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• SOLUTION OF THE INVERSE PROBLEM OF SPECTRAL GRAPH THEORY IN THE ABSENCE OF OBSERVABLE VARIABLES

  А.N. Tselykh , V. S. Vasilev , L.А. Tselykh , S.А. Barkovskii

  163-173

  2025-10-01

  Abstract ▼

  The article is devoted to solving the main inverse problem of spectral graph theory – determining the main parameters of a graph based on the spectrum of its eigenvalues. The article studies cognitive causal graph models of complex systems with unknown dynamics of variables. Non-stochastic graph models with non-numeric values of nodes and links, as well as poorly defined system factors are considered. In the absence of initial data, solving the inverse problem for a directed weighted signed graph is significantly complicated. When graphs have the same topology but different weights on arcs, their spectra form a set of fuzzy collinear vectors in the solution space. The straight lines of these vectors diverge in the vector space due to their directionality to different vertices. The article proposes to use an algorithm that allows one to accurately restore the weights of a cognitive graph when the conditional principal eigenvector and the topological structure of the adjacency matrix are known. This algorithm takes into account an important feature of the adjacency matrix of the graph - the direction of the main eigenvector to the target vertex, which allows finding the correct solution from a set of fuzzy collinear vectors in the solution space. To achieve complete restoration of the graph weights with acceptable accuracy, it is proposed to combine the graph spectrum and the effective control model with the combinatorial optimization problem. Restoring the adjacency matrix weights using our approach, we compare them with the given graph. The comparison takes into account such graph parameters as the graph spectrum, similarity coefficients of the restored matrix, response and control vectors

• THE ADJACENCY MATRIX RECONSTRUCTION ALGORITHM FOR CAUSAL GRAPH MODELS IN THE ABSENCE OF OBSERVABLE VARIABLES

  A. N. Tselykh , V.S. Vasilev, L. A. Tselykh

  2021-11-14

  Abstract ▼

  The paper deals with the problem of modeling complex systems in the absence of observable
  variables. To solve this problem, it is proposed to use causal graph models. The class of causal
  models considered here is defined as non-stochastic causal models with unobservable variables.
  These models are presented in the form of a directed graph, created on the basis of human mental
  representations. In this case, on the arcs, causality is expressed in the form of some marks with a
  sign that determines the direction of change in the state of the system. The considered causal models
  include heterogeneous, complex and qualitative types of variables that illustrate the nonnumerical
  nature of nodes and links and, as a consequence, the absence and impossibility of obtaining
  time series data. In the absence of observable variables and the impossibility of conducting
  experiments, the problem of reconstructing the adjacency matrix of the causal graph model becomes
  much more complicated. It is required to obtain a model with a certain spectral decomposition
  that implements the main function of the modeled system. Based on this concept, a new method
  for reconstructing the adjacency matrix is proposed, implemented on the basis of the corresponding
  causal propagation matrix or transmission matrix. The idea is to use combinatorial optimization
  based on spectral graph theory to generate data from a qualitative non-stochastic causal
  model and reconstruct an adjacency matrix using that data. In this case, the eigenvectors are
  identified as key objectives of the matrix reconstruction process, which postulates a fundamental
  approach based on the spectral properties of the graph. The results of computational experiments
  on solving the problem of reconstructing the adjacency matrix for causal graph models in the absence
  of observable variables using the developed algorithm have shown that the algorithm effectively
  reconstructs matrices from the given parameters with admissible similarity indices. The
  convergence of the approximation to the solution of the matrix reconstruction algorithm is proved
  no slower than with the speed of a geometric progression. From a technical point of view, the
  advantage of the algorithm is the implementation of a tool for automatic adjustment of the regularization
  parameter, suitable for users without prior mathematical knowledge.

• ALGORITHM OF EFFECTIVE CONTROLS FOR NONSTOCHASTIC CAUSAL MODELS IN THE ABSENCE OF OBSERVABLE VARIABLES FOR SYSTEMS OF DECISION MAKING CONTROL

  A.N. Tselykh, V.S. Vasilev , L.A. Tselykh

  2021-11-14

  Abstract ▼

  The paper deals with the problem of reproducing the decision-making process by a person under
  conditions of uncertainty and incompleteness of the initial data. The decision-maker relies on his
  belief system, which includes a shared vision of the system in relation to which the decision is being
  made. The system is presented in the form of a causal model created on the basis of human mental
  representations. These models are directed graphs, on the arcs of which the causal relationship is
  expressed in the form of labels with a sign that determines the direction of change in the state of the
  system. The vertices of this directed graph are high-level abstraction concepts. This graph simulates
  the functioning of a real system. Thus, we investigate the problem of predicting and controlling human
  actions based on non-stochastic causal models in the absence of observable variables for use in
  decision support systems and expert systems. Decision-making is considered from the point of view of
  the choice of objects of application of managerial influences - the factors of the model. In this study,
  we show that the application of the proposed algorithm can facilitate decision-making regarding the
  choice of control actions that support the achievement of the tactical and strategic goals of the decision
  maker. It should be noted that the algorithm implements an automatic selection of the regularization
  parameter, which makes the development and application of the proposed algorithm available
  to users who do not have sufficient mathematical training. The convergence of the sequence of Lagrange
  multipliers of an effective control algorithm is proved. The theorem on resonance in a nonstochastic
  causal mod-el, represented by a directed graph, which is determined by the range of admissible
  values of the damping coefficient in the control model, is proved. It is expected that the introduction
  of this tool into decision support systems will in-crease the reliability of decisions regarding
  the operation of the system as a whole. The choice of control actions using the proposed algorithm
  has high efficiency and productivity. Thus, the results presented in the study can be useful for
  developing applications in intelligent systems.

