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.
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.
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.
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.
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.
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