Confidence Probability Research Articles

Validation of Reliability Indices during Experimental Development of a Complex Technical Series System

Introduction. The article studies the problem of validating the specified levels of reliability during experimental development of a complex technical series system. Such tasks arise when it is required to make a decision on testing the system as part of a larger one or on the completion of experimental development and the start of series production. The study is aimed at validating the reduction of the experimental development time. The task is to determine whether the hypothesis Но is accepted or rejected.Materials and Methods. To implement the research objective and task, a critical area described by the inequality was constructed based on the test results. The formulation of the requirements validation task was based on well-known approaches to testing statistical hypotheses. The conceptual apparatus of information theory, probability, and statistics was involved. The theoretical and applied literature on mathematical methods in reliability theory was studied. The particular tasks of the work were solved by known ways. Thus, the probability of obtaining the exact number of successful outcomes in a certain number of experiments was determined by the Bernoulli scheme. The exact confidence interval based on the binomial distribution was derived from the Clopper-Pearson relation. The theorem of A.D. Solovyov and R. A. Mirny made it possible to assess the system reliability based on the test results of its components.Results. Control rules adequate to the stage of experimental development (with insufficient data on the technical system) and the stage of series production were mathematically defined. The probability of a successful outcome when testing technical systems was represented by:– the probability of event for a system element;– confidence value;– required scope of tests.In these terms, the null and alternative hypotheses and the corresponding reliability control procedures were investigated. Two provisions were considered. The first one provided using the null confidence hypothesis Но = {Р ≥ РТ} and an alternative Н = { Р < РТ} to confirm the requirements (РТ, γ) for the reliability indicator of one parameter for any (РТ, γ). In this case, one trouble-free test was enough. The second provision considered a sequential technical system with independent elements that were tested separately from the system according to the Bernoulli scheme for one parameter. We considered the requirements for the system in the form of a set of values (РТ, γ) and the requirements for any of its elements (РТi, γ). They coincided when the planned outcome of the tests corresponded to the cases when the ratio Р= lim 1≤i≤N : Р i = Р m was fulfilled, and the null alternative hypothesis was selected from the theory of statistical hypothesis testing.Discussion and Conclusions. The experimental development strategy should be implemented in two stages: the search and validation of the reliability of the elements through a series of fail-safe tests. In this case, the planned scope of tests of each element is determined taking into account the confidence probability, the lower limit of the confidence interval, and the requirements for reliability indices of one parameter of the technical system. If the use of the null confidence hypothesis is acceptable, one fail-safe test is sufficient to confirm the requirements for the reliability index.

MAGDM Model Using the Exponential Similarity Measure of Neutrosophic Confidence Cubic Sets in a Single-Valued Neutrosophic Multivalued Circumstance

Probability estimation of small sample data is a key tool to ensure the probability that sample data fall within the confidence interval at a certain confidence level and probability distribution, which shows its advantages in practical engineering applications. Then, regarding a group decision-making (GDM) problem in the situation of indeterminacy and inconsistency, several experts/decision makers will assign several true, false, and indeterminate fuzzy values to the evaluation values of each alternative over different attributes, and then form a single-valued neutrosophic multivalued set (SvNMVS) as their assessed information. To ensure some confidence level of the evaluation values in the circumstance of SvNMVSs and GDM reliability, this paper aims to propose a conversion technique from SvNMVS to a neutrosophic confidence cubic set (NCCS) and a GDM model using the exponential similarity measure of NCCSs in the circumstance of SvNMVSs. First, we give the definition of NCCS, which is transformed from SvNMVS in terms of average values and confidence intervals of true, false, and indeterminate fuzzy sequences subject to the conditions of the normal distribution and confidence levels. Second, we present the exponential similarity measure of NCCSs and the weighted exponential similarity measure of NCCSs and their characteristics. Third, a GDM model is developed by using the weighted exponential similarity measure of NCCSs in the circumstance of SvNMVSs. Fourth, the developed GDM model is applied to a choice case of landslide treatment schemes in the circumstance of SvNMVSs to reveal its usability and suitability in actual GDM problems. Compared with the existing GDM models, the developed GDM model indicates its superiorities in decision flexibility and credibility/reliability subject to 90%, 95%, and 99% confidence levels.

