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  8. 48-2

Electronic modeling

Vol 48, No 2 (2026)

CONTENTS

Mathematical modeling and Computation Methods

  KRASILNIKOV O.I.
The Excess Coefficient Analysis of Kaplansky's Generalized Distributions
3-23

Informational Technologics

  HORBULIN V.P., DODONOV O.G.
On the Survival of Automated Organizational Management Systems
24-50
  KLIUZKO O.
Energy AI Software System for Forecasting the Electricity Procurement Portfolio of a Supplier
51-68
  PAZININ A.S.
Proactive Auto-Scaling of Kubernetes Services Based on Machine Learning
69-86

Application of Modeling Methods and Facilities

  KOROBEYNIKOV F., MATVIEIEV S., MOKHOR V.
High-Impact Low-Probability Risks and the Limits of Anticipation: From Known Knowns to Zero-Precedent Uncertainty
87-102
  MARTYNIUK I., ZAIKA N., KOMAROV M., MARTYNIUK H.
Intelligent Analytics for Enhancing the Resilience of Critical Infrastructure
103-114
  NIKOLYUK P.K., MYSHKIVSKA Y.V., OVCHAR M.I.
Multimodal Object Recognition System Based on Modified Yolo Architecture
115-128

The Excess Coefficient Analysis of Kaplansky's Generalized Distributions

O.I. Krasilnikov
ORCID: https://orcid.org/0000-0001-5666-6459https://orcid.org/0000-0001-5666-6459

Èlektron. model. 2026, 48(2):03-23

ABSTRACT

The probability densities I ( ) p x , …, IV( ) p x , given in Kaplansky's report (1945), as examples refuting the interpretation of the excess coefficient as a measure of the sharpness of distributions are analyzed. Kaplan's generalized distributions K1, ..., K4 are defined, whose probability densities I ( ; ) p x p , …, IV( ; ) p x p are a group of two-component mixtures of sym metric distributions with an arbitrary weight coefficient. The dependence of the properties of probability densities I ( ; ) p x p , …, IV( ; ) p x p and their excess coefficient 4( )  p on the weight coefficient p is investigated. A comparison is made between the zero values of the standar dized probability densities I ( ; ) p x p , …, IV( ; ) p x p and the value of the standard normal distri bution. The results obtained allow for mathematical and computer modeling of a multitude of examples of non-Gaussian symmetric probability densities, which refute the interpretation of the excess coefficient as a measure of the sharpness of distributions.

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KEYWORDS

non-Gaussian symmetric distributions, excess kurtosis, two-component mixtures of distributions, cumulant coefficients, cumulant analysis.

REFERENCES

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  5. Krasilnikov, A.I., Beregun, V.S. & Polobyuk, T.A. (2019). Kumuliantnye metody v zadachakh shumovoi diagnostiki teploenergeticheskogo oborudovaniia [Cumulant methods in the problems of noise diagnostics of heat-and-power equipment] (A.I. Krasilnikov, Ed.). Kyiv: Osvita Ukrainy (in Russian).
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  16. Krasilnikov, A.I. (2017). Class of Non-Gaussian Symmetric Distributions with Zero Coefficient of Kurtosis. Elektronnoe modelirovanie, 39(1), 3-17. https://doi.org/10.15407/39.01.003 (in Russian).
  17. Krasylnikov, O.I. (2023). Classification of models of two-component mixtures of symmetrical distributions with zero kurtosis coefficient. Elektronne modeliuvannia, 45(5), 20-38. DOI: https://doi.org/10.15407/emodel.45.05.020 (in Ukrainian).
  18. Krasylnikov, O.I. (2024). Modeling of Two-component Mixtures of Shifted Distributions with Zero Cumulant Coefficients. Elektronne modeliuvannia, 46(4), 19-38. https://doi.org/10.15407/emodel.46.04.019 (in Ukrainian).
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On the Survival of Automated Organizational Management Systems

V.P. Horbulin
ORCID: https://orcid.org/0000-0002-7195-8684
O.G. Dodonov
ORCID: https://orcid.org/0009-0006-1650-1629

Èlektron. model. 2026, 48(2):24-50

ABSTRACT

This article addresses the issue of ensuring the survivability of automated organizational management systems (AOMS). It considers the features of AOMS, their basic functions, and threats that could disrupt the functioning of the system. The concept of survivability and the technologies for ensuring it are defined, and the main directions and basic requirements for ASOM to ensure their survivability under adverse conditions and emergencies are proposed.

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KEYWORDS

automated organizational management system, unified information space, survivability, threat, modeling, negative impact, technology.

REFERENCES

  1. Glushkov, M. (1964). Introduction to Cybernetics. monografiia. Kyiv: Publishing house of the Academy of Sciences of the Ukrainian SSR, 324 p.
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Energy AI Software System for Forecasting the Electricity Procurement Portfolio of a Supplier

O. Kliuzko
ORCID: https://orcid.org/0009-0000-3313-0547

Èlektron. model. 2026, 48(2):51-68

ABSTRACT

The Energy AI software system is proposed as an integrated tool to support operational planning and risk management for energy supply companies in the Ukrainian electricity market. The software system combines short-term hourly consumption forecasting (STLF) with subsequent LP/MILP optimization of the procurement portfolio in market segments (RDD/RDN/VDR/BR). The forecasting module provides hourly consumption profiling using the Random Forest method, and the model parameters are tuned using Optuna. The forecast results are used by the Energy AI optimization module to form a procurement portfolio, taking into account limits, product activity masks, discretization steps, and supplier policies. An example of the system's application is given with an assessment of the effectiveness of the supplier's procurement strategy and the impact of imbalances.

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KEYWORDS

Energy AI, consumption forecasting, portfolio optimization, Random Forest, load-shedding, Optuna, LP/MILP, electricity supplier.

REFERENCES

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Proactive Auto-Scaling of Kubernetes Services Based on Machine Learning

A.S. Pazinin
ORCID: https://orcid.org/0009-0002-9506-953https://orcid.org/0009-0002-9506-953

Èlektron. model. 2026, 48(2):69-86

ABSTRACT

To optimize the use of computing resources, reactive and proactive approaches to service autoscaling in Kubernetes are considered: the standard reactive Horizontal Pod Autoscaler (HPA) and a proactive autoscaler based on machine learning using LSTM. A controller has been developed and proposed that collects CPU metrics from Prometheus, trains and updates the model, predicts short-term load dynamics, and adjusts the number of replicas via the Kubernetes API. Metrics for predictions and decisions are sent to Pushgateway and visualized in Grafana. Experimental studies in an Azure Kubernetes Service cluster with controlled container load showed a 30 % reduction in total vCPU usage compared to HPA while maintaining the same service level, reducing scaling latency (scaling up in 30-60 s versus 75-90 s; shrink time of 60-90 s versus 90-150 s) and elimination of “jitter.” The results confirm the effectiveness of applying proactive Kubernetes service autoscaling based on machine learning methods for services with stable or seasonal traffic patterns.

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KEYWORDS

Kubernetes, autoscaling, HPA, LSTM, Prometheus, Pushgateway, Grafana.

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