Applied Mathematics and Control Sciences

Digitalization of various spheres of economic and social life is accompanied by the emergence of large amounts of data, processing of which is necessary to identify certain dependencies, build models of processes and systems. The study is devoted to the development and research of a mathematical model for the classification of data on medical care in the medical organization of Lipetsk region. As inputs there were used indicators of medical care, divided into five groups (data describing patient; data describing the medical organization in which the care was provided; indicators of the disease; data on health employee that assisted; indicators characterizing the specific features of the patient's visits to a particular specialist). The volume of records on which the study was conducted is more than one million records of the facts. The purpose of the study is to propose models and approaches for identifying erroneous records, as well as cases of falsification. The paper presents a statement of the binary classification problem. Anomaly detection refers to the problem of finding data that does not correspond to some expected process behavior or indicator that occurs in the system. When building systems for detecting anomalous observations, much attention must be paid to the model underlying the system. The study is devoted to the construction of a model for detecting anomalous values of a fixed indicator based on a combination of an isolation forest algorithm to estimatie the observation anomaly index and the subsequent application of a neural network classifier. The study contains the results of computational experiments to determine the threshold value for dividing records into classes of anomalous observations and data that do not have signs of abnormality. To evaluate which factors should be passed to the input of the neural network classifier (in order to increase the time efficiency of data processing), the approach to the reduction of the neural network model based on Sensitivity Analysis was proposed. The classical approach when considering the sensitivity of systems is to find the sensitivity by the parameter of the system under study, however, there is also a direction of Sensitivity Analysis that involves using its factors as the estimated parameters of the system. The proposed approach is based on applying Analysis of Finite Fluctuation. This analysis is based on replacing the mathematical model of the dependence of the system output on factors with a model of the dependence of the finite fluctuation in output on the finite fluctuations of factors. In Mathematical Analysis such a structure is known - this is Lagrange mean value theorem. The approach allows us to determine the values of the so-called factor loads. The paper presents a new approach to averaging the obtained values of factor loads and constructing interval characteristics for their estimation. A study of the stability of the proposed procedure for calculating the sensitivity coefficients of the model is presented.

A new multi-model approach to assessing the influence of the level of intellectualization of target selection procedures on a set of alternatives implemented through the use of information management systems is proposed. The methodological basis of decision-making procedures in these systems is human intuition, which divided into two types: Inside and Intueri. The first type related to the innate natural ability of people to make choices, based on their acquired life experience and is the most common. The second type constructed in the information environment as a composition/superposition of Inside options in order to increase the level of intellectualization of target choosing procedures. It is suggested that in developing rules of output stages of decision making they should be evaluated negentropically, the unit of measurement that should be "bit". After generalizing all the output procedures, this will allow a comparative analysis of the levels of intellectualization of ranking procedures, which are a preliminary stage in the implementation of the choosing process. Multivariance of solutions to the set tasks requires solving the problem of listing effective choices, their formalizing, modeling, and developing effectiveness criteria. To solve these problems, proposed a new multi-model approach. These approaches include linguistic contextual representations of ranking procedures based on the set of meanings (semantics) and "triangles" by N. Chomsky; formal systems for listing effective ranking procedures based on generating context-free grammar in the form of metalinguistic formulas and variables; mathematical algorithms for evaluating the levels of intellectualization of choice procedures using the negentropic principle. Solution of both simple and complex tasks selection is represented as a formal output system. The focus is on three classes of intelligent selection procedures: intuition-based selection of the Inside type; procedures for building artificial intelligence with the connection of intuition like Intueri; intelligent procedures for choosing alternatives using artificial intelligence. The classes of these intellectual procedures are presented as the resultant conclusions of the same "theorem", but differ in the efficiency of performing ranking / selection tasks and the level of their intellectualization. The solution of a simple choice problem characterized by low speed, low level of non-manipulability and documentability. Low effectiveness of ranking procedures leads to the need to introduce a large number of restrictions on the complexity parameters of the choice problems to solve. A high level of intellectualization of this procedure can be reveal in a variety of classes of problems to solved, which is due to the erudition of the subject of control. Realization of the second class of intelligent procedures can become the basis for the development of various options for using artificial intelligence. When once obtained algorithmic constructions can be available for repeated use by organizing standard access to these models. There will be an effect of "amortization" as an expenditure of intellectual resource when delegating authority for a new or repeated assignment. Intelligent alternative selection procedures using artificial intelligence are decision-making algorithms designed for multiple use, within its "authority" as a limited subject area.

