Kolmogorov-Gabor Polynomial Research Articles

Predicting COVID-19 Hospital Stays with Kolmogorov–Gabor Polynomials: Charting the Future of Care

Optimal allocation of ward beds is crucial given the respiratory nature of COVID-19, which necessitates urgent hospitalization for certain patients. Several governments have leveraged technology to mitigate the pandemic’s adverse impacts. Based on clinical and demographic variables assessed upon admission, this study predicts the length of stay (LOS) for COVID-19 patients in hospitals. The Kolmogorov–Gabor polynomial (a.k.a., Volterra functional series) was trained using regularized least squares and validated on a dataset of 1600 COVID-19 patients admitted to Khorshid Hospital in the central province of Iran, and the five-fold internal cross-validated results were presented. The Volterra method provides flexibility, interactions among variables, and robustness. The most important features of the LOS prediction system were inflammatory markers, bicarbonate (HCO3), and fever—the adj. R2 and Concordance Correlation Coefficients were 0.81 [95% CI: 0.79–0.84] and 0.94 [0.93–0.95], respectively. The estimation bias was not statistically significant (p-value = 0.777; paired-sample t-test). The system was further analyzed to predict “normal” LOS ≤ 7 days versus “prolonged” LOS > 7 days groups. It showed excellent balanced diagnostic accuracy and agreement rate. However, temporal and spatial validation must be considered to generalize the model. This contribution is hoped to pave the way for hospitals and healthcare providers to manage their resources better.

Patterns of winter wheat ear productivity formation depending on the content of trace elements in the soil

The study of patterns of the formation of ear productivity depending on the content of potentially bioavailable Fe, Mn, Zn, Cu in the soil, the stochastic formalization of such patterns are important for a more profound understanding of the conceptual and mechanistic aspects of the dependence of yield development on the levels of nutrient supply of winter wheat under the conditions of environmentally friendly fertilization systems. The purpose of this study was to find statistically significant interdependencies, significant and relevant univariate or multivariate regression equations of the dependence of the mass of grains of ear-1 of winter wheat on the content of potentially bioavailable Fe, Mn, Zn, Cu in the soil, arguments and explanations of such subordinations under the conditions of environmentally friendly fertilization systems. The following methods were used in the study: field, laboratoryanalytical, mass-spectrometric, mathematical-statistical (Student’s t-test, ANOVA, correlational, single- and multivariate regression analyses). The applied green fertilization systems based on pea straw or pea straw + N30P45K45, or N60P90K90, only N60P90K90 caused an increase in the weight of grains of one ear of winter wheat, the content of mobile forms of Fe, Mn, Zn, Cu in the grey forest soil under this culture (earing phase), compared to the control (without fertilizers). Substantial and significant Pearson correlation coefficients between the mass of grains of an ear of wheat and the content of mobile Fe, Mn, Zn, Cu in the soil, the corresponding contents of Mn and Zn, Cu and Zn, as well as the coefficients of partial correlation of the mass of grains of ear-1 of wheat – Cu, Mn – Zn testified to the complex structure of interdependencies between the traits under study. Reliable, relevant single- and multifactorial regression dependences of the mass of grains of ear-1 on linear combinations of products of independent variables (the content of mobile Fe, Mn, Zn, Cu in the soil) and/or such variables in indicators of natural powers 2-4 (fragments of the Kolmogorov-Gabor polynomial) were found. The coverage of regularities in the formation of the productivity of the ear of winter wheat depending on the content of potentially bioavailable microelements in the soil under the conditions of environmentally friendly fertilization systems will enable the theoretical substantiation and development of the latest strategies of mineral and ecological engineering of agricultural systems to maintain prominent levels and biological safety of the harvest of the specified crop

The Impact of the Organization of Public Health Systems on the Ability of Countries to Resist the COVID-19 Pandemic: The Experience of Developed Countries of the World and Ukraine.