Development and approbation of an analytical method for the quantitative determination of carbon tetrachloride in freons used in the composition of medicines in the form of an aerosol

Aim to develop and test an analytical method for the quantitative determination of carbon tetrachloride in freons used in the composition of medicines in the form of an aerosol.
 Material and methods. Carbon tetrachloride (tetrachloromethane, Freon-10) - CCl4, M.m. = 153.81, heavy, colorless, volatile liquid with a sweet smell reminiscent of chloroform. Melting point - 22.96 С, boiling point - 76.75 C, relative density at 20 - [d]420 1.595. Poorly soluble in water (0.5 g/l), unrestrictedly miscible with alcohol, ether, acetone, benzene (chemically pure grade).
 To determine the tests for the presence and quantitative determination of carbon tetrachloride in propellant gases used in medicinal preparations, we chose the drug "Salbutamol-Pharmstandard". To identify and quantify carbon tetrachloride in propellants used in medicinal products, the gas-liquid chromatography method with electron capture detection with a capillary column was applied.
 Results. The developed method was used to determine carbon tetrachloride in the test preparation "Salbutamol". The results were statistically processed and showed that the content of carbon tetrachloride in the test preparation was 0.01580.0007 mg/l. The error of a single experiment with a confidence probability P = 95% was 4.42%
 Conclusion. We proposed a method for estimating the content of carbon tetrachloride impurities in aerosol dosage forms by gas-liquid chromatography with an electron capture detector. The technique involved the gas chromatographic separation of a sample, taken from an aerosol can, on a capillary chromatographic column. The most appropriate detector in this case turned out to be an electron capture detector.

Planning of rolling stock operation considering specific features of road traffic management when transporting goods in the Far North

Introduction. The operation practice for the rolling stock of road transport during the transportation of goods in the harsh conditions of the Far North (Republic of Sakha (Yakutia)) shows the necessity to organize measures related to ensuring road safety on road sections with ups and downs. To prevent rolling stock from running off the road and overturning, tractor equipment is used as a tractor for road transport, the use of which is time-consuming. The purpose of this article is to develop a new theoretical toolkit for planning the work of the rolling stock, which makes it possible to determine the time spent on transportation.Materials and methods. The study uses field observations for trips, during which tractor equipment was used as a tractor for road transport on cargo transportation routes, where movement was carried out on descents and ascents.Methods of probability theory and mathematical statistics were used to determine the probability of occurrence of an event, the values of confidence intervals for the time of movement of the rolling stock, taking into account the confidence probability of 0.95. As the basis of the performed research, the scientific work of scientists on the planning of the work of the rolling stock was used, taking into account the peculiarities of the organization of road traffic during the transportation of goods in difficult operating conditions.Results. The authors determined the time spent on the transportation of goods using tractor equipment as a tractor for planning the work of IVECO-AMT 733910 С/Т rolling stock on six routes. The value of the probability of using tractor equipment on the studied routes for planning the operation of IVECO-AMT 733910C/T rolling stock has been established.Conclusions. The presented values of the movement time of the IVECO-AMT 733910 С/Т rolling stock when transporting goods using tractor equipment as a tractor can be used for practical use in planning from December to March when transporting collapsible structural elements of drilling rigs and property of drilling crews.

Mathematical model of agricultural aggregate movement based on the Autotractor

The paper presents theoretical studies of the movement of the agricultural unit on the basis of the MEZ-330 «Autotractor». An equivalent dynamic model of an agricultural unit on the basis of MEZ-330 «Autotractor» is presented. A system of differential equations has been compiled, which makes it possible to describe the interrelation of the main structural parameters of the unit and its operating modes. The results of modeling the motion of the MEZ-330 «Autotractor» on the implementation of technological operations are given. According to the simulation results, the dependences describing the influence of the mass of the MEZ-330 «Autotractor» on the coefficient of slipping of its wheels were established. It is established that the obtained theoretical dependences are adequate and correlate with experimental data with a 95% confidence probability.

