Algebraic Model Of Constructive Logic Research Articles

ОЦЕНКА ЗАВИСИМОСТИ СРЕДНЕЙ ПРОДОЛЖИТЕЛЬНОСТИ ЖИЗНИ НАСЕЛЕНИЯ ТУЛЬСКОЙ ОБЛАСТИ, ПРОЖИВАЮЩЕГО НА ТЕРРИТОРИЯХ С ВЫСОКИМ СОДЕРЖАНИЕМ ТЯЖЕЛЫХ МЕТАЛЛОВ В ПОЧВЕ

The article presents the relevance of the problem, defines the research purpose: to compare the average life expectancy of the population in the areas of the Tula region with different contents of heavy metals in the class of causes of death “Respiratory diseases ”. The authors used the data of the regional mortality register, the results of analyzes of the content of heavy metals (copper, lead, zinc, nickel) in the soil by atomic absorption spectroscopy, and the calculation of the average life expectancy by the algebraic model of constructive logic. The results indicate a decrease in average life expectancy due to the presence of heavy metals in the soil, but the average life expectancy in both contaminated and non-contaminated areas is gradually increasing.

Metrological assessment of the averaged phase cardiocycle in solving problems of rehabilitation and sports medicine

To determine the possibility of measuring the myocardial biosignal using the averaged cardiocycle of a single-channel ECG in the phase space. Registration and analysis of the averaged biosignal obtained by converting a single-channel ECG in phase space, taking into account age and gender characteristics, was carried out using the FAZAGRAF software and hardware complex, which implements the original information technology for processing an electrocardiogram in phase space using computer graphics ideas and automatic pattern recognition methods. The parameters of the phase averaged cycle were subject to an analytical assessment: duration and amplitude characteristics of the P, Q, R, S, T waves (ms). The construction of a nonlinear mathematical model is carried out using an algebraic model of constructive logic based on predicate logic, followed by a multivariate assessment of the influence of each factor. The massive of verified data is represented by 58 016 values of indicators of the cardiovascular system in 1568 study participants aged 20 to 65 years. All subjects were divided into 2 groups: group 1 - 1087 conditionally healthy patients, group 2 - 471 patients with a verified diagnosis of pathology of the cardiovascular system. The information content of the QTc indicator was determined using ROC analysis. The age-related features of some parameters of the averaged phase cycle were examined in a cohort of 218 conditionally healthy schoolchildren aged 6-17 in Simferopol. The study of the adaptive features of the circulatory system was carried out in 40 sportsmen aged 14-15 with different profile orientation of training activity, which was divided into 2 cohorts. The first cohort included 20 wrestlers, the second - amounted to 20 football players. The gender characteristics of the reaction to natural aroma effects were studied in 30 conditionally healthy young people aged 17-18 (15 boys and 15 girls). The most significant parameters of the averaged phase cardiocycle for assessing the states and characteristics of their values were revealed. The obtained parameters of the averaged phase cardiocycle with a quantitative assessment of ranges with a significant number of subjects were used to solve preventive (predictive) problems of rehabilitation and sports medicine.

Подготовка данных для многофакторного анализа в медицине и биологии с помощью алгебраической модели конструктивной логики

An algebraic model of constructive logic is intended to build multivariate non-linear logical mathematical model and is widely used in analytical studies in medicine and biology. An important stage of its construction is the data preparation in accordance with the following requirements:
 ▪ The optimal choice of the analyzed factors with the following features: the pursuit of the researcher to involve the largest possible number of factors is a common mistake; factors must be independent; it is advisable to select only those factors that meet the research objectives; the ability of the algorithm to exclude certain fac-tors from the resulting mathematical model, it is observed, when the array of data input is sufficiently complete; the ability to use both continuous variables and discrete; the mathematical model is a more compact, if less factors are used, this model is easier to analyze and identify the characteristics of the test process.
 ▪ Verification of the data is the identification and correction of errors at the stage of entering the informa-tion into the database; using the built-in intelligent tools that facilitate the process of correct coding of medical information; additional data verification by using special techniques, such as the analytical testing method in the database records.
 ▪ Selecting of objective study with the following features: the goal can be represented not only two dis-crete (the goal is achieved or not achieved), but also a large number of them; the more discrete, the amount of base should be larger; possibility to use calculated target value by using various criteria.
 ▪ Presence of the necessary number of entries for a full analysis, it is necessary to ensure compliance with each of the target case (corresponding to the goal) at least two cases of non-target (not corresponding to the goal).
 ▪ Choice of software options is adequate available data.
 These requirements will allow to performing the analytical studies in accordance with the required relia-bility.