• CONSTRUCTION OF AN OPTIMAL CONTROL TRAJECTORY IN AN INTELLIGENT SYSTEM IN THE ABSENCE OF OBSERVABLE VARIABLES

  А.N. Tselykh , V. S. Vasilev , L.А. Tselykh , Е.S. Podoplelova

  224-233

  2025-07-24

  Abstract ▼

  Constructing optimal control in the complete absence of data on the system dynamics is a pressing problem. In this paper, we propose a solution to a finite-horizon linear quadratic problem (LCP) for a time-invariant system with a graph dynamics matrix. Unlike the control problem, stability and complete controllability of the system are not assumed. The construction of the control trajectory is controlled by the direction of increase in the change in the state of variables over a small number of steps, which is determined by the conditional principal eigenvector of the adjacency matrix of the graph model. The solution of classical optimal control is carried out in an autonomous mode and requires complete knowledge of the system dynamics. In the absence of complete knowledge of the system dynamics, solving optimal control problems for systems with uncertainty, including discrete linear systems, has attracted considerable interest in recent years. The main approach when complete information about the system is unavailable is the design of optimal control, in which the system parameters are initially determined, and then an algebraic equation in the dual space is solved. An important difference from the standard discrete control problem is that the control model was modified to estimate changes in the state of variables under controls transmitted through the dynamics matrix. The proposed algorithm using a graph matrix implements recurrent calculations of dynamic and adjoint equations, as well as the Powell method for solving a system of linear algebraic equations (SLAE). The authors introduced a new interpretation of the mathematical construction of the system dynamics matrix in a standard discrete control problem on a finite time interval, which can be used to design any controlled dynamic system with unobservable parameters.

• APPLYING DEEP LEARNING TO EXTRACT CAUSALITY FROM TEXT USING SYNTHETIC DATA

  А.N. Tselykh, I. А. Valukhov, L.А. Tselykh

  2025-01-30

  Abstract ▼

  This article addresses the problem of developing a causal full-tuples extraction model from unstructured
  texts to represent decision-making situations in complex social and humanitarian environments.
  We present a causal full-tuples extraction model using a pre-trained BERT with additional feature-based
  special fine-tuning. To refine the causal classification, the model uses two types of features (verb causality
  and cause-and-effect quality metrics) to recognize a causal tuple, automatically extracts semantic features
  from sentences, increasing the accuracy of extraction. Text preprocessing is performed using the open
  source SpaCy library. The extracted cause-and-effect tuples in the format <cause phrase, verb phrase,
  effect phrase, polarity> are easily transformed into the corresponding elements of the graph <outgoing
  graph node, graph arc direction, incoming graph node, graph connection weight sign> and can then be
  used to construct a directed weighted signed graph with deterministic causality on arcs. In order to reduce
  dependence on external knowledge, synthetic generated annotated datasets are used to fine-tune and test
  the BERT model. Experimental results show that the accuracy of extracting cause-and-effect relationships
  on synthetic data reaches 94%, and the F1 value is 95%. The advantages of the presented technological
  solution are that the model does not require high operating costs, is implemented on a computer with
  standard characteristics, uses free software, which makes it accessible to a wide variety of users. It is
  expected that the proposed model can be used to automate text analysis and support decision-making in
  conditions of high uncertainty, which is especially important for social and humanitarian environments.

