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The approaches used in biomedicine to analyze epidemics take into account features such as exponential growth in the early stages, slowdown in dynamics upon saturation, time delays in spread, segmented spread, evolutionary adaptations of the pathogen, and preventive measures based on universal communication protocols. All these characteristics are also present in modern cyber epidemics. Therefore, adapting effective biomedical approaches to epidemic analysis for the investigation of the development of cyber epidemics is a promising scientific research task. The article is dedicated to researching the problem of predicting the development of cyber epidemics at early stages. In such conditions, the available data is scarce, incomplete, and distorted. This situation makes it impossible to use artificial intelligence models for prediction. Therefore, the authors propose an entropy-extreme model, defined within the machine learning paradigm, to address this problem. The model is based on estimating the probability distributions of its controllable parameters from input data, taking into account the variability characteristic of the last ones. The entropy-extreme instance, identified from a set of such distributions, indicates the most uncertain (most negative) trajectory of the investigated process. Numerical methods are used to analyze the generated set of investigated process development trajectories based on the assessments of probability distributions of the controllable parameters and the variability characteristic. The result of the analysis includes characteristic predictive trajectories such as the average and median trajectories from the set, as well as the trajectory corresponding to the standard deviation area of the parameters' values. Experiments with real data on the infection of Windows-operated devices by various categories of malware showed that the proposed model outperforms the classical competitor (least squares method) in predicting the development of cyber epidemics near the extremum of the time series representing the deployment of such a process over time. Moreover, the proposed model can be applied without any prior hypotheses regarding the probabilistic properties of the available data., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors.)

Rerouting of direct information traffic under the WiMax-1/2 technology control in the case of licensed frequency spectrum overload ensures communication continuity in the smart city's critical infrastructure. The support of such a process in the WiMax-1/2 cluster has its specificity, worthy of analytical formalization. The article presents a mathematical apparatus that allows the average service duration of an information message during its transfer from the terminal to the WiMax-1/2 base station to be estimated. Unlike analogues, the presented concept adequately describes the investigated process for any number of terminals, taking into account both the queuing effect on their side and the functioning of the cumulative query transmission mechanism inherent in WiMax-1/2 technology. Therefore, the proposed mathematical apparatus, describing the process of servicing an information message, takes into account both the average duration accompanied by potential collisions in the process of sending a request for the allocation of communication resources for its transmission to the base station, and the average duration of the information message's stay in the terminal queue. Experimental studies demonstrated the adequacy of the proposed mathematical apparatus for describing the investigated process. The experimental section also formulates the optimization problem of the investigated process resulting from the management of competitive access parameters., Competing Interests: We declare we have no competing interests., (© 2024 The Authors.)

The formalization of dependencies between datasets, taking into account specific hypotheses about data properties, is a constantly relevant task, which is especially acute when it comes to small data. The aim of the study is to formalize the procedure for calculating optimal estimates of probability density functions of parameters of linear and nonlinear dynamic and static small data models, created taking into account specific hypotheses regarding the properties of the studied object. The research methodology includes probability theory and mathematical statistics, information theory, evaluation theory, and stochastic mathematical programming methods. The mathematical apparatus presented in the article is based on the principle of maximization of information entropy on sets determined as a result of a small number of censored measurements of "input" and "output" entities in the presence of noise. These data structures became the basis for the formalization of linear and nonlinear dynamic and static models of small data with stochastic parameters, which include both controlled and noise-oriented input and output measurement entities. For all variants of the above-mentioned small data models, the tasks of determining the optimal estimates of the probability density functions of the parameters were carried out. Formulated optimization problems are reduced to the forms canonical for the stochastic linear programming problem with probabilistic constraints., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors. Published by Elsevier Ltd.)

A typical element of the smart city's information and communication space is a 5G cluster, which is focused on serving both new and handover requests because it is an open system. In an ordinary 5G smart city cluster, Ultra-Reliable Low-Latency Communications (URLLC) and enhanced Mobile BroadBand (eMBB) traffic types prevail. The formation of an effective QoS policy for such an object (taking into account the potentially active slicing technology) is an urgent problem. As a baseline, this research considers a Quality of Service (QoS) policy with constraints for context-defined URLLC and eMBB classes of incoming requests. Evaluating the QoS policy instance defined within the framework of the basic concept requires the formalization of both a complete qualitative metric and a computationally efficient mathematical apparatus for its calculation. The article presents accurate and approximate methods of calculating such quality parameters as the probability of loss of typed requests and the utilization ratio of the communication resource, which depend on the implementation of the estimated QoS policy. At the same time, the original parametric space includes both fixed characteristics (amount of available communication resources, load according to request classes) and controlled characteristics due to the specifics of the implementation of the basic QoS concept. The paper empirically proves the adequacy of the presented mathematical apparatus for evaluating the QoS policy defined within the scope of the research. Also, in the proposed qualitative metric, a comparison of the author's concept with a parametrically close analogue (the well-known QoS policy scheme, which takes into account the phenomenon of reservation of communication resources), determined taking into account the reservation of communication resources, was made. The results of the comparison testify in favour of the superiority of the author's approach in the proposed metrics., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Kovtun et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

This study was conducted to determine the thyroid function in severe pre-eclamptic patients compared with healthy controls. Twenty-seven women with severe pre-eclampsia and 26 healthy normotensive controls were studied prospectively. Both groups were matched according to three gestational age subgroups; 30-33,34-37 and 38-41 weeks. Serum concentrations of free thyroxine(Fr4), free triiodothyronine (FT3) and thyroid-stimulating hormone (TSH) were measured by immunochemoluminiscence using an automated analyser (Immulite 2000). Pre-eclamptic women obviously showed a statistically significant increase in terms of systolic BP, diastolic BP, levels of urinary albumin and uric acid compared with the healthy controls. There were no significant differences in the levels of FT4, FT3 and TSH between the two study groups in the various gestational age subgroups. We conclude that the thyroid function is not altered in severe pre-clampsia, therefore it does not reflect the severity of pre-eclampsia.