Целевая направленность многофакторного анализа с использованием алгебраической модели конструктивной логики

Multivariate analysis, including algebraic model of constructive logic, is often used in medical practice and biological research. To carry out such studies, it is necessary a array of source information (analyzed cases) and purpose, which is most often selected one of the values of the factors. At the same time, in the practice of analytical calculations there are cases when the target value cannot be set explicitly. The aim of this work is to provide a method of calculating target values for specific cases of morbidity and mortality.
 The proposed method is based on counting the number of instances of each value of each factor and their share in the total number of cases. The product of the assessed values of each involved factor, compared with the set of the threshold value, determines a value corresponding to the achievement of the goal. To confirm the proposed method on the array of 208269 deaths, the authors built a mathematical model using algebraic model of constructive logic. Evaluation of a mathematical model confirmed the performance of the proposed method of calculating the target value, since the simulation results are most consistent with known estimates obtained by other methods.

Формирование аналитических массивов данных для многофакторного анализа с использованием алгебраической модели конструктивной логики

Mathematical device of algebraic model of constructive logic has been used for many years for multivariate analysis in medicine and biology. The resulting mathematical model is represented by a set of output components in the form of factors indicating the detection restrictions, which are united by the sign of con-junction (indicating joint influence). Each resulting component is characterized by a capacity, which is the es-sence of the number of rows in the table with the same factors and their intervals of definition. These capacities characterize the degree of influence of the resulting component on the overall result. The input table must not contain contradictions (when the goal is achieved and not achieved when the same values of the factors). For this purpose, the computer program provides for an exception to those target lines, which coincide with non-target rows. However, this is not always acceptable in cases of a large number of matching target lines and unit numbers of non-target rows or vice versa, because a large number of cases is excluded because of a single non-target rows or single target lines. These contradictions arise, primarily, due to the probabilistic nature of the cases. This is clearly seen in the monitoring of mortality.
 In this article the authors propose three ways optimum yield conflicting source data, based on the excess multiplicity of frequencies matching target and non-target cases and estimates of confidence intervals. The pro-posed methods are examined by analyzing data on deaths of persons aged 18 years and older, residents of the Tula region for 2007-2014 (total 208269 cases). An age cohort 45-54 years is a goal of study.
 The application of methods of optimum yield conflicting source data is a necessity, which not only im-proves the mathematical model, but, in some cases, is the only way to perform multivariate analysis. All pro-posed methods have their own scope of use, depending on the circumstances.

К вопросу прогнозирования показателей смертности в Тульской области

Despite the positive trend to a decrease in the mortality rate from the Tula region remains high compared to middle-russian indicator. The decline in mortality is included in the Concept target demographic policy of the Russian Federation until 2025. It can be achieved by reducing mortality by leading causes of death, such as cardiovascular diseases and cancer and injuries. The aim is to study the influence of environmental fac- tors on mortality and the choice of method for predicting mortality. When forecasting the following methods: regression analysis, algebraic model of constructive logic, group method of artificial neural networks. We used and analyzed mortality rates for 1996 - 2012 years, as well as details of the radiation situation, air emissions, soil and water, do not meet state standards. The study found that the greatest impact on mortality have not meet state standards food, the release of pollutants into the atmosphere and content of radionuclides in food. It was found that the method of stepwise regression reveals multifactor linear relationship. However, in the case of the nonli- near dependence of the method little- competent, and require the use of other methods of forecasting, such as neural networks.

Совершенствование методов исследования здоровья населения с использованием алгебраической модели конструктивной логики

Algebraic model of constructive logic is developed in Russia and is used for many years in medicine and biology for multivariate analysis and for building expert systems. In the process of improving the algorithm of the algebraic model of constructive logic and software, the methods of the study of population health with the use of these models are improved. The tasks of providing a compact representation of the mathematical model are solved, the version of algorithms and programs with different reaction to incomplete source data is created, an analytical and methodological support of research is developed. The article presents the results of practical work to improve the working methods of the study of population health. It covers the issues of verification of source data, an obtainment a compact mathematical models, the valuation and completeness of the source data, the main highlight of the resulting components, the exclusion of inconsistencies in the source data, the absorption of the analyzed factors, the principles of the analysis of the factors in mathematical models and principles of construction of expert systems. The authors showed that the classical and modernized versions of the algebraic model of constructive logic have their applications and are not exclusive of each other. This article also provides recommendations and explanations that facilitate the realization of analytical studies using algebraic models of constructive logic.

