Scientific Journal of KubSAU

Classical combinatorial formula to calculate the number of combinations from n on m: C(n,m)=n!/(m!(nm)!) involves the intermediate calculation of factorials, which is often impossible when n>170, due to limitations in the capacity of numbers that are used in programming languages and created through these systems. However, in some cases it is necessary to calculate the number of combinations for n and m much larger than this limit, such as when a value greater than 10000. In such cases, there is a definite problem, which manifests itself, for example in the fact that many on-line services meant to calculate the number of combinations with these parameters do not work properly. In this article, we present its solution in the form of an algorithm and software implementation. The essence of the approach is to first decompose the factorials into prime factors and reduce them, and then to produce multiplication. This approach differs from those cited in the Internet

In criminology, there are actual problems of determining the type (machine gun, rifle, large caliber, pistol) and a particular model of small rifle for its ammunition, in particular, discovered in the use of weapons. The article proposes a solution to this problem with the use of a new innovative method of artificial intelligence: automated system-cognitive analysis (ASCanalysis) and its programmatic toolkit – a universal cognitive analytical system called "Eidos". In the system of "Eidos", we have implemented a software interface that provides input to the system images, and the identification of their external contours on the basis of luminance and color contrast. Typing by multiparameter contour images of specific ammunition, we create and verify the system-cognitive model, with the use of which (if the model is sufficiently reliable), we can solve problems of system identification, classification, study of the simulated object by studying its model and others. For these tasks we perform the following steps: 1) enter the images of ammunitions into the system of "Eidos" and create mathematical models of their contours; 2) synthesis and verification of models of the generalized images of ammunition for types of weapons based on the contour images of specific munitions (multivariate typology); 3) quantification of the similarities-differences of the specific ammunition with generalized images of ammunition of various types and models of small rifle (system identification); 4) quantification of the similarities-differences of the types of munitions, i.e. cluster-constructive analysis

To increase the validity of conclusions about the impact of the environment on the quality of life we need to move from generalities to the application of quantitative modeling techniques. This requires the joint processing environmental databases and databases depicting various aspects of quality of life. These databases are needed to be handled not just together, but in a comparable form approach, including technology and methodology, and to be implemented in one software system. For the first time in the environmental studies, it has been planned to be done with the application of the ASK-analysis and the system called "Eidos". Previously, the authors have set the goals and the objectives of the application of the ASK-analysis to study the effect of environmental factors on the quality of life of the population of the region. The article reveals the urgency of this study; the requirements for the method of conducting the study, the choice of a research method; as well as the contents of the objectives of the study. The proposed work is at the edge of mathematical ecology and mathematical modeling of quality of life (which refers to mathematical and instrumental methods of Economics), resulting from expected synergies, consists in obtaining of new knowledge in these fields that is relevant to both ecology and economy. This knowledge will make it more meaningful and justified for the application of environmental criteria and concepts in the economy. This work contains a description of the basic data sources for the study of the impact of environmental factors on various aspects of quality of life of the region's population, the source data for this study, the characteristics of the original data, substantiation of requirements to the method of research, choosing research methods appropriate to requirements; the development of steps to achieve the objectives of the study

The article proposes to use the automated systemcognitive analysis (ASC-analysis) and its software tool which is "Eidos" system to solving multiparameter typing, system identification and cartographic visualization of spatially-distributed natural, environmental and socio-economic systems. Imagine, that we have an original point cloud with coordinates (X,Y,Z), each with known values of gradation descriptive scales of nominal, ordinal, or numeric type S(s1,s2,...,sn). Then the "Eidos" system provides: 1) building a model that contains generalized knowledge about the strength and the direction of the influence of descriptive gradations of scales at Z=M(S); 2) estimation of the values of Z for points (X,Y) described in the same descriptive scales S(s1,s2,...,sn), but not a part of the original point cloud; 3) a cartographic visualization of the spatial distribution of values of the function Z=M(S) for points outside the initial cloud, using Delaunay triangulation. Basically, this means that the "Eidos" system ensures recovery of the unknown function values on the grounds of the argument and implements it in a generic setting, independent of subject area. We propose a new scientific concept called "Geo-cognition system", which is defined as a software system that provides conversion of source data into information, and knowledge in visualization and mapping of this knowledge, resulting in the cognitive map becomes graphics. This feature can be used to quantify the degree of suitability of the watersheds for cultivation of certain crops, the evaluation of the ecological situation on particular territories on the structure and intensity of anthropogenic load, visualization of results of forecasting of earthquakes and other unwanted risks or emergencies, as well as for solving many other similar mathematical essence of tasks in a variety of subject areas. We have also shown a simple numerical example

Classic quantitative measure of the reliability of the models: F-measure by van Rijsbergen is based on counting the total number of correctly and incorrectly classified and not classified objects in the training sample. In multiclass classification systems, the facility can simultaneously apply to multiple classes. Accordingly, when the synthesis of the model description is used for formation of generalized images of many of the classes it belongs to. When using the model for classification, it is determined by the degree of similarity or divergence of the object with all classes, and a true-positive decision may be the membership of the object to several classes. The result of this classification may be that the object is not just rightly or wrongly relates or does not relate to different classes, both in the classical F-measure, but rightly or wrongly relates or does not relate to them in varying degrees. However, the classic F-measure does not count the fact that the object may in fact simultaneously belongs to multiple classes (multicrossover) and the fact that the classification result can be obtained with a different degree of similarity-differences of object classes (blurring). In the numerical example, the author states that with true-positive and true-negative decisions, the module similarities-differences of the object classes are much higher than for false-positive and false-negative decisions. It would therefore be rational to the extent that the reliability of the model to take into account not just the fact of true or false positive or negative decisions, but also to take into account the degree of confidence of the classifier in these decisions. In the intellectual system called "Eidos", which is a software toolkit for the automated system-cognitive analysis (ASC-analysis), we use initially proposed by its developers measure of the reliability of the models, which is essentially a fuzzy multiclass generalization of the classical F-measure (it is proposed to call it the L-measure). In this article, L-measure is mathematically described and its application is demonstrated on a simple numerical example