Bayesian network modeling of risk and prodromal markers of Parkinson's disease.

Parkinson's disease (PD) is characterized by a long prodromal phase with a multitude of markers indicating an increased PD risk prior to clinical diagnosis based on motor symptoms. Current PD prediction models do not consider interdependencies of single predictors, lack differentiation by subtypes of prodromal PD, and may be limited and potentially biased by confounding factors, unspecific assessment methods and restricted access to comprehensive marker data of prospective cohorts. We used prospective data of 18 established risk and prodromal markers of PD in 1178 healthy, PD-free individuals and 24 incident PD cases collected longitudinally in the Tübingen evaluation of Risk factors for Early detection of NeuroDegeneration (TREND) study at 4 visits over up to 10 years. We employed artificial intelligence (AI) to learn and quantify PD marker interdependencies via a Bayesian network (BN) with probabilistic confidence estimation using bootstrapping. The BN was employed to generate a synthetic cohort and individual marker profiles. Robust interdependencies were observed for BN edges from age to subthreshold parkinsonism and urinary dysfunction, sex to substantia nigra hyperechogenicity, depression, non-smoking and to constipation; depression to symptomatic hypotension and excessive daytime somnolence; solvent exposure to cognitive deficits and to physical inactivity; and non-smoking to physical inactivity. Conversion to PD was interdependent with prior subthreshold parkinsonism, sex and substantia nigra hyperechogenicity. Several additional interdependencies with lower probabilistic confidence were identified. Synthetic subjects generated via the BN based representation of the TREND study were realistic as assessed through multiple comparison approaches of real and synthetic data. Altogether our work demonstrates the potential of modern AI approaches (specifically BNs) both for modelling and understanding interdependencies between PD risk and prodromal markers, which are so far not accounted for in PD prediction models, as well as for generating realistic synthetic data.

SGLT2 inhibitors among patients with heart failure with preserved ejection fraction: a meta analysis of randomised controlled trials

Abstract Funding Acknowledgements Type of funding sources: None. Background Sodium glucose co-transporter 2 (SGLT2) inhibitors have been recommended in the practice guidelines for the treatment of patients with heart failure with reduced ejection fraction, however their effects among patients with preserved ejection fraction has been debatable. Objective We aim to evaluate the SGLT2 inhibitor effect among patients with HFpEF including DELIVER and EMPEROR-Preserved trials. Methods We performed a systematic literature search using the PubMed, Embase, Scopus, and Cochrane libraries for relevant articles from inception until August 30th, 2022. Statistical analysis was performed by calculating hazard ratio (HR) using the random effect model with 95% confidence interval (CI) and probability value (P). Statistical significance was met if 95% CI doesn’t cross numeric "1" and p <0.05. Results A total of 4 studies with 30418 patients (15390 SGLT2 inhibitor vs 15028 placebo) were included in our analysis. The average age and percentage of females were comparable between groups, with a mean age of 68.3 years and 39.7% of females in the SGLT2 inhibitor group, whereas 67.7 years and 40.5% of females in the placebo group. Most common comorbidities among the SGLT2 inhibitor group included diabetes mellitus (78.8% vs 78.4%). Mean follow-up duration was 2.92 years. SGLT2 inhibitors reduced composite cardiovascular death or first hospitalisation for heart failure (HR, 0.82(95%CI: 0.75-0.89), P<0.001, heart failure hospitalisation (HR, 0.74(95%CI: 0.67-0.82), P<0.001) compared with placebo. However, all-cause mortality (HR, 0.97(95%CI: 0.89-1.06), P=0.54), and cardiovascular mortality (HR, 0.96(95%CI: 0.82-1.13), P=0.66) were comparable between the both groups on SGLT2 inhibitor and placebo. Conclusion SGLT2 inhibitors reduced the risk of cardiovascular death and hospitalisation for heart failure. The results suggest patients with HFpEF have almost similar outcomes compared with previous studies on HFrEF. Hence SGLT2 inhibitors can be used among patients with reduced and preserved ejection fraction.

Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

Multi-task supply-demand prediction and reliability analysis for docked bike-sharing systems via transformer-encoder-based neural processes

With the rise of sharing economy, bike-sharing systems (BSSs) have gained heated attention, and their operations require accurate prediction of bike usage. Although many deep learning methods have been exploited to predict bike usage, they generally provide point predictions of average bike usage, neglecting the stochasticity in BSSs. Due to the analytically explainable properties and linear computational costs with respect to data size, neural processes (NPs) have recently attracted increasing interest. An NP model learns a Gaussian process (GP) by mapping the input–output observations to a probabilistic distribution over functions. Each function is a distribution of the outputs given an input, conditioned on the arbitrary size of observed data. NPs provide probabilistic confidence in predicted results, which overcomes the point prediction issue faced by other models and provides insights for operational strategies in stochastic scenarios. This paper originally proposes a transformer-encoder-based NP (TENP) model to fit the distribution of bike usage in BSSs. To the best of our knowledge, this work is among the first to incorporate transformer encoders into NPs, enhancing the capability of extracting relevant information in a targeted manner. Based on the Citi Bike datasets in New York City, the TENP method is adopted in a multi-task learning task that simultaneously fits the number of pickups and returns. The proposed TENP model outperforms the conventional NP method and its extensions and prevalent machine learning models in terms of prediction accuracy. Armed with the probabilistic confidence provided by the TENP, reliability analysis is conducted, and thoughtful guidance is provided for bike-sharing operations, such as dynamic bike rebalancing.

Gambling Under Unknown Probabilities as Proxy for Real World Decisions Under Uncertainty

The subject of decisions under uncertainty about future events, if lacking sufficient theory or data to make confident probability assessments, poses a challenge for any quantitative analysis. This article suggests one way to first look at this subject. We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler’s perceived advantage based on their perceived probability, and their accuracy in estimating true probabilities is measured by mean-squared-error. Within this framework one can study the cost of estimation errors, and seek to formalize the “obvious” notion that in competitive interactions between agents whose actions depend on their perceived probabilities, those who are more accurate at estimating probabilities will generally be more successful than those who are less accurate. This article is an extended version of the Brouwer Medal talk at the 2021 Nederlands Mathematisch Congres.

МОДЕЛЬ ОЦІНКИ МАТЕМАТИЧНОГО СПОДІВАННЯ ШВИДКОСТІ ВИТРАТИ ПАЛЬНОГО ПІДРОЗДІЛОМ ЗБРОЙНИХ СИЛ УКРАЇНИ

The study of the experience of conducting an anti-terrorist operation (ATO) and an operation of the United Forces (OUF) in the war against the Russian Federation allows us to conclude that today the use of modern means of fire damage in combination with new approaches to intelligence conducting has had a significant effect on increasing the intensity and speed of troops movement during hostilities. In such conditions, random (unforeseen) consumption of fuel may appear with a simultaneous sudden decrease in its reserves below the specified (acceptable) norms. An unexpected drop in fuel reserves in military equipment can be related to many factors and, as a result, create conditions that will not allow to perform tasks in the offensive, during the development of success and when solving other combat tasks in the next day of hostilities. In order to ensure the fulfillment of combat missions by units and subunits of the Armed Forces and to prevent the limitation of their combat capability in connection with an unforeseen shortage of fuel during the operation, there is a need to develop a mathematical model, the use of which in the future will allow to calculate the time after which the level of fuel reserves will decrease below the permissible norm, and in the dynamics of the work of the logistics headquarters, it contributes to the timely provision of the troops needs. In the article, for the first time, simple expressions were obtained for calculating the required sample volume of a random fuel consumption value in the UAF subunits and for the error of estimating the mathematical expectation of this value in the sample, which guarantees the fulfillment of the requirements for the accuracy of calculations with a sample size significantly smaller than the traditional one and without using the concepts of "confidence interval" and "confidence probability", and corresponds to the limited capabilities of the Ukraine Armed Forces subunits to collect statistics during hostilities. The developed model can be used for further development of mathematical tools for predicting possible fuel consumption, for predicting needs and for providing the troops with fuel up to the established standards in a timely manner.