Способ выявления ограничений анализируемого метода лечения с помощью алгебраической модели конструктивной логики на примере гипербарической оксигенотерапии при онкогинекологической патологии

Mathematical device of algebraic model of constructive logic has been used for many years for multivariate analysis in medicine and biology most often to identify causal relationships. This mathematical apparatus can be used for more complex analysis schemes for the purpose of determining the contingent of patients who require this method of treatment. The proposed method is a two-step analysis using algebraic model of constructive logic with different specified purposes and subsequent analysis of the resulting final components of the mathematical model. As a result, it is possible to identify restrictions and to quantify the number of patients who need to analyzed method of treatment. The proposed method is explained by an analytical study of hyperbaric oxygen therapy in oncological pathology. Analysis of the results revealed 7,87-39,35% of patients requiring hyperbaric oxygen therapy. The authors revealed the restrictions presented resulting final components of the mathematical model in the form of limits of detection of the combined factors. The equity analysis of values of the resulting components of the mathematical model is associated with the need to calculate the maximum possible total power of the resulting components of the mathematical model, used in expert systems.

Совершенствование алгоритма алгебраической модели конструктивной логики

For many years, algebraic constructive logic model is used for multivariate analysis in medicine and biology. The classic version of this model includes the exclusion of contradictory accounts, i.e. when the target is achieved and not achieved in the presence of the same values of the factors. In this case, the lines as appropriate to achieving target, and its failure are removed, including significant proportions. Another feature of this algorithm is the partial overlap of the intervals to determine the factors resulting in components in achieving a target and not achieving despite the exclusion of contradictory accounts. The authors explain this by the fact that the classical algorithm generates the detection limits of the factors in resulting components with some capture values that are related to the lines of not achieving the target (up to inappropriate values). To some extent this reduces the accuracy of the mathematical model. A further feature of the algorithm is the necessary to optimize mathematical model by excluding re-coating lines. This is acceptable, but not optimal. This requires additional procedures at the final stage of formation of the mathematical model.
 
 The proposed version of the algebraic model of constructive logic allows to eliminating the above drawbacks. This is achieved the measure of approximation and a way of combining the cases in the resulting components. The proposed algorithm was tested using specially designed software that allows to exclude controversial cases and to form a mathematical model. Testing showed that the proposed algorithm is better than the classic version and meets the objectives of multivariate analysis in medicine and biology.

Гендерные особенности смертности больных сахарным диабетом в Тульской области

A multivariate analysis of mortality of inhabitants of the Tula region from diabetes was carried out. In the analysis the authors used data from the register of population mortality 184 646 deaths for the period 2007 to 2013; in 3424 cases the initial cause of death was diabetes mellitus. The reliability of the coding of multiple causes of death was achieved by the module acme.exe (CDC, USA) automatically determination of the initial cause of death register of death, and by analytical testing. On the basis of these data using the upgraded version of the algebraic model of constructive logic, the authors created a mathematical model.
 
 Analysis of the obtained mathematical model demonstrates that the mortality of women of 20.9 times higher than the mortality of men, 36.7% were between the ages of 60-64 years and 31.7% were aged 70-74 years. Women in a registered marriage, died a decade early in comparison with unmarried, mostly aged 60-64 years - 49,2%, 65-69 years is 14.5%, 70-74 years - 18.7%. Among unmarried women, the critical age was five years from 70-74 years, death occurred in 56.1% of women.
 
 Women (among married women 67,7% and among unmarried 61.4%) had no education.
 
 There was greatest number of deaths among women with the general education, among men with professional primary education. The greatest number of deaths was in married women with general basic education.