The purpose of the study is to analyze the presence of functional interrelationships between the level of funding of the healthcare sector and the country's ability to withstand any pandemic, using the example of the COVID-19 pandemic. Official indicators presented by the WHO, analytical reports by Numbeo (the world's largest cost-of-living database), and the Global Health Security Index were used for the study. Using these indicators, the authors analyzed the following: the level of the spread of coronavirus infections in the world's countries, the share of public expenditures on the development of the medical sphere in the GDP of the countries, and the development of the healthcare sector in 12 developed countries and Ukraine. These countries were grouped into three groups, based on the model of the organization of the healthcare sector (Beveridge model, Bismark model, Market (private) model). The Farrar-Glauber method was used to check for multicollinearity in the input dataset, and thirteen relevant indicators were selected. These indicators took part in the formation of the generalized characteristics of the country's medical sphere and the ability to resist the pandemic. The state of readiness of countries to resist the spread of coronavirus infections was assessed using the country's index of vulnerability to COVID-19 and the integral index of the development of medicine. Additive convolution was used in combination with sigma-limited parameterization to form an integral index of the country's vulnerability to COVID-19 and to determine the weights of each indicator. The convolution of indicators according to the Kolmogorov-Gabor polynomial was used to construct an integral index of the development of medicine. Thus, while analyzing the ability of countries to resist the pandemic in terms of models of organization of the healthcare sector, it should be noted that none of the models demonstrated absolute effectiveness in the fight against the mass spread of COVID-19. The calculations made it possible to determine the nature of the relationship between the integral indices of the development of medicine and the vulnerability of countries to COVID-19, as well as a country's potential ability to resist any pandemic and prevent the mass spread of infectious diseases.

Predicting hydrodynamic forces on heave plates using a data-driven modelling architecture

Prior work has modelled heave forces on surface piercing bodies in real time for 2D, convex and static geometries using a Hammerstein framework. In this work, the modifications needed to make that framework suitable for a representative heave plate geometry in irregular waves are investigated in order to facilitate force prediction for heaving wave energy converters. Two candidate models are compared. The first introduces a Bouc–Wen model to the conventional internal force calculation in the Hammerstein framework. The second further modifies the dynamic block by replacing the linear ARX dynamic calculation with a nonlinear Kolmogorov–Gabor polynomial (KGP) structure. The addition of the Bouc–Wen model introduces velocity and acceleration dependence and a new hysteresis contribution to the internal force predictions to capture the form drag and inertial loads known to occur around heave plates from the entrained fluid. This addition reduces the average error in the internal force calculation by up to 70% for kinematically controlled bodies in irregular waves. Using the revised internal force in the system dynamic block identification process, it was found that the resulting models provided significant improvements (up to 38%) in prediction of the hydrodynamic heave force when using both the linear and nonlinear ARX formulations.

Mathematical model of structural and topological optimization of logistics networks

The subject of research in the article is the topological structures of closed-loop logistics networks. The goal of the article is to increase the efficiency of centralized logistics networks by developing a mathematical model for a two-criteria problem of optimizing topological structures in the process of their reengineering. The article solves the following tasks: analysis of the current state of the problem of structural and topological optimization of logistics networks; formalization of the problem of optimization of logistics networks as geographically distributed objects; synthesis of objective functions of the mathematical model of a two-criterion optimization problem for centralized three-level topological structures of closed logistics networks at the reengineering stage; development of a system of constraints of the mathematical model of the problem of optimizing centralized three-level topological structures of closed logistics networks; a function for evaluating the overall utility of options based on the Kolmogorov-Gabor polynomial is offered. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: the analysis of the current state of the problem of system optimization of logistics networks, mathematical models and methods for its solution was carried out; formalization of the problem of structural and topological optimization of logistics networks as geographically distributed objects; a mathematical model of a two-criterion task of reengineering of three-level topological structures of logistics networks in terms of costs and efficiency with integrated points of production and processing has been developed (originality). Conclusions: Based on the results of the analysis of the problem of optimizing the topological structures of logistics systems, it has been established that the problems of direct and reverse logistics are still considered as conditionally independent, which does not allow obtaining effective global solutions. In the context of expanding the network of consumers, changes in delivery volumes, the introduction of environmental restrictions, it is proposed to reengineer the networks, which provides for their radical redesign. The formulated statement and the developed mathematical model of a two-criterion (in terms of cost and efficiency) optimization problem for three-level topological structures for combined production and processing points will increase the efficiency of logistics networks with reverse flows by reducing the cost of reengineering (practical value).

