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• LOW-RESOURCE ABSTRACTIVE TEXT SUMMARIZATION VIA CONTRASTIVE UNSUPERVISED LEARNING WITH A ROUGE-ORIENTED LOSS FUNCTION

  I. Е. Lysenko

  91-101

  2026-09-10

  Abstract ▼

  The relevance of this work is motivated by the fact that in specialized domains and low-resource languages obtaining a sufficient number of “document-summary” pairs for effective abstractive text summarization is expensive and often practically infeasible, whereas modern deep learning models require large labeled corpora and large volumes of text remain unused. The aim of this study is to develop a new training method for abstractive summarization models in low-resource (10-shot and 100-shot) settings that improves quality by fine-tuning the model on unlabeled data using unsupervised contrastive learning with input augmentation. The research tasks include designing a new contrastive loss function and comparing the proposed approach with existing methods of low-resource abstractive summarization. The methods and approaches comprise a new loss function for fine-tuning a transformer that includes a contrastive generative component based on a differentiable approximation of the ROUGE-3 metric. Two variants of the method are proposed – the sequential “DiffROUGE-seq” and the semi-supervised “DiffROUGE-sim”. BART-large is used as the base model, while input augmentations are generated by FLAN-T5-large in a zero-shot regime. Experiments are conducted on popular datasets AESLC, Gigaword, XSum, and Reddit. The proposed method achieves substantial improvements in ROUGE scores in successful cases, with average gains of 2.69 in the 10-shot setting and 2.13 in the 100-shot setting. In summary, the newly proposed low-resource abstractive summarization method that leverages both labeled and unlabeled data is significantly more effective in terms of ROUGE than existing approaches

• NEURAL NETWORK APPROXIMATION OF MODEL-PREDICTIVE CONTROL FOR A DYNAMIC OBJECT STABILIZATION SYSTEM

  B.А. Komarov , S.V. Leonov , Т.Е. Mamonova

  276-287

  2025-12-30

  Abstract ▼

  Relevance. When solving problems of stabilization of dynamic objects, classical model predictive control is widely used. It provides high quality control by solving the optimization problem at each step, but it has significant computing costs, which limits its application in real-time systems with high requirements for update frequency. Therefore, the question of investigating the applicability of a neural network regulator trained on a model predictive regulator (MPC) when solving the problem of stabilizing the position of a dynamic object with a limited computational and time resource is relevant. Goal.  The purpose of the presented work was to develop and study a neural network regulator trained on the basis of an MPC regulator to stabilize the position of a dynamic object on a mobile platform. Methods. When performing the work, methods of system analysis, simulation modeling, as well as experimental tests on the bench were used. Results and conclusions. As part of the study, a neural network regulator was developed and trained that approximates the behavior of MPC based on data obtained when controlling a real balancing platform. The training was conducted on the input and output data of the MPC without using the internal model of the system, which made it possible to reproduce the dynamics of the regulator at significantly lower computational costs. Experimental results showed that the neural network model provides a stabilization quality comparable to the original MPC, while the calculation time was reduced from 47 ms to
  1.6 ms, which amounted to an acceleration value of 29 times. The proposed approach demonstrates the potential of neural network control methods in the problems of replacing complex optimization regulators for systems with limited computing resources.

• FORMATION OF THE IMPULSE RESPONSE OF A RECURSIVE LOW-PASS FILTER WITH FINITE IMPULSE RESPONSE AS A SUM OF QUASI-HARMONICS OF A TRUNCATED FOURIER SERIES

  D.I. Bakshun , I.I. Turulin

  221-228

  2025-12-30

  Abstract ▼

  The problem of reducing the number of arithmetic operations in digital filtering algorithms is highly relevant, as it directly impacts power consumption, processing speed, and hardware costs. Under strict power efficiency requirements for mobile and embedded systems, minimizing multiplication and addition operations becomes a critical design factor. This paper presents a method for implementing a recursive filter with a finite impulse response (FIR) based on a truncated sinc function smoothed by a window (weighting function), represented as a sum of quasi-harmonic functions. These quasi-harmonic functions with different frequencies are polynomials of degree r. The study adopts a second-degree polynomial as a baseline and proposes a numerical method for increasing the polynomial order to improve the accuracy of the approximation. Accuracy analysis demonstrates that using 4th- and 6th-order polynomials achieves an approximation error of less than 1%. The coefficients of the non-recursive part of the filter are computed via inverse finite differences of the original FIR impulse response. These coefficients are integers whose values depend on the number of samples (length) of the half-period of the quasi-sinusoidal function, simplifying the implementation of such a recursive FIR (RFIR) filter on a field-programmable gate array (FPGA). Numerical analysis of finite differences for each quasi-sinusoid revealed that quadratic approximation requires only 16 samples but results in relatively high side-lobe levels (–30 dB). Switching to 4th-order approximation increases the number of non-zero coefficients to 20 and significantly reduces
  (by 13 dB) the stopband magnitude of the frequency response, reaching –43 dB.