Оптимизация базы данных для многофакторного анализа с помощью алгебраической модели конструктивной логики

The paper considers the stage of preparing the database for multi-factor analysis by means of the algebraic model of constructive logic that has been used successfully since 1999 to perform the analysis in medicine and biology. Initial data for model building is a table. Each line in this table is treated as a case where the values of factors and their impacts are marked. The resulting model is represented by a set of result components in the form of factors indicating the limit of detection combined by conjunction sing (pointing to the combined effect). Each resulting component is characterized by the capacity is the essence of the number of lines in the table, which correspond to the specified limits of determining factors in their joint action. The resulting logical expression is characterized by a combination of factors (indicating the detection limits of each of them) in their capacity as the degree of influence on the result. The initial table data should not have contradictions (when the aim is achieved and isn´t achieved by the same values of the factors). To this aim, the program envisages the exception of those targeted lines of which coincide with non-target strings. However, this isn´t always acceptable
 
 in cases of a large number of matching target lines and the singular numbers of non-target strings. Then a large number of cases due to the single non-target line are excluded. The analysis of the coincidences of target and non-target lines to select a single non-target line, to remove them from the database on the example of connective tissue dysplasia with magnesium therapy has been proposed. Comparative analysis of the obtained mathematical models was carried out. The effect of improvement of mathematical model on the basis of algebraic model of constructive logic was demonstrated.

Программа для выделения главных результирующих составляющих в алгебраической модели конструктивной логики

The article presents the program to determine the principal components resulting in the algebraic model of constructive logic, which is designed for construction multivariate nonlinear mathematical models. The resulting mathematical model is represented by a set of resulting components as factors indicating the detection limits, combined mark of conjunction (indicating joint impact). Each resulting component is characterized by power, which is the essence of the number of rows in the table that match the specified detection limits factors in their joint action. The program provides two methods to determine the main result components. The first method is based on determining the minimum difference between increasing amounts of capacity resulting components of the top and bottom. The second method is based on the determination of the inflection point of the curve decreasing capacity of the resulting components. The authors give recommendations on the choice of allocation method the main result components. If the curve changes power has a dedicated point of inflection and more like a straight line, it is recommended to use method 1. If the curve changes power has a dedicated point of inflection, it is recommended to use method 2. The program should be used in the package of analytical programs
 algebraic model of constructive logic when performing complex analytical calculations in biophysics, medicine and biology.

Оптимизация алгебраической модели конструктивной логики

The authors proposed and evaluated options of optimization of the algebraic model of constructive logic, designed to construct multichannel non-linear mathematical model often used in Russia in the in-depth analysis in medicine and biology. In the basis of optimization of this model are procedures for finding duplicate cases (rows base), relevant to the achievement of goals, and excluding those resulting components that are duplicated other cases the resulting components.
 
 Procedures for reviewing the results of the components of a top-down or bottom-up and comparing the numbers corresponding to achievement of objectives are the basis of optimization. If all the numbers viewing the resulting component will be present in other watched the resulting components, then it is removed as redundant. As a result of identifying and eliminating redundant coatings target lines are reducing the number of resulting parts. Reduction of number of resulting components is achieved by identifying and eliminating redundant coatings target lines.
 
 The results of two variants of optimization of mathematical model are shown on the example of the mathematical model identification features of the method of oxygen therapy in the treatment of oncological pathology. The authors suggested the possibility of practical use of various optimization algorithms to choose model with a minimal number of components of the resulting/

Опыт выполнения аналитических расчетов с использованием алгебраической модели конструктивной логики в медицине и биологии

This paper describes the experience of analytical calculations in medicine and biology using the mathematical apparatus of algebraic model of constructive logic, created with Russia in 1983. Basically it is a model intuitionism calculus, displaying the inductive part of the thinking - formulation of a relatively small set of summary of the information arrays of large dimension. The initial data to build the model is a table. Each row in this table is treated as a case in which the values of the factors are listed in the form of any numeric value, and the result of their exposure. The resulting model is represented by a set of the resulting components as factors indicating the detection limits, combined mark conjunction (pointing to the joint effect). Each resulting component characterized by the capacity, which is the essence of the number of rows in the table that meet the specified limits of the determining factors in their joint action defined by algebraic model of constructive logic. Optimality is demonstrated by a comparison with a dead-end disjunctive form, as not allowing further simplification in the synthesis of combinational logical schema. The algorithm has the potential partial avoidance of the impact of hidden variables that are slowly evolve over time.
 
 The stages of the analysis, including the building of the expert system, are demonstrated and also the ways of further improvement of the algorithm are specified. An algebraic model of constructive logic of their capabilities is not inferior to neural network algorithms for analytical capabilities, convenient in use and doesn´t require the training phase. An algebraic model of constructive logic is fundamentally different from many well-known algorithms including neural network algorithms. Its use along with other allows to reach greater confidence in the assessment of the results.