Анализ тематик выпускных квалификационных работ студентов переводческих специальностей и их корреляции с потребностями рынка труда

Problem Statement. This study contains a statistical analysis of the translation market by translation type and domain and the distribution of translation student graduation project subjects. The purpose of this study is to improve the translation teaching quality through a better match between the graduation project subjects and the translation market demand. Materials and Methods. The authors reviewed the demand statistics for the Russian, EU, and US translation markets. We also collected a large database of translation graduation projects defended in Russian universities in 2018–2020. The series contains 245 projects. It covers 8 % of the relevant universities, which makes it representative with a 20 % confidence interval and 85 % confidence probability. The subjects of the graduation projects were divided into the following domains: audiovisual translation; theoretical linguistics; game and software localization; medical translation; research and technical translation; political journalism; advertising; interpretation; fiction; legal translation. Results and Discussion. It was found that the university-level translator training does not match the actual market demand. The maximum discrepancies were found in the following categories: “fiction” (21.66 % excess), “research and technical translation” (20.08 % deficiency), and “political journalism” (16.32 % excess). In addition, we analyzed the subjects of 138 graduation papers submitted to the Translator Creativity and Education International Contest in 2022. The lack of positive dynamics was found: the share of fiction reached 34.06% while the research and technical translation category reduced to just 11.59 %. Conclusions. The following corrective measures are proposed: harmonization of the graduation paper subjects with the market demand, engaging practicing translators as instructors, internships with LSPs, personalized learning paths, and interdepartmental projects.

The aircraft hydraulic system units and pipelines heat exchange parameters study

A method of mathematical simulation of the aircraft hydraulic system thermal state is proposed. The mathematical model is a system of partial differential equations for carbon-fiber composite thermal insulation and ordinary differential equations for hydraulic system elements that describe their heat exchange with the air and surrounding surfaces. To solve the direct problem of the hydraulic system elements thermal state, that is, to solve stiff ordinary differential equations, a Rosenbrock-type second order approximation numerical scheme for non-autonomous systems and the solution of a system of partial differential equations, the Monte Carlo method based on a probabilistic representation of the solution in the form of a diffusion process functional expectation were used. The inverse problem of the hydraulic system elements thermal state is solved by the composition of the steepest descent method, the Newton method and the quasi-Newton method of Broyden-Fletcher-Goldfarb-Shanno. A thermal state mathematical model of the hydraulic system unit in an aircraft unpressurized compartment has been developed and the confidence intervals of each of the required model coefficients have been estimated using 12 at a confidence probability = 0.95.

Data-Driven Stability Certificate of Interconnected Homogeneous Networks via ISS Properties

This letter is concerned with a compositional data-driven approach for stability certificate of interconnected homogeneous networks with (partially) unknown dynamics while providing 100% correctness guarantees (as opposed to probabilistic confidence). The proposed framework enjoys input-to-state stability (ISS) properties of subsystems described by ISS Lyapunov functions. In our data-driven scheme, we first reformulate the corresponding conditions of ISS Lyapunov functions as a robust optimization program (ROP). Due to appearing unknown dynamics of subsystems in the constraint of ROP, we propose a scenario optimization program (SOP) by collecting data from trajectories of each unknown subsystem. We solve SOP and construct an ISS Lyapunov function for each subsystem with unknown dynamics. We accordingly leverage a compositional technique based on -type small-gain reasoning and construct a Lyapunov function for an unknown interconnected network based on ISS Lyapunov functions of individual subsystems. We demonstrate the efficacy of our data-driven approach over a room temperature network containing 1000 rooms with unknown dynamics. Given collected data from each unknown room, we verify that the unknown interconnected network is globally asymptotically stable (GAS) with 100% correctness guarantee.