The article describes a numerical example of creating intellectual application designed to predict solar flares of different classes on the basis of the history of their development in the environment of "Eidos" system. As the source data, we used the database of UCI repository

The article discusses the application of automated system-cognitive analysis (ASC-analysis), its mathematical model which is system theory of information and its software tool, which is intellectual system called "Eidos" for solving problems related to identification of types and models of aircraft by their silhouettes on the ground, to be more precise, their external contours: 1) digitization of scanned images of aircraft and creation of their mathematical models; 2) formation of mathematical models of specific aircraft with the use of the information theory; 3) modeling of the generalized images of various aircraft types and models and their graphic visualization; 4) comparing an image of a particular plane with generalized images of various aircraft types and models, and quantifying the degree of similarities and differences between them, i.e., the identification of the type and model of airplane by its silhouette (contour) on the ground; 5) quantification of the similarities and differences of the generalized images of the planes with each other, i.e., clusterconstructive analysis of generalized images of various aircraft types and models. The article gives a new approach to digitizing images of aircraft, based on the use of the polar coordinate system, the center of gravity of the image and its external contour. Before digitizing images, we may use their transformation, standardizing the position of the images, their sizes (resolution, distance) and the angle of rotation (angle) in three dimensions. Therefore, the results of digitization and ASC-analysis of the images can be invariant (independent) relative to their position, dimensions and turns. The shape of the contour of a particular aircraft is considered as a noise information on the type and model of aircraft, including information about the true shape of the aircraft type and its model (clean signal) and noise, which distort the real shape, due to noise influences, both of the means of countering detection and identification, and environment. Software tool of ASC-analysis, i.e. Eidos intellectual system, provides identification of the type and the model of airplane by its silhouette, as it was shown in a simplified numerical example

The article discusses the application of automated system-cognitive analysis (ASC-analysis), its mathematical model is a system of information theory and implements, its software tools – intellectual system called "Eidos" for solving one of the important tasks of ampelography: to quantify the similarities and differences of different clones of grapes using contours of the leaves. To solve this task we perform the following steps: 1) digitization of scanned images of the leaves and creation their mathematical models; 2) formation mathematical models of specific leaves with the application of information theory; 3) modeling the generalized images of leaves of different clones on the basis of specific leaves (multiparameter typing); 4) verification of the model by identifying specific leaf images with generic clones, i.e., classes (system identification); 5) quantification of the similarities and differences of the clones, i.e. cluster-constructive analysis of generalized images of leaves of various clones. The specific shape of the contour of the leaf is regarded as noise information on the clone to which it relates, including information about the true shape of a leaf of this clone (clean signal) and noise, which distort the real shape, due to the random influence of the environment. Software tools of ASA-analysis which is intellectual "Eidos" system provides the noise suppression and the detection of a signal about the true shape of a leaf of each clone on the basis of a number of noisy concrete examples of the leaves of this clone. This creates a single image of the shape of the leaf of each clone, independent of their specific implementations, i.e. "Eidos" of these images (in the sense of Plato) - the prototype or archetype (in the Jungian sense) of the images

The researchers obtained data on the morphological, biochemical and trace element composition of the blood of bull-calves of Hereford breed of different sizes. In this regard, scientists and business executives have three natural questions: 1) whether it is possible to predict the size and thus the meat productivity of bulls using these blood indicators; what are the strength and direction of the influence of certain values of blood indicators on the size and weight of bulls; what blood indicators are similar in meaning, and what are different and how much (to what extent). The article is devoted to the reasoned answers to these questions by applying modern methods of mathematical and numerical modeling to solve the corresponding problems. The results of the study can be used by anyone, due to the fact that Eidos the universal automated system, which is a tool of ask-analysis, is in full open free access on the author's website at: http://lc.kubagro.ru/aidos/_Aidos-X.htm, and numerical examples of solving the mentioned problems with the use of artificial intelligence technologies are placed as a cloud Eidos-application #133

In complex multiparameter technical systems there are numerous and varied physical processes which, on the one hand, have a significant impact on the performance of those systems, and on the other hand, it is extremely difficult amenable to description in the form of meaningful analytical models based on equations, because these models must take into account the specific features of the systems. As a consequence, the development of conceptual analytical models is a "hand-made work" and it is associated with a large number of simplifying assumptions that reduce their versatility and reliability. But there is also another principle of modeling: the construction of phenomenological information models, i.e. models that do not have analytical forms of representation that describes the simulated system superficially as a "black box". Such models can be built directly based on empirical data and with the appropriate software it can be a standard technology much faster and much less time consuming than developing meaningful analytical models. On the other hand, the phenomenological information model can be sufficient to determine the rational design features and parameters of the modes of operation of complex technical systems. Besides, such phenomenological models can be viewed as the first stage in the development of meaningful analytical models. It is proposed to use a new universal innovative method of artificial intelligence for creating phenomenological models of complex technical systems: automated system-cognitive analysis (ASC-analysis) and its programmatic Toolkit which is a universal cognitive analytical system called "Eidos". In the system of "Eidos" we have implemented a software interface that provides direct input into the system large amounts of empirical data from an Excel file. The system of "Eidos" can directly (based on empirical (experimental) data) calculate how much information about the results of the technical systems is contained in the facts of possessing certain specific structural elements and certain values of the parameters modes of its work. On this basis, the system provides research-based and appropriate recommendations for the rational choice of design features and parameters of the operation modes of the simulated system