COMPARATOR IDENTIFICATION OF THE MULTI-FACTOR EVALUATION MODEL OF ALTERNATIVES USING THE BAGGING METHOD

Proponent one step before the solution of the problem to induce a mathematical model of a multi-factor assessment of alternatives, which is based on the ideas of the theory of comparator identification. Methods of structural and parametric identification are seen. The structure of the model is established within the framework of the Kolmogorov-Gabor polynomial, which allows the synthesis of both traditional additive and multiplicative, as well as models of a multi-factor assessment of alternatives to present folding. To increase the accuracy of the model, a victorious ensemble of models is proposed, aggregating that work on the basis of the running method. The results of a computer model have been introduced, which will confirm the effectiveness of the described approach. Propagation of ideas based on the prospect of advancing the effectiveness of the identification of models for expert assessment of alternatives.

Identification of dynamic models for a wave energy converter from experimental data

This paper addresses the issue of hydrodynamic model identification from recorded tank test data, for a prototype wave energy device. The study focusses on nonlinear Kolmogorov–Gabor polynomial models, with linear models also used as a baseline reference. Six different experimental data sets are employed for model identification and validation, all derived from a JONSWAP input sea state. Compared to identification on numerical data, this study shows that the determination of model structure and orders is not so straightforward, but that consistent and useful computationally efficient models can be obtained. For the particular tests undertaken, in which the prototype device generally behaves as a wave follower, the nonlinear models only show very marginal performance improvement over the linear ones.

Development of the Non-Iterative Supervised Learning Predictor Based on the Ito Decomposition and SGTM Neural-Like Structure for Managing Medical Insurance Costs

The paper describes a new non-iterative linear supervised learning predictor. It is based on the use of Ito decomposition and the neural-like structure of the successive geometric transformations model (SGTM). Ito decomposition (Kolmogorov–Gabor polynomial) is used to extend the inputs of the SGTM neural-like structure. This provides high approximation properties for solving various tasks. The search for the coefficients of this polynomial is carried out using the fast, non-iterative training algorithm of the SGTM linear neural-like structure. The developed method provides high speed and increased generalization properties. The simulation of the developed method’s work for solving the medical insurance costs prediction task showed a significant increase in accuracy compared with existing methods (common SGTM neural-like structure, multilayer perceptron, Support Vector Machine, adaptive boosting, linear regression). Given the above, the developed method can be used to process large amounts of data from a variety of industries (medicine, materials science, economics, etc.) to improve the accuracy and speed of their processing.

Development of machine learning method of titanium alloy properties identification in additive technologies

Based on the experimentally established data on the parameters of microstructure, elemental and fractional composition of titanium alloy powders, four classes of their conformity (a material with excellent properties, optimal properties, possible defects in the material and defective material) as source raw materials for the additive technologies are identified. The basic characteristics of the material, which determine its belonging to a certain class, are established. Training and test samples based on 20 features that characterize each of the four classes of titanium alloy powders for the implementation of machine learning procedures were built. The developed method for identification of the class of material, based on the use of the second-order Kolmogorov-Gabor polynomial and the Random Forest algorithm, is described. An experimental comparison of the developed method work results with existing methods: Random Forest, Logistic Regression, and Support Vectors Machines based on the accuracy of their work in the training and application modes was made. The visualization of the results of all the investigated methods was given. The developed supervised learning method allows constructing models for processing a large number of each input vector characteristics. In this case, the Random Forest algorithm provides satisfactory generalization properties while retaining the advantages of an additional increase of the accuracy based on the Kolmogorov-Gabor polynomial. The main advantages of the developed method, in particular, regarding the additional increase of the accuracy of the classification task solution, are experimentally determined. The developed method allows increasing the modeling accuracy by 34.38, 33.34 and 3.13 % compared with the methods: Support Vectors Machine, Logistic Regression, and Random Forest respectively. The obtained results allow one to considerably reduce financial and time expenses during the manufacture of products by additive technologies methods. The use of artificial intelligence tools can reduce the complexity and energy efficiency of experiments to determine the optimum characteristics of powder materials.