Development of physiologically-based gut absorption model for probabilistic prediction of environmental chemical bioavailability.

Absorption in the gastrointestinal tract is a key factor determining the bioavailability of chemicals after oral exposure but is frequently assumed to have a conservative value of 100% for environmental chemicals, particularly in the context of high-throughput toxicokinetics for in vitro-to-in vivo extrapolation (IVIVE). For pharmaceutical compounds, the physiologically based advanced compartmental absorption and transit (ACAT) model has been used extensively to predict gut absorption but has not generally been applied to environmental chemicals. Here we develop a probabilistic environmental compart­mental absorption and transit (PECAT) model, adapting the ACAT model to environmental chemicals. We calibrated the model parameters to human in vivo, ex vivo, and in vitro datasets of drug permeability and fractional absorption by con­sidering two key factors: (1) differences between permeability in Caco-2 cells and in vivo permeability in the jejunum, and (2) differences in in vivo permeability across different gut segments. Incorporating these factors probabilistically, we found that given Caco-2 permeability measurements, predictions of the PECAT model are consistent with the (limited) available gut absorption data for environmental chemicals. However, the substantial chemical-to-chemical variability observed in the cal­ibration data often led to wide probabilistic confidence bounds in the predicted fraction absorbed and resulting steady state blood concentration. Thus, while the PECAT model provides a statistically rigorous, physiologically based approach for incor­porating in vitro data on gut absorption into toxicokinetic modeling and IVIVE, it also highlights the need for more accurate in vitro models and data for measuring gut segment-specific in vivo permeability of environmental chemicals.

Estimation of Driver’s Gaze Region From Head Position and Orientation Using Probabilistic Confidence Regions

Visual attention is one of the most important aspects related to driver distraction. Estimating the driver’s visual attention can help a vehicle understand the awareness state of the driver, providing important contextual information. While estimating the exact gaze direction is difficult in the car environment, a coarse estimation of the visual attention can be obtained by tracking the head pose. Since the relation between head pose and gaze direction is not one-to-one, this paper proposes a formulation based on probabilistic models to create salient regions describing the driver’s visual attention. The area of the estimated region is small when the model has high confidence, which is directly learned from the data. We use <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gaussian process regression</i> (GPR) to implement the framework, comparing the performance with different regression formulations such as linear regression and neural network based methods. We evaluate these frameworks by studying the tradeoff between spatial resolution and accuracy of the probability map using naturalistic recordings collected with the UTDrive platform. We observe that the GPR method produces the best result creating accurate estimations with localized salient regions. For example, the 95% confidence region is defined by an area covering 3.77% region of a sphere surrounding the driver.

Methodological approaches to the assessment of public opinion during the overhaul of apartment buildings

In the article, using the example of a survey of residents of apartment houses (AH) on the quality of capital repairs, methodological approaches to assessing public opinion are considered. Processing the results of the survey showed that the definition of the coefficient of concordance is insufficient. It is shown that in order to assess the reliability of surveys conducted by the Delphi method, one should focus on achieving a greater confidence probability, and not on the value of the concordance coefficient. The survey showed that the priority factor for residents of apartment buildings of all ages and genders when assessing major repairs is the use of quality materials. For women of all ages, the issue of the cost of repairs was very important. Its importance for this group of respondents turned out to be almost at the level of the importance of the quality of materials. For the practical application of the results obtained, the weight coefficients of each studied factor were calculated for the total sample of respondents, which made it possible to create a methodology for express assessment of the quality of ongoing overhauls based on Harrington's verbal-numerical scales.