• THE PROBLEM OF CHOOSING A DUMPING FACTOR IN THE EFFECTIVE CONTROL MODEL FOR DIRECTED WEIGHTED SIGNED GRAPHS

  A.N. Tselykh, V.S. Vasilev, L.A. Tselykh

  2020-07-20

  Abstract ▼

  The paper deals with the problem of choosing a dumping factor in the effective control model
  based on maximizing the transfer of impacts for fuzzy cognitive models represented by directed
  weighted signed graphs. To transfer influence, a management model is used that implements the
  development of the system. An effective control algorithm is based on solving the optimization
  problem of finding a vector of external influences that maximizes the accumulated increase in
  increments of vertex indicators. The optimal control effect is considered to be a control that provides
  the maximum ratio of the square of the norm of the response vector of the system to the
  square of the norm of the control vector. The dumping factor of this model controls the comparative
  scale of the direct and indirect influence of all intrafactor relationships of the system as a
  whole. The purpose of the study is to determine such areas of acceptable values for the obtained
  solutions, in which (i) the condition of consistency of the result is met; (ii) the change of vertex
  ranks is slow. By the sequence of results, we mean satisfaction with the rules of the system as a
  whole. These rules can be expressed in imposing restrictions on the status of vertices, on the sign
  of impacts and responses. Set the damping factor, called the resonance, where resonance occurs a
  surge in the value of the objective function the problem of maximization of the impact when there
  is no alignment between the resonant response and caused its effect. The choice of the dumping
  factor affects the value of the target function of the impact maximization problem and the vector of
  effective management on which this solution is achieved. The value of the resonant damping coefficient
  can be interpreted as the limit of the possible controllability of the system, i.e. limit the
  potential impact on the system without harming it. The proposed solution is evaluated based on the
  degree of stability of the rank of model nodes depending on the influence of changes in the damping
  coefficient, the algorithmization of determining the range of its acceptable values and the
  shape of the resonance within the values of the damping coefficient.

• A NEURAL NETWORK-BASED METHOD FOR EXTRACTING CAUSAL RELATIONS USING COMPARATIVE ANALYSIS OF SYNTHETIC AND OPEN CORPORA

  А.N. Tselykh , I. А. Valukhov

  160-169

  2026-09-10

  Abstract ▼

  The automatic extraction of causal relations is critically important for decision support systems, but its development is hindered by the scarcity of annotated corpora. The aim of this study is to comparatively analyze the effectiveness of three types of training data: open expert corpora, a manually annotated political corpus, and synthetic data generated by a large language model. Experiments were conducted using the DistilBERT architecture with token-level BIOES tagging. Synthetic data were generated with the Llama-3 LLM by encapsulating causes and effects in XML markers, followed by deterministic conversion into the BIOES format. For comparison, two expert corpora (EventStoryLine and SemEval-2010 Task 8), the expert-annotated political corpus PolitiCAUSE, and a synthetic sample of 1,100 balanced examples were used. The model trained on synthetic data achieved a Macro F1 score of 0.736, which is 6.7% higher than the result obtained from training on the expert corpora (0.690). Training on the political corpus PolitiCAUSE (24,417 examples) yielded a substantially lower result, with a Macro F1 score of 0.367. This discrepancy is attributed to class imbalance (approximately 15% causal tokens versus 50% in the synthetic sample) and to differences in task formulation: PolitiCAUSE is oriented toward binary sentence-level classification of causal presence, whereas the present study addresses token-level span labeling. The hypothesis that annotation quality and class balance are more important than data volume is confirmed. The proposed LLM-generation pipeline makes it possible to create training datasets that outperform expert corpora without direct manual annotation costs. The method is recommended for rapid deployment of causal relation extraction systems in new domains.

• ABOUT THE REAL POSSIBILITIES OF MODERN COMPUTING SYSTEMS FOR DISTRIBUTED MULTIPLICATION OF LARGE-DIMENSIONAL MATRICES

  V.М. Glushan, L.А. Popov, А.А. Tselykh

  2025-01-14

  Abstract ▼

  The needs of practice constantly require improving the performance of computing systems. For
  quite a long time, multiprocessor systems have been the main way to build ultra-high performance computing
  systems. When creating such systems, many difficult problems arise. They are related to the need to
  parallelize the computing process in order to efficiently load the system processors, overcome conflicts
  when several processors try to use the same system resource, reduce the impact of conflicts on system
  performance, etc. With microelectronics overcoming the milestone of a billion transistors on a silicon
  chip, a new paradigm of multicore processors has emerged. At the same time, the problem of the ratio of
  multicore and multithreading in modern computers arose. This is due to the dilemma of preference between
  them. A multicore processor contains two or more electronic computing cores placed on a single
  semiconductor crystal. Each core of a multicore processor is a full-fledged microprocessor. Multicore is
  an obvious and traditional method of distributed solution of many complex tasks. But this cannot be said
  about multithreading, which relies on the use of very fast cache memory associated with the main memory
  and serves to reduce the average access time to the main memory of the processor. The relative novelty of
  modern approaches to the construction of computing systems requires comparative experimental studies
  of their capabilities. A promising and convenient mathematical object for these purposes is the distributed
  multiplication of matrices of large dimensions. The article presents practical results of distributed multiplication
  of square matrices with sizes from 300*300 to 2000*2000 and randomly generated values of
  elements in the matrices in the range from -100 to +100. Based on the experimental data presented in the
  corresponding tables and graphs, hyperbolic relations are obtained for the dependence of the matrix multiplication
  time on the number of virtual machines (cores) in the laptop used. Similar results were obtained
  by multiplying square matrices on single-processor computers connected to a local network. Analytical
  expressions in this case also represent hyperbolic time dependencies. But the numerical values in
  them significantly exceed those for the hyperbolic formula obtained for the laptop. Based on the results
  obtained, the conducted research allows us to conclude that the use of a single-processor computer connected
  to a local network for multiplying matrices of large dimensions is inferior to the performance of a
  laptop. This is due to the significant time spent moving data over the local network.