OF EXACT APPROXIMATIONS OF STATISTICS PROBABILITY DISTRIBUTIONS

  А.К. Melnikov, I.I. Levin, А.I. Dordopulo, I.V. Pisarenko

  6-19

  2021-10-05

  Abstract ▼

  In the paper we consider the solution of a computationally expensive problem such as calcu-lation of statistics probability distribution with the help of modern computer technologies. To re-duce computational complexity and to provide a sufficient level of criteria efficiency not less than the specified threshold, we suggest to use Δ-exact approximations. To calculate exact approxima-tions, we use the method of second order, based on solution of a system of linear equations. Owing to this method, it is possible to calculate exact approximations for the maximum values of sample parameters for available computational resource. The most laborious part of the method of second order is the procedure of sequential detection of the vectors of possible solutions and test if the vectors belong to the set of solutions. The system solution set membership test for the vectors of possible solutions is data independent, so the algorithm can be data-parallelized. We give the al-gorithm complexity equation for calculation of exact approximations of statistics probability dis-tributions. Using this equation, we calculated the complexity of modern practical problems for the samples with the parameters (N, n) of the alphabet power and the sample size: (256,1280), (128,640), (128, 320), and (192,3200) for the accuracy of calculations =10-5. The computational complexity is 9.68·1022-1.60·1052 operations, and its average value is about 4.55·1025 operations, the number of tested vectors is 6.50·1023-1.39·1050, and the number of solutions is 4.67·1012-5.60·1025, respectively. The total solution time for clock-round duration of calculations cannot exceed 30 days or 2.592·106 sec. For the obtained complexity evaluation, we analysed abilities of modern cluster computer systems based on general-purpose processors, graphic accelerators, and FPGA-based reconfigurable computer systems. For each technology, we determined the number of computational nodes needed for calculation of exact approximations with the specified parameters during the specified time. We proved that it is impossible to obtain a solution for the required pa-rameters of exact approximations of statistics probability with the help of the reviewed modern computer technologies. In conclusion, we claim that it is necessary to analyse the abilities of ad-vanced computer technologies based of quantum and photonic computers, and also hybrid com-puter systems for calculation of exact approximations of statistics probability distributions with the specified parameters during reasonable time

• METHODOLOGY FOR ANALYZING THE FAULT SAFETY OF SYSTEMS AND AGGREGATES OF A MULTI-AGENT GROUP OF AIRCRAFT

  A.S. Boldyrev, A.L. Verevkin, L.C. Verevkina

  2022-01-31

  Abstract ▼

  Areas of application of CALS technologies are considered to be: improvement of activities
  in the field of heterogeneous processes occurring at all stages of the life cycle (LC) of products;
  supply chain management throughout the entire LC of products (from the creation of the product
  concept to its disposal); electronic integration of organizations (enterprises) involved in these
  processes at various stages of LC; management of support for LC products One of the most relevant
  areas of development in the aviation industry are: multi-agent technologies for improving the
  efficiency of aircraft (aircraft of various types in a group and a single mission) and CALS technologies.
  The article proposes a methodology for analyzing the fault safety of systems and aggregates
  of the multi-agent group of aircraft as a whole, by types of aircraft, their systems, and aggregates.
  The methodology is given on the example of statistical data of AP and PAP 16 systems: flight navigation,
  exhaust, ignition, fuel, control, power supply, air conditioning; hydraulic, radio communication
  equipment, control devices, and aggregates: engine, propellers, wings, windows, lantern,
  ten aircraft AN-2, L-410, Yak-40, An-24, Tu-134, Yak-42, Tu-154, IL-62, IL-62M, IL-86. In the
  proposed methodology for analyzing statistical data of AP and PAP, transformations with matrices
  are used, which allow not to be limited to the number of systems, aggregates, and the aircraft
  themselves. The operating time before the functional failure of systems and aggregates by types of
  aircraft was calculated, the average probability of functional failure of each of the systems and
  aggregates in a multi-agent group was determined, and the time before the functional failure of a
  multi-agent group of 10 aircraft as a whole, which was 132.5 hours, and it was determined that
  PAP and AP are more likely to occur with the chassis and engine of the aircraft. The given methodology
  allows: to correlate quantitative reliability requirements for systems and aggregates,
  taking into account random factors and uncertainty factors; to assess the feasibility of the established
  reliability requirements; to conduct a comparative analysis and justification of the choice of
  a rational variant of the composition of the aircraft group.