Development of neural network model of the multiparametric technological object

At present, there are a large number of methods for identifying the technological objects on the basis of data of their industrial operation [1-3]. The most promising direction is the construction of a model, which will allow to take into account the multifactorial nature of the object, and the nonlinearity of interrelation between variables. This will make it possible to control the object, taking into account the change in its states, and based on the current data,to predict the change in the output value with different input characteristics[4-6]. All this will provide the opportunity to create an operating system, based on the currently measured technological indicators. In order to implement this approach, a comparative study of the regression analysis models, using polynomials of various types and neural network algorithms, for the synthesis of a complex technological unit model, was carried out in the work. In the regression analysis, the following models were investigated: polynomials, linear, fractional and exponential functions, Kolmogorov-Gabor polynomial. In the process of the research of neural networks to solve this problem, their structure was varied, with subsequent learning according to the Levenberg-Marcardt algorithm. In the process of simulation of the object models in the Matlab package, the degree of similarity of the outputs for each of the obtained models and the actual output of the object were estimated. Quadratic criterion and the coefficient of correlation were calculated, that made it possible to judge the accuracy of the constructed models. The best structure of the model was established for identifying a complex multiparameter object, using the example of statistics for the operation of a ball mill. It was a network with three hidden layers and 50, 35 and 25 neurons in them, with activation functions, respectively by layers - hyperbolic tangent, sigmoid function in 2 layers, and a linear activation function in the output layer. The vector, including 15 parameters, was supplied to the network input: the volume of ore supply to the mill, the volume of water supply to the mill and the mill’strommel, the signals with the first-, the second-, and the third-order lags, and the signal of current with the first-, the second-, and the third-order lags. This approach to identification has increased the accuracy of the object model, that ultimately will affect the quality of the developed control system of the unit as a whole, allowing to improve the quality of the ball millcontrol.

PARAMETRIC SYNTHESIS OF MODELS FOR MULTICRITERIAL ESTIMATION OF TECHNOLOGICAL SYSTEMS

The subject matter of the article is the problem of multicriteria estimation of the properties of technological systems (TS) in the process of their structural-parametric optimization. The goal of the study is to increase the efficiency of procedures for multicriteria estimation of TS properties at the stages of their design and reengineering using the technology of comparative parametric identification of the preferences of a decision maker. The objectives are: to increase the adequacy of the additive-multiplicative model of multifactor estimation of variants of building a TS based on the Kolmogorov-Gabor polynomial; to develop an efficient method of parametric synthesis of additive-multiplicative models of multifactor estimating and selecting variants of building a TS based on a decision maker’s preferences; to carry out the analysis and give recommendations on the practical use of the suggested method of parametric synthesis of models of multicriteria TS estimation. The methods used are: system analysis, decision theory, identification theory, multicriteria optimization methods. The following results are obtained: to increase the adequacy of the models of TS multifactor estimation, it is suggested to use the utility function of partial criteria that makes it possible to realize not only linear, convex or concave, but also S (Z)-like dependencies on their values. To solve the problem of parametric synthesis of models of multicriteria TS estimation, the method of comparative identification of a decision maker’s preferences is improved on the basis of the procedures for calculating the Chebyshev point and the residual vector. The experimental study of the efficiency of the suggested variant of the method is carried out. Conclusions. The application of the suggested function in additive-multiplicative models of TS multi-factor estimation does not change the methods for selecting their parameters. The suggested improvement of the method of comparative identification of a decision maker’s preferences on the basis of the procedures for calculating the Chebyshev point and the residual vector for the parametric synthesis of models of TS multicriteria estimation enables covering all practically important situations of selection described by binary relations of equivalence, strict, and nonstrict preferences. The experimental study of the method confirms the increase in the efficiency of the procedures of parametric synthesis of models built on its basis in comparison with the method of group accounting of arguments on the basis of genetic algorithms. Practical application of the results obtained in the support systems for making multicriteria design and management decisions will improve their accuracy and, on this basis, increase the functional and cost efficiency of modern TS.