Математична модель емпіричного закону розподілу виходу з ладу силових трансформаторів через пошкодження обмоток

The work is devoted to the identification of the law of distribution according to statistical data of failure of power transformers of 6–10 kV due to damage to their windings for a three-year period: from 2018 to 2020. According to statistical data, it has been established that there is a tendency to reduce damage to power transformers by almost two times. But the number of these failures still remains quite large. The main cause of power transformers failure is damage to their windings, which accounts for 82.17 % of other causes. Therefore, the statistics that characterize the failure of power transformers due to damage to the windings were taken for research. It was established that in 2018 and 2019, the largest number of damages to power transformer windings occurred in April—July with a peak in June, and in 2020, the maximum damages were recorded in November and December. The prerequisite for building mathematical models for predicting the failure of power transformers due to the damage to the windings in order to ensure the necessary number of spare parts for their quick recovery is the study of the nature of the failure of transformers. The following methods were used to solve the tasks: passive experiment — to collect information about the failure of power transformers; statistical analysis — to build an empirical law of distribution. After analyzing the view of the histogram of the variation series of the sample of failure of power transformers due to damage to the windings, a hypothesis was put forward about the logarithmic normal distribution law of the failure of transformers due to damage to the windings. Pearson's c2-test was used to check it. As a result of the study, the proposed hypothesis was confirmed. Using Student's tables and the c2-distribution table with a confidence probability of g2 = 0.98, confidence intervals were determined for statistical estimates of the mean value, variance and root mean square deviation, which characterize the failure of power transformers due to damage to the windings. With further research, it will be possible to build mathematical models for predicting the failure of power transformers due to damage to the windings.

Devising a procedure for defining the general criteria of abnormal behavior of a computer system based on the improved criterion of uniformity of input data samples

The object of this study was the process of detecting anomalies in computer systems. The task to timely detect anomalies in computer systems was solved, based on a mathematical model underlying which is the criteria for uniformity of samples of input data. The necessity and possibility to devise a universal and at the same time scientifically based approach to tracking the states of the system were determined. Therefore, the purpose of this work was to develop a methodology for determining the general criterion of anomaly in the behavior of a computer system depending on the input data. This will increase the reliability of identifying the anomaly in the behavior of the system, which, in turn, should increase its safety. To solve the problem, a mathematical model for detecting anomalies in the behavior of a computer system has been built. The mathematical model differs from the well-known ones in the possibility of isolating a series of observations, the results of which show the anomaly in the behavior of the computer system. This made it possible to ensure the necessary level of reliability of the results of monitoring and research. In the process of modeling, the criteria for uniformity of samples of input data have been investigated and improved. The expediency of using the improved criterion of uniformity of samples of input data in the case of a significantly unequal distribution of values from the sensors of computer systems has been proved. An algorithm for the functioning of the software test tool has been developed. The results of the study showed that the confidence probability that the value of the statistical values of the shift in a certain criterion does not deviate from the mathematical expectation by more than 0.05 is approximately equal to 0.94. The scope of the obtained results is systems for detecting anomalies of computer systems. A necessary condition for the use of the proposed results is the presence of a series of observations of the state of the computer system

The whole slide breast histopathology image detection based on a fused model and heatmaps

The analysis of whole slide breast histopathology image is one of the most effective techniques in the current breast cancer diagnosis. However, the size of whole slide image(WSI) is too large to be processed directly by machine learning or deep learning based classifier. To solve the problem of WSI-based computer aided diagnosis, a novel classification framework with three stages is proposed in this paper to locate and classify tumor region in the whole slide images. This framework contains three parts: patch-based classification, tumor region segmentation and location, and WSI-based classification. In the period of data processing, the Cycle-GAN(Cycle Generative Adversarial Network) model is firstly adopted to normalize the colors of the images. Then an improved DPN68(Dual Path Networks) based classifier and a Swin-Transformer based classifier are combined to improve the accuracy of patch-based classification. With the malignant confidence probability output by the fused model, the whole slide heatmap is generated to segment, locate and visually display the tumor regions. Statistical features are computed and selected from the heatmap based on medical diagnosis indicators, and then an SVM(Support Vector Machines) based classifier is applied to implement WSI-based classification to further confirm the tumor. Experimental results on the Camelyon16 dataset show that our proposed framework can effectively classify the whole slide breast histopathology image with high-precision.