• LIMITING THE NUMBER OF DIFFERENT TEST VECTORS TO OBTAIN ALL SOLUTIONS OF A SYSTEM OF THE SECOND MULTIPLICITY LINEAR EQUATIONS ON MULTIPROCESSOR COMPUTER SYSTEM

  А.К. Melnikov

  2021-07-18

  Abstract ▼

  In the paper we consider calculation of all integer nonnegative solutions of a linear equation
  system (LES) of the second types order by a method of sequential vector testing. The method
  checks whether a vector is a solution of the LES. We consider different vectors and test if they
  belong to the set of the LES solutions. As a result, after such testing we obtain all solutions of the
  LES. The LES testing vector consists of the elements which are the numbers of some alphabet signs
  with the same number of occurrences in the sample. The LES unites the number of occurrences of
  the elements of all types into the considering sample, the power of the alphabet, the size of the
  sample, and the limitation for the maximum number of occurrences of the alphabet signs into the
  sample. The LES solution is the base for calculation of exact statistics probability distributions
  and their exact approximations by the method of the second types order. Here, the exact approximations
  are Δexact distributions. The difference between the Δexact distributions and the exact
  distributions does not exceed the predefined arbitrary small value Δ. The number of test vectors is
  one of those which defines algorithmic complexity of the method of second types order. Without it,
  it is impossible to define the parameters of samples, and to calculate exact distributions and their
  exact approximations for limited hardware resource. We consider various test vectors for the limited
  maximum number of occurrences of the alphabet signs in the sample, and for the unlimited
  one. We have obtained formulas to calculate the number of tests for various vectors. Here, the
  values of the power of the alphabet, the size of the sample, and the limitations for the maximum
  number of occurrences of the alphabet signs into the sample can be arbitrary. Using the obtained
  formulas, we can get all integer nonnegative solutions of the LES of the second types order. We
  can use the obtained formula for analysis of algorithmic complexity of calculations of exact distributions
  and their exact approximations with the predefined accuracy Δ.

• ERROR ESTIMATION FOR MULTIPLE COMPARISON OF NOISY IMAGES

  A.N. Karkishchenko, V. B. Mnukhin

  2021-07-18

  Abstract ▼

  The aim of this work is to study the effect of noise on the image on the quality of comparison of a
  finite set of images of the same shape and size. This task inevitably arises when analyzing scenes, detecting
  individual objects, detecting symmetry, etc. The noise factor must be taken into account, since the
  difference between digital objects can be caused not only by the mismatch of the compared images of
  real objects, but also by distortions due to noise, which is almost always takes place. This differenceturns out to be proportional to the level of the noise component. The main result of this article is an
  analytical estimate for the probability of a given level of error, which may arise in the multiple comparison
  of a finite set of commensurate digital images. This estimate is based on a low-level comparison,
  which is a pixel-by-pixel calculation of image differences using the Euclidean metric. In this case, a
  standard assumption is made about the independent normal noise of image intensities with zero mathematical
  expectation and a priori established standard deviation in each pixel. The evidence presented in
  the article allows us to assert that the obtained estimate should be regarded as sufficiently "cautious"
  and it can be expected that in reality the scatter of the measure caused by noise in the image will be
  significantly less than the theoretically found boundary. The estimates obtained in this work are also
  useful for detecting various types of symmetry in images, which, as a rule, lead to the need to calculate
  the difference of an arbitrary number of commensurate digital areas. In addition, they can be used as
  theoretically grounded threshold values in tasks requiring a decision on the coincidence or difference of
  images. Such threshold values inevitably appear at various stages of processing noisy images, and the
  question of their specific values, as a rule, remains open; at best, heuristic considerations are proposed
  for their selection.

• ANALYSIS OF ADVANCED COMPUTER TECHNOLOGIES FOR CALCULATION OF EXACT APPROXIMATIONS OF STATISTICS PROBABILITY DISTRIBUTIONS

  А.К. Melnikov, I.I. Levin, А.I. Dordopulo, L.M. Slasten

  2022-11-01

  Abstract ▼

  The paper is devoted to the evaluation of the hardware resource of computer systems for
  solving a computational-expensive problem such as calculation of the probability distributions of
  statistics by the second multiplicity method based on Δ-exact approximations for samples with a
  size of 320-1280 characters and an alphabet power of 128-256 characters, and with an accuracy
  of Δ=10-5. The total solution time should not exceed 30 days or 2.592·106 seconds for 24/7 computing.
  Owing to the use of the properties of the second multiplicity method, the computational complexity
  of the calculations can be brought to the range of 9.68·1022-1.60·1052 operations with the
  number of tested vectors of 6.50·1023-1.39·1050. The solution of this problem for the specified parameters
  of samples during the given time requires the hardware resource which cannot be provided
  by modern computer means such as processors, graphics accelerators, programmable logic
  integrated circuits. Therefore, in the paper we analyze the possibilities of promising quantum and
  photon technologies for solving the problem with the given parameters. The main advantage of
  quantum computer systems is the high speed of calculations for all possible parameter values.
  However, quantum acceleration will not be achieved to calculate the probability distributions of
  statistics due to the need to check all the obtained solutions. Here, the number of obtained solutions
  corresponds to the dimension of the problem. In addition, due to the current development
  level of the quantum hardware components, it is impossible to create and use the 120-qubit quantum
  computers for the solution of the considered problem. Photon computers can provide high
  computation speed at low power consumption and require the smallest number of nodes to solve
  the considered problem. However, unsolved problems with the physical implementation of efficient
  memory elements and the lack of available hardware components make the use of photon computer
  technologies impossible for calculation of the probability distributions of statistics in the near
  future (5-7 years). Therefore, it is most reasonable to use hybrid computer systems containing
  nodes of different architectures. To solve the problem on various hardware platforms (generalpurpose
  processors, GPUs, FPGAs) and configurations of hybrid computer systems, we suggest to
  use an architecture independent high-level programming language SET@L. The language combines
  the representation of calculations as sets and collections (based on the alternative set theory
  of P. Vopenka), the absolutely parallel form of the problem represented as an information graph,
  and the paradigm of aspect-oriented programming.