A systematic approach to the synthesis of forecasting mathematical models for interrelated non-stationary time series

The study presents a schematic diagram suitable to describe almost any presently known combined, hybrid or decomposition model for forecasting time series. The diagram has laid the basis for the suggested methods of structural identification of sparse nonlinear models of interrelated non-stationary time series on the basis of “Caterpillar”-SSA methods, fast orthogonal search, a group accounting method, and SARIMA models. Often a plurality of measured features is insufficient for building a model of satisfactory quality. It is necessary to extend the set of features by means of functional transformations of initial signs to decrease the uncertainty of the linear model. The study suggests that components of the “Caterpillar”-SSA method expansion, applied to the forecast and exogenous time series, should be viewed as generated variables. In one of the suggested models, the method of fast orthogonal search is used for optimal thinning. In the other––the method of group arguments accounting is applied to thin the Kolmogorov-Gabor polynomial, which is built on the expansion components of the “Caterpillar”-SSA method that is applied to the forecast and exogenous time series. To correct the forecasts in both models, we used the seasonal model of auto-regression––the integrated moving average. The analysis and modeling of the considered method prove its effectiveness in the search of an optimal model structure, and the time for determining the model parameters considerably shortens alongside. Therefore, a systematic approach is a set of methods and tools that facilitates overall researching of the properties and structure of the interrelated non-stationary time series and presents them as systems with all complex inter-element relationships.

Modified Criterion for Economic Efficiency Estimation of Heat Pumps

In this work the cost-effectiveness of coal mine waste water low potential heat utilization and integration in the enterprise local heating network by the bivalent parallel scheme is investigated. It is shown that the additive criterion of economic efficiency is not always sensitive to the target value because of the reason of non-linear coupling between the arguments of the target function. Several cases were considered from the viewpoint of cost-effectiveness criterion. Moreover, the arguments of the target function are also nonlinear, depending on technological parameters of the heat pump (HP) equipment. As a more effective criteria were proposed the modified canonical additive-multiplicative function and Kolmogorov-Gabor polynomial function to obtain the generalized multivariate estimation of alternatives in two stages procedure.

Using Genetic Algorithms for Solving the Comparison-Based Identification Problem of Multifactor Estimation Model

In this paper the statement and the methods for solving the comparison-based structure-parametric identification problem of multifactor estimation model are addressed. A new method that combines heuristics methods with genetic algorithms is proposed to solve the problem. In order to overcome some disadvantages of using the classical utility functions, the use of nonlinear Kolmogorov-Gabor polynomial, which contains in its composition the first as well as higher characteristics degrees and all their possible combinations is proposed in this paper. The use of nonlinear methods for identification of the multifactor estimation model showed that the use of this new technique, using as a utility function the nonlinear Kolmogorov-Gabor polynomial and the use of genetic algorithms to calculate the weights, gives a considerable saving in time and accuracy performance. This method is also simpler and more evident for the decision maker (DM) than other methods.

Performance Assessment for a Class of Nonlinear Systems

In this paper, a class of specified nonlinear systems are concerned. The nonlinear process model can be considered as a simplified Kolmogorov–Gabor polynomial model, which is motivated by considering the actuator nonlinearity and the process output nonlinearity. In terms of this nonlinear system, the analytical performance benchmark and the associated benchmark controller are established by minimizing the variance of the measurement output. The existence conditions of feedback invariant are discussed. The calculation of performance index, based on correlation analysis, is proposed. To facilitate assessment, a filtering or whitening method is presented. The white noise sequence is estimated by dynamic principal component analysis (DPCA), based on the nonlinear autoregressive exogenous (NARX) model. The numerical examples are given to illustrate the effectiveness of the proposed assessment method.

Forecasting with Nonlinear Time Series Models

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econometrics are presented and some of their properties discussed. This includes two models based on universal approximators: the Kolmogorov-Gabor polynomial model and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive)method for this purpose is mentioned as well. Forecasting with complex dynamic systems, albeit less frequently applied to economic forecasting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using differenttime series models are discussed, and the paper also contains a small imulation study comparing recursive and direct forecasts in a particular case where the data-generating process is a simple artificial neural network model. Suggestions for further reading conclude the paper.