A political science-mathematical model has been built, designed to assess the possibility of maintaining order in the state. The model is based on a neural network trained on data on the state of many countries in different historical periods. The adequacy of the model is shown by comparing the simulation results with the real course of historical processes. The model was used to estimate the significance of the input parameters. It was found that the most significant parameters that have the greatest impact on the situation in the country are taxes, the state of the economy, and the availability of essential goods. The influence of the most significant parameters on the course of historical events is demonstrated by examples of the situation in France in the period 1629-1634 and in the Ottoman Empire during 1799-1804. Computer experiments were carried out by the scenario forecasting method: using a neural network, calculations were performed by enumerating the values of one parameter, or a small fixed group of parameters, while the values of the other parameters remained unchanged. An attempt has been made to predict the development of the situation in Venezuela for the next five years. A large number of options for forecasts of the development of events were carried out, depending on various combinations of possible measures taken by the government to stabilize the situation. Based on these forecasts, the most effective measures were selected to reduce tensions in the country. The practical value of the study lies in the fact that the created political science and mathematical model can be used to assess the possibility of maintaining order in modern states and to determine the steps necessary to prevent or trigger revolutions, civil wars, etc.

At the moment, there is an increase in the importance of efficiency in another sector of the economy. Evaluating the efficiency of an enterprise makes it possible to implement a correct and profitable resource allocation strategy, which shows its potential level. In connection with the annual increase in the number of bankrupt enterprises, the problem of assessing the efficiency of enterprises' activities is relevant both for their owners and managers, and for creditors. There are various methods and models for assessing the efficiency of enterprises. One study focuses on the improvement of a parametric method for assessing the performance of objects - the SFA (Stochastic Frontier Analysis) method. The classical SFA method is based on the production function of an enterprise, linking the volume of output with the volume of consumed resources. In this case, the SFA model uses several input (volumes of consumed resources) and only one output parameter - the volume of output. The essence of the proposed modification of the model based on the SFA method is to use financial indicators of enterprises' activities instead of data on consumed resources and output, on the basis of evaluating the financial activity of the economic objects under study. The developed model of the situation for assessing the efficiency of the enterprise in terms of its financial indicators.

In the issue we consider socio-economic processes modeling based on first and second order finite differences models. Since commonly used modeling methods have drawbacks and thus are not universal it was necessary to develop alternative methods which are better in some aspects. Specifically multiple linear regression models have limited prediction abilities, and differential regression coefficient evaluation method is quite complex and have some economically uninterpreted excess tunings. In our research we replaced first and second order derivatives in differential regression models with their finite differences equivalents and thus gained a multiple linear regression model modification which includes first and second order auto regression items. Estimation of their parameters can be done using a modification of least-squares method in which we demand that factor coefficients signs for models with and without auto regression items are the same. Due to additional items in the modified linear regression models their approximation capacity is greater than of a common model. However for application purposes model forecasting capacity is more important, i.e. the forecasting efficiency criterion is the most significant for a decision making. In order to estimate forecasting potential of modified multiple linear regression models we performed coefficient estimation of unmodified and modified equations for 59 various socio-economic data sets. We used shortened time series, so we could calculate model values and compare them to actual data. It was determined that modified multiple linear regression models allowed to make better predictions in 49 (76.3 %) cases. We can now assume that addition of auto regression items into multiple linear regression model can increase short-term forecasting efficiency.