• THEORETICAL STUDY OF ESTIMATING THE PROBABILITY OF A CONNECTION IN SYSTEMS WITH BROADBAND SIGNALS AND FHSS

  D.I. Konkov , А. А. Schmidt , D.N. Polyakov , V.R. Bikbulatov

  285-294

  2025-07-24

  Abstract ▼

  The article is devoted to a theoretical study of the probabilistic characteristics of communication systems with broadband signals and pseudorandom tuning of the operating frequency in a complex electromagnetic environment. An analytical tool for calculating the communication probability is presented, taking into account the complex effects of multipath propagation, frequency-selective fading, and intentional interference. The dependence of the communication probability on the signal-to-noise ratio is investigated using integral expressions that take into account the normal power distribution at the input of the receiving device. A mathematical analysis of the transmission function of the communication channel as a complex characteristic describing the amplitude-frequency and phase distortions during signal propagation is performed. Theoretical models of synchronization processes are developed, including the stages of signal search, capture, and tracking, using the Markum function to describe the probability of signal detection against the background of Gaussian noise. Methods for optimizing the key parameters of the RFP system, such as the frequency tuning period, the total number of frequency channels, and the width of the protective frequency interval, are proposed. The theoretical foundations of adaptive control based on the maximum likelihood method and recursive filtering for estimating the parameters of the channel\are described. The energy efficiency of systems with RFP is studied, taking into account the frequency tuning losses and the necessary adjustment of the signal-to-noise ratio. A comprehensive indicator of the quality of a communication system combining probabilistic, energy, and time characteristics of the system is proposed. Analytical expressions are developed for estimating the intensity of synchronization failure based on statistical analysis of experimental data and calculation of the covariance matrix of measurement noise. The expediency of using reference signals to increase the reliability of measurements of communication channel parameters in adaptive control of the system is justified. Relations are derived for determining the duration of the synchronization window, taking into account the maximum allowable time of entering synchronism and the margin factor, which takes into account possible frequency instabilities of the reference generators.  The influence of the protective frequency interval on preventing inter-channel interference and ensuring electromagnetic compatibility of neighboring channels is analyzed. The presented theoretical results provide a scientific basis for the design of radio systems with increased noise immunity and can be used in the development of adaptive algorithms for controlling RF control systems in a dynamically changing electromagnetic environment, ensuring a balance between the reliability of information transmission and the efficiency of using frequency-time resources of the communication system.

• ENERGY MODEL OF THE QUANTUM BACKBONE NETWORK

  А.P. Pljonkin

  256-264

  2025-07-24

  Abstract ▼

  Already today, quantum communications networks are being actively deployed and created in Russia and around the world, and standards in the field of quantum technologies are being developed. As part of the roadmap for the development of quantum communications in Russia, the length of quantum networks is more than 7 thousand km, and by 2030 it is planned to be more than 15 thousand km. Quantum communications today are, in fact, a technology of quantum key distribution, which is at the stage of intensive scientific research and development. With regard to backbone quantum networks, the technology of secret key distribution requires new approaches to implementation, since the use of equipment from various vendors and the length of fiber-optic communication lines impose surmountable restrictions on the topology of backbone networks. An important aspect in the design of quantum networks is the calculation of losses in optical communication channels. Attenuations introduced by various passive and active elements are usually calculated individually for each section of the network and ultimately form a comprehensive energy model. The article considers several topologies of backbone quantum networks and presents the calculation of optical losses for fiber-optic communication channels of these topologies. In general, a method for detecting an optical signal in quantum communication networks is presented. The purpose of the article is a comparative analysis of energy models of backbone quantum networks and a presentation of a variant of implementing a section of an urban quantum network. The work describes a generalized principle of operation of a quantum key distribution system both in a two-pass version and in a single-pass configuration. The results of the analysis of the energy model and the calculation of average losses in a quantum channel are presented. In conclusion, we propose for consideration a possible variant of the topology of a quantum network.