• THE METHOD OF PIECEWISE APPROXIMATION OF STATIC CHARACTERISTICS OF DEEP-LYING HYDROLITHOSPHERIC PROCESSES

  I. А. Bondin

  81-89

  2025-12-30

  Abstract ▼

  This paper addresses the problem of describing the static characteristics of hydrolithospheric processes in deep-lying aquifers using the Essentuki mineral groundwater field, classified as a Category IV deposit in terms of geological complexity, as a case study. It is shown that classical methods for approximating distributed transfer functions, widely applied in the analysis and design of control systems for shallow aquifers at depths of 50–400 m, are not applicable to deep-lying conditions. This limitation is caused by high gas saturation of groundwater, pronounced structural heterogeneity of reservoirs, complex and often nonlinear hydraulic interaction between production and observation wells, as well as spatial and temporal variability of hydrochemical parameters. A modified method of piecewise approximation of static characteristics of hydrolithospheric processes is proposed. The method is based on the separate identification of parameters of approximating elements over individual distance intervals between wells using the results of pumping tests. The approach was implemented for the Cenomanian–Maastrichtian aquifer of the Novoblagodarnensky area of the Essentuki field, where hydraulic interaction coefficients between wells were calculated and static transfer functions were constructed for different spatial intervals, taking into account actual geological and filtration conditions. The results demonstrate that the use of piecewise approximation provides a better agreement with experimental data compared to homogeneous models and allows spatial variability of filtration properties to be taken into account. The obtained results form a methodological basis for forecasting hydrodynamic and gas–hydrochemical changes, assessing the stability of operating regimes, and developing and synthesizing control systems for regulating discharge rates of deep mineral groundwater wells. The practical significance of the study lies in the applicability of the proposed method to substantiating pilot industrial operation parameters, adjusting design solutions, interpreting monitoring and pumping test data, and formulating scientifically grounded recommendations for groundwater abstraction management, reduction of technogenic disturbances, and preservation of the stability of hydrolithospheric systems under conditions of intensive field development.

• PHOTODETECTOR WITH CONTROLLED RELOCATION: DRIFT-DIFFUSION MODEL AND APPLICATION IN OPTICAL INTERCONNECTIONS

  I.V. Pisarenko, Е.А. Ryndin

  2020-07-20

  Abstract ▼

  Previously, we proposed an injection laser with a double AIIIBV nanoheterostructure for the
  generation and modulation of light in optical interconnections for integrated circuits. To convert
  short optical pulses generated by the laser-modulator into electrical signals, a technologically
  compatible photodetector with subpicosecond response time is needed. Traditional designs of
  photosensitive semiconductor devices do not meet the specified requirements. Therefore, we developed
  a promising concept of a high-speed photodetector with controlled relocation of carrier density
  peaks within specially organized quantum regions. This optoelectronic device includes a longitudinal
  photosensitive p-i-n junction and a transverse control heterostructure, which containstwo low-temperature-grown layers and two control junctions. Before the trail of an optical pulse,
  the photodetector operates as a classical p-i-n photodiode. Transverse electric field is activated
  only during the back edge of a laser pulse. It relocates the peaks of electron and hole densities
  from the absorbing region to the regions with low carrier mobility and short lifetime. This process
  leads to the decrease in response time to a subpicosecond value. In our previous papers, we estimated
  the performance of the considered device using a quantum mechanical combined model that
  had not taken into account certain aspects of charge carrier transport in its structure. This paper
  is aimed at a proper semiclassical analysis of transients in the photodetector with controlled relocation
  by means of a two-dimensional drift-diffusion model. For the numerical implementation of
  the model, we develop a finite difference simulation technique based on the explicit method and
  applied software. According to the obtained results, it is reasonable to use the differential connection
  principle in order to compensate displacement currents in the supply circuit of the device. In
  view of this feature, we propose a circuit of optical receiver that provides the generation of resultant
  electrical signal as well as the required mode of the control voltage application to the
  photodetector contacts, and a driver circuit for the lasers-modulators.

• 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

• 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.

• ANALYSIS OF CERTAIN WEIGHT FUNCTIONS (WINDOWS) AND THEIR APPROXIMATIONS FOR IMPLEMENTATION OF CONTROLLED RECURSIVE LOW-PASS FILTERS WITH A FINITE IMPULSE RESPONSE ON THEIR BASIS

  T.V. Shushkevich , А.А. Morozov, I. I. Turulin

  2021-11-14

  Abstract ▼

  There are various types of weighting functions, the so-called windows in digital signal processing,
  such as rectangular (Dirichlet window), triangular (Bartlett window), Vallee-Poussin window,
  Kaiser-Bessel window, Barsilon-Temesh window, Hann, Bohman, Blackman, Gauss (Weierstrass),
  Dolph - Chebyshev, Hamming windows and many others and ideal characteristics of standard filters
  such as low-pass, high-pass, bandpass filters. The purpose of this review article is to determine the most
  suitable weighting function for implementation on its basis of a controlled recursive low-pass filter with
  a finite impulse response. This article presents an analysis of only some of the above windows and their
  approximations, namely the Dolph - Chebyshev window, the Gauss (Weierstrass) window and the
  Hamming window. In addition to the analysis, the synthesis of recursive filters with a finite impulse
  response for weighting data based on the selected windows and their approximations was considered.
  The method of synthesis of Dolph-Chebyshev windows is considered. The implementation of the Gauss
  (Weierstrass) window is considered. Methods for approximating the Hamming window and methods
  and several algorithms for developing filters with FIR in the form of this window are considered. The
  estimation of parameters dependencies some quick window of the maximum level of the side lobes.
  Based on the data obtained, conclusions were drawn about the selection of the most suitable and
  demonstrating maximum performance windows, suitable for implementation on its basis of a controlled
  recursive low-pass filter with a finite impulse response.

• SELECTING FEATURES OF THE MODEL TRANSFORMATION CHARACTERISTICS FOR AN INTELLIGENT PHYSICAL QUANTITY SENSOR

  S. I. Klevtsov

  2021-11-14

  Abstract ▼

  The paper discusses the issues of choosing the type and parameters of the model of the transformation
  characteristic of an intelligent sensor of physical quantities using the example of a pressure
  sensor. The transformation characteristic of an intelligent sensor is a mathematical, algorithmic
  and software for calculating a physical quantity based on electrical signals that come from the measuring
  channels of the sensor. The model of the conversion characteristic should be adapted to the
  configuration of the conversion function of the sensor's sensitive element and the behavior of this
  function under the influence of external destabilizing factors. The paper considers various models of
  the conversion characteristics, identifies the features of their application, advantages and disadvantages,
  attainable levels of approximation error of the real characteristic, which affect the final
  measurement accuracy of the smart sensor. Smart sensors are used for measuring physical quantities
  in various technical systems and the requirements for measurement accuracy in real-life tasks are
  different. The measurement accuracy is largely determined by the degree of approximation of the real
  characteristics of the sensor by its mathematical model. The more complex the model, the more difficult
  it is to implement in the sensor, and the higher the measurement cost. Therefore, it is important
  to control the conversion characteristic approximation error in order to use the sensor efficiently. To
  control the approximation error of the transformation characteristic of an intelligent pressure sensor,
  it is proposed to use the method of multi-segment spatial approximation, and use models of linear or
  nonlinear spatial elements as segments. The basic mathematical expressions, the error control
  scheme are determined. The results of modeling are presented, which show the possibility and advantages
  of using the method for the formation of spatial models of the transformation characteristics,
  which are adaptive to changes in the real transformation function of the sensor, take into account
  the influence of external factors on the measurement results. In addition, the method allows you
  to modify the current spatial approximation model by changing the types of local spatial elements
  and, thus, to control the measurement error

• SELECTION OF THE SENSOR CONVERSION CHARACTERISTIC MODEL FOR CONTROLLING THE ERROR IN THE MEASUREMENT OF PHYSICAL QUANTITIES

  S.I. Klevtsov

  2022-08-09

  Abstract ▼

  On the example of a pressure sensor, the problem of selecting a model and parameters of
  the conversion function of a microprocessor sensor is considered. The conversion function is
  based on a mathematical model that associates the electrical signal coming from the sensor's
  measuring transducer with the value of a physical quantity. The model of the conversion function
  of a microprocessor sensor must repeat the real spatial dependence of the electrical signal on the
  measured value and take into account the influence of external factors, such as temperature. Microprocessor
  sensors are used to measure the parameters of an object with a given accuracy. The
  main contribution to the measurement error is made by the inaccuracy of the approximation of the
  real transformation function by its model. The need to achieve the optimal level of parameter
  measurement error in the system, taking into account the complexity and cost of measurements,
  requires the control of the sensor error. For this purpose, various models and methods of approximation
  are presented. For efficient error control, a method of multi-segment spatial approximation
  based on models of linear or non-linear spatial elements is proposed. The error control procedure
  is formulated. The procedure for using the model of multi-segment spatial approximation
  of the transformation characteristic for pressure calculations taking into account the influence of
  temperature is based on the combined use of linear and non-linear spatial elements within the
  same model. The segment type selection procedure should begin with an assessment of the possibility
  of using a linear spatial element first, and if it is impossible to meet the accuracy requirements,
  an analysis of the use of a non-linear element. The method allows you to change the types
  and configuration of spatial elements and in this way influence the measurement error. The advantages
  of this approach are confirmed by the simulation